An update on polar magnetotaxis: Insights from hanging drop assays and microcosm experiments

An update on polar magnetotaxis: Insights from hanging drop assays and microcosm experiments | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article An update on polar magnetotaxis: Insights from hanging drop assays and microcosm experiments Xuegang Mao, Ramon Egli, Nikolai Petersen, Xiuming Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4320581/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted 13 You are reading this latest preprint version Abstract Magnetotactic bacteria (MTB) combine passive alignment with the Earth magnetic field with a chemotactic response (magneto-chemotaxis) to reach their optimal living depth in chemically stratified environments. Current magneto-aerotaxis models fail to explain the occurrence of MTB far below the oxic-anoxic interface and the coexistence of MTB cells with opposite magnetotactic polarity at depths that are unrelated with the redox gradient. Here we propose a modified model of polar magnetotaxis which explains these observations, as well as the distinct concentration profiles and magnetotactic advantages of two types of MTB inhabiting a freshwater sediment: Magnetobacterium bavaricum (MB) and a group unidentified, wild-type cocci (MC). This model assumed that magnetotactic polarity is set by a threshold mechanism in counter gradients of oxygen and a second group of repellents, with, in case of MB, includes H + ions. Depending on the position of the two repellent thresholds in a vertical redox gradient, MTB possessing this type of polar magnetotaxis either accumulate around a preferred depth where the opposed stimuli set by the two repellents are equivalent, or shuttle between two limit depths across the redox gradient (redox taxis). We show that MB belongs to the latter category, as previously postulated for MB and other members of the Nitrospirae group. Microcosm experiments suggest that redox taxis might be assisted by a partial control of magnetotactic polarity by cell metabolism, which helps maintaining a consistent polarity bias during shuttling. Our model of polar magnetotaxis supports a large variety of magnetotactic behaviors, depending on the position of the two repellent thresholds in a redox gradient, enabling different types of MTB to occupy different ecological niches in the same environment. Biological sciences/Biophysics Biological sciences/Microbiology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 INTRODUCTION Magnetotactic bacteria (MTB) contain intracellular chains of nano-sized magnetite and/or greigite crystals, which ensure a passive alignment with the Earth’s magnetic field ( 1 – 3 ), known as magnetotaxis. Combination of this alignment with the swimming direction determined by surrounding environment (chemotaxis) yields a one-dimensional displacement along magnetic field lines, reducing a three-dimensional search problem of ordinary chemotaxis to one of a single dimension ( 4 ). Magneto-chemotaxis is therefore more efficient than chemotaxis alone in all situations where the magnetic field component along the sought direction of displacement exceeds few µT ( 5 ). This magnetotactic advantage is also available to MTB living in sediment, despite the poor (~ 1–3%) alignment with the Earth’s magnetic field caused by the limited space available in sediment pores ( 6 ). Many MTB are sensitive to oxygen and show a behavior known as magneto-aerotaxis ( 7 ), either through a temporal sensing mechanism, as in Magnetospirillum magnetotacticum strain MS-1, or a threshold mechanism, as in Magnetococcus marinus strain MC-1 ( 8 ). The temporal sensing mechanism, which measures concentration gradients, produces an axial response to the magnetic field (axial magnetotaxis), such that changing the field polarity will not disrupt the cell concentration profile that forms the aerotactic band in cultures grown in a semi-solid medium. The threshold mechanism, which is concentration-sensitive, gives a polar response to the magnetic field (polar magnetotaxis), such that a field reversal will disperse the aerotactic band that forms at the oxic-anoxic interface (OAI). The preferred swimming direction relative to the magnetic field in a hanging drop assay, where oxygen is nearly saturated, determines the magnetotaxis polarity, that is, north-seeking (NS) if swimming towards the magnetic North, or south-seeking (SS) otherwise. MTB performing axial magnetotaxis react randomly to the absence of an oxygen gradient, undertaking frequent changes of the swimming direction that impart a characteristic oscillatory motion parallel to the magnetic field. MTB performing polar magnetotaxis, on the other hand, are in a well-defined sensory state dictated by oxygen saturation, which yields a predominant NS polarity. Both axial and polar magnetotaxis are believed to help MTB in maintaining themselves within a preferred depth range in horizontally stratified environments where the oxygen concentration decreases with depth. In the case of polar magnetotaxis, most cells retrieved in the northern hemisphere are NS when exposed to large oxygen concentrations and SS in the southern hemisphere, since these polarities makes them swim downwards along the inclined field lines. Equal amounts of NS and SS MTB have been found in proximity of the magnetic equator ( 9 ), where the field lines are horizontal. The direction of the Earth’s magnetic field relative to chemical gradients is therefore considered to be responsible for MTB polarity selection ( 7 , 10 ). A second sensory state is needed to switch the magnetotactic polarity, making cells swim upwards when located too deep, albeit such a polarity switching has never been observed in controlled experiments ( 11 ). The second sensory state might be triggered by a lower oxygen threshold ( 8 ), or by a chemorepellent response associated with excessively reducing conditions. The threshold sensory mechanism might also depend on metabolic states of the cell. A metabolic control of magnetotaxis would have the benefit of avoiding unnecessary displacements ( 11 ); however, fast chemotactic responses are still needed to escape potentially damaging conditions. Cell metabolism is expected to play an important role in redox taxis ( 11 ): for instance, MTB from the Nitrospirae phylum accumulate elemental sulfur (S 0 ) through sulfate reduction while resting in the reducing zone, until a “reduced” internal state triggers the magnetotactic polarity reversal required to move up to the microaerobic zone, where S 0 can be oxidized ( 12 ). Complete consumption of S 0 would switch the cell to an “oxidized” state that makes it migrate again to the reduced zone. More complicated forms of magneto-aerotaxis have been described. For instance, strains of Magnetospirillum freshly isolated from environmental samples display a form of semi-polar magnetotaxis where the typical oscillatory motion of axial magnetotaxis is biased, resulting in the accumulation of cells along one edge of the hanging drop assay ( 11 ). The marine vibrio MV-1, on the other hand, performs axial magnetotaxis in the oxic zone and polar magnetotaxis in the anoxic zone of gradient cultures ( 13 ). These observations suggest that axial and polar magnetotaxis might be the idealized endmembers of a range of intermediate responses to chemical gradients. Furthermore, magnetotaxis is also affected by light (phototaxis) and physical contact ( 14 – 18 ). Non-chemical stimuli might provide additional clues for navigation in the water column and in the sediment. Current models of magnetotaxis are challenged by the observation of MTB with opposite magnetotactic polarity coexisting in at the same depths in horizontally stratified water columns, and the lack of a consistent relation between polarity and position in the redox gradient ( 16 , 19 – 21 ). On the other hand, hanging drop assays on wild-type MTB retrieved from sediment, including Magnetobacterium bavaricum , the model MTB for which redox taxis has been postulated ( 22 – 24 ), yielded always the polarity expected in the case of oxygen saturation, regardless of sampling depth, also when sampling and observations were performed under strictly anoxic conditions and in the dark ( 25 ). These results cannot be explained by an aerotactic or a metabolic control of the swimming direction, or a combination of both. In the present study, we observe the response of wild-type cells of Magnetobacterium bavaricum (MB) and unidentified magnetic cocci (MC) to pH gradients, and show, for the first time, that the magnetotactic polarity of MB can be switched by a pH-driven threshold sensing mechanism. Our result suggests that polar magnetotaxis is controlled by at least two chemorepellents, or groups of chemorepellents, associated with natural redox gradients. Using results obtained from previous experiments with MB and MC cells from the same sediment ( 6 , 25 ), we develop a new model of polar magnetotaxis that resolves the abovementioned inconsistencies between theory and observations. MATERIALS AND METHODS Freshwater sediment was collected using a grab sampler from a small pond (30×7×0.5m) in Niederlippach, Germany, (48°35’14.98” N, 12°04’43.71” E, Fig. 1 , A) ( 25 , 26 ), and transferred to glass aquaria that were kept at room temperature (Fig. 1 , B) in the Earth’s magnetic field. A new sediment stratification and oxygen gradient was reestablished after ~ 10 days. After complete stabilization, mini cores (3–5 cm long) were taken from the sediment using a plastic drinking straw (diameter: 5 mm) and sliced in 1 mm increments. Each slice was diluted with distilled water (~ 200 µL) and prepared for a hanging drop assay on a rubber O-ring to prevent rapid evaporation (insert of Fig. 1 , C). MTB cells swimming out of the sediment were observed and counted under a special optical microscope ( 6 ) equipped with Helmholtz coils for producing a stable magnetic field (Fig. 1 , C). The quasi totality of MTB observed with this apparatus belonged to two groups: the giant rod-shaped MB (Fig. 1 , E, F), previously identified in the same pond ( 24 ), and MC cells containing one or more chains of prismatic or tooth-shaped magnetosomes (Fig. 1 , D). Despite their diversity, MC cells were characterized by a homogeneous magnetotactic behavior. The presence of sulfur inclusions (Fig. 1 , F) in MB cells was confirmed by energy-dispersive X-ray spectroscopy (EDS) (Fig. 1 , G). MTB cells freshly retrieved from the sediment present strong tactile responses and a tendency to decrease their motility with time, or upon transferring them to another setup once they left the sediment. Attempts to transfer MTB cells into microfluidic devices, where controlled chemical gradients can be created, were not successful. Therefore, a modified version of the hanging drop assay has been used to observe the motion of MB cells in a pH gradient, under conditions that were as close as possible to the classic hanging drop assay used here as control experiment. The modified hanging drop assay (Fig. 2 , A) was prepared as follows: ~0.5 mL of MTB-containing sediment was taken with a micropipette from an aquarium and transferred to a glass slide (2.6×7.6 cm). Then, ~ 1 mL distilled water (pH 7) was added on the top of the sediment drop to create a clear water rim around the sediment. Placement of a cover glass (2×2 cm) onto the sediment-water preparation creates a thin film of homogeneous thickness. A series of aqueous solutions with pH values ranging from 1 to 12 have been prepared by successive dilution of 1 M HCl or NaOH with distilled water. The pH value of each solution was confirmed with a pH sensor from Unisense. About 0.1 mL of the as-prepared pH solution was deposited onto one side of the cover glass, providing a reservoir that is in contact with the fluid under the cover glass (Fig. 2 , A). The thin fluid layer below the cover glass prevents turbulent mixing, so that a pH gradient forms by diffusion and propagates toward the other end of the cover glass. This setup does not allow to monitor actual pH values; however, as discussed later, a qualitative assessment of the pH gradient is sufficient to elucidate the magnetotactic response, which is therefore simply described by the pH value of the added solution. A rough assessment of the pH gradient is obtained from the solution of the one-dimensional diffusion equation $$\frac{{\partial C}}{{\partial t}}=D\frac{{{\partial ^2}C}}{{\partial {x^2}}}$$ 1 inside the fluid layer below the cover glass, where C = C ( x , t ) is the concentration of H + or OH − ions as a function of the distance x from the cover slide edge where the solution was added at the time t = 0, and D ≈ 2.3×10 − 9 m 2 /s is the self-diffusion coefficient of water at room temperature. The initial condition \(C(x,t)={C_0}H(x),\) where C 0 is the concentration of ions and H is the Heaviside unit step function, describes the addition of the pH solution at t = 0. Suitable boundary conditions must be set at x = 0 and at the opposed side x = − L of the cover slide ( L ≈ 2 cm). Because the added drop of pH solution is much thicker than the fluid layer under the cover slide, we assume an infinite reservoir with \(C(0,t)={C_0}\) at x = 0. The other end of the cover slide is a physical barrier with no flux, whence \(\partial C{\kern 1pt} /{\kern 1pt} \partial x=0\) for x = L . Numerical solutions of Eq. ( 1 ) are shown in Fig. 2 , B (H + ions) and Fig. 2 , C (pH) for a 2-cm-wide cover slide and a pH 3 solution ([H + ] 0 = 10 − 3 ). These solutions show that a pH front with decreasing sharpness propagates under the cover slide for the first ~ 30 min. During this time, the left-hand side of the cover slide is unaffected by the pH solution. The pH front disappears completely after 2 hours, when the pH of the entire water film starts to decrease until it equilibrates with the added solution. Accordingly, we expect a pH gradient along x to be present during the first ~ 30 min, so that MTB cells exiting the sediment will swim from a near-neutral environment into a < 1 mm-wide diffusion front. All observations were performed within 30 min from preparation, after placing the glass slide under the optical microscope in a controlled magnetic field. Motile cells can be observed for several hours, which means that evaporation is not an issue in these experiments. RESULTS Control experiments and loss of cell motility A series of pH solutions (pH 1–12) have been used to test the MTB response to a pH gradient. Addition of a pH 7 solution, which is similar to the near-neutral pH of the sediment used in our experiments ( 24 ), did not produce a noticeable change in the swimming behavior of both MTB types with respect to simple hanging drop assays, with cells being consistently NS (Table 1 ). In rare cases, few (< 1%) MB engaged an oscillatory motion (Movie S1). This control experiment shows that the one-sided addition of an aqueous solution to the hanging drop setup does not modify, per se, the magnetotactic polarity of MB and MC cells. Table 1 Summary of results obtained from hanging drop assays. Numbers indicate cell counts. Added solution NS Oscillating SS Full stop (immobile) Full stop (vibrating) Control a ~ 400 (99.3%) 3 (0.7%) 0 0 0 pH 1 0 0 0 ~ 300 (100%) 0 pH 2 b 9 (6.4%) 0 131 (93.6%) not observed not observed pH 2 c 37 (3.2%) 955 (83.5%) 102 (8.9%) 50 (4.4%) 0 pH 3 15 (28.8%) 37 (71.2%) 0 not observed not observed pH 4 0 0 0 2 (8.3%) 22 (91.7%) pH 5 0 0 0 0 100 (100%) pH 6 2 (5.3%) 0 0 0 36 (94.7%) pH 7 45 (97.8%) 0 0 0 1 (2.2%) pH 8 7 (25%) 0 0 0 21 (75%) pH 12 0 0 0 ~ 300 (100%) 0 a Standard assay b Before oscillating cells were observed c While oscillating cells were observed Nearly all MTB cells lose their motility with a complete stop of the flagellar motor upon adding very acidic (pH 1) or alkaline (pH 12) solutions once they reach the diffusion front (Movie S2). Motility was not resumed upon reversing and/or rotating the magnetic field. On the other hand, the addition mild solutions (pH 4–6 and 8) triggered a different response, with MB cells slowing down to a full stop after reaching the diffusion front. After stopping, rapid lateral vibrations of the cell body (Movie S3), indicate that the flagellar motor was still active, but flagella were no longer arranged in a way that supported forward propulsion ( 27 ). Lateral vibrations are produced by random torques that would make the cell tumble in absence of a magnetic field. Tumbling is a typical chemotactic response of motile bacteria ( 28 ), which, in the case of MTB, might serve other purposes. Normal swimming was not resumed by reversing or by rotating the magnetic field. Magnetotactic polarity switching A distinct swimming pattern that included magnetotactic polarity switching (Movie S4) was observed only in the case of MB cells approaching the pH gradients created by adding moderately acidic solutions (pH 2–3). This pattern is best described by dividing the cover slide into three zones, labeled as A, B, and C, according to the increasing proximity to the side where the solution was added (Fig. 2 , A). In zone A, which extends from the sediment to a certain distance from the diffusion front, cells maintained the usual NS behavior (Movie S4, 0’4”–0’6”), eventually approaching the pH front. In the pH 2 experiment, few (4.4%) MB cells continued to swim along the same direction until reaching zone C, closest to the side where the solution was added, until the flagellar motor suddenly stopped. Motility could not be resumed by reversing and/or rotating the magnetic field (Movie S4, 0’9”–0’12”), alike the experiments with pH 1 solutions. Most MB cells, however, reversed their swimming direction in zone C, effectively becoming SS (Movie S4, 0’50”–2’10”). These SS cells occasionally reverted to NS for short periods of time (0.5–1 s), however, the net swimming direction was SS (Movie S4, 0’50”–2’10”). The SS motility triggered in zone C did not cease until cells reached again zone B, where they engaged a distinct back-forward motion (referred to as oscillating in the following) by switching their flagellar motor every 0.15–0.6 s, with no systematic bias in favor of either direction (Movie S4, 0’17”–0’33” and 2’15”–2’22”). The oscillating motion maintained these cells in zone B for several minutes. In the pH 3 experiment, most MB cells engaged the same oscillating motion as soon as they reached zone B (Table 1 ). After reversing the magnetic field (Movie S4, 0’33”), MB in zone B stop to oscillate, resuming their normal swimming behavior (Movie S4, 0’33”–0’40”), mostly (~ 91%) with NS polarity, and the remaining part (~ 9%) with SS polarity (Movie S4, 2’41”–2’49”). NS cells eventually reached back into zone A, while SS cells advanced towards zone C. If the original magnetic field direction was restored (Movie S4, 0’42”), both NS and SS cells returned to zone B and engaged the same oscillatory motion observed before (Movie S4, 0’43”–0’46”). If the magnetic field was turned by 90° (Movie S4, 2’53”), all MB cells became NS, stopping the periodic polarity reversal (Movie S4, 2’53”–3’11”). Zeroing the magnetic field made MB cells swim randomly, with no preferred direction (Movie S5 0’2”–0’41”). Tracking periodic magnetotactic polarity reversals Detailed insights into the periodic motion of MB cells in zone B have been obtained by digitizing individual swimming paths in Movie S4 (0’29”–0’36”). The first example (Fig. 3 , A) depicts a large cell that oscillates with an unusually large amplitude. Its swimming path is composed of discrete sections characterized by constant swimming velocities with alternating sign, as deduced from the saw-tooth pattern of the x -coordinate x ( t ). The y -coordinate, on the other hand, remains nearly constant, up to small random fluctuations, as expected from the strong alignment of MB cells ( 6 ) in the ~ 0.1 mT field parallel applied along x . The asymmetry of the saw-tooth pattern is caused by the swimming velocity of SS tracks being ~ 37% smaller than that of NS tracks. This pattern clearly shows that oscillations around a mean position are not random, being caused by flagellar motor reversals occurring at two fixed positions along the pH gradient. Most MB cells in zone B oscillate much more rapidly, as seen in Fig. 3 , B. In these cases, the rapid (~ 6 Hz) alternation of the swimming direction prevents a precise discrimination between NS and SS velocities. In both examples, the magnetic field was reversed while the cells were NS. Thereafter, cells continued to be NS and swam away from the diffusion front. The last example (Fig. 3 , C) depicts two oscillating cells that are only ~ 50 µm apart from each other, which means that they move inside the same chemical gradient roughly oriented along x . The field was reversed when both cells were NS, yet one cell remained NS, while the other cell became SS and swam toward the pH front. Because of identical external conditions, the different behaviors of the two cells must be attributed to cell-internal factors, due for instance to a memory effect ( 29 ). pH sensitivity The above observations can be summarized as follows: (a) The addition of solutions with pH values close to the natural sedimentary environment (pH 7) did not produce any visible difference with respect to the regular hanging drop assay; (b) the addition of highly acidic or alkaline solutions (pH 1 and 12) led to a complete stop of the flagellar motor once passing through the diffusion front (zone C); (c) the addition of weakly acidic or alkaline solutions (pH 4–6 and 8) led to a progressive slowdown and stop once passing through the diffusion front (zone C), however, the flagellar motor was still active; (d) the addition of moderately acidic solutions (pH 2–3) triggered a magnetotactic polarity reversal in most cells, which led to an oscillatory motion either directly in zone B (pH 3), or after a first reversal in zone C (pH 2); (e) a magnetic field reversal brings ~ 91% of the oscillating cells back to their usual NS state, while the remaining ~ 9% becomes SS; (f) reverting the magnetic field to the original polarity resumes the oscillatory behavior once the cells returned to zone B. Finally, MC cells were either unaffected, or they slowed down and lost their motility upon encountering a sufficiently strong pH gradient (Movie S6), suggesting that pH does not trigger a magnetotactic polarity reversal in this type of MTB. DISCUSSION pH-driven polar magnetotaxis switching The periodic swimming direction reversal engaged by MB cells in properly set pH gradients differ from changes of the magnetotactic behavior triggered by other stimuli, such light as tactile responses. For instance, the bounce and ping-pong motion of multicellular magnetotactic prokaryotes (MMPs), which is triggered by UV light (phototaxis) or tactile stimuli ( 15 – 18 ) is irregular and depends on the sampling season, storage time in the laboratory, observation duration, and on the magnetic field strength ( 30 , 31 ). Our observations, on the other hand, depend on the presence of a pH gradient, this gradient being the only difference with control experiments. The response of MB cells to pH gradients, which enables them to escape very acidic or alkaline conditions, is analogous to that of other neutrophilic bacteria ( 32 , 33 ). The oscillatory motion of MB in zone B resembles the axial magnetotaxis of spirilla ( 7 , 11 ). However, the cause is completely different: in absence of a chemical gradient, the temporal sensing mechanism of spirilla is subjected to random fluctuations and measures essentially noise, triggering swimming direction reversals at random times. The oscillation of MB in zone B, on the other hand, is very regular (Fig. 3 ), and it occurs in proximity of zone C, where excessively acidic conditions suppress cell motility. This means that the concentration of H + ions in zone B abundantly exceeds the noise level of the sensory mechanism, so that changes in swimming direction are triggered deterministically either by a concentration gradient or by a concentration threshold. In case of spatiotemporal sensing mechanisms ( 34 ), cells compare the concentrations C 1 = C ( x ( t )) and C 2 = C ( x ( t + ∆ t )) of a repellent – in our case H + -ions – along the swimming path x ( t ) over successive time intervals ∆ t , therefore effectively sensing a spatial gradient G ( x ) = ( C 2 – C 1 )/ v Δ t along x , with v being the swimming velocity. In this case, the only role played by the magnetic field is that of determining the axis along which the gradient is sensed, so that the response to a field polarity reversal is purely axial ( 7 ). However, our experiments show that the periodic change of the swimming direction by cells that engage an oscillatory motion in zone B ceases immediately after reversing the field polarity, yielding NS or SS cells with the normal swimming behavior observed without a pH gradient. This observation proves that MB cells do not react to pH gradients via a spatiotemporal sensing mechanism. The threshold sensing model ( 8 ) assumes that the swimming direction of MB cells is switched by a repellent threshold concentration detected by external ( 35 ) or internal ( 36 ) receptors. We assume that the capture of repellant molecules and the transmission of signals to the flagellar motor produces a certain delay between the actual concentration C ( x ( t )) along the swimming path x ( t ) of the cell, and the sensed concentration C s ( t ), which might be controlled by a diffusive process ( 35 ), or by a reaction rate ( 37 ). To keep the conceptual model as simple as possible, we use a one-dimensional model of tracer diffusion across planar sheet of thickness 2 d that surrounds the receptors located at z = 0. The exact geometry of the problem is irrelevant, because the thickness of the sheet and its diffusion coefficient combine into a single parameter τ d = d 2 / D which controls the time dependence of the tracer concentration profile c ( z , t ) across the sheet ( 38 ). With these settings, C s ( t ) = c ( z = 0, t ), where c is the solution of the one-dimensional diffusion equation with boundary condition c(± d , t ) = C ( x ( t )), and x ( t ) the swimming path and C the tracer concentration outside the cell. Since d 2 / D and the pH profiles of the hanging drop experiments are unknown, all simulations results discussed below are expressed in arbitrary units assuming D = 1, d = 1, and v = 1. The initial condition for a cell that just left the sediment and swims towards the diffusion front (zone A) is C = C s ≈ 0. The cell is initially NS, so that x ( t ) = v NS t , where v NS > 0 is the NS swimming velocity. In zone B, C ( x ( t )) starts to increase, and the same occurs for C s ( t ) with some delay caused by diffusion across d (Fig. 4 , A). When C s ( t ) reaches a critical threshold \(C_{{\text{s}}}^{ * }\) (assumed to be 0.2 in the unitless simulations of Fig. 4 ), the swimming direction is reversed and the cell becomes SS, moving back towards the starting point. C s initially continues to increase while C is decreasing, but the trend is inverted after passing the point where C s = C . If the cell remains SS, C s will eventually cross a threshold that makes the cell becoming NS again. For convenience, we assume this threshold to be identical to \(C_{{\text{s}}}^{ * }\) . While the cell is moving again towards the repellent, C s continues to decrease for a while, until the increase of C reverses this trend. At a certain point, C s exceeds \(C_{{\text{s}}}^{ * }\) a second time, and the cell becomes again SS. This cycle is repeated indefinitely, as long as C ( x ) is constant, producing the periodic functions x ( t ), C ( x ( t )) and C s ( t ) in Fig. 4 , B. The periodicity of x ( t ) represents the oscillatory behavior of the cell around a mean position close to the point where \(C=C_{{\text{s}}}^{ * }\) . The qualitative characteristics of the periodic motion depend only on the existence of (a) a sensed threshold \(C_{{\text{s}}}^{ * }\) that triggers a magnetotactic polarity reversal and determines the mean position of the cell with respect to the pH gradient, and (b) a delay between C and C s , which controls the period ~ d 2 / D of the motion. Sensing mechanisms depend in a complex manner on the input and its past evolution, generating hysteretic responses that reduce the flagellar motor chatter in case inputs close to the noise level ( 39 ). In this case, the response is apparently controlled by two thresholds C 1,2 of the external concentration ( 40 ), depending on whether the sensed concentration increases ( C 0 ), or decreases ( C 1 < C 0 ). The sensory mechanism itself might possess two different internal thresholds, as it has been postulated for the oxygen concentration in magneto-aerotaxis ( 7 ). Addition of a second internal threshold \(>C_{{\text{s}}}^{ * }\) in the above model moves the NS → SS turning point further to the right, making the cycle depicted in Fig. 4 , A, B more symmetric. Cells, however, would continue to oscillate between two points of the unknown pH gradient. The above model also explains the response of oscillating cells to a field polarity reversal. Figure 4 , C–F depicts four cases where the field polarity is reversed at different points of the cell trajectory: two cases when the cell is NS and two cases when the cell is SS. Depending on the instantaneous value of C s during the field polarity reversal, and the subsequent evolution of C s while the cell is swimming in the opposite direction, the magnetotactic polarity might or might not be switched another time. The outcome is either a NS cell in the reversed field, which moves away from the repelling zone, or a SS cell in the reversed field, which swims towards the repelling zone. Because oscillating cells spend most of their time in a region where the repellent concentration is \(<C_{{\text{s}}}^{ * },\) the probability to end in a SS state after field reversal is much lower (~ 9%) than that of ending in a NS state. This probability is exactly reflected by our observations of MB cells in zone B, with ~ 9% of all oscillating cells becoming SS in the reversed field. The evident disproportion between NS and SS cells produced by the field reversal suggests that the magnetotactic polarity is switched by a single internal threshold or by two similar ones, since the symmetric cycle produced by largely different thresholds gives a 50% chance for either polarity. Chemotactic response rescaling Chemotactic sensory systems rescale their response sensitivity (adaptation) so to sense small concentrations differences at concentration levels ranging over several orders of magnitude ( 41 – 43 ). Accordingly, a chemotactic response is triggered by a minimum relative concentration change with respect to a background concentration. The adaptation process takes some time ranging from seconds to minutes ( 44 ) and is sensitive to both the sign and the rate of concentration changes ( 45 ). The adaptation and de-adaptation process of motile non-magnetotactic bacteria such as E . coli is reflected by the frequency of tumbling intervals, defined as intervals of random cell rotation obtained by reversing the flagellar motor ( 46 ). A different type of adaptation can be observed in the hanging drop experiments performed with a pH 2 solution. In this case, most MB cells will first swim to zone C, where they become SS, and then swim back to zone B, where they begin a periodic reversal of the magnetotactic polarity around a mean position. This behavior implies that the first NS → SS trigger in zone C occurs at a much larger H + concentration than the subsequent triggers in zone B. The associated threshold change can be explained by the initial adaptation of the sensory mechanism to the concentration increase above the background level of zone A. A delay of few seconds, roughly corresponding the time required to move from zone B to zone C, explains why all cells swim to zone C and lose their motility when stronger pH gradients are used: in these cases, tolerable H + concentrations are exceeded before the sensory mechanism can adapt. This does not occur with a pH 3 solution, probably because the gradient formed in this case is shallow enough for the sensory mechanism to switch the flagellar motor already in zone B. We could not measure the instantaneous pH value that causes a motility loss in our experimental setting, however, as a term of comparison, the flagellar motor of E. coli is completely stopped in an external pH of 5 ( 47 ). Intermediate responses The response of MB cells to the addition of mildly acidic or alkaline solutions consisted in an initial slowdown of the flagellar motor, as shown by the decreasing NS swimming speed (Movie S3), followed by a reversal. The reversed rotation speed was not sufficient to sustain the backward motion observed in SS cells obtained with the other experiments. Some studies indicate that the speed of the flagellar motor can be modulated by a variety of molecular mechanisms when circumstances call for a less vigorous motility ( 48 ). In our experiments, this slowdown might represent a reduced response to weak repellent concentrations. Because cell tumbling is prevented by the magnetic torque, slower flagellar rotation in “backward” mode might be used to stop cell motion under conditions where a displacement is not useful. A simple model for two different forms of polar magnetotaxis Our hanging drop experiments show, for the first time, that the magnetotactic polarity of MB cells is switched by the chemotactic response to a repellent different from oxygen. The presence of two repellents, in our case O 2 and H + , of which at least one forms a gradient that is correctly oriented with respect to the magnetic field, is sufficient to constrain the cell position within limits determined by the repellent concentrations and the sensing thresholds. This model of polar magnetotaxis works similarly magneto-aerotaxis ( 8 ), except that the trigger for setting cells in a “reduced state” is given by a different repellent, rather than a lower [O 2 ] threshold. Natural environments inhabited by MTB are characterized by counter gradients of oxidized and reduced species that form a redox gradient. In this case, at least one repellent capable of switching the magnetotactic polarity is required for each counter gradient. Repellents encountered in the oxic zone, such as O 2 , trigger the magnetotactic polarity that makes cells swim downwards along the Earth’s magnetic field, that is, NS in the northern hemisphere and SS in the southern hemisphere. We refer to this polarity simply as down-seeking (DS). Repellents encountered in the reducing zone trigger the opposite polarity, called upward-seeking (US). In the natural environments inhabited by MB, H + belongs to the family of repellents associated with the reducing zone, as seen by the pH decrease across the OAI ( 25 ). The pH threshold required to switch the magnetotactic polarity of MB under natural conditions is likely not the same of our hanging drop experiments, because the strong NS response triggered by oxygen saturation, and because of the role played by adaptation. The polar magnetotaxis model illustrated above defines two types of responses to redox gradients characterized by a combined concentration R ox ( z ) of oxidizing repellents, which decrease with depth, and a combined concentration R red ( z ) of oxidizing repellents, which increase with depth. If the R ox threshold required to trigger the DS polarity occurs at the same depth or at a greater depth z ox than the depth z red of the R red threshold required to trigger the US polarity, cells located either above z red or below z ox receive consistent stimuli that direct them toward the ( z red , z ox ) depth range (Fig. 5 , A). Once within this depth range, stimuli that trigger opposed magnetotactic polarities overlap, leading either to a mixed polarity state characterized by frequent polarity changes, with a bias determined by the stronger stimulus, as observed with freshly isolated strains of Mangetospirillum ( 11 ), or to a cell motility slowdown, as observed in our hanging drop experiments with mildly acidic or alkaline solutions. In both cases, cells are expected to reach an equilibrium depth within ( z red , z ox ), which depends on how the R ox and R red stimuli are combined. Because of the phenotypic heterogeneity of chemotactic sensitivity ( 49 ), a MTB population subjected to the conditions shown in Fig. 5 is expected to produce a bell-shaped cell concentration profile with mean depth controlled by the mean chemotactic response to the given redox gradient, and width reflecting the population heterogeneity (Fig. 5 , B). If, on the other hand, z ox < z red , as for instance in the case for mutually exclusive repellents in the oxic and reducing zones, respectively, cells will always possess a well-defined magnetotactic polarity, regardless of depth, provided that the magnetotactic polarity set by the R ox threshold is maintained for as long as the R red threshold is not exceeded, and vice versa (Fig. 6 , A). This hypothesis is consistent with the observation that lack of oxygen in hanging drop assays performed under anoxic conditions did not switch the NS polarity of MB and MC cells ( 25 ). Possible mechanisms that help cells maintaining a consistent magnetotactic polarity is discussed in the next section. In the configuration of Fig. 6 , A, a cell initially located above z ox will be set into a DS state that produces a downward migration, until z red is reached. At this point, the cell will be set into an US state, and the migration direction is reversed, until z ox is reached again and the cycle is repeated. As a result, cells shuttle continuously between z ox and z red , as postulated by the redox taxis model ( 11 ). Under stationary environmental conditions, MTB pauseless shuttling between z ox and z red are expected to be homogeneously distributed between these limiting depths, yielding a uniform cell density profile proportional to the box function \(\Pi ((z - {z_{{\text{red}}}})/({z_{{\text{red}}}} - {z_{{\text{ox}}}})),\) with Π( x ) = 1 for 0 ≤ x ≤ 1, and Π( x ) = 0 otherwise. Because of unavoidable environmental and phenotypic heterogeneities, a more realistic representation of the expected concentration profile is given by a smoothed version of the box function, obtained by convolving Π( x ) with a bell-shaped distribution g ( x ) of z ox and z red values, is (Fig. 6 B). If redox taxis is used to satisfy different metabolic requirements across the redox gradient, such as the accumulation of elemental sulfur (S 0 ) under reducing conditions, and the oxidation of S 0 under microaerobic conditions ( 12 ), it is reasonable to assume that cell migration is paused at the limiting horizons z ox and z red for the time required to complete chemical reactions associated with redox cycling (Fig. 6 , C). In this case, two peaks of the form \(g(z - {z_{\text{c}}})\,{T_{\text{c}}}{\kern 1pt} v{\kern 1pt} /{\kern 1pt} ({z_{{\text{red}}}} - {z_{{\text{ox}}}}),\) centered at z c = z ox and z c = z red , respectively, reproduce the concentration profiles of pausing cells, which overlap with the box-shaped distribution of migrating cells (Fig. 6 , D). The factor \({T_{\text{c}}}v{\kern 1pt} /{\kern 1pt} ({z_{{\text{red}}}} - {z_{{\text{ox}}}})\) corresponds to the ratio between the time T c spent at z c and the time spent between z red and z ox , respectively. The total numbers N ox and N red of cells pausing at z ox and z red , respectively, as well as the proportion of DS and US polarities of migrating cells, is dictated by the population balance equations $$\begin{gathered} \frac{{{\text{d}}{N_{{\text{ox}}}}}}{{{\text{d}}t}}=({r_{{\text{ox}}}} - {\psi _{{\text{ds}}}}){N_{{\text{ox}}}}+{\psi _{{\text{us}}}}{\eta _{{\text{us}}}}{N_{{\text{red}}}} \hfill \\ \frac{{{\text{d}}{N_{{\text{red}}}}}}{{{\text{d}}t}}=({r_{{\text{red}}}} - {\psi _{{\text{us}}}}){N_{{\text{red}}}}+{\psi _{{\text{ds}}}}{\eta _{{\text{ds}}}}{N_{{\text{ox}}}} \hfill \\ \end{gathered}$$ 2 , where r ox , r red are the cell growth rates, ψ ds , ψ us the fractions of pausing cells that resume DS and US migration per unit of time, and η ds , η us the fractions of migrating cells that reach the target layer, escaping, for instance, predation. Stationary solutions (d N ox /d t = d N red /d t = 0) exist only if \({\psi _{{\text{ds}}}}\,>{r_{{\text{ox}}}},\) \({\psi _{{\text{us}}}}\,>{r_{{\text{red}}}},\) and \({\psi _{{\text{ds}}}}{\psi _{{\text{us}}}}{\eta _{{\text{ds}}}}{\eta _{{\text{us}}}}=({r_{{\text{ox}}}} - {\psi _{{\text{ds}}}})({r_{{\text{red}}}} - {\psi _{{\text{us}}}})\) . In this case, the fractions \({p_{{\text{us}}}}({z_{{\text{ox}}}})=({\psi _{{\text{ds}}}} - {r_{{\text{ox}}}})\,/\) \((2{\psi _{{\text{ds}}}} - {r_{{\text{ox}}}})\) and \({p_{{\text{us}}}}({z_{{\text{red}}}})={\psi _{{\text{us}}}}{\kern 1pt} /{\kern 1pt} (2{\psi _{{\text{us}}}} - {r_{{\text{red}}}})\) of US cells near z ox and z red are comprised between 0 and 50%, and between 50 and 100%, respectively. Exactly 50% of all migrating cells are US, regardless of depth (Fig. 6 , B) in case of pauseless shuttling ( \({r_{{\text{ox}}}}/{\kern 1pt} {\psi _{{\text{ox}}}}={r_{{\text{red}}}}/{\kern 1pt} {\psi _{{\text{red}}}}=0\) ). More generally, p us ( z ) can be any function comprised between 0 and 100% if the population is not stationary, which means that the in-situ magnetotactic polarity of migrating cells is not systematically related to the redox conditions. Several observations provide indirect evidence in support of the two polar magnetotaxis models described above (Table 2 ). The first evidence comes from MB and MC concentration profiles measured over several months in the same stable microcosms that served as MTB source for this work ( 25 , 50 ). The shape of these profiles depends on the depth-integrated cell concentration N , which ranges from 1800 cells/mm 2 . The average of MB profiles with N < 450 cells/mm 2 is nearly constant between z 1 ≈ 3 mm and z 2 ≈ 17 mm (Fig. 6 , E), resembling the theoretical box function expected from pauseless shuttling between two limit depths (Fig. 6 , B). The concentration plateau increases with N , but remains within the same limit depths, up to N ≈ 1500 cells/mm 2 . Two distinct peaks, centered at z 1 ≈ 6 mm and z 2 ≈ 17 mm, respectively, emerge for the average of profiles with N > 1800 cells/mm 2 . This average resembles the concentration profile predicted for cells that pause at both limit depths (Fig. 6 , D). The upper peak is comprised between z ≈ 4 mm, which is the depth where oxygen drops to zero, and ~ 10 mm, while the less pronounced lower peak is slightly broader. The two peaks occur independently of each other, as seen from individual profiles featuring only one maximum that coincides with the upper or the lower peak position (Fig. 7 ). MC concentration profiles are relatively flat at low N ( N 400 cells/mm 2 ), instead of two distinct peaks (Fig. 5 , C). Table 2 Characteristics of polar magnetotaxis deduced from microscope observations and from microcosm experiments. Process Microscope observations Microcosm experiments Lower [O 2 ] threshold No • assay in anoxic conditions No • MTB well below the OAI Second repellant pH (MB), unknown (MC) Unknown (pH-compatible) Threshold sensing Yes • polar magnetotaxis Possible - sensitivity to field reversal Threshold adaptation Yes • pH 3 experiments Not observable Tumbling/stop a Yes (MB) • cell vibration at pH 6 and 8 Yes (MB) • redox taxis with pause Stationary MA b — Yes (MB), No (MC) • microcosms in zero field Dynamic MA c — Yes (MB and MC) • migration experiments Redox taxis — Yes (MB), No (MC) • depth distribution • S 0 inclusions • stationary MA Metabolism-driven chemotaxis — Yes (MB), No (MC) • redox taxis with pause • Better migration of MB vs. MC • Migration in reversed field US fraction d (in situ) Variable (0 to ~ 100%) e • unrelated to redox gradient Adaptable • Migration experiments a Flagellar motion that would make the cell tumble in null field. b Magnetotactic advantage (MA) for a stationary MTB population c Magnetotactic advantage (MA) identified with the capability to follow a macroscopic OAI offset. d US = SS in the northern hemisphere, and US = NS in the southern hemisphere. e For hanging drop assays or other observation methods that preserve, at least partially the original chemical conditions. MC and MB concentration profiles are well explained by the magnetotactic models of Fig. 5 and Fig. 6 , respectively. The role played by polar magnetotaxis in determining the distinct concentration profiles of MB and MC is further confirmed by the in-situ magnetotactic advantage of these two MTB populations. Magnetotactic advantages are defined here by the role played by the magnetic field in helping cells to (a) keep their preferred depth range under stationary conditions (stationary advantage), and (b) react to sudden changes of the surrounding environment (dynamic advantage). The stationary advantage has been investigated by monitoring the evolution of the two MTB populations while the microcosms were placed in a null field ( 25 , 50 ): while MC was practically unaffected by the field removal, depth-integrated counts of MB declined by 50%. The difference can be explained by considering how MTB cells migrate in sediment: because of the poor magnetic alignment caused by the limited pore space, motile cells perform a biased random walk, rather than displacing along straight lines, even when keeping the same magnetotactic polarity ( 6 ). Numerical simulations show that the random walk component dominates small (< 0.2 mm) displacements, while the advective component, which depends on the magnetic alignment, becomes dominant over larger distances. Hence, the small adjustments needed to maintain a preferred living depth in the model of Fig. 5 do not benefit significantly from the alignment induced by Earth-like magnetic fields, explaining the lack of a static magnetotactic advantage for MC cells. On the other hand, MB cells migrate over distances of the order of 1 cm or more during redox taxis (Fig. 6 ), well within the range where the magnetic alignment becomes important. Finally, both MTB populations possess also a dynamic magnetotactic advantage, as seen by their ability to follow a macroscopic displacement of the OAI ( 25 ). In the case of MB, this ability persists, in a much-reduced form, also after reversing the field, while MC cells are incapable to follow the OAI in a reversed field. The adverse effects of a field reversal in these experiments provide an in-situ confirmation of the polar character of magnetotaxis in these two MTB populations. On the other hand, the partial ability of MB to overcome a field reversal requires additional considerations, as explained below. Metabolism-dependent chemotaxis Classical models of chemotaxis assume that the flagellar motor is controlled by a sensorimotor pathway that provides a relatively rapid response to external stimuli ( 51 ). The adaptation capability of this pathway ( 45 ) provides cells with a memory that enhances navigation in rugged chemical gradients by extracting information from environmental correlations ( 29 ). Maximal advantage is achieved when the memory effect is comparable with the time scale of fluctuations as perceived during swimming. In sediment, the diffusive component of MTB displacement, which is similar to the path generated by simple chemotaxis, dominates over length scales < 0.2 mm and corresponding time scales < 20 min ( 6 ). Displacements over such small scales can therefore benefit from adaptation times of the order of minutes ( 45 ). On the other hand, a much longer memory, of the order of days, would be required to keep the same magnetotactic polarity, or at least a consistent polarity bias, during the time required to sustain redox taxis. The two-repellant sensing mechanism of Fig. 6 does not need a memory effect, provided that the polarity triggered by the R ox threshold is maintained until the R red threshold is attained, and vice versa. This mechanism, however, is not robust against rugged gradients, as any local heterogeneity that exceeds one of the thresholds makes shuttling cells return to the layer that they just left, instead of completing their migration. Adaptation of the R ox and R red thresholds according to the time-averaged repellent concentrations encountered by migrating cells would not help redox taxis either: for instance, the magnetotactic polarity of a DS cell located near z ox would be prematurely switched by a smaller R red threshold, and vice versa. A metabolism-based control of chemotaxis ( 51 ) might generate the long-term memory required to make redox taxis less sensitive to rugged redox gradients. Such a mechanism could set MB cells pausing at z red in a US state as soon as the sulfur accumulation capacity is exhausted, and cells pausing at z ox in a DS state as soon as the accumulated sulfur has been completely oxidized. The observation of fast chemical responses in our hanging drop assays suggests that external stimuli can override a hypothetical metabolism-based chemotaxis. A combination of metabolism-independent and metabolism-dependent controlling mechanisms, by which cells react rapidly to strong external triggers, but maintain a bias dictated their internal state, for instance through a modulation of the R ox and R red thresholds, explains the apparent inconsistencies between observed and expected magnetotactic polarities reported in the literature ( 19 – 21 ). These observations were obtained from hanging drop assays with no added water ( 19 ), or with a special apparatus that minimizes the introduction of oxygen during recovery of wild-type MTB ( 20 , 52 ). Both sampling procedures are expected to maintain, at least in part, the oxidation-reduction potential of the stratified water column, so that a strong magnetotactic polarity bias triggered by oxygen might be avoided, especially if the DS polarity is controlled by the oxidation-reduction potential ( 10 ). Under such conditions, a metabolic bias can preserve the in-situ magnetotactic polarity of individual cells, which, as discussed above, is not related to the position within the redox gradient. Additional indirect evidence for a metabolic control of magnetotaxis is given by the partial ability of MB cells to follow the OAI after a field reversal ( 25 ). In these experiments, the OAI was moving upwards by ~ 3.5 mm/day, as estimated from the MTB displacement observed with the normal field polarity. For comparison, the estimated migration speed of cells with constant magnetotactic polarity is ~ 12 mm/day ( 6 ), meaning that MTB can adjust their depth in sediment synchronously with the moving OAI. In case of experiments performed in a reversed field, cells are expected to move in the wrong direction ( 8 ), leading to the population decline observed with MC cells ( 25 ). Redox taxis assisted by a metabolic memory, on the other hand, permits a limited displacement towards the correct direction, as seen with the example of an US cell located just below to z ox . When the field is reversed, this cell starts to move downwards, away from the R ox threshold that would switch its magnetotactic polarity. Meanwhile, metabolism brings this cell to the next stage of redox taxis, which is the pause that would normally occur at z ox . As a result, the cell pauses somewhere below z ox , but still close enough to support oxidative reactions. When this pause comes to an end, the cell is set in a DS state, which makes it migrate upwards in the reversed field, instead of downwards. During the pause near z ox , the redox gradient moves up, so that the cell will cross the R ox threshold and leave the optimal depth range at a later point, closer to the sediment surface. The maximum vertical displacement attainable in this way is of the order of the distance covered during ordinary redox taxis. Indeed, the maximum MB displacement of ~ 1 cm observed in the reversed field, just before a complete disappearance of motile cells, is compatible with z red − z ox estimated from MB concentration profiles ( 25 ). Environmental and phylogenetic implications The combination of metabolism-independent and metabolism-based magneto-chemotaxis can generate a rich variety of responses by different types of MTB, enabling to exploit multiple ecological niches. This concept is best exemplified by the differences in depth distribution, migration ability, magnetotactic advantage, and chemotactic responses of MB and MC populations living inside the same sediment. Chemotactic responses that do not involve oxygen might have played an important role for supporting navigation of phylogenetically deep-branching MTB, of which MB is an example, in ancient anoxic environments, such as the Archean oceans ( 53 ). CONCLUSIONS Current magneto-aerotaxis models are challenged by (a) the lack of a consistent relation between magnetotactic polarity and position in the redox gradient, (b) the existence of substantial differences in the migration capability of different wild-type MTB, despite apparently identical aerotactic responses, and (c) the lack of a magnetotactic polarity switching mechanisms that support cell shuttling during redox taxis. Altogether, these observations can be explained by a threshold-driven, two-repellent model of magnetotaxis, where magnetotactic polarity is controlled by two groups of repellents with opposed concentration gradients. The first group includes oxygen and triggers the polarity that makes cells swim downwards (DS), as expected from magneto-aerotaxis models. The second group triggers the opposite polarity (US). We were able, for the first time, to observe a systematic magnetotactic polarity switching of MB cells, from DS to US and vice-versa, under the combined action of oxygen saturation and a pH gradient. In our experiments, acidic conditions acted as second repellent, which, in the chemical stratification of the sediment from which MB was retrieved, forms a counter gradient with respect to oxygen. The response of MB cells to mildly acidic or alkaline conditions includes a slowdown of the flagellar motor and subsequent reversal that is compatible with tumbling in the chemotaxis of non-magnetic bacteria. The magnetotactic polarity of MC could not be reversed by a pH gradient, demonstrating the different chemotactic response of these two MTB populations. The two-repellent model of magnetotaxis supports two fundamentally different magnetotactic behaviors, depending on the depths z ox and z red where the concentration thresholds of oxidizing ( R ox ) and reducing ( R red ) repellents set the magnetotactic polarity to a DS and an US state, respectively. If z red ≤ z ox , MTB tend to accumulate around a mean depth comprised between z ox and z red , where the overlapping and opposed stimuli of R ox and R red cancel any bias in favor of one or the other magnetotactic polarity. The resulting concentration profile is unimodal and comprised between z ox and z red , as observed for MC. If z ox < z red , MTB shuttle between z ox and z red , performing redox taxis. The resulting concentration profile is either flat, when cells do not pause, or bimodal with peaks near the limiting depths of redox taxis if cells pause near z ox and near z red . Both profile types are compatible with MB. Several observations, summarized in Table 2 , support these two scenarios. In both cases, the threshold triggering mechanism of polar magnetotaxis makes it less sensitive to random polarity reversals caused by rugged chemical gradients. Redox taxis might be further stabilized by a metabolism-driven magnetotactic polarity bias. Our model of polar magnetotaxis supports a large variety of magnetotactic behaviors, depending on the position of the R ox and R red thresholds in a redox gradient, enabling different types of MTB, such as MB and MC, to occupy different ecological niches inside the same environment. Declarations DECLARATION OF COMPETING INTEREST The authors declare no competing interests. Author Contribution X. M. and R. E. conducted the experiments. X. M, R. E., N. P., and X. L. analyzed of the data., X. M., R.E. and N.P. made the modeling. X.M. and R.E. wrote the paper. R.E. and X. L. supervised the work. ACKNOWLEDGMENTS This work is supported by National Natural Science Foundation of China (Grant No. 41602184, 42130507, 41772180), Natural Science Foundation of Fujian Province (Grant No. 2020J01141), and German Research Foundation (Grant No. EG 294/1–1 and EG 294/2 − 1). References Blakemore, R.P. 1975. Magnetotactic bacteria. Annu. Rev. Microbiol. 190: 217–238. Faivre, D., and D. Schüler. 2008. Magnetotactic bacteria and magnetosomes. Chem. Rev. 108: 4875–4898. Lefèvre, C. T., D. A. Bazylinski. 2013. Ecology, diversity, and evolution of magnetotactic bacteria. Microbiology and Molecular Biology Reviews 77: 497–526. Frankel, R.B. 1984. Magnetic guidance of organisms. 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Simple homemade apparatus for harvesting uncultured magnetotactic microorganisms. Brazilian Journal of Microbiology 34: 111–116. Lin, W., G.A. Paterson, Q. Zhu, Y. Wang, E. Kopylova, Y. Li, R. Knight, D.A. Bazylinski, R. Zhu, J.L. Kirschvink, and Y. Pan. 2017. Origin of microbial biomineralization and magnetotaxis during the Archean. Proceedings of the National Academy of Sciences . 114:2171–2176. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 09 Nov, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 09 Sep, 2024 Reviews received at journal 07 Sep, 2024 Reviews received at journal 28 Aug, 2024 Reviewers agreed at journal 19 Aug, 2024 Reviewers agreed at journal 19 Aug, 2024 Reviews received at journal 07 Aug, 2024 Reviewers agreed at journal 26 Jul, 2024 Reviewers agreed at journal 25 Jul, 2024 Reviewers invited by journal 25 Jul, 2024 Editor assigned by journal 29 Apr, 2024 Editor invited by journal 26 Apr, 2024 Submission checks completed at journal 26 Apr, 2024 First submitted to journal 24 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4320581","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":297457669,"identity":"75037254-f7cf-4d1c-9787-6659074e0145","order_by":0,"name":"Xuegang Mao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYHADxsYHCRU1JGlhbjZ4cOYYSVrY2yQftjATVqfbfviYNE9Frbw5/8K2isQGNgb+9u4EvFrMzqQlG/OcOW64c8bDthuJO2QYJM6c3YBfy4Ecw8e8bccYN9w4CNRyho3BQCKXgJbzbwwO8/47Zg/SUpDYxkyElhsgWxpqEjecb2xjIFLLs2TDOccOJG+4wdgskXDmGA9hv5xPPibxpqbOdsP54w8//qiokeNv78WvBQoOMzBIJIBZPMQoB4E6Bgb+A8QqHgWjYBSMgpEGALzsUobelEMKAAAAAElFTkSuQmCC","orcid":"","institution":"Fujian Normal University","correspondingAuthor":true,"prefix":"","firstName":"Xuegang","middleName":"","lastName":"Mao","suffix":""},{"id":297457671,"identity":"03d7c126-5d35-41f6-bc6f-ce0d5b3c4797","order_by":1,"name":"Ramon Egli","email":"","orcid":"","institution":"GeoSphere Austria","correspondingAuthor":false,"prefix":"","firstName":"Ramon","middleName":"","lastName":"Egli","suffix":""},{"id":297457673,"identity":"5fe3ba8e-ce2d-476e-9349-e7dc3e69eb05","order_by":2,"name":"Nikolai Petersen","email":"","orcid":"","institution":"Ludwig-Maximilians University","correspondingAuthor":false,"prefix":"","firstName":"Nikolai","middleName":"","lastName":"Petersen","suffix":""},{"id":297457675,"identity":"4df0fecb-435e-4337-8cce-8046e2eba075","order_by":3,"name":"Xiuming Liu","email":"","orcid":"","institution":"Fujian Normal University","correspondingAuthor":false,"prefix":"","firstName":"Xiuming","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2024-04-24 23:38:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4320581/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4320581/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-78946-7","type":"published","date":"2024-11-09T15:56:59+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":55765590,"identity":"266295e3-4a62-48c4-9ed1-70ab02bb8a65","added_by":"auto","created_at":"2024-05-02 20:07:31","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":580839,"visible":true,"origin":"","legend":"\u003cp\u003eMTB sampling and characterization. (\u003cem\u003eA\u003c/em\u003e) Sediment mud collection from the Nieder­lippach pond using a grab. (\u003cem\u003eB\u003c/em\u003e) Glass aquarium (30×20×20 cm) filled with pond sediment. Living MTB cells were found in the topmost 3 cm (dashed line). (\u003cem\u003eC\u003c/em\u003e) Hanging drop assay (insert), observed under an optical microscope equipped by two pairs of Helmholtz coils. MB cells performing polar magnetotaxis accumulate at the N side of the horizontal field produced by the Helmholtz coils (right side of the monitor). (\u003cem\u003eD\u003c/em\u003e) Transmission electron micrograph (TEM) image of a MC cell. (\u003cem\u003eE\u003c/em\u003e, \u003cem\u003eF\u003c/em\u003e) TEM images of MB with several chains of bullet-shaped magnetosomes (\u003cem\u003eE\u003c/em\u003e, insert). MB contains empty (\u003cem\u003eE\u003c/em\u003e) or filled sulfur inclusions (\u003cem\u003eF\u003c/em\u003e, arrow), as indicated by energy dispersive spectroscopy (\u003cem\u003eG\u003c/em\u003e).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/000fea98569255ca631d7a2e.png"},{"id":55765614,"identity":"aa97a6cf-b048-4201-8dfe-47270952f985","added_by":"auto","created_at":"2024-05-02 20:07:33","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":147607,"visible":true,"origin":"","legend":"\u003cp\u003eHanging drop assays with a pH gradient. (\u003cem\u003eA\u003c/em\u003e) Setup for observing MTB in a pH gradient (top view and side view, not to scale). See the text for the definition of zones A, B, and C. (\u003cem\u003eB\u003c/em\u003e, \u003cem\u003eC\u003c/em\u003e) Simulated profiles of [H\u003csup\u003e+\u003c/sup\u003e] and pH in the liquid film under the glass cover, for selected times after the addition of a pH 3 solution at the right end of the cover slide.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/72487ea48eb4f7f68bc8f96f.png"},{"id":55765611,"identity":"ad386969-4de4-4798-bef0-ecd85140a571","added_by":"auto","created_at":"2024-05-02 20:07:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":76466,"visible":true,"origin":"","legend":"\u003cp\u003eOscillatory swimming paths of selected MB cells in the [H\u003csup\u003e+\u003c/sup\u003e] gradient created in zone B by the addition of a pH 3 solution. Left plots: swimming paths digitized from Movie S4. Arrows indicate the field direction before and after the field reversal. The point of the path where the reversal occurred is indicated by an asterisk. Right plots: \u003cem\u003ex\u003c/em\u003e- and \u003cem\u003ey\u003c/em\u003e-coordinates of the digitized paths (circles), as a function of time. The vertical dashed line indicates the field reversal at \u003cem\u003et\u003c/em\u003e = 37.8 s. The path coordinates \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) and \u003cem\u003ey\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) have been fitted with straight segments corresponding to a constant swim­ming velocity. Before the field is reversed, positive and negative slopes of \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) represent NS and SS magnetotactic polarities, respectively, while the opposite is true after field reversal. (\u003cem\u003eA\u003c/em\u003e) Large MB cell performing unusually large oscillations. The asymmetric saw-tooth pattern in \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) defines the NS and SS swimming velocities \u003cem\u003ev\u003c/em\u003e\u003csub\u003eNS\u003c/sub\u003e = 0.40 ± 0.02 mm/s and \u003cem\u003ev\u003c/em\u003e\u003csub\u003eSS\u003c/sub\u003e = 0.25 ± 0.03 mm/s, respectively, which are switched with a frequency \u003cem\u003ef\u003c/em\u003e = 1.7 Hz. The cell was NS when the field has been reversed. (\u003cem\u003eB\u003c/em\u003e) Same as (A) for a smaller cell performing faster oscillations (\u003cem\u003ev\u003c/em\u003e\u003csub\u003emean\u003c/sub\u003e = 0.33 ± 0.1 mm/s, \u003cem\u003ef\u003c/em\u003e = 6.6 Hz). (\u003cem\u003eC\u003c/em\u003e) Same as (A) for two close cells (\u003cem\u003ev\u003c/em\u003e\u003csub\u003emean\u003c/sub\u003e = 0.33 ± 0.1 mm/s, \u003cem\u003ef\u003c/em\u003e = 6.4 Hz). In this case one cell becomes SS when the field is switched, and therefore continues to swim towards the pH front.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/906b7cb519b141514fd8ce8d.png"},{"id":55765612,"identity":"e2b548ab-0c48-4dea-8353-d496a73ae8e6","added_by":"auto","created_at":"2024-05-02 20:07:33","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":215685,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/e174e6b348603d45f3aa698f.png"},{"id":55765613,"identity":"18558e04-cdd6-45c6-a39a-2ffa2b6939b8","added_by":"auto","created_at":"2024-05-02 20:07:33","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":53469,"visible":true,"origin":"","legend":"\u003cp\u003eModel of two-threshold polar magnetotaxis with overlapping repellent counter gradients. (\u003cem\u003eA\u003c/em\u003e) Repellent concentrations \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e (shaded) and corresponding magnetotactic polarity swit­ching thresholds (asterisks). \u003cstrong\u003eB\u003c/strong\u003e represent the inclined field lines in the northern hemisphere. MTB are set to a DS and to an US state above the \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e and below the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e threshold, respectively. Both states coexist between the two thresholds. The magnetotactic polarity is determined by CCW or CW flagellar rotation. (\u003cem\u003eB\u003c/em\u003e) Idealized cell concentration profile. (\u003cem\u003eC\u003c/em\u003e) Measured oxygen concentration (da­shed line) and MC concentration profiles (solid lines) in sediment (data from ref. 25). The three MC profiles correspond to the average of individual measurements with depth-integrated total concen­trations \u003cem\u003eN\u003c/em\u003e \u0026lt; 200 cells/mm\u003csup\u003e2\u003c/sup\u003e (lowest curve), \u003cem\u003eN\u003c/em\u003e \u0026gt; 500 cells/mm\u003csup\u003e2\u003c/sup\u003e (highest curve), and 200 \u0026lt; \u003cem\u003eN\u003c/em\u003e \u0026lt; 500 cells/mm\u003csup\u003e2\u003c/sup\u003e (intermediate curve).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/5d4dfe8152c7eddfad78e36e.png"},{"id":55765615,"identity":"5b845510-f960-4c97-9f97-495a12b314b2","added_by":"auto","created_at":"2024-05-02 20:07:33","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":82181,"visible":true,"origin":"","legend":"\u003cp\u003eModel of two-threshold polar magnetotaxis with non-overlapping repellent counter gra­dients. (\u003cem\u003eA\u003c/em\u003e) Repellent concentrations \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e (shaded) and corresponding magnetotactic polarity switching thresholds (asterisks). \u003cstrong\u003eB\u003c/strong\u003e represent the inclined field lines in the northern hemisphere. MTB are set to a DS and to an US state at the \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e and at the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e thresholds, respectively, making the cells shuttle along \u003cstrong\u003eB\u003c/strong\u003e, between two limiting depths defined by the thresholds. The magnetotactic polarity is determined by CCW or CW flagellar rotation. Cell shading indicates the progress of metabolic pro­cesses performed under reducing (darkening) and oxidizing (lightening) conditions. (\u003cem\u003eB\u003c/em\u003e) Idealized cell concentration profile corresponding to (\u003cem\u003eA\u003c/em\u003e). (\u003cem\u003eC\u003c/em\u003e) Same as (\u003cem\u003eA\u003c/em\u003e), for the case where cells pause near the \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e thresholds. (\u003cem\u003eD\u003c/em\u003e) Cell concentration profile corresponding to (\u003cem\u003eC\u003c/em\u003e). (\u003cem\u003eE\u003c/em\u003e) Measured oxygen concentration (dashed line) and MB concentration profiles (solid lines) in sediment (data from ref. 25). The three MB profiles correspond to the average of individual measurements with depth-integra­ted total concentrations \u003cem\u003eN\u003c/em\u003e \u0026lt; 450 cells/mm\u003csup\u003e2\u003c/sup\u003e (lowest curve), \u003cem\u003eN\u003c/em\u003e \u0026gt; 1500 cells/mm\u003csup\u003e2\u003c/sup\u003e (highest curve), and 450 \u0026lt; \u003cem\u003eN\u003c/em\u003e \u0026lt; 1500 cells/mm\u003csup\u003e2\u003c/sup\u003e (intermediate curve).\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/112f5ae197599b718b99cd9f.png"},{"id":55765610,"identity":"6a3eec5c-6c5c-426a-8c5b-4b10871bad08","added_by":"auto","created_at":"2024-05-02 20:07:32","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":210874,"visible":true,"origin":"","legend":"\u003cp\u003eVariability of MB profiles in a sediment microcosm (data from ref. 25). (\u003cem\u003eA\u003c/em\u003e) Forty-four individual profiles taken with 1 mm resolution over several months. Lines are color-coded according to the depth-integrated cell concentration, from blue (lowest) to red (highest). Notice the nonlinear scale used to represent profiles with amplitudes that vary over two orders of magnitude. (\u003cem\u003eB\u003c/em\u003e–\u003cem\u003eD\u003c/em\u003e) Same as (\u003cem\u003eA\u003c/em\u003e) for selected profiles with pronounced upper peak, lower peak, and both. The thick line is the average of the plotted profiles.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/a7358de7391a23867d2262a0.png"},{"id":68749902,"identity":"fd282b5d-46b0-44b1-ab58-c3a2977f170f","added_by":"auto","created_at":"2024-11-11 16:07:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2383283,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4320581/v1/d5b7c030-d977-4277-8403-ade0f748d678.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An update on polar magnetotaxis: Insights from hanging drop assays and microcosm experiments","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eMagnetotactic bacteria (MTB) contain intracellular chains of nano-sized magnetite and/or greigite crystals, which ensure a passive alignment with the Earth\u0026rsquo;s magnetic field (\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e), known as magnetotaxis. Combination of this alignment with the swimming direction determined by surrounding environment (chemotaxis) yields a one-dimensional displacement along magnetic field lines, reducing a three-dimensional search problem of ordinary chemotaxis to one of a single dimension (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). Magneto-chemotaxis is therefore more efficient than chemotaxis alone in all situations where the magnetic field component along the sought direction of displacement exceeds few \u0026micro;T (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e). This magnetotactic advantage is also available to MTB living in sediment, despite the poor (~\u0026thinsp;1\u0026ndash;3%) alignment with the Earth\u0026rsquo;s magnetic field caused by the limited space available in sediment pores (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Many MTB are sensitive to oxygen and show a behavior known as magneto-aerotaxis (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e), either through a temporal sensing mechanism, as in \u003cem\u003eMagnetospirillum magnetotacticum\u003c/em\u003e strain MS-1, or a threshold mechanism, as in \u003cem\u003eMagnetococcus marinus\u003c/em\u003e strain MC-1 (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). The temporal sensing mechanism, which measures concentration gradients, produces an axial response to the magnetic field (axial magnetotaxis), such that changing the field polarity will not disrupt the cell concentration profile that forms the aerotactic band in cultures grown in a semi-solid medium. The threshold mechanism, which is concentration-sensitive, gives a polar response to the magnetic field (polar magnetotaxis), such that a field reversal will disperse the aerotactic band that forms at the oxic-anoxic interface (OAI). The preferred swimming direction relative to the magnetic field in a hanging drop assay, where oxygen is nearly saturated, determines the magnetotaxis polarity, that is, north-seeking (NS) if swimming towards the magnetic North, or south-seeking (SS) otherwise. MTB performing axial magnetotaxis react randomly to the absence of an oxygen gradient, undertaking frequent changes of the swimming direction that impart a characteristic oscillatory motion parallel to the magnetic field. MTB performing polar magnetotaxis, on the other hand, are in a well-defined sensory state dictated by oxygen saturation, which yields a predominant NS polarity.\u003c/p\u003e \u003cp\u003eBoth axial and polar magnetotaxis are believed to help MTB in maintaining themselves within a preferred depth range in horizontally stratified environments where the oxygen concentration decreases with depth. In the case of polar magnetotaxis, most cells retrieved in the northern hemisphere are NS when exposed to large oxygen concentrations and SS in the southern hemisphere, since these polarities makes them swim downwards along the inclined field lines. Equal amounts of NS and SS MTB have been found in proximity of the magnetic equator (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e), where the field lines are horizontal. The direction of the Earth\u0026rsquo;s magnetic field relative to chemical gradients is therefore considered to be responsible for MTB polarity selection (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e). A second sensory state is needed to switch the magnetotactic polarity, making cells swim upwards when located too deep, albeit such a polarity switching has never been observed in controlled experiments (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). The second sensory state might be triggered by a lower oxygen threshold (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e), or by a chemorepellent response associated with excessively reducing conditions. The threshold sensory mechanism might also depend on metabolic states of the cell. A metabolic control of magnetotaxis would have the benefit of avoiding unnecessary displacements (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e); however, fast chemotactic responses are still needed to escape potentially damaging conditions. Cell metabolism is expected to play an important role in redox taxis (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e): for instance, MTB from the \u003cem\u003eNitrospirae\u003c/em\u003e phylum accumulate elemental sulfur (S\u003csup\u003e0\u003c/sup\u003e) through sulfate reduction while resting in the reducing zone, until a \u0026ldquo;reduced\u0026rdquo; internal state triggers the magnetotactic polarity reversal required to move up to the microaerobic zone, where S\u003csup\u003e0\u003c/sup\u003e can be oxidized (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). Complete consumption of S\u003csup\u003e0\u003c/sup\u003e would switch the cell to an \u0026ldquo;oxidized\u0026rdquo; state that makes it migrate again to the reduced zone.\u003c/p\u003e \u003cp\u003eMore complicated forms of magneto-aerotaxis have been described. For instance, strains of \u003cem\u003eMagnetospirillum\u003c/em\u003e freshly isolated from environmental samples display a form of semi-polar magnetotaxis where the typical oscillatory motion of axial magnetotaxis is biased, resulting in the accumulation of cells along one edge of the hanging drop assay (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). The marine vibrio MV-1, on the other hand, performs axial magnetotaxis in the oxic zone and polar magnetotaxis in the anoxic zone of gradient cultures (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e). These observations suggest that axial and polar magnetotaxis might be the idealized endmembers of a range of intermediate responses to chemical gradients. Furthermore, magnetotaxis is also affected by light (phototaxis) and physical contact (\u003cspan additionalcitationids=\"CR15 CR16 CR17\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e). Non-chemical stimuli might provide additional clues for navigation in the water column and in the sediment.\u003c/p\u003e \u003cp\u003eCurrent models of magnetotaxis are challenged by the observation of MTB with opposite magnetotactic polarity coexisting in at the same depths in horizontally stratified water columns, and the lack of a consistent relation between polarity and position in the redox gradient (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e). On the other hand, hanging drop assays on wild-type MTB retrieved from sediment, including \u003cem\u003eMagnetobacterium bavaricum\u003c/em\u003e, the model MTB for which redox taxis has been postulated (\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e), yielded always the polarity expected in the case of oxygen saturation, regardless of sampling depth, also when sampling and observations were performed under strictly anoxic conditions and in the dark (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). These results cannot be explained by an aerotactic or a metabolic control of the swimming direction, or a combination of both. In the present study, we observe the response of wild-type cells of \u003cem\u003eMagnetobacterium bavaricum\u003c/em\u003e (MB) and unidentified magnetic cocci (MC) to pH gradients, and show, for the first time, that the magnetotactic polarity of MB can be switched by a pH-driven threshold sensing mechanism. Our result suggests that polar magnetotaxis is controlled by at least two chemorepellents, or groups of chemorepellents, associated with natural redox gradients. Using results obtained from previous experiments with MB and MC cells from the same sediment (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e), we develop a new model of polar magnetotaxis that resolves the abovementioned inconsistencies between theory and observations.\u003c/p\u003e"},{"header":"MATERIALS AND METHODS","content":"\u003cp\u003eFreshwater sediment was collected using a grab sampler from a small pond (30\u0026times;7\u0026times;0.5m) in Niederlippach, Germany, (48\u0026deg;35\u0026rsquo;14.98\u0026rdquo; N, 12\u0026deg;04\u0026rsquo;43.71\u0026rdquo; E, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, A) (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e), and transferred to glass aquaria that were kept at room temperature (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, B) in the Earth\u0026rsquo;s magnetic field. A new sediment stratification and oxygen gradient was reestablished after ~\u0026thinsp;10 days. After complete stabilization, mini cores (3\u0026ndash;5 cm long) were taken from the sediment using a plastic drinking straw (diameter: 5 mm) and sliced in 1 mm increments. Each slice was diluted with distilled water (~\u0026thinsp;200 \u0026micro;L) and prepared for a hanging drop assay on a rubber O-ring to prevent rapid evaporation (insert of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, C). MTB cells swimming out of the sediment were observed and counted under a special optical microscope (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e) equipped with Helmholtz coils for producing a stable magnetic field (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, C). The quasi totality of MTB observed with this apparatus belonged to two groups: the giant rod-shaped MB (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, E, F), previously identified in the same pond (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e), and MC cells containing one or more chains of prismatic or tooth-shaped magnetosomes (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, D). Despite their diversity, MC cells were characterized by a homogeneous magnetotactic behavior. The presence of sulfur inclusions (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, F) in MB cells was confirmed by energy-dispersive X-ray spectroscopy (EDS) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, G).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMTB cells freshly retrieved from the sediment present strong tactile responses and a tendency to decrease their motility with time, or upon transferring them to another setup once they left the sediment. Attempts to transfer MTB cells into microfluidic devices, where controlled chemical gradients can be created, were not successful. Therefore, a modified version of the hanging drop assay has been used to observe the motion of MB cells in a pH gradient, under conditions that were as close as possible to the classic hanging drop assay used here as control experiment. The modified hanging drop assay (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, A) was prepared as follows: ~0.5 mL of MTB-containing sediment was taken with a micropipette from an aquarium and transferred to a glass slide (2.6\u0026times;7.6 cm). Then, ~\u0026thinsp;1 mL distilled water (pH 7) was added on the top of the sediment drop to create a clear water rim around the sediment. Placement of a cover glass (2\u0026times;2 cm) onto the sediment-water preparation creates a thin film of homogeneous thickness.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA series of aqueous solutions with pH values ranging from 1 to 12 have been prepared by successive dilution of 1 M HCl or NaOH with distilled water. The pH value of each solution was confirmed with a pH sensor from Unisense. About 0.1 mL of the as-prepared pH solution was deposited onto one side of the cover glass, providing a reservoir that is in contact with the fluid under the cover glass (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, A). The thin fluid layer below the cover glass prevents turbulent mixing, so that a pH gradient forms by diffusion and propagates toward the other end of the cover glass. This setup does not allow to monitor actual pH values; however, as discussed later, a qualitative assessment of the pH gradient is sufficient to elucidate the magnetotactic response, which is therefore simply described by the pH value of the added solution.\u003c/p\u003e \u003cp\u003eA rough assessment of the pH gradient is obtained from the solution of the one-dimensional diffusion equation\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\frac{{\\partial C}}{{\\partial t}}=D\\frac{{{\\partial ^2}C}}{{\\partial {x^2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003einside the fluid layer below the cover glass, where \u003cem\u003eC\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e) is the concentration of H\u003csup\u003e+\u003c/sup\u003e or OH\u003csup\u003e\u0026minus;\u003c/sup\u003e ions as a function of the distance \u003cem\u003ex\u003c/em\u003e from the cover slide edge where the solution was added at the time \u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0, and \u003cem\u003eD\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;2.3\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e m\u003csup\u003e2\u003c/sup\u003e/s is the self-diffusion coefficient of water at room temperature. The initial condition \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C(x,t)={C_0}H(x),\\)\u003c/span\u003e\u003c/span\u003e where \u003cem\u003eC\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the concentration of ions and \u003cem\u003eH\u003c/em\u003e is the Heaviside unit step function, describes the addition of the pH solution at \u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0. Suitable boundary conditions must be set at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0 and at the opposed side \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;\u003cem\u003eL\u003c/em\u003e of the cover slide (\u003cem\u003eL\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;2 cm). Because the added drop of pH solution is much thicker than the fluid layer under the cover slide, we assume an infinite reservoir with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C(0,t)={C_0}\\)\u003c/span\u003e\u003c/span\u003e at \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0. The other end of the cover slide is a physical barrier with no flux, whence \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\partial C{\\kern 1pt} /{\\kern 1pt} \\partial x=0\\)\u003c/span\u003e\u003c/span\u003e for \u003cem\u003ex\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eL\u003c/em\u003e. Numerical solutions of Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, B (H\u003csup\u003e+\u003c/sup\u003e ions) and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, C (pH) for a 2-cm-wide cover slide and a pH 3 solution ([H\u003csup\u003e+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e = 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e). These solutions show that a pH front with decreasing sharpness propagates under the cover slide for the first\u0026thinsp;~\u0026thinsp;30 min. During this time, the left-hand side of the cover slide is unaffected by the pH solution. The pH front disappears completely after 2 hours, when the pH of the entire water film starts to decrease until it equilibrates with the added solution. Accordingly, we expect a pH gradient along \u003cem\u003ex\u003c/em\u003e to be present during the first\u0026thinsp;~\u0026thinsp;30 min, so that MTB cells exiting the sediment will swim from a near-neutral environment into a\u0026thinsp;\u0026lt;\u0026thinsp;1 mm-wide diffusion front. All observations were performed within 30 min from preparation, after placing the glass slide under the optical microscope in a controlled magnetic field. Motile cells can be observed for several hours, which means that evaporation is not an issue in these experiments.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eControl experiments and loss of cell motility\u003c/h2\u003e \u003cp\u003eA series of pH solutions (pH 1\u0026ndash;12) have been used to test the MTB response to a pH gradient. Addition of a pH 7 solution, which is similar to the near-neutral pH of the sediment used in our experiments (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e), did not produce a noticeable change in the swimming behavior of both MTB types with respect to simple hanging drop assays, with cells being consistently NS (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In rare cases, few (\u0026lt;\u0026thinsp;1%) MB engaged an oscillatory motion (Movie S1). This control experiment shows that the one-sided addition of an aqueous solution to the hanging drop setup does not modify, per se, the magnetotactic polarity of MB and MC cells.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of results obtained from hanging drop assays. Numbers indicate cell counts.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdded solution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOscillating\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFull stop (immobile)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFull stop (vibrating)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eControl \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e~\u0026thinsp;400 (99.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3 (0.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;300 (100%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 2 \u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9 (6.4%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e131 (93.6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003enot observed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003enot observed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 2 \u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e37 (3.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e955 (83.5%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e102 (8.9%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e50 (4.4%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15 (28.8%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e37 (71.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003enot observed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003enot observed\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2 (8.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e22 (91.7%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e100 (100%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2 (5.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e36 (94.7%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e45 (97.8%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1 (2.2%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7 (25%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e21 (75%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003epH 12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e~\u0026thinsp;300 (100%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003csup\u003ea\u003c/sup\u003e Standard assay\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003csup\u003eb\u003c/sup\u003e Before oscillating cells were observed\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003csup\u003ec\u003c/sup\u003e While oscillating cells were observed\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eNearly all MTB cells lose their motility with a complete stop of the flagellar motor upon adding very acidic (pH 1) or alkaline (pH 12) solutions once they reach the diffusion front (Movie S2). Motility was not resumed upon reversing and/or rotating the magnetic field. On the other hand, the addition mild solutions (pH 4\u0026ndash;6 and 8) triggered a different response, with MB cells slowing down to a full stop after reaching the diffusion front. After stopping, rapid lateral vibrations of the cell body (Movie S3), indicate that the flagellar motor was still active, but flagella were no longer arranged in a way that supported forward propulsion (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e). Lateral vibrations are produced by random torques that would make the cell tumble in absence of a magnetic field. Tumbling is a typical chemotactic response of motile bacteria (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e), which, in the case of MTB, might serve other purposes. Normal swimming was not resumed by reversing or by rotating the magnetic field.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eMagnetotactic polarity switching\u003c/h2\u003e \u003cp\u003eA distinct swimming pattern that included magnetotactic polarity switching (Movie S4) was observed only in the case of MB cells approaching the pH gradients created by adding moderately acidic solutions (pH 2\u0026ndash;3). This pattern is best described by dividing the cover slide into three zones, labeled as A, B, and C, according to the increasing proximity to the side where the solution was added (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, A). In zone A, which extends from the sediment to a certain distance from the diffusion front, cells maintained the usual NS behavior (Movie S4, 0\u0026rsquo;4\u0026rdquo;\u0026ndash;0\u0026rsquo;6\u0026rdquo;), eventually approaching the pH front. In the pH 2 experiment, few (4.4%) MB cells continued to swim along the same direction until reaching zone C, closest to the side where the solution was added, until the flagellar motor suddenly stopped. Motility could not be resumed by reversing and/or rotating the magnetic field (Movie S4, 0\u0026rsquo;9\u0026rdquo;\u0026ndash;0\u0026rsquo;12\u0026rdquo;), alike the experiments with pH 1 solutions. Most MB cells, however, reversed their swimming direction in zone C, effectively becoming SS (Movie S4, 0\u0026rsquo;50\u0026rdquo;\u0026ndash;2\u0026rsquo;10\u0026rdquo;). These SS cells occasionally reverted to NS for short periods of time (0.5\u0026ndash;1 s), however, the net swimming direction was SS (Movie S4, 0\u0026rsquo;50\u0026rdquo;\u0026ndash;2\u0026rsquo;10\u0026rdquo;). The SS motility triggered in zone C did not cease until cells reached again zone B, where they engaged a distinct back-forward motion (referred to as oscillating in the following) by switching their flagellar motor every 0.15\u0026ndash;0.6 s, with no systematic bias in favor of either direction (Movie S4, 0\u0026rsquo;17\u0026rdquo;\u0026ndash;0\u0026rsquo;33\u0026rdquo; and 2\u0026rsquo;15\u0026rdquo;\u0026ndash;2\u0026rsquo;22\u0026rdquo;). The oscillating motion maintained these cells in zone B for several minutes. In the pH 3 experiment, most MB cells engaged the same oscillating motion as soon as they reached zone B (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAfter reversing the magnetic field (Movie S4, 0\u0026rsquo;33\u0026rdquo;), MB in zone B stop to oscillate, resuming their normal swimming behavior (Movie S4, 0\u0026rsquo;33\u0026rdquo;\u0026ndash;0\u0026rsquo;40\u0026rdquo;), mostly (~\u0026thinsp;91%) with NS polarity, and the remaining part (~\u0026thinsp;9%) with SS polarity (Movie S4, 2\u0026rsquo;41\u0026rdquo;\u0026ndash;2\u0026rsquo;49\u0026rdquo;). NS cells eventually reached back into zone A, while SS cells advanced towards zone C. If the original magnetic field direction was restored (Movie S4, 0\u0026rsquo;42\u0026rdquo;), both NS and SS cells returned to zone B and engaged the same oscillatory motion observed before (Movie S4, 0\u0026rsquo;43\u0026rdquo;\u0026ndash;0\u0026rsquo;46\u0026rdquo;). If the magnetic field was turned by 90\u0026deg; (Movie S4, 2\u0026rsquo;53\u0026rdquo;), all MB cells became NS, stopping the periodic polarity reversal (Movie S4, 2\u0026rsquo;53\u0026rdquo;\u0026ndash;3\u0026rsquo;11\u0026rdquo;). Zeroing the magnetic field made MB cells swim randomly, with no preferred direction (Movie S5 0\u0026rsquo;2\u0026rdquo;\u0026ndash;0\u0026rsquo;41\u0026rdquo;).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eTracking periodic magnetotactic polarity reversals\u003c/h2\u003e \u003cp\u003eDetailed insights into the periodic motion of MB cells in zone B have been obtained by digitizing individual swimming paths in Movie S4 (0\u0026rsquo;29\u0026rdquo;\u0026ndash;0\u0026rsquo;36\u0026rdquo;). The first example (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, A) depicts a large cell that oscillates with an unusually large amplitude. Its swimming path is composed of discrete sections characterized by constant swimming velocities with alternating sign, as deduced from the saw-tooth pattern of the \u003cem\u003ex\u003c/em\u003e-coordinate \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e). The \u003cem\u003ey\u003c/em\u003e-coordinate, on the other hand, remains nearly constant, up to small random fluctuations, as expected from the strong alignment of MB cells (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e) in the ~\u0026thinsp;0.1 mT field parallel applied along \u003cem\u003ex\u003c/em\u003e. The asymmetry of the saw-tooth pattern is caused by the swimming velocity of SS tracks being ~\u0026thinsp;37% smaller than that of NS tracks. This pattern clearly shows that oscillations around a mean position are not random, being caused by flagellar motor reversals occurring at two fixed positions along the pH gradient. Most MB cells in zone B oscillate much more rapidly, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, B. In these cases, the rapid (~\u0026thinsp;6 Hz) alternation of the swimming direction prevents a precise discrimination between NS and SS velocities. In both examples, the magnetic field was reversed while the cells were NS. Thereafter, cells continued to be NS and swam away from the diffusion front. The last example (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, C) depicts two oscillating cells that are only\u0026thinsp;~\u0026thinsp;50 \u0026micro;m apart from each other, which means that they move inside the same chemical gradient roughly oriented along \u003cem\u003ex\u003c/em\u003e. The field was reversed when both cells were NS, yet one cell remained NS, while the other cell became SS and swam toward the pH front. Because of identical external conditions, the different behaviors of the two cells must be attributed to cell-internal factors, due for instance to a memory effect (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003epH sensitivity\u003c/h2\u003e \u003cp\u003eThe above observations can be summarized as follows: (a) The addition of solutions with pH values close to the natural sedimentary environment (pH 7) did not produce any visible difference with respect to the regular hanging drop assay; (b) the addition of highly acidic or alkaline solutions (pH 1 and 12) led to a complete stop of the flagellar motor once passing through the diffusion front (zone C); (c) the addition of weakly acidic or alkaline solutions (pH 4\u0026ndash;6 and 8) led to a progressive slowdown and stop once passing through the diffusion front (zone C), however, the flagellar motor was still active; (d) the addition of moderately acidic solutions (pH 2\u0026ndash;3) triggered a magnetotactic polarity reversal in most cells, which led to an oscillatory motion either directly in zone B (pH 3), or after a first reversal in zone C (pH 2); (e) a magnetic field reversal brings\u0026thinsp;~\u0026thinsp;91% of the oscillating cells back to their usual NS state, while the remaining\u0026thinsp;~\u0026thinsp;9% becomes SS; (f) reverting the magnetic field to the original polarity resumes the oscillatory behavior once the cells returned to zone B. Finally, MC cells were either unaffected, or they slowed down and lost their motility upon encountering a sufficiently strong pH gradient (Movie S6), suggesting that pH does not trigger a magnetotactic polarity reversal in this type of MTB.\u003c/p\u003e \u003c/div\u003e"},{"header":"DISCUSSION","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003epH-driven polar magnetotaxis switching\u003c/h2\u003e \u003cp\u003eThe periodic swimming direction reversal engaged by MB cells in properly set pH gradients differ from changes of the magnetotactic behavior triggered by other stimuli, such light as tactile responses. For instance, the bounce and ping-pong motion of multicellular magnetotactic prokaryotes (MMPs), which is triggered by UV light (phototaxis) or tactile stimuli (\u003cspan additionalcitationids=\"CR16 CR17\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e) is irregular and depends on the sampling season, storage time in the laboratory, observation duration, and on the magnetic field strength (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e). Our observations, on the other hand, depend on the presence of a pH gradient, this gradient being the only difference with control experiments. The response of MB cells to pH gradients, which enables them to escape very acidic or alkaline conditions, is analogous to that of other neutrophilic bacteria (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe oscillatory motion of MB in zone B resembles the axial magnetotaxis of spirilla (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). However, the cause is completely different: in absence of a chemical gradient, the temporal sensing mechanism of spirilla is subjected to random fluctuations and measures essentially noise, triggering swimming direction reversals at random times. The oscillation of MB in zone B, on the other hand, is very regular (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), and it occurs in proximity of zone C, where excessively acidic conditions suppress cell motility. This means that the concentration of H\u003csup\u003e+\u003c/sup\u003e ions in zone B abundantly exceeds the noise level of the sensory mechanism, so that changes in swimming direction are triggered deterministically either by a concentration gradient or by a concentration threshold.\u003c/p\u003e \u003cp\u003eIn case of spatiotemporal sensing mechanisms (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e), cells compare the concentrations \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)) and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e + ∆\u003cem\u003et\u003c/em\u003e)) of a repellent \u0026ndash; in our case H\u003csup\u003e+\u003c/sup\u003e-ions \u0026ndash; along the swimming path \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) over successive time intervals ∆\u003cem\u003et\u003c/em\u003e, therefore effectively sensing a spatial gradient \u003cem\u003eG\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) = (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e \u0026ndash; \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e)/\u003cem\u003ev\u003c/em\u003eΔ\u003cem\u003et\u003c/em\u003e along \u003cem\u003ex\u003c/em\u003e, with \u003cem\u003ev\u003c/em\u003e being the swimming velocity. In this case, the only role played by the magnetic field is that of determining the axis along which the gradient is sensed, so that the response to a field polarity reversal is purely axial (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). However, our experiments show that the periodic change of the swimming direction by cells that engage an oscillatory motion in zone B ceases immediately after reversing the field polarity, yielding NS or SS cells with the normal swimming behavior observed without a pH gradient. This observation proves that MB cells do not react to pH gradients via a spatiotemporal sensing mechanism.\u003c/p\u003e \u003cp\u003eThe threshold sensing model (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e) assumes that the swimming direction of MB cells is switched by a repellent threshold concentration detected by external (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e) or internal (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e) receptors. We assume that the capture of repellant molecules and the transmission of signals to the flagellar motor produces a certain delay between the actual concentration \u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)) along the swimming path \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) of the cell, and the sensed concentration \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e), which might be controlled by a diffusive process (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e), or by a reaction rate (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e). To keep the conceptual model as simple as possible, we use a one-dimensional model of tracer diffusion across planar sheet of thickness 2\u003cem\u003ed\u003c/em\u003e that surrounds the receptors located at \u003cem\u003ez\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0. The exact geometry of the problem is irrelevant, because the thickness of the sheet and its diffusion coefficient combine into a single parameter \u003cem\u003eτ\u003c/em\u003e\u003csub\u003ed\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ed\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e/\u003cem\u003eD\u003c/em\u003e which controls the time dependence of the tracer concentration profile \u003cem\u003ec\u003c/em\u003e(\u003cem\u003ez\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e) across the sheet (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e). With these settings, \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003ec\u003c/em\u003e(\u003cem\u003ez\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0, \u003cem\u003et\u003c/em\u003e), where \u003cem\u003ec\u003c/em\u003e is the solution of the one-dimensional diffusion equation with boundary condition c(\u0026plusmn;\u0026thinsp;\u003cem\u003ed\u003c/em\u003e, \u003cem\u003et\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)), and \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) the swimming path and \u003cem\u003eC\u003c/em\u003e the tracer concentration outside the cell. Since \u003cem\u003ed\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e/\u003cem\u003eD\u003c/em\u003e and the pH profiles of the hanging drop experiments are unknown, all simulations results discussed below are expressed in arbitrary units assuming \u003cem\u003eD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1, and \u003cem\u003ev\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.\u003c/p\u003e \u003cp\u003eThe initial condition for a cell that just left the sediment and swims towards the diffusion front (zone A) is \u003cem\u003eC\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e \u0026asymp; 0. The cell is initially NS, so that \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;\u003cem\u003ev\u003c/em\u003e\u003csub\u003eNS\u003c/sub\u003e \u003cem\u003et\u003c/em\u003e, where \u003cem\u003ev\u003c/em\u003e\u003csub\u003eNS\u003c/sub\u003e \u0026gt; 0 is the NS swimming velocity. In zone B, \u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)) starts to increase, and the same occurs for \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e) with some delay caused by diffusion across \u003cem\u003ed\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, A). When \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e) reaches a critical threshold \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C_{{\\text{s}}}^{ * }\\)\u003c/span\u003e\u003c/span\u003e (assumed to be 0.2 in the unitless simulations of Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), the swimming direction is reversed and the cell becomes SS, moving back towards the starting point. \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e initially continues to increase while \u003cem\u003eC\u003c/em\u003e is decreasing, but the trend is inverted after passing the point where \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e = \u003cem\u003eC\u003c/em\u003e. If the cell remains SS, \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e will eventually cross a threshold that makes the cell becoming NS again. For convenience, we assume this threshold to be identical to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C_{{\\text{s}}}^{ * }\\)\u003c/span\u003e\u003c/span\u003e. While the cell is moving again towards the repellent, \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e continues to decrease for a while, until the increase of \u003cem\u003eC\u003c/em\u003e reverses this trend. At a certain point, \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e exceeds \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C_{{\\text{s}}}^{ * }\\)\u003c/span\u003e\u003c/span\u003e a second time, and the cell becomes again SS. This cycle is repeated indefinitely, as long as \u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) is constant, producing the periodic functions \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e), \u003cem\u003eC\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e)) and \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(\u003cem\u003et\u003c/em\u003e) in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, B. The periodicity of \u003cem\u003ex\u003c/em\u003e(\u003cem\u003et\u003c/em\u003e) represents the oscillatory behavior of the cell around a mean position close to the point where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C=C_{{\\text{s}}}^{ * }\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe qualitative characteristics of the periodic motion depend only on the existence of (a) a sensed threshold \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C_{{\\text{s}}}^{ * }\\)\u003c/span\u003e\u003c/span\u003e that triggers a magnetotactic polarity reversal and determines the mean position of the cell with respect to the pH gradient, and (b) a delay between \u003cem\u003eC\u003c/em\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e, which controls the period\u0026thinsp;~\u0026thinsp;\u003cem\u003ed\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e/\u003cem\u003eD\u003c/em\u003e of the motion. Sensing mechanisms depend in a complex manner on the input and its past evolution, generating hysteretic responses that reduce the flagellar motor chatter in case inputs close to the noise level (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e). In this case, the response is apparently controlled by two thresholds \u003cem\u003eC\u003c/em\u003e\u003csub\u003e1,2\u003c/sub\u003e of the external concentration (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e), depending on whether the sensed concentration increases (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e), or decreases (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003eC\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e). The sensory mechanism itself might possess two different internal thresholds, as it has been postulated for the oxygen concentration in magneto-aerotaxis (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). Addition of a second internal threshold \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\u0026gt;C_{{\\text{s}}}^{ * }\\)\u003c/span\u003e\u003c/span\u003e in the above model moves the NS \u0026rarr; SS turning point further to the right, making the cycle depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, A, B more symmetric. Cells, however, would continue to oscillate between two points of the unknown pH gradient.\u003c/p\u003e \u003cp\u003eThe above model also explains the response of oscillating cells to a field polarity reversal. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, C\u0026ndash;F depicts four cases where the field polarity is reversed at different points of the cell trajectory: two cases when the cell is NS and two cases when the cell is SS. Depending on the instantaneous value of \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e during the field polarity reversal, and the subsequent evolution of \u003cem\u003eC\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e while the cell is swimming in the opposite direction, the magnetotactic polarity might or might not be switched another time. The outcome is either a NS cell in the reversed field, which moves away from the repelling zone, or a SS cell in the reversed field, which swims towards the repelling zone. Because oscillating cells spend most of their time in a region where the repellent concentration is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\u0026lt;C_{{\\text{s}}}^{ * },\\)\u003c/span\u003e\u003c/span\u003e the probability to end in a SS state after field reversal is much lower (~\u0026thinsp;9%) than that of ending in a NS state. This probability is exactly reflected by our observations of MB cells in zone B, with ~\u0026thinsp;9% of all oscillating cells becoming SS in the reversed field. The evident disproportion between NS and SS cells produced by the field reversal suggests that the magnetotactic polarity is switched by a single internal threshold or by two similar ones, since the symmetric cycle produced by largely different thresholds gives a 50% chance for either polarity.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eChemotactic response rescaling\u003c/h2\u003e \u003cp\u003eChemotactic sensory systems rescale their response sensitivity (adaptation) so to sense small concentrations differences at concentration levels ranging over several orders of magnitude (\u003cspan additionalcitationids=\"CR42\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e). Accordingly, a chemotactic response is triggered by a minimum relative concentration change with respect to a background concentration. The adaptation process takes some time ranging from seconds to minutes (\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e) and is sensitive to both the sign and the rate of concentration changes (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e). The adaptation and de-adaptation process of motile non-magnetotactic bacteria such as \u003cem\u003eE\u003c/em\u003e. \u003cem\u003ecoli\u003c/em\u003e is reflected by the frequency of tumbling intervals, defined as intervals of random cell rotation obtained by reversing the flagellar motor (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e). A different type of adaptation can be observed in the hanging drop experiments performed with a pH 2 solution. In this case, most MB cells will first swim to zone C, where they become SS, and then swim back to zone B, where they begin a periodic reversal of the magnetotactic polarity around a mean position. This behavior implies that the first NS \u0026rarr; SS trigger in zone C occurs at a much larger H\u003csup\u003e+\u003c/sup\u003e concentration than the subsequent triggers in zone B. The associated threshold change can be explained by the initial adaptation of the sensory mechanism to the concentration increase above the background level of zone A. A delay of few seconds, roughly corresponding the time required to move from zone B to zone C, explains why all cells swim to zone C and lose their motility when stronger pH gradients are used: in these cases, tolerable H\u003csup\u003e+\u003c/sup\u003e concentrations are exceeded before the sensory mechanism can adapt. This does not occur with a pH 3 solution, probably because the gradient formed in this case is shallow enough for the sensory mechanism to switch the flagellar motor already in zone B. We could not measure the instantaneous pH value that causes a motility loss in our experimental setting, however, as a term of comparison, the flagellar motor of \u003cem\u003eE. coli\u003c/em\u003e is completely stopped in an external pH of 5 (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eIntermediate responses\u003c/h2\u003e \u003cp\u003eThe response of MB cells to the addition of mildly acidic or alkaline solutions consisted in an initial slowdown of the flagellar motor, as shown by the decreasing NS swimming speed (Movie S3), followed by a reversal. The reversed rotation speed was not sufficient to sustain the backward motion observed in SS cells obtained with the other experiments. Some studies indicate that the speed of the flagellar motor can be modulated by a variety of molecular mechanisms when circumstances call for a less vigorous motility (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e). In our experiments, this slowdown might represent a reduced response to weak repellent concentrations. Because cell tumbling is prevented by the magnetic torque, slower flagellar rotation in \u0026ldquo;backward\u0026rdquo; mode might be used to stop cell motion under conditions where a displacement is not useful.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eA simple model for two different forms of polar magnetotaxis\u003c/h2\u003e \u003cp\u003eOur hanging drop experiments show, for the first time, that the magnetotactic polarity of MB cells is switched by the chemotactic response to a repellent different from oxygen. The presence of two repellents, in our case O\u003csub\u003e2\u003c/sub\u003e and H\u003csup\u003e+\u003c/sup\u003e, of which at least one forms a gradient that is correctly oriented with respect to the magnetic field, is sufficient to constrain the cell position within limits determined by the repellent concentrations and the sensing thresholds. This model of polar magnetotaxis works similarly magneto-aerotaxis (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e), except that the trigger for setting cells in a \u0026ldquo;reduced state\u0026rdquo; is given by a different repellent, rather than a lower [O\u003csub\u003e2\u003c/sub\u003e] threshold. Natural environments inhabited by MTB are characterized by counter gradients of oxidized and reduced species that form a redox gradient. In this case, at least one repellent capable of switching the magnetotactic polarity is required for each counter gradient. Repellents encountered in the oxic zone, such as O\u003csub\u003e2\u003c/sub\u003e, trigger the magnetotactic polarity that makes cells swim downwards along the Earth\u0026rsquo;s magnetic field, that is, NS in the northern hemisphere and SS in the southern hemisphere. We refer to this polarity simply as down-seeking (DS). Repellents encountered in the reducing zone trigger the opposite polarity, called upward-seeking (US). In the natural environments inhabited by MB, H\u003csup\u003e+\u003c/sup\u003e belongs to the family of repellents associated with the reducing zone, as seen by the pH decrease across the OAI (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). The pH threshold required to switch the magnetotactic polarity of MB under natural conditions is likely not the same of our hanging drop experiments, because the strong NS response triggered by oxygen saturation, and because of the role played by adaptation.\u003c/p\u003e \u003cp\u003eThe polar magnetotaxis model illustrated above defines two types of responses to redox gradients characterized by a combined concentration \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e(\u003cem\u003ez\u003c/em\u003e) of oxidizing repellents, which decrease with depth, and a combined concentration \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e(\u003cem\u003ez\u003c/em\u003e) of oxidizing repellents, which increase with depth. If the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e threshold required to trigger the DS polarity occurs at the same depth or at a greater depth \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e than the depth \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e of the \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e threshold required to trigger the US polarity, cells located either above \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e or below \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e receive consistent stimuli that direct them toward the (\u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e) depth range (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, A). Once within this depth range, stimuli that trigger opposed magnetotactic polarities overlap, leading either to a mixed polarity state characterized by frequent polarity changes, with a bias determined by the stronger stimulus, as observed with freshly isolated strains of \u003cem\u003eMangetospirillum\u003c/em\u003e (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e), or to a cell motility slowdown, as observed in our hanging drop experiments with mildly acidic or alkaline solutions. In both cases, cells are expected to reach an equilibrium depth within (\u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e), which depends on how the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e stimuli are combined. Because of the phenotypic heterogeneity of chemotactic sensitivity (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e), a MTB population subjected to the conditions shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e is expected to produce a bell-shaped cell concentration profile with mean depth controlled by the mean chemotactic response to the given redox gradient, and width reflecting the population heterogeneity (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, B).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIf, on the other hand, \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e \u0026lt; \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, as for instance in the case for mutually exclusive repellents in the oxic and reducing zones, respectively, cells will always possess a well-defined magnetotactic polarity, regardless of depth, provided that the magnetotactic polarity set by the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e threshold is maintained for as long as the \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e threshold is not exceeded, and vice versa (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, A). This hypothesis is consistent with the observation that lack of oxygen in hanging drop assays performed under anoxic conditions did not switch the NS polarity of MB and MC cells (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). Possible mechanisms that help cells maintaining a consistent magnetotactic polarity is discussed in the next section. In the configuration of Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, A, a cell initially located above \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e will be set into a DS state that produces a downward migration, until \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e is reached. At this point, the cell will be set into an US state, and the migration direction is reversed, until \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e is reached again and the cycle is repeated. As a result, cells shuttle continuously between \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, as postulated by the redox taxis model (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e). Under stationary environmental conditions, MTB pauseless shuttling between \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e are expected to be homogeneously distributed between these limiting depths, yielding a uniform cell density profile proportional to the box function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\Pi ((z - {z_{{\\text{red}}}})/({z_{{\\text{red}}}} - {z_{{\\text{ox}}}})),\\)\u003c/span\u003e\u003c/span\u003e with Π(\u003cem\u003ex\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;1 for 0\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003ex\u003c/em\u003e\u0026thinsp;\u0026le;\u0026thinsp;1, and Π(\u003cem\u003ex\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;0 otherwise. Because of unavoidable environmental and phenotypic heterogeneities, a more realistic representation of the expected concentration profile is given by a smoothed version of the box function, obtained by convolving Π(\u003cem\u003ex\u003c/em\u003e) with a bell-shaped distribution \u003cem\u003eg\u003c/em\u003e(\u003cem\u003ex\u003c/em\u003e) of \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e values, is (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIf redox taxis is used to satisfy different metabolic requirements across the redox gradient, such as the accumulation of elemental sulfur (S\u003csup\u003e0\u003c/sup\u003e) under reducing conditions, and the oxidation of S\u003csup\u003e0\u003c/sup\u003e under microaerobic conditions (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e), it is reasonable to assume that cell migration is paused at the limiting horizons \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e for the time required to complete chemical reactions associated with redox cycling (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, C). In this case, two peaks of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(g(z - {z_{\\text{c}}})\\,{T_{\\text{c}}}{\\kern 1pt} v{\\kern 1pt} /{\\kern 1pt} ({z_{{\\text{red}}}} - {z_{{\\text{ox}}}}),\\)\u003c/span\u003e\u003c/span\u003e centered at \u003cem\u003ez\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e = \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, respectively, reproduce the concentration profiles of pausing cells, which overlap with the box-shaped distribution of migrating cells (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, D). The factor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({T_{\\text{c}}}v{\\kern 1pt} /{\\kern 1pt} ({z_{{\\text{red}}}} - {z_{{\\text{ox}}}})\\)\u003c/span\u003e\u003c/span\u003e corresponds to the ratio between the time \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e spent at \u003cem\u003ez\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e and the time spent between \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e, respectively. The total numbers \u003cem\u003eN\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eN\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e of cells pausing at \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, respectively, as well as the proportion of DS and US polarities of migrating cells, is dictated by the population balance equations\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} \\frac{{{\\text{d}}{N_{{\\text{ox}}}}}}{{{\\text{d}}t}}=({r_{{\\text{ox}}}} - {\\psi _{{\\text{ds}}}}){N_{{\\text{ox}}}}+{\\psi _{{\\text{us}}}}{\\eta _{{\\text{us}}}}{N_{{\\text{red}}}} \\hfill \\\\ \\frac{{{\\text{d}}{N_{{\\text{red}}}}}}{{{\\text{d}}t}}=({r_{{\\text{red}}}} - {\\psi _{{\\text{us}}}}){N_{{\\text{red}}}}+{\\psi _{{\\text{ds}}}}{\\eta _{{\\text{ds}}}}{N_{{\\text{ox}}}} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e,\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003er\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e, \u003cem\u003er\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e are the cell growth rates, \u003cem\u003eψ\u003c/em\u003e\u003csub\u003eds\u003c/sub\u003e, \u003cem\u003eψ\u003c/em\u003e\u003csub\u003eus\u003c/sub\u003e the fractions of pausing cells that resume DS and US migration per unit of time, and \u003cem\u003eη\u003c/em\u003e\u003csub\u003eds\u003c/sub\u003e, \u003cem\u003eη\u003c/em\u003e\u003csub\u003eus\u003c/sub\u003e the fractions of migrating cells that reach the target layer, escaping, for instance, predation. Stationary solutions (d\u003cem\u003eN\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e/d\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;d\u003cem\u003eN\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e/d\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0) exist only if \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\psi _{{\\text{ds}}}}\\,\u0026gt;{r_{{\\text{ox}}}},\\)\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\psi _{{\\text{us}}}}\\,\u0026gt;{r_{{\\text{red}}}},\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\psi _{{\\text{ds}}}}{\\psi _{{\\text{us}}}}{\\eta _{{\\text{ds}}}}{\\eta _{{\\text{us}}}}=({r_{{\\text{ox}}}} - {\\psi _{{\\text{ds}}}})({r_{{\\text{red}}}} - {\\psi _{{\\text{us}}}})\\)\u003c/span\u003e\u003c/span\u003e. In this case, the fractions \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p_{{\\text{us}}}}({z_{{\\text{ox}}}})=({\\psi _{{\\text{ds}}}} - {r_{{\\text{ox}}}})\\,/\\)\u003c/span\u003e\u003c/span\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((2{\\psi _{{\\text{ds}}}} - {r_{{\\text{ox}}}})\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p_{{\\text{us}}}}({z_{{\\text{red}}}})={\\psi _{{\\text{us}}}}{\\kern 1pt} /{\\kern 1pt} (2{\\psi _{{\\text{us}}}} - {r_{{\\text{red}}}})\\)\u003c/span\u003e\u003c/span\u003e of US cells near \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e are comprised between 0 and 50%, and between 50 and 100%, respectively. Exactly 50% of all migrating cells are US, regardless of depth (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, B) in case of pauseless shuttling (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r_{{\\text{ox}}}}/{\\kern 1pt} {\\psi _{{\\text{ox}}}}={r_{{\\text{red}}}}/{\\kern 1pt} {\\psi _{{\\text{red}}}}=0\\)\u003c/span\u003e\u003c/span\u003e). More generally, \u003cem\u003ep\u003c/em\u003e\u003csub\u003eus\u003c/sub\u003e(\u003cem\u003ez\u003c/em\u003e) can be any function comprised between 0 and 100% if the population is not stationary, which means that the in-situ magnetotactic polarity of migrating cells is not systematically related to the redox conditions.\u003c/p\u003e \u003cp\u003eSeveral observations provide indirect evidence in support of the two polar magnetotaxis models described above (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The first evidence comes from MB and MC concentration profiles measured over several months in the same stable microcosms that served as MTB source for this work (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e). The shape of these profiles depends on the depth-integrated cell concentration \u003cem\u003eN\u003c/em\u003e, which ranges from \u0026lt;\u0026thinsp;10 to \u0026gt;\u0026thinsp;1800 cells/mm\u003csup\u003e2\u003c/sup\u003e. The average of MB profiles with \u003cem\u003eN\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;450 cells/mm\u003csup\u003e2\u003c/sup\u003e is nearly constant between \u003cem\u003ez\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;3 mm and \u003cem\u003ez\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;17 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, E), resembling the theoretical box function expected from pauseless shuttling between two limit depths (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, B). The concentration plateau increases with \u003cem\u003eN\u003c/em\u003e, but remains within the same limit depths, up to \u003cem\u003eN\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;1500 cells/mm\u003csup\u003e2\u003c/sup\u003e. Two distinct peaks, centered at \u003cem\u003ez\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;6 mm and \u003cem\u003ez\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;17 mm, respectively, emerge for the average of profiles with \u003cem\u003eN\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;1800 cells/mm\u003csup\u003e2\u003c/sup\u003e. This average resembles the concentration profile predicted for cells that pause at both limit depths (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, D). The upper peak is comprised between \u003cem\u003ez\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;4 mm, which is the depth where oxygen drops to zero, and ~\u0026thinsp;10 mm, while the less pronounced lower peak is slightly broader. The two peaks occur independently of each other, as seen from individual profiles featuring only one maximum that coincides with the upper or the lower peak position (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). MC concentration profiles are relatively flat at low \u003cem\u003eN\u003c/em\u003e (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;150 cells/mm\u003csup\u003e2\u003c/sup\u003e), like MB ones, but a single, broad peak centered at \u003cem\u003ez\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;8 mm develops at higher concentrations (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;400 cells/mm\u003csup\u003e2\u003c/sup\u003e), instead of two distinct peaks (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, C).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCharacteristics of polar magnetotaxis deduced from microscope observations and from microcosm experiments.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProcess\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMicroscope observations\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMicrocosm experiments\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLower [O\u003csub\u003e2\u003c/sub\u003e] threshold\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; assay in anoxic conditions\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; MTB well below the OAI\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSecond repellant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003epH (MB), unknown (MC)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eUnknown (pH-compatible)\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThreshold sensing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eYes\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; polar magnetotaxis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003ePossible\u003c/b\u003e\u003c/p\u003e \u003cp\u003e- sensitivity to field reversal\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThreshold adaptation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eYes\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; pH 3 experiments\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNot observable\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTumbling/stop \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eYes (MB)\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; cell vibration at pH 6 and 8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eYes (MB)\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; redox taxis with pause\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStationary MA \u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eYes (MB), No (MC)\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; microcosms in zero field\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDynamic MA \u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eYes (MB and MC)\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; migration experiments\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRedox taxis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eYes (MB), No (MC)\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; depth distribution\u003c/p\u003e \u003cp\u003e\u0026bull; S\u003csup\u003e0\u003c/sup\u003e inclusions\u003c/p\u003e \u003cp\u003e\u0026bull; stationary MA\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetabolism-driven chemotaxis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eYes (MB), No (MC)\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; redox taxis with pause\u003c/p\u003e \u003cp\u003e\u0026bull; Better migration of MB vs. MC\u003c/p\u003e \u003cp\u003e\u0026bull; Migration in reversed field\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eUS fraction \u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(in situ)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eVariable (0 to ~\u0026thinsp;100%)\u003c/b\u003e \u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; unrelated to redox gradient\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eAdaptable\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u0026bull; Migration experiments\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003csup\u003ea\u003c/sup\u003e Flagellar motion that would make the cell tumble in null field.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003csup\u003eb\u003c/sup\u003e Magnetotactic advantage (MA) for a stationary MTB population\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003csup\u003ec\u003c/sup\u003e Magnetotactic advantage (MA) identified with the capability to follow a macroscopic OAI offset.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003csup\u003ed\u003c/sup\u003e US\u0026thinsp;=\u0026thinsp;SS in the northern hemisphere, and US\u0026thinsp;=\u0026thinsp;NS in the southern hemisphere.\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"3\"\u003e\u003csup\u003ee\u003c/sup\u003e For hanging drop assays or other observation methods that preserve, at least partially the original chemical conditions.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMC and MB concentration profiles are well explained by the magnetotactic models of Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, respectively. The role played by polar magnetotaxis in determining the distinct concentration profiles of MB and MC is further confirmed by the in-situ magnetotactic advantage of these two MTB populations. Magnetotactic advantages are defined here by the role played by the magnetic field in helping cells to (a) keep their preferred depth range under stationary conditions (stationary advantage), and (b) react to sudden changes of the surrounding environment (dynamic advantage). The stationary advantage has been investigated by monitoring the evolution of the two MTB populations while the microcosms were placed in a null field (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e): while MC was practically unaffected by the field removal, depth-integrated counts of MB declined by 50%. The difference can be explained by considering how MTB cells migrate in sediment: because of the poor magnetic alignment caused by the limited pore space, motile cells perform a biased random walk, rather than displacing along straight lines, even when keeping the same magnetotactic polarity (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Numerical simulations show that the random walk component dominates small (\u0026lt;\u0026thinsp;0.2 mm) displacements, while the advective component, which depends on the magnetic alignment, becomes dominant over larger distances. Hence, the small adjustments needed to maintain a preferred living depth in the model of Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e do not benefit significantly from the alignment induced by Earth-like magnetic fields, explaining the lack of a static magnetotactic advantage for MC cells. On the other hand, MB cells migrate over distances of the order of 1 cm or more during redox taxis (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), well within the range where the magnetic alignment becomes important.\u003c/p\u003e \u003cp\u003eFinally, both MTB populations possess also a dynamic magnetotactic advantage, as seen by their ability to follow a macroscopic displacement of the OAI (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). In the case of MB, this ability persists, in a much-reduced form, also after reversing the field, while MC cells are incapable to follow the OAI in a reversed field. The adverse effects of a field reversal in these experiments provide an in-situ confirmation of the polar character of magnetotaxis in these two MTB populations. On the other hand, the partial ability of MB to overcome a field reversal requires additional considerations, as explained below.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eMetabolism-dependent chemotaxis\u003c/h2\u003e \u003cp\u003eClassical models of chemotaxis assume that the flagellar motor is controlled by a sensorimotor pathway that provides a relatively rapid response to external stimuli (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e). The adaptation capability of this pathway (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e) provides cells with a memory that enhances navigation in rugged chemical gradients by extracting information from environmental correlations (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e). Maximal advantage is achieved when the memory effect is comparable with the time scale of fluctuations as perceived during swimming. In sediment, the diffusive component of MTB displacement, which is similar to the path generated by simple chemotaxis, dominates over length scales\u0026thinsp;\u0026lt;\u0026thinsp;0.2 mm and corresponding time scales\u0026thinsp;\u0026lt;\u0026thinsp;20 min (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Displacements over such small scales can therefore benefit from adaptation times of the order of minutes (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e). On the other hand, a much longer memory, of the order of days, would be required to keep the same magnetotactic polarity, or at least a consistent polarity bias, during the time required to sustain redox taxis. The two-repellant sensing mechanism of Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e does not need a memory effect, provided that the polarity triggered by the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e threshold is maintained until the \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e threshold is attained, and vice versa. This mechanism, however, is not robust against rugged gradients, as any local heterogeneity that exceeds one of the thresholds makes shuttling cells return to the layer that they just left, instead of completing their migration. Adaptation of the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e thresholds according to the time-averaged repellent concentrations encountered by migrating cells would not help redox taxis either: for instance, the magnetotactic polarity of a DS cell located near \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e would be prematurely switched by a smaller \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e threshold, and vice versa.\u003c/p\u003e \u003cp\u003eA metabolism-based control of chemotaxis (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e) might generate the long-term memory required to make redox taxis less sensitive to rugged redox gradients. Such a mechanism could set MB cells pausing at \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e in a US state as soon as the sulfur accumulation capacity is exhausted, and cells pausing at \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e in a DS state as soon as the accumulated sulfur has been completely oxidized. The observation of fast chemical responses in our hanging drop assays suggests that external stimuli can override a hypothetical metabolism-based chemotaxis. A combination of metabolism-independent and metabolism-dependent controlling mechanisms, by which cells react rapidly to strong external triggers, but maintain a bias dictated their internal state, for instance through a modulation of the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e thresholds, explains the apparent inconsistencies between observed and expected magnetotactic polarities reported in the literature (\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e). These observations were obtained from hanging drop assays with no added water (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e), or with a special apparatus that minimizes the introduction of oxygen during recovery of wild-type MTB (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e). Both sampling procedures are expected to maintain, at least in part, the oxidation-reduction potential of the stratified water column, so that a strong magnetotactic polarity bias triggered by oxygen might be avoided, especially if the DS polarity is controlled by the oxidation-reduction potential (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e). Under such conditions, a metabolic bias can preserve the in-situ magnetotactic polarity of individual cells, which, as discussed above, is not related to the position within the redox gradient.\u003c/p\u003e \u003cp\u003eAdditional indirect evidence for a metabolic control of magnetotaxis is given by the partial ability of MB cells to follow the OAI after a field reversal (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). In these experiments, the OAI was moving upwards by ~\u0026thinsp;3.5 mm/day, as estimated from the MTB displacement observed with the normal field polarity. For comparison, the estimated migration speed of cells with constant magnetotactic polarity is ~\u0026thinsp;12 mm/day (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e), meaning that MTB can adjust their depth in sediment synchronously with the moving OAI. In case of experiments performed in a reversed field, cells are expected to move in the wrong direction (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e), leading to the population decline observed with MC cells (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). Redox taxis assisted by a metabolic memory, on the other hand, permits a limited displacement towards the correct direction, as seen with the example of an US cell located just below to \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e. When the field is reversed, this cell starts to move downwards, away from the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e threshold that would switch its magnetotactic polarity. Meanwhile, metabolism brings this cell to the next stage of redox taxis, which is the pause that would normally occur at \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e. As a result, the cell pauses somewhere below \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e, but still close enough to support oxidative reactions. When this pause comes to an end, the cell is set in a DS state, which makes it migrate upwards in the reversed field, instead of downwards. During the pause near \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e, the redox gradient moves up, so that the cell will cross the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e threshold and leave the optimal depth range at a later point, closer to the sediment surface. The maximum vertical displacement attainable in this way is of the order of the distance covered during ordinary redox taxis. Indeed, the maximum MB displacement of ~\u0026thinsp;1 cm observed in the reversed field, just before a complete disappearance of motile cells, is compatible with \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e \u0026minus; \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e estimated from MB concentration profiles (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eEnvironmental and phylogenetic implications\u003c/h2\u003e \u003cp\u003eThe combination of metabolism-independent and metabolism-based magneto-chemotaxis can generate a rich variety of responses by different types of MTB, enabling to exploit multiple ecological niches. This concept is best exemplified by the differences in depth distribution, migration ability, magnetotactic advantage, and chemotactic responses of MB and MC populations living inside the same sediment. Chemotactic responses that do not involve oxygen might have played an important role for supporting navigation of phylogenetically deep-branching MTB, of which MB is an example, in ancient anoxic environments, such as the Archean oceans (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"CONCLUSIONS","content":"\u003cp\u003eCurrent magneto-aerotaxis models are challenged by (a) the lack of a consistent relation between magnetotactic polarity and position in the redox gradient, (b) the existence of substantial differences in the migration capability of different wild-type MTB, despite apparently identical aerotactic responses, and (c) the lack of a magnetotactic polarity switching mechanisms that support cell shuttling during redox taxis. Altogether, these observations can be explained by a threshold-driven, two-repellent model of magnetotaxis, where magnetotactic polarity is controlled by two groups of repellents with opposed concentration gradients. The first group includes oxygen and triggers the polarity that makes cells swim downwards (DS), as expected from magneto-aerotaxis models. The second group triggers the opposite polarity (US). We were able, for the first time, to observe a systematic magnetotactic polarity switching of MB cells, from DS to US and vice-versa, under the combined action of oxygen saturation and a pH gradient. In our experiments, acidic conditions acted as second repellent, which, in the chemical stratification of the sediment from which MB was retrieved, forms a counter gradient with respect to oxygen. The response of MB cells to mildly acidic or alkaline conditions includes a slowdown of the flagellar motor and subsequent reversal that is compatible with tumbling in the chemotaxis of non-magnetic bacteria. The magnetotactic polarity of MC could not be reversed by a pH gradient, demonstrating the different chemotactic response of these two MTB populations.\u003c/p\u003e \u003cp\u003eThe two-repellent model of magnetotaxis supports two fundamentally different magnetotactic behaviors, depending on the depths \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e where the concentration thresholds of oxidizing (\u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e) and reducing (\u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e) repellents set the magnetotactic polarity to a DS and an US state, respectively. If \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e \u0026le; \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e, MTB tend to accumulate around a mean depth comprised between \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, where the overlapping and opposed stimuli of \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e cancel any bias in favor of one or the other magnetotactic polarity. The resulting concentration profile is unimodal and comprised between \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, as observed for MC. If \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e \u0026lt; \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, MTB shuttle between \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e, performing redox taxis. The resulting concentration profile is either flat, when cells do not pause, or bimodal with peaks near the limiting depths of redox taxis if cells pause near \u003cem\u003ez\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and near \u003cem\u003ez\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e. Both profile types are compatible with MB. Several observations, summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, support these two scenarios. In both cases, the threshold triggering mechanism of polar magnetotaxis makes it less sensitive to random polarity reversals caused by rugged chemical gradients. Redox taxis might be further stabilized by a metabolism-driven magnetotactic polarity bias.\u003c/p\u003e \u003cp\u003eOur model of polar magnetotaxis supports a large variety of magnetotactic behaviors, depending on the position of the \u003cem\u003eR\u003c/em\u003e\u003csub\u003eox\u003c/sub\u003e and \u003cem\u003eR\u003c/em\u003e\u003csub\u003ered\u003c/sub\u003e thresholds in a redox gradient, enabling different types of MTB, such as MB and MC, to occupy different ecological niches inside the same environment.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDECLARATION OF COMPETING INTEREST\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eX. M. and R. E. conducted the experiments. X. M, R. E., N. P., and X. L. analyzed of the data., X. M., R.E. and N.P. made the modeling. X.M. and R.E. wrote the paper. R.E. and X. L. supervised the work.\u003c/p\u003e\u003ch2\u003eACKNOWLEDGMENTS\u003c/h2\u003e \u003cp\u003eThis work is supported by National Natural Science Foundation of China (Grant No. 41602184, 42130507, 41772180), Natural Science Foundation of Fujian Province (Grant No. 2020J01141), and German Research Foundation (Grant No. EG 294/1\u0026ndash;1 and EG 294/2\u0026thinsp;\u0026minus;\u0026thinsp;1).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBlakemore, R.P. 1975. Magnetotactic bacteria. Annu. Rev. Microbiol. 190: 217\u0026ndash;238.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFaivre, D., and D. Sch\u0026uuml;ler. 2008. Magnetotactic bacteria and magnetosomes. Chem. Rev. 108: 4875\u0026ndash;4898.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLef\u0026egrave;vre, C. T., D. A. Bazylinski. 2013. Ecology, diversity, and evolution of magnetotactic bacteria. 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Origin of microbial biomineralization and magnetotaxis during the Archean. \u003cem\u003eProceedings of the National Academy of Sciences\u003c/em\u003e. 114:2171\u0026ndash;2176.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4320581/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4320581/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMagnetotactic bacteria (MTB) combine passive alignment with the Earth magnetic field with a chemotactic response (magneto-chemotaxis) to reach their optimal living depth in chemically stratified environments. Current magneto-aerotaxis models fail to explain the occurrence of MTB far below the oxic-anoxic interface and the coexistence of MTB cells with opposite magnetotactic polarity at depths that are unrelated with the redox gradient. Here we propose a modified model of polar magnetotaxis which explains these observations, as well as the distinct concentration profiles and magnetotactic advantages of two types of MTB inhabiting a freshwater sediment: \u003cem\u003eMagnetobacterium bavaricum\u003c/em\u003e (MB) and a group unidentified, wild-type cocci (MC). This model assumed that magnetotactic polarity is set by a threshold mechanism in counter gradients of oxygen and a second group of repellents, with, in case of MB, includes H\u003csup\u003e+\u003c/sup\u003e ions. Depending on the position of the two repellent thresholds in a vertical redox gradient, MTB possessing this type of polar magnetotaxis either accumulate around a preferred depth where the opposed stimuli set by the two repellents are equivalent, or shuttle between two limit depths across the redox gradient (redox taxis). We show that MB belongs to the latter category, as previously postulated for MB and other members of the \u003cem\u003eNitrospirae\u003c/em\u003e group. Microcosm experiments suggest that redox taxis might be assisted by a partial control of magnetotactic polarity by cell metabolism, which helps maintaining a consistent polarity bias during shuttling. Our model of polar magnetotaxis supports a large variety of magnetotactic behaviors, depending on the position of the two repellent thresholds in a redox gradient, enabling different types of MTB to occupy different ecological niches in the same environment.\u003c/p\u003e","manuscriptTitle":"An update on polar magnetotaxis: Insights from hanging drop assays and microcosm experiments","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-02 20:07:24","doi":"10.21203/rs.3.rs-4320581/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-09-09T06:04:55+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-07T06:09:34+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-28T10:33:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"16875629902430495710863144855895795137","date":"2024-08-20T00:56:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"209353833991794979924126182716281983379","date":"2024-08-19T13:50:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-07T18:53:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"102343657333076752751888260049386142683","date":"2024-07-26T06:36:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"187306639059412175983894885383282929636","date":"2024-07-25T20:50:36+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-25T19:07:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-29T04:30:42+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-04-26T05:16:57+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-26T05:10:39+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-04-24T23:30:18+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"1b341540-cd0e-47a7-8b8e-dc447a8a9f2c","owner":[],"postedDate":"May 2nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":31380360,"name":"Biological sciences/Biophysics"},{"id":31380361,"name":"Biological sciences/Microbiology"}],"tags":[],"updatedAt":"2024-11-11T16:00:56+00:00","versionOfRecord":{"articleIdentity":"rs-4320581","link":"https://doi.org/10.1038/s41598-024-78946-7","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-11-09 15:56:59","publishedOnDateReadable":"November 9th, 2024"},"versionCreatedAt":"2024-05-02 20:07:24","video":"","vorDoi":"10.1038/s41598-024-78946-7","vorDoiUrl":"https://doi.org/10.1038/s41598-024-78946-7","workflowStages":[]},"version":"v1","identity":"rs-4320581","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4320581","identity":"rs-4320581","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}