Neutrons reveal the dynamics of leaf thylakoids in living plants

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Evans, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4437351/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted 12 You are reading this latest preprint version Abstract The study is the first known exploration of photosynthetic membranes dynamics in living plants by high resolution inelastic neutron scattering spectroscopy. We characterized in vivo thylakoid membranes mobility in Lemna minor plants. Excess dynamics at length scales corresponding to both the membrane stacks and membrane thickness were observed and described by classical biophysical models to assess the undulation modes, the rigidity of the membranes, and how the structural variations affect the observed dynamics. The stacks of thylakoids in Lemna minor are rigid systems with an apparent bending coefficient in the upper range observed for surfactant membranes, while the single thylakoid leaflet is very flexible situated well within the bi-continuous surfactant phases dynamics. These observations further our understanding of the relationship between photosynthesis and the cellular architecture, while simultaneously opening more questions and the need for further investigations at extended q -and-time regimes. Biological sciences/Biological techniques Biological sciences/Biophysics Biological sciences/Plant sciences Physical sciences/Physics Physical sciences/Physics/Applied physics Physical sciences/Physics/Biological physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction The light reaction of photosynthesis occurs within the intricate membranous structures known as thylakoids. It has been shown previously in the unicellular cyanobacteria, where the photosynthetic membranes form concentric layers that follow the shape of the cell envelope, that thylakoids are highly flexible structures, and their dynamics is tightly connected with the electron transfer between photosynthetic reaction centers and the associated electrochemical proton gradient across the membrane 1,2 . However, in higher plants the thylakoid membranes are organized in a different fashion. Each leaf cell contains several chloroplasts in which thylakoid membranes are stacked in closed appressed structures ensuring a large area-to-volume ratio and a high stability of the photosynthetic ultrastructure, with remarkable flexibility and adaptability to environmental conditions. 3,4 To date, detailed information about thylakoids macro-structure in their native environment in leaf cells is available using non-invasive Small Angle Neutron Scattering (SANS) 5–7 . These elegant and thorough structural studies suggest that thylakoid membranes within chloroplasts can also exhibit a great amount of flexibility and very complex dynamics patterns related to the photosynthetic process 8–11 . In respect of that view our aim was to observe and characterize noninvasively the dynamics of plant thylakoids and assess their flexibility as bending and thickness fluctuations, in a similar way as previously done for single-cell photosynthetic microorganisms 1,2 and standard bilayer phospholipid membranes 12–15 . Neutron Spin-Echo (NSE) spectroscopy is the high-resolution spectroscopic technique that has already proved to be very successful in capturing the structure and dynamics of bilayer lipid membranes with no damage inflicted to membranes 1,12,16,17 . A variety of theoretical models also exist to characterize the undulation, bending and thickness fluctuations of the lipid membranes 18–23 . The main challenge for this study was to find a suitable plant that can fulfill all the following vital requirements: i) fast growing in confined lab space to supply plentitude of fresh, intact leaves over a relatively short period of time ii) could survive for extended soaking time in D 2 O, which is necessary to enhance the contrast, iii) has thin leaves that allow fast gas diffusion and D 2 O exchange, iv) is biologically relevant and, preferably, v) it has been investigated thoroughly by SANS which demonstrated that its diffraction pattern shows correlation peaks in the spin-echo accessible q -range. Common duckweed ( Lemna minor) is a small aquatic plant that belongs to the Lemnaceae family. It is one of the smallest flowering plants in the world and can be found floating on the surface of still or slow-moving freshwater bodies like ponds and lakes. Lemna minor has tiny, oval-shaped leaf called fronds of a few millimeters in size. Due to its rapid growth and its ability to efficiently absorb nitrogen and phosphorus from the water, duckweed is often used in wastewater treatment 24,25 . Lemna minor also provides habitat and food for various aquatic organisms. Its ability to cover large water surfaces can also reduce evaporation and inhibit the growth of harmful algae by shading the water. Duckweed plays a fascinating role in aquatic ecosystems and has practical applications in environmental and agricultural contexts with the potential to be used for biofuel production 26 , protein-rich animal feed 27 and phytoremediation 28 . In contrast to most terrestrial plants, Lemna minor can tolerate and grow in relatively high concentrations of D 2 O 29 and has been grown in 50% D 2 O for production of deuterated biomass 30 for metabolic studies 31 , and for probing localization of lipid biosynthesis 32 . In this work, we observe and characterize the mobility of the thylakoid membranes encapsuled by chloroplasts in cell fronds of living Lemna minor plants by neutron spin-echo spectroscopy. Results and Discussion Assessment of the internal dynamics of thylakoids. The result of neutron spin-echo spectroscopy measurements is the normalized intermediate scattering function I ( q , τ ) / I ( q , 0) describing the pair-correlation distances observed in reciprocal space q = 2π/ d and the time-dependent relaxation of such correlations due to the internal mobility of the sample investigated. As the first step in the analysis, the normalized intermediate scattering functions experimentally obtained, were fitted by a stretched exponential function with the stretching exponent β as a free fitting parameter. Figure 1 shows the q dependence of the stretching exponent. The values of β range between 0.2 and 0.4 in the small q -regime ≤ 0.07Å −1 with the rest of β around 0.6 for higher q values. One can also observe the large β -errors, providing insights how stretched exponential function with a free exponent might not be the correct model to describe the experimental relaxation curves, especially for the data in the high q -regime. Therefore, in the next step of the evaluation we fixed the value of β = 2/3 according to Zilman & Granek 18,19 model (abbreviated ZG from here on) proposed for bilayer membrane dynamics and the intermediate scattering function observed by NSE were fitted accordingly. ZG model provided a reasonable description of the NSE experimental data, with χ 2 = 0.019 per degree of freedom, see Fig. 2 . The corresponding time information obtained is expressed as either relaxation time τ or inversely, as relaxation rates Γ ZG and calculated using Eq. 1 , see Methods. In the following we used the spatial dependence of the relaxation rate Γ ZG to characterize the dynamics of our system (Fig. 3 , both panels). The Γ ZG behavior as a function of q shows different patterns between the small q -range (black symbols) and the large q -range (red symbols) in Fig. 3 , left panel. In the small q -range, there is no change in the relaxation rate values as a function of q . This points toward a relaxation process restricted by space, like diffusion in confined geometry. In the large q -range the relaxation rate is characterized a by a power law with the exponent of m = 3.88. A linear fit of all data yields a power law with the exponent of m = 3.28, when all Γ ZG values are used. Given the value of the exponent close to m = 3, the Γ ZG / q 3 behavior as a function of q is commonly represented to observe the linear dependence at high q -values, a typical signature of pure undulation motions in lipid bilayer membranes that helps extract the effective bending modulus of the membranes. It should come as no surprise that the dependence displayed in Fig. 3 , right panel, shows a poor linearity between the relaxation rates Γ ZG / q 3 at high q -values, ≥ 0.07Å −1 . This points to additional relaxation due to superimposed dynamic processes on top of the simple undulation motions. The complex nature of the relaxation rate pattern arises from the complexity of the thylakoids stacked architecture within the chloroplast of the leaf and its intricate dynamical behavior. The photosynthetic membranes closely appressed together and enclosed in chloroplast feel the presence of other neighboring membranes in terms of fluctuation dynamics and one cannot easily deconvolute the single bilayer membrane undulation dynamics from the overall bilayer-bilayer interaction within the stack. The original ZG model is expected to be valid in the high q -regime, where 1/ q < < interthylakoidal distance. The deviations observed in Γ ZG /q 3 vs q represents a limitation of the ZG model for characterizing bending fluctuation in complex architectural membrane structures, especially in living thylakoids where a multitude of other components beside bilayers are present and may contribute with additional relaxation modes. Characteristics of bending fluctuations. The q 3 dependence of the relaxation rate Γ ZG is controlled by the elastic modulus \(\stackrel{\sim}{\kappa }\) , with higher bending coefficients corresponding to smaller relaxation rates 18,20 . The effective bending coefficient was calculated according to Eq. 2 from the intercept value y 0 in Fig. 3 , right panel (linear regression with slope = 0 depicted by the green dashed line) and expressed in units of thermal energy. Large value of \(\stackrel{\sim}{\kappa }\) >> k B T ( \(\stackrel{\sim}{\kappa }\) = 1669.7 k B T ) indicates a rigid system, a stack of membranes closely appressed together or membranes encapsulated in a tight structure with restricted space for free undulation motions, as well as it can indicate the presence of other structures like macromolecules grafted on the surface of the surfactant membranes that act like fluctuation suppressors 18,20 . All these are valid if we consider the architecture of thylakoids encapsuled by chloroplasts in the cells of Lemna minor leaf. The effective bending coefficient in stacked membranes depends also strongly on the viscosity of the solvent confined between membranes, as shown previously in numerous studies 33 . A rescaling of the bulk D 2 O viscosity, η D2O , to 3· η D2O as suggested by these studies brings the effective bending coefficient to \(\stackrel{\sim}{{\kappa }}\) = 185 k B T (Table 1 ), well within the extensive range observed for surfactant membranes, where values between 0.1–2000 k B T have been reported by various research. Table 1 Characteristics of bending fluctuations. The bending modulus was calculated for η D2O = 0.00125 kg·m·s − 1 as D 2 O viscosity at 20°C, and for 3· η D2O as suggested by literature 20,33 . Sample name Γ/q 3 (Å 3 /ns) \(\stackrel{\sim}{\varvec{\kappa }}\) (k B T) \(\stackrel{\sim}{\varvec{\kappa }}\) for 3 · η D2O (k B T) Lemna Minor 1.98 ± 0.33 1669.7 ± 556.6 185.5 ± 61.8 Given the above, an analogy can be made between the observed excess dynamics of thylakoids and the excess dynamics related to shape fluctuations in oriented lamellar phase microemulsions 34,35 . Dynamics of oriented lamellar phases model implemented in the software Jscatte r 36,37 calculates the coherent intermediate scattering function arising from dynamics of oriented lamellar phases at the length scale of the intermembrane distance (see Eq. 16 in reference Mihailescu et al ., 2002 34 ). In our case the model provided information on the single membrane apparent bending modulus in thermal energy units, the membrane thickness, and solvent viscosity, using the film-to-film distance (241.65Å, first SANS peak @ q ~ 0.026Å −1 ) representing the periodicity of the structure as input parameter (Fig. 4 ). The best fit was obtained assuming q -dependence of the bending modulus and solvent viscosity, with χ 2 = 0.017 per degree of freedom (117 dof, with 31 parameters fitted simultaneously for the ten experimental scattering functions, i.e. q ’s). The bending modulus calculated for single membrane varies between 0.59 k B T and 3.72 k B T (Fig. 5 ), higher but not too different from values determined for bi-continuous surfactant phases 38 (~ 1.3–1.5 k B T ). Single bilayer thickness calculated is 65 Å ± 24 Å and strongly corelated with the solvent viscosity. In the analysis only bulk apparent viscosity was assumed and fitted for each q to account for local viscosity fluctuations. These variations can be seen in Fig. 5 . A mean value of 0.75 mPa*s (with a large standard deviation of 0.75) can be calculated from the viscosity values, falling well within the range observed for the n-alkanes and chloroalkanes, as well as aqueous solution with high solutes concentration 39 . We theorized that the sensitivity of the calculated model parameters to observable bulk viscosity represents a qualitative description of local viscosity fluctuations due to anchored proteins on the membrane surfaces, increased local friction with the solvent and variabilities in the membrane internal viscosity due to variations in lipids concentration. Characteristics of local fluctuations. The spatial dependence of the decay rate Γ shows excess mobility in addition to the underlying q 3 -dependent undulation dynamics. To quantify these deviations we used the approach established by Nagao and collaborators 13,21 where the excess motion is described as local shape and thickness fluctuations with peristaltic and protrusion motions, see Eq. 3 in Methods. The intent is to describe the trend of the relaxation rate by Lorentz functions, using the previous peak model analysis used for photosynthetic cells 1 based on simulation results for thickness fluctuations 21 and protein-induced deformations in lipid bilayers 20,40 . There are two strong deviations identifiable, one in the small to intermediate q -range where we sample distances proportional to the center-to-center bilayer distance, and another deviation in the high q -regime at distances in the range of a single membrane thickness. In the past, similar excess dynamics have been attributed to swelling of the membrane pair, e.g. , thickness fluctuations, bilayer-bilayer interactions, and dynamics due to protrusion and diffusion of proteins at the membrane surface. The decay rate Γ experimentally obtained fit was separated again, for the purpose of this study, in two q -regimes: a high q -regime ≥ 0.07Å −1 (red data in Fig. 6 ) and a small q -regime ≤ 0.07Å −1 (black data in Fig. 6 ) and two Lorentzian were used for the analysis of the two q -regimes. The best fit was obtained by Lorentzian functions having the peak center situated around the same position as the first and the last observable SANS correlation peaks: q ~ 0.027Å −1 and q ~ 0.11Å −1 . This is a clear indication of excess dynamics occurring at length scales corresponding to both: bilayer periodicity and single membrane thickness. The calculated parameters from the Lorentz fit are presented in Table 2 . The large difference observed in the decay rate of the local fluctuations, A · q 0 3 , between small and high q -regime is a good indication of the underlaying dynamical process. In the small q -regime the faster decay rate points toward longer relaxation times and slower motions. These slow motions can be attributed to progressive swelling of the thylakoid pair stack as well and to adjacent bilayer repulsive interactions. The photosynthetic membrane pair is a living structure, and a certain amount of flexibility is needed to adjust to the active photosynthetic process. The swelling of the thylakoid pair happens within the restricted space of the chloroplast, up to the point where is contracted by the adjacent bilayer swelling. Although we lack a more discrete refinement of Γ vs q dependence, as well as values at the very low q , we can still formulate some hypothesis on a reasonable behavior for living photosynthetic membranes under restricted spatial architecture within chloroplasts. Table 2 Characteristics of local thickness fluctuations. A = damping frequency of the peristaltic mode, ξ = the peristaltic mode amplitude, q 0 = the peak maximum position, local length scale of thickness fluctuations. The product A · q 0 3 describes the decay rate of the local fluctuations. * Note that the parameters are calculated for each peak displayed in Fig. 6 using the intercept value y 0 = Γ ZG /q 3 = 0.89 of the two Lorentzian. Sample name Γ ZG /q 3 (Å 3 /ns) q 0 (Å −1 ) A (Å 3 /ns) ξ (Å) A*q 0 3 x 10 − 4 (ns − 1 ) χ 2 Peak1 0.89 ± 0.02 0.027 0.24 ± 0.002 0.03 ± 2.5E-4 0.045 ± 0.0004 3.4E-4 Peak2 0.89 ± 0.02 0.109 0.13 ± 0.03 0.04 ± 0.01 1.74 ± 0.035 0.42 With increasing distance from the marked high q = 0.11Å −1 ( d ≈ 50Å) to the marked low q = 0.027Å −1 ( d ≈ 250Å), the field of view changes from the local single membrane leaflet to center-to-center distance of adjacent bilayer membrane-pair stack. The thermal fluctuations can induce collisions between neighboring membranes. These collisions give rise to repulsive bilayer-bilayer interactions caused by the reduction of entropy, called Helfrich steric repulsion 41 . Experimental work on lamellar microemulsion of sodium dodecyl sulfate (SDS) of Safinya et al ., 42 showed that for intermembrane distances between ~ 40Å and ~ 170Å Helfrich steric interaction is the dominant interaction. The q- window that NSE was able to sample during the measurements on Lemna minor 0.04Å −1 < q < 0.13Å −1 with corresponding distances of 157Å < d < 48Å sits within the exact region of steric repulsion described above. In the high q -regime, however, the larger decay rate A · q 0 3 (38-fold faster), points toward much faster motions. The sole existence of an observable deviation at higher q (distances in the range of a single membrane thickness, ~ 50Å), points toward short-range dynamics due perhaps to protrusion and diffusion of large proteins anchored on the surface of the single leaflet membrane, that contaminate the observed NSE relaxation time window. Future planned experiments at extended q -range with the characteristic dynamical trends combined with a thorough analysis of the SANS correlations peaks under variable illumination conditions are planned and will expand further our understating of these photosynthetic membranes dynamics over an extended q -scale. Methods Sample preparation and setup . Lemna minor (6-DW138, purchased from the Rutgers Duckweed Stock Cooperative, Rutgers State University New Jersey, New Brunswick, NJ, USA) was grown in H 2 O-based medium (3.2 g/L Schenk and Hildebrandt Basal Salt Mixture at pH4.2, Millipore Sigma, USA) at 24°C and 100 µE light intensity with a 12h/12h day/night cycle. Before the NSE experiment, the plants were transferred to D 2 O and equilibrated overnight. The plants were combined in a final sample batch before the NSE experiment, and the duckweeds were gently harvested and placed in NSE quartz cells of 4mm thickness as shown in Fig. 7 . In the final step pure D 2 O was added as solvent and couple of hours of equilibration were allowed for D 2 O exchange to improve the contrast. Two identical samples were prepared consecutively and used during the NSE measurements to make sure the plants are alive, and the thylakoids are functionally intact. NSE experiment and data reduction. To investigate the collective dynamics we used SNS-NSE, the NSE spectrometer at the Spallation Neutron Source 43,44 , Oak Ridge National Laboratory. Measurements were carried out in 4mm-path quartz cells at 20°C. The NSE data acquisition setup included a combination of incident wavelengths of 8Å and 11Å, accessing a dynamical range of 0.1 ≤ τ max ≤ 130ns Fourier time for different momentum transfers. Five solid angles between 0.035Å −1 and 0.12Å −1 , as minimum momentum transfer, were set to cover most of the correlation peaks observed in the SANS experiment, Fig. 8 . The characteristic peaks observable on the SANS scattering curve are originating from the periodic thylakoid membrane structure. This has been demonstrated through a series of experiments following the isolation protocol of thylakoid membranes from intact leaves 45 which preserves the diffraction features. Ideally, the correlation peak at ~ 0.027Å −1 , which relates to the first order Bragg peak of the periodic membrane system would be at the center of the NSE study, but this falls outside the q -range of the SNS-NSE spectrometer for the 8Å and 11Å incident wavelengths where the neutron flux is statistically acceptable. Therefore, as a compromise between neutron flux, reliable statistics, and beam-time availability, the next Bragg peaks in the Lemna minor diffraction pattern were selected (Fig. 8 ). Graphite foil and Al 2 O 3 were used as a standard elastic reference and pure D 2 O as solvent. The entire experiment was ~ 130 hours, with a change of sample in between, to provide fresh Lemna minor plants. The NSE raw data from the two Lemna minor samples were combined and reduced using DrSpine SNS-NSE reduction software 46 . The reduced data populated a Q- & -tau space histogram displayed in Fig. 9 , with ten momentum transfers collected with good statistics, for a different number of Fourier times as allowed by the time-of-flight nature of the SNS-NSE data. NSE data analysis. The intermediate scattering functions obtained from the NSE data reduction were fitted at first by a stretched exponential function with a stretching exponent of 2/3 predicted by Zilman & Granek 18,19 for single membrane using the python package PySEN 47 developed by P. Zolnierczuk for the SNS-NSE data analysis: $$\frac{\text{S}(\text{q},\text{t})}{\text{S}(\text{q},0)}=\text{exp}\left[-{\left({\Gamma }\text{t}\right)}^{2/3}\right]$$ 1 were Γ is the relaxation rate. Using this initial approach for fitting the NSE data any additional diffusion contributions and intermembrane interactions are neglected. The Zilman & Granek 18,19 model explains the dependence of the relaxation rate Γ with q 3 for systems where the hydrodynamic interactions dominate and the wavelengths are shorter than the characteristic correlation length, in our case 1/q < < inter-thylakoidal distance: $${{\Gamma }}_{\text{Z}\text{G}}=\text{0.025}{\alpha }\sqrt{\frac{{\text{k}}_{\text{B}}\text{T}}{\stackrel{\sim}{{\kappa }}}}\cdot \frac{{\text{k}}_{\text{B}}\text{T}}{{{\eta }}_{\text{D}2\text{O}}}\cdot {\text{q}}^{3}$$ 2 where: Γ ZG is the decay rate due to bending fluctuations, \(\stackrel{\sim}{\kappa }\) is the effective bending modulus, α is an angle factor = 1 for NSE, k B T is the thermal energy, and η D2O is the viscosity of the D 2 O solvent at T = 20°C. To assess the characteristics of thickness and local fluctuations we apply further the model used by Nagao M., 2009 21 in which shape fluctuations are taken into account together with bending fluctuations using a well-known analogy with the shape fluctuations of droplet micro-emulsions 48 : $$\frac{{\Gamma }}{{\text{q}}^{3}}=\frac{{{\Gamma }}_{\text{Z}\text{G}}}{{\text{q}}^{3}}+\frac{\text{A}}{1+{\left(\text{q}-{\text{q}}_{0}\right)}^{2}\cdot {{\xi }}^{2}}$$ 3 where: Γ is the effective relaxation rate due to both bending motions, Γ ZG , and local thickness fluctuations, Γ TF , with A the damping frequency of the peristaltic mode, A = Γ TF / q 0 3 , ξ is the mode amplitude and q 0 is the membrane thickness at which the excess motions associated with local shape fluctuations are observed 48 . In the final step the data were treated using the dynamics structure factor for a stack of oriented lamellar phases at the length scale of the intermembrane distance, as opposed to single membrane dynamics 34,35 . This model implemented in Jscatter software 36,37 allows the evaluation of membrane curvature elasticity, bending elastic modulus \(\kappa\) , compression modulus, and the dissipation related to the viscosity of the solvent according to Eq. 16 in Mihailescu et al ., 34 . Declarations Author Contributions Statement L.-R.S. developed and performed the experiment, methodology, data reduction and analysis, wrote the original draft, reviewed, and introduced co-authors editing; prepare the manuscript for submission. G.N. grew the plants and help with sample preparation and experiment setup. B.R.E. provided the original duck weed specimens. C.-H. L. helped with data error calculations. All authors reviewed and edited the manuscript. Author Contribution L.-R.S. developed and performed the experiment, methodology, data reduction and analysis, wrote the original draft, reviewed, and introduced co-authors editing; prepare the manuscript for submission. G.N. grew the plants and help with sample preparation and experiment setup. B.R.E. provided the original duck weed specimens. C.-H. L. helped with data error calculations. All authors reviewed and edited the manuscript. Acknowledgement Neutron beam time for this research at ORNL’s Spallation Neutron Source was allocated through the ScientificUser Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. SANS data were previouslyobtained using resources at the High Flux Isotope Reactor sponsored by the Scientific User Facilities Division,Office of Basic Energy Sciences and by the Office of Biological and Environmental Research, U.S. Department ofEnergy. The authors acknowledge Dr. K. Weiss for biochemistry lab support. Data Availability The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. Notice : This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/doe-public-access-plan). References Stingaciu, L.-R. et al. Revealing the Dynamics of Thylakoid Membranes in Living Cyanobacterial Cells. Sci. Rep. 6, 19627 (2016). Stingaciu, L.-R., O’Neill, H. M., Liberton, M., Pakrasi, H. B. & Urban, V. S. Influence of Chemically Disrupted Photosynthesis on Cyanobacterial Thylakoid Dynamics in Synechocystis sp. PCC 6803. Sci. Rep. 9, (2019). Allen, J. F. & Forsberg, J. Molecular recognition in thylakoid structure and function. Trends in Plant Science vol. 6 317–326 (2001). Mustárdy, L., Buttle, K., Steinbach, G. & Garab, G. The three-dimensional network of the thylakoid membranes in plants: Quasihelical model of the granum-stroma assembly. Plant Cell vol. 20 2552–2557 (2008). Posselt, D. et al. Small-angle neutron scattering study of the ultrastructure of chloroplast thylakoid membranes - Periodicity and structural flexibility of the stroma lamellae. in Biochimica et Biophysica Acta - Bioenergetics vol. 1817 1220–1228 (2012). Ünnep, R. et al. Thylakoid membrane reorganizations revealed by small-angle neutron scattering of Monstera deliciosa leaves associated with non-photochemical quenching: Membrane reorganizations in vivo and NPQ. Open Biol. (2020) doi: 10.1098/rsob.200144rsob200144 . Nagy, G. et al. Kinetics of structural reorganizations in multilamellar photosynthetic membranes monitored by small-angle neutron scattering. Eur. Phys. J. E 36, (2013). Nagy, G. et al. Dynamic properties of photosystem II membranes at physiological temperatures characterized by elastic incoherent neutron scattering. Increased flexibility associated with the inactivation of the oxygen evolving complex. Photosynth. Res. 111, 113–124 (2012). Nagy, G. et al. Chloroplast remodeling during state transitions in Chlamydomonas reinhardtii as revealed by noninvasive techniques in vivo. Proc. Natl. Acad. Sci. U. S. A. (2014) doi: 10.1073/pnas.1322494111 . Ünnep, R. et al. Low-pH induced reversible reorganizations of chloroplast thylakoid membranes — As revealed by small-angle neutron scattering. Biochim. Biophys. Acta - Bioenerg. (2017) doi: 10.1016/j.bbabio.2017.02.010 . Ünnep, R. et al. Thylakoid membrane reorganizations revealed by small-angle neutron scattering of Monstera deliciosa leaves associated with non-photochemical quenching. Open Biol. (2020) doi: 10.1098/rsob.200144 . Nagao, M., Kelley, E. G., Ashkar, R., Bradbury, R. & Butler, P. D. Probing elastic and viscous properties of phospholipid bilayers using neutron spin echo spectroscopy. J. Phys. Chem. Lett. (2017) doi: 10.1021/acs.jpclett.7b01830 . Woodka, A. C., Butler, P. D., Porcar, L., Farago, B. & Nagao, M. Lipid bilayers and membrane dynamics: Insight into thickness fluctuations. Phys. Rev. Lett. (2012) doi: 10.1103/PhysRevLett.109.058102 . Yi, Z., Nagao, M. & Bossev, D. P. Bending elasticity of saturated and monounsaturated phospholipid membranes studied by the neutron spin echo technique. J. Phys. Condens. Matter (2009) doi: 10.1088/0953-8984/21/15/155104 . Nagao, M. Temperature and scattering contrast dependencies of thickness fluctuations in surfactant membranes. J. Chem. Phys. (2011) doi: 10.1063/1.3625434 . Nickels, J. D. et al. Bacillus subtilis Lipid Extract, A Branched-Chain Fatty Acid Model Membrane. J. Phys. Chem. Lett. (2017) doi: 10.1021/acs.jpclett.7b01877 . Gupta, S. et al. Dynamics of Phospholipid Membranes beyond Thermal Undulations. J. Phys. Chem. Lett. (2018) doi: 10.1021/acs.jpclett.8b01008 . Zilman, A. G. & Granek, R. Undulations and dynamic structure factor of membranes. Phys. Rev. Lett. 77, 4788–4791 (1996). Zilman, A. G. & Granek, R. Membrane dynamics and structure factor. Chem. Phys. 284, 195–204 (2002). Watson, M. C. & Brown, F. L. H. Interpreting membrane scattering experiments at the mesoscale: The contribution of dissipation within the bilayer. Biophys. J. (2010) doi: 10.1016/j.bpj.2009.11.026 . Nagao, M. Observation of local thickness fluctuations in surfactant membranes using neutron spin echo. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. (2009) doi: 10.1103/PhysRevE.80.031606 . Ashkar, R. et al. Tuning Membrane Thickness Fluctuations in Model Lipid Bilayers. Biophys. J. (2015) doi: 10.1016/j.bpj.2015.05.033 . Mihailescu, M. et al. Neutron spin-echo investigation of the microemulsion dynamics in bicontinuous, lamellar and droplet phases. Appl. Phys. A Mater. Sci. Process. 74, (2002). Iqbal, J., Javed, A. & Baig, M. A. Growth and nutrient removal efficiency of duckweed (lemna minor) from synthetic and dumpsite leachate under artificial and natural conditions. PLoS One 14, (2019). Paolacci, S., Stejskal, V. & Jansen, M. A. K. Estimation of the potential of Lemna minor for effluent remediation in integrated multi-trophic aquaculture using newly developed synthetic aquaculture wastewater. Aquac. Int. 29, 2101–2118 (2021). Zhao, X. et al. Enzymatic saccharification of duckweed (Lemna minor) biomass without thermophysical pretreatment. Biomass and Bioenergy 47, 354–361 (2012). Demann, J. et al. Nutritional Value of Duckweed as Protein Feed for Broiler Chickens—Digestibility of Crude Protein, Amino Acids and Phosphorus. Animals 13, 130 (2022). Ali, S. et al. Application of floating aquatic plants in phytoremediation of heavy metals polluted water: A review. Sustain. 12, (2020). Cope; B. T.; Bose; S..; Crespi; H. L.; Katz; J. J. Growth of Lemna in H2O-D2O mixtures: Enhancement by kinetin. Bot. Gaz. 126, 214–221 (1965). Evans, B. R., Foston, M., O’Neill, H. M., Reeves, D., Rempe, C., McGrath, K., Ragauskas, A. J., and Davison, B. H. Production of Deuterated Biomass by Cultivation of Lemna minor (duckweed) in D2O. Planta 249, 1465–1475 (2019). Cooke, R. J., Grego, S., Olivier, J., Davies, D. D. The effect of deuterium oxide on protein turnover in Lemna minor. Planta 146, 229–236 (1979). Tat, VT; Lee, Y. Spatiotemporal study of galactolipid biosynthesis in duckweed with mass spectrometry imaging and in vivo isotope labeling. Plant Cell Physiol. (2024) doi: 10.1093/pcp/pcae032 . Yi, Z., Nagao, M. & Bossev, D. P. Bending elasticity of saturated and monounsaturated phospholipid membranes studied by the neutron spin echo technique. J. Phys. Condens. Matter 21, 155104 (2009). Mihailescu, M. et al. Neutron scattering study on the structure and dynamics of oriented lamellar phase microemulsions. Phys. Rev. E 66, (2002). Holderer, O. et al. Dynamic properties of microemulsions modified with homopolymers and diblock copolymers: The determination of bending moduli and renormalization effects. J. Chem. Phys. 122, (2005). Biehl, R. Jscatter, a Program for Evaluation and Analysis of Experimental Data. Ralf Biehl. Jscatter, a program for evaluation and analysis of experimental data. PLoS One. Mihailescu, M. et al. Dynamics of bicontinuous microemulsion phases with and without amphiphilic block-copolymers. J. Chem. Phys. 115, 9563–9577 (2001). https:// en.wikipedia.org/wiki/List_of_viscosities . Brannigan, G. & and F. L. Brown. A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayers. (2006). Helfrich, W. Steric Interaction of Fluid Membranes in Multilayer Systems. Zeitschrift für Naturforsch. A 33, 305–315 (1978). Safinya, C. R. et al. Steric Interactions in a Model Multimembrane System: A Synchrotron X-Ray Study. Phys. Rev. Lett. 57, 2718–2721 (1986). Ohl, M. et al. The high-resolution neutron spin-echo spectrometer for the SNS with τ ≥ 1 µs. in Physica B: Condensed Matter (2004). doi: 10.1016/j.physb.2004.04.014 . Kämmerling, P. et al. SNS-NSE control and data acquisition system for the neutron spin echo spectrometer at the spallation neutron source. in SEI 2013 – 104. Tagung der Studiengruppe Elektronische Instrumentierung im Fruhjahr 2013 (2013). Ünnep, R. et al. The ultrastructure and flexibility of thylakoid membranes in leaves and isolated chloroplasts as revealed by small-angle neutron scattering. Biochim. Biophys. Acta - Bioenerg. (2014) doi: 10.1016/j.bbabio.2014.01.017 . Zolnierczuk, P. A. et al. Efficient data extraction from neutron time-of-flight spin-echo raw data. J. Appl. Crystallogr. 52, 1022–1034 (2019). Zolnierczuk, P. PySEN: A Python Package for Aiding Experiments at the SNS Neutron Spin Echo Spectrometer . https://doi.org/10.2172/1987766 (2023) doi:10.2172/1987766. Milner, S. T. & Safran, S. A. Dynamical fluctuations of droplet microemulsions and vesicles. Phys. Rev. A 36, 4371–4379 (1987). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Nov, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 08 Jul, 2024 Reviews received at journal 30 Jun, 2024 Reviews received at journal 26 Jun, 2024 Reviewers agreed at journal 24 Jun, 2024 Reviews received at journal 05 Jun, 2024 Reviewers agreed at journal 26 May, 2024 Reviewers agreed at journal 22 May, 2024 Reviewers invited by journal 22 May, 2024 Editor assigned by journal 22 May, 2024 Editor invited by journal 22 May, 2024 Submission checks completed at journal 21 May, 2024 First submitted to journal 17 May, 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-4437351","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":309450627,"identity":"08d89d07-2bd6-4cc5-9d0c-b8b15641d4b9","order_by":0,"name":"Laura-Roxana Stingaciu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYFACxgYQycPAzsD4AMiQIayDDaaFmYHZAMwgrAXGYGZgkyBKi/z85raHX2rsZAwO8z6r+LjnDg8D/+JjEvi0GBxjbDeWOZbMY3CY3ezmjGfPeBgknqXh18LG2CYtwXYAqIWN7TbPgcNALWeMDfA6rA2k5R9ESzFRWhiOMbZJfmyDaGEGa+HvMXyA3y+JbdKMfck8kofZmCVnALWwSbAl4tUi33z8meSPb3b2fMfbGD98OHBYjp//8IEDeB0GBMwoccEmkUBIAzDJ/EDh8hO0YxSMglEwCkYYAAC+7EJZteJOQAAAAABJRU5ErkJggg==","orcid":"","institution":"Oak Ridge National Laboratory","correspondingAuthor":true,"prefix":"","firstName":"Laura-Roxana","middleName":"","lastName":"Stingaciu","suffix":""},{"id":309450628,"identity":"67c12c2a-7b84-4869-8855-3fb755d3d6b2","order_by":1,"name":"Hugh O’Neill","email":"","orcid":"","institution":"Oak Ridge National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Hugh","middleName":"","lastName":"O’Neill","suffix":""},{"id":309450629,"identity":"831c4d96-72e9-4e65-96d7-b3bf5a51fa92","order_by":2,"name":"Chung-Hao Liu","email":"","orcid":"","institution":"Oak Ridge National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Chung-Hao","middleName":"","lastName":"Liu","suffix":""},{"id":309450630,"identity":"798ee987-23fd-49f5-99c1-96e40473f422","order_by":3,"name":"Barbara R. Evans","email":"","orcid":"","institution":"Oak Ridge National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Barbara","middleName":"R.","lastName":"Evans","suffix":""},{"id":309450631,"identity":"900411d1-72cc-409c-9e7c-e0ae00760da1","order_by":4,"name":"Gergely Nagy","email":"","orcid":"","institution":"Oak Ridge National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Gergely","middleName":"","lastName":"Nagy","suffix":""}],"badges":[],"createdAt":"2024-05-17 14:31:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4437351/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4437351/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-22747-z","type":"published","date":"2025-11-05T15:57:25+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":57640937,"identity":"5e9208e1-9076-4c81-8656-932204231fce","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":144060,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-dependence of the stretching exponent \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eβ \u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003efrom KWW fit\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003e.\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e \u003c/em\u003eThe red dotted line is a visual mark for Zilman-Granek\u003csup\u003e18,19\u003c/sup\u003e exponent,\u003cem\u003e β \u003c/em\u003e= 2/3\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/f658a7cd9683d2cefb01683e.jpeg"},{"id":57640938,"identity":"703cd083-c03f-4b01-b0bf-f899bbfdf7b7","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":609350,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eI\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e (\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e, \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eτ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e) / \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eI \u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e(\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e, 0) of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eLemna minor \u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003emodeled by ZG.\u003c/strong\u003e Solid lines in same color represent the stretched exponential function fitting with the stretching exponent of 2/3, according to ZG. In the inset the scattering functions have been shifted by for better visualization. The lower graph is the fit residuals.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/37c38204042980b0ce50571e.jpeg"},{"id":57640940,"identity":"92561afb-26a3-4c78-9262-8ee94e3c80a3","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":898433,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003csup\u003e\u003cstrong\u003e \u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003edependence of the decay rate (left panel) and \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003csup\u003e\u003cstrong\u003e3 \u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003edependence of the decay rate (right panel) from ZG fit (\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eΓ\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cstrong\u003eZG\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e).\u003c/strong\u003e The vertical dashed lines mark the positions of the corresponding SANS correlation peaks from the SANS profile superimposed in blue circles. Linear regression fit was applied to the data in the left panel using all \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e values (blue), small \u003cem\u003eq\u003c/em\u003e-range (black) and large \u003cem\u003eq\u003c/em\u003e-range (red). \u0026nbsp;The horizontal green line in the right panel represents the linear fit of all relaxation rate \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e/\u003cem\u003e q\u003c/em\u003e\u003csup\u003e3 \u003c/sup\u003evalues with slope = 0 and intercept value = \u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e to access the apparent bending modulus of the membranes.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/7cf3996903b53884467e0d11.jpeg"},{"id":57641245,"identity":"1eb3e61b-9bb1-4f64-ab76-ec2bf3b2acac","added_by":"auto","created_at":"2024-06-03 17:28:59","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":567311,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eI\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e (\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e, \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eτ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e) / \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eI \u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e(\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e, 0) of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eLemna minor\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e modeled by oriented lamellar phases. \u003c/strong\u003eSolid lines represent the fitting by dynamics of oriented lamellar phases model according to Mihailescu \u003cem\u003eet al., \u003c/em\u003e2002\u003csup\u003e34\u003c/sup\u003e. In the inset scattering functions have been shifted by -0.05 for better visualization. The lower graph is the fit residuals.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/292ea4246703c043a1ae7474.jpeg"},{"id":57640944,"identity":"a6e9333a-5da3-449d-9624-6aafc1b02db1","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":339285,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe single membrane apparent bending modulus (black) with superimposed solvent viscosity (green). \u003c/strong\u003eValues were calculated using the dynamics of oriented lamellar phases model for T =20°C and a film-to-film distance = 241.65Å corresponding to the first SANS correlation peak. The dashed green line represents H\u003csub\u003e2\u003c/sub\u003eO dynamic viscosity ~ 1 mPa*s.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/de96784797fd80a7c1b6626f.jpeg"},{"id":57640943,"identity":"18aa32f0-6ca1-4900-8f7a-f02e17065547","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":431738,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eEmpirical Lorentz description of excess dynamics attempted on the \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eq\u003c/strong\u003e\u003c/em\u003e\u003csup\u003e\u003cstrong\u003e3 \u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003edependence of the decay rate \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eΓ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e from ZG fit. \u003c/strong\u003eThe vertical lines and circle marks show the position of the corresponding SANS correlation peaks. The horizontal green line represents the intercept value of the Lorentzian functions.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/df172696b09e444d6d120116.jpeg"},{"id":57640941,"identity":"3919e902-8e8d-44fb-92e2-e2784d11450e","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":64051,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eLemna minor\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e sample preparation. \u003c/strong\u003eLeft-side panels show representative batches during growing and harvesting phase; Middle and right-side panels show the two NSE samples collected in quartz cells and mounted on the NSE sample holder frame together with the D\u003csub\u003e2\u003c/sub\u003eO solvent sample. Note that the NSE samples were interchanged in the middle of the NSE experiment to ensure fresh living plants for the entire length of the measurement.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/773175e17a53550abdee31cb.jpeg"},{"id":57640942,"identity":"66285e21-e374-49a7-a403-db750567eb25","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":606563,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003e\u003cstrong\u003eLemna minor \u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003eSANS diffraction pattern. \u003c/strong\u003eSeveral correlation peaks are observed due to membrane stack periodicity and were sampled as solid angles during the NSE measurement.\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/1e4a6139766108815316032f.jpeg"},{"id":57640946,"identity":"2429ad06-73b6-433e-b007-0a2dac0fb419","added_by":"auto","created_at":"2024-06-03 17:20:59","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":330519,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCoverage of \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eQ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e-\u0026amp;-\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eτ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e space showing the evaluated \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eQ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e and \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eτ\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e points alongside the corresponding weighted detector pixel contributions. \u003c/strong\u003eThe histogram was populated reducing raw echo data from both \u003cem\u003eLemna minor\u003c/em\u003e samples combined for the 5 solid angles measured.\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/0749fd353b00e64375834174.jpeg"},{"id":95564129,"identity":"8de8a933-08b8-47f9-9b34-56074651fd3d","added_by":"auto","created_at":"2025-11-10 16:08:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5085305,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4437351/v1/fa5416d5-1a19-4f4d-b1b3-b4c04ef03f3b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Neutrons reveal the dynamics of leaf thylakoids in living plants","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe light reaction of photosynthesis occurs within the intricate membranous structures known as thylakoids. It has been shown previously in the unicellular cyanobacteria, where the photosynthetic membranes form concentric layers that follow the shape of the cell envelope, that thylakoids are highly flexible structures, and their dynamics is tightly connected with the electron transfer between photosynthetic reaction centers and the associated electrochemical proton gradient across the membrane\u003csup\u003e1,2\u003c/sup\u003e. However, in higher plants the thylakoid membranes are organized in a different fashion. Each leaf cell contains several chloroplasts in which thylakoid membranes are stacked in closed appressed structures ensuring a large area-to-volume ratio and a high stability of the photosynthetic ultrastructure, with remarkable flexibility and adaptability to environmental conditions.\u003csup\u003e3,4\u003c/sup\u003e To date, detailed information about thylakoids macro-structure in their native environment in leaf cells is available using non-invasive Small Angle Neutron Scattering (SANS)\u003csup\u003e5\u0026ndash;7\u003c/sup\u003e. These elegant and thorough structural studies suggest that thylakoid membranes within chloroplasts can also exhibit a great amount of flexibility and very complex dynamics patterns related to the photosynthetic process\u003csup\u003e8\u0026ndash;11\u003c/sup\u003e. In respect of that view our aim was to observe and characterize noninvasively the dynamics of plant thylakoids and assess their flexibility as bending and thickness fluctuations, in a similar way as previously done for single-cell photosynthetic microorganisms\u003csup\u003e1,2\u003c/sup\u003e and standard bilayer phospholipid membranes\u003csup\u003e12\u0026ndash;15\u003c/sup\u003e. Neutron Spin-Echo (NSE) spectroscopy is the high-resolution spectroscopic technique that has already proved to be very successful in capturing the structure and dynamics of bilayer lipid membranes with no damage inflicted to membranes\u003csup\u003e1,12,16,17\u003c/sup\u003e. A variety of theoretical models also exist to characterize the undulation, bending and thickness fluctuations of the lipid membranes\u003csup\u003e18\u0026ndash;23\u003c/sup\u003e. The main challenge for this study was to find a suitable plant that can fulfill all the following vital requirements: i) fast growing in confined lab space to supply plentitude of fresh, intact leaves over a relatively short period of time ii) could survive for extended soaking time in D\u003csub\u003e2\u003c/sub\u003eO, which is necessary to enhance the contrast, iii) has thin leaves that allow fast gas diffusion and D\u003csub\u003e2\u003c/sub\u003eO exchange, iv) is biologically relevant and, preferably, v) it has been investigated thoroughly by SANS which demonstrated that its diffraction pattern shows correlation peaks in the spin-echo accessible \u003cem\u003eq\u003c/em\u003e-range.\u003c/p\u003e \u003cp\u003eCommon duckweed (\u003cem\u003eLemna minor)\u003c/em\u003e is a small aquatic plant that belongs to the Lemnaceae family. It is one of the smallest flowering plants in the world and can be found floating on the surface of still or slow-moving freshwater bodies like ponds and lakes. \u003cem\u003eLemna minor\u003c/em\u003e has tiny, oval-shaped leaf called fronds of a few millimeters in size. Due to its rapid growth and its ability to efficiently absorb nitrogen and phosphorus from the water, duckweed is often used in wastewater treatment\u003csup\u003e24,25\u003c/sup\u003e. \u003cem\u003eLemna minor\u003c/em\u003e also provides habitat and food for various aquatic organisms. Its ability to cover large water surfaces can also reduce evaporation and inhibit the growth of harmful algae by shading the water. Duckweed plays a fascinating role in aquatic ecosystems and has practical applications in environmental and agricultural contexts with the potential to be used for biofuel production\u003csup\u003e26\u003c/sup\u003e, protein-rich animal feed\u003csup\u003e27\u003c/sup\u003e and phytoremediation\u003csup\u003e28\u003c/sup\u003e. In contrast to most terrestrial plants, \u003cem\u003eLemna minor\u003c/em\u003e can tolerate and grow in relatively high concentrations of D\u003csub\u003e2\u003c/sub\u003eO\u003csup\u003e29\u003c/sup\u003e and has been grown in 50% D\u003csub\u003e2\u003c/sub\u003eO for production of deuterated biomass\u003csup\u003e30\u003c/sup\u003e for metabolic studies\u003csup\u003e31\u003c/sup\u003e, and for probing localization of lipid biosynthesis\u003csup\u003e32\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this work, we observe and characterize the mobility of the thylakoid membranes encapsuled by chloroplasts in cell fronds of living \u003cem\u003eLemna minor\u003c/em\u003e plants by neutron spin-echo spectroscopy.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003e \u003cb\u003eAssessment of the internal dynamics of thylakoids.\u003c/b\u003e The result of neutron spin-echo spectroscopy measurements is the normalized intermediate scattering function \u003cem\u003eI\u003c/em\u003e (\u003cem\u003eq\u003c/em\u003e, \u003cem\u003eτ\u003c/em\u003e) / \u003cem\u003eI\u003c/em\u003e (\u003cem\u003eq\u003c/em\u003e, 0) describing the pair-correlation distances observed in reciprocal space \u003cem\u003eq\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2π/\u003cem\u003ed\u003c/em\u003e and the time-dependent relaxation of such correlations due to the internal mobility of the sample investigated. As the first step in the analysis, the normalized intermediate scattering functions experimentally obtained, were fitted by a stretched exponential function with the stretching exponent \u003cem\u003eβ\u003c/em\u003e as a free fitting parameter. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the \u003cem\u003eq\u003c/em\u003e dependence of the stretching exponent. The values of \u003cem\u003eβ\u003c/em\u003e range between 0.2 and 0.4 in the small \u003cem\u003eq\u003c/em\u003e-regime\u0026thinsp;\u0026le;\u0026thinsp;0.07\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e with the rest of \u003cem\u003eβ\u003c/em\u003e around 0.6 for higher \u003cem\u003eq\u003c/em\u003e values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOne can also observe the large \u003cem\u003eβ\u003c/em\u003e-errors, providing insights how stretched exponential function with a free exponent might not be the correct model to describe the experimental relaxation curves, especially for the data in the high \u003cem\u003eq\u003c/em\u003e-regime. Therefore, in the next step of the evaluation we fixed the value of \u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2/3 according to Zilman \u0026amp; Granek\u003csup\u003e18,19\u003c/sup\u003e model (abbreviated ZG from here on) proposed for bilayer membrane dynamics and the intermediate scattering function observed by NSE were fitted accordingly. ZG model provided a reasonable description of the NSE experimental data, with χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.019 per degree of freedom, see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe corresponding time information obtained is expressed as either relaxation time \u003cem\u003eτ\u003c/em\u003e or inversely, as relaxation rates \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e and calculated using Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, see Methods. In the following we used the spatial dependence of the relaxation rate \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e to characterize the dynamics of our system (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, both panels). The \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e behavior as a function of \u003cem\u003eq\u003c/em\u003e shows different patterns between the small \u003cem\u003eq\u003c/em\u003e-range (black symbols) and the large \u003cem\u003eq\u003c/em\u003e-range (red symbols) in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, left panel. In the small \u003cem\u003eq\u003c/em\u003e-range, there is no change in the relaxation rate values as a function of \u003cem\u003eq\u003c/em\u003e. This points toward a relaxation process restricted by space, like diffusion in confined geometry. In the large \u003cem\u003eq\u003c/em\u003e-range the relaxation rate is characterized a by a power law with the exponent of \u003cem\u003em\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.88. A linear fit of all data yields a power law with the exponent of \u003cem\u003em\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.28, when all \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e values are used.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eGiven the value of the exponent close to \u003cem\u003em\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3, the \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e /\u003cem\u003eq\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e behavior as a function of \u003cem\u003eq\u003c/em\u003e is commonly represented to observe the linear dependence at high \u003cem\u003eq\u003c/em\u003e-values, a typical signature of pure undulation motions in lipid bilayer membranes that helps extract the effective bending modulus of the membranes. It should come as no surprise that the dependence displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, right panel, shows a poor linearity between the relaxation rates \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e /\u003cem\u003eq\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e at high \u003cem\u003eq\u003c/em\u003e-values, \u0026ge; 0.07\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e. This points to additional relaxation due to superimposed dynamic processes on top of the simple undulation motions. The complex nature of the relaxation rate pattern arises from the complexity of the thylakoids stacked architecture within the chloroplast of the leaf and its intricate dynamical behavior. The photosynthetic membranes closely appressed together and enclosed in chloroplast feel the presence of other neighboring membranes in terms of fluctuation dynamics and one cannot easily deconvolute the single bilayer membrane undulation dynamics from the overall bilayer-bilayer interaction within the stack. The original ZG model is expected to be valid in the high \u003cem\u003eq\u003c/em\u003e-regime, where 1/\u003cem\u003eq\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026lt;\u0026thinsp;interthylakoidal distance. The deviations observed in \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e \u003cem\u003e/q\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e vs \u003cem\u003eq\u003c/em\u003e represents a limitation of the ZG model for characterizing bending fluctuation in complex architectural membrane structures, especially in living thylakoids where a multitude of other components beside bilayers are present and may contribute with additional relaxation modes.\u003c/p\u003e \u003cp\u003e \u003cb\u003eCharacteristics of bending fluctuations.\u003c/b\u003e The \u003cem\u003eq\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e dependence of the relaxation rate \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e is controlled by the elastic modulus \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{\\kappa }\\)\u003c/span\u003e\u003c/span\u003e, with higher bending coefficients corresponding to smaller relaxation rates\u003csup\u003e18,20\u003c/sup\u003e. The effective bending coefficient was calculated according to Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e from the intercept value \u003cem\u003ey\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, right panel (linear regression with slope\u0026thinsp;=\u0026thinsp;0 depicted by the green dashed line) and expressed in units of thermal energy. Large value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{\\kappa }\\)\u003c/span\u003e\u003c/span\u003e \u0026gt;\u0026gt; \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{\\kappa }\\)\u003c/span\u003e\u003c/span\u003e = 1669.7 \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e) indicates a rigid system, a stack of membranes closely appressed together or membranes encapsulated in a tight structure with restricted space for free undulation motions, as well as it can indicate the presence of other structures like macromolecules grafted on the surface of the surfactant membranes that act like fluctuation suppressors\u003csup\u003e18,20\u003c/sup\u003e. All these are valid if we consider the architecture of thylakoids encapsuled by chloroplasts in the cells of \u003cem\u003eLemna minor\u003c/em\u003e leaf. The effective bending coefficient in stacked membranes depends also strongly on the viscosity of the solvent confined between membranes, as shown previously in numerous studies\u003csup\u003e33\u003c/sup\u003e. A rescaling of the bulk D\u003csub\u003e2\u003c/sub\u003eO viscosity, \u003cem\u003eη\u003c/em\u003e\u003csub\u003eD2O\u003c/sub\u003e, to 3\u0026middot;\u003cem\u003eη\u003c/em\u003e\u003csub\u003eD2O\u003c/sub\u003e as suggested by these studies brings the effective bending coefficient to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{{\\kappa }}\\)\u003c/span\u003e\u003c/span\u003e = 185 \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), well within the extensive range observed for surfactant membranes, where values between 0.1\u0026ndash;2000 \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e have been reported by various research.\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\u003e\u003cb\u003eCharacteristics of bending fluctuations.\u003c/b\u003e The bending modulus was calculated for \u003cem\u003eη\u003c/em\u003e\u003csub\u003eD2O\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.00125 kg\u0026middot;m\u0026middot;s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e as D\u003csub\u003e2\u003c/sub\u003eO viscosity at 20\u0026deg;C, and for 3\u0026middot;\u003cem\u003eη\u003c/em\u003e\u003csub\u003eD2O\u003c/sub\u003e as suggested by literature\u003csup\u003e20,33\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample\u003c/p\u003e \u003cp\u003ename\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eΓ/q\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(\u0026Aring;\u003csup\u003e3\u003c/sup\u003e/ns)\u003c/p\u003e\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{\\varvec{\\kappa }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e(k\u003csub\u003eB\u003c/sub\u003eT)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{\\varvec{\\kappa }}\\)\u003c/span\u003e\u003c/span\u003e for 3 \u0026middot; \u003cem\u003eη\u003c/em\u003e\u003csub\u003eD2O\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(k\u003csub\u003eB\u003c/sub\u003eT)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLemna Minor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.98\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1669.7\u0026thinsp;\u0026plusmn;\u0026thinsp;556.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e185.5\u0026thinsp;\u0026plusmn;\u0026thinsp;61.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eGiven the above, an analogy can be made between the observed excess dynamics of thylakoids and the excess dynamics related to shape fluctuations in oriented lamellar phase microemulsions\u003csup\u003e34,35\u003c/sup\u003e. Dynamics of oriented lamellar phases model implemented in the software Jscatte\u003cem\u003er\u003c/em\u003e\u003csup\u003e36,37\u003c/sup\u003e calculates the coherent intermediate scattering function arising from dynamics of oriented lamellar phases at the length scale of the intermembrane distance (see Eq.\u0026nbsp;16 in reference Mihailescu \u003cem\u003eet al\u003c/em\u003e., 2002\u003csup\u003e34\u003c/sup\u003e). In our case the model provided information on the single membrane apparent bending modulus in thermal energy units, the membrane thickness, and solvent viscosity, using the film-to-film distance (241.65\u0026Aring;, first SANS peak @ \u003cem\u003eq\u003c/em\u003e\u0026thinsp;~\u0026thinsp;0.026\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e) representing the periodicity of the structure as input parameter (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe best fit was obtained assuming \u003cem\u003eq\u003c/em\u003e-dependence of the bending modulus and solvent viscosity, with χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.017 per degree of freedom (117 dof, with 31 parameters fitted simultaneously for the ten experimental scattering functions, \u003cem\u003ei.e. q\u003c/em\u003e\u0026rsquo;s). The bending modulus calculated for single membrane varies between 0.59 \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e and 3.72 \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), higher but not too different from values determined for bi-continuous surfactant phases\u003csup\u003e38\u003c/sup\u003e (~\u0026thinsp;1.3\u0026ndash;1.5 \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e). Single bilayer thickness calculated is 65 \u0026Aring; \u0026plusmn; 24 \u0026Aring; and strongly corelated with the solvent viscosity. In the analysis only bulk apparent viscosity was assumed and fitted for each \u003cem\u003eq\u003c/em\u003e to account for local viscosity fluctuations. These variations can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. A mean value of 0.75 mPa*s (with a large standard deviation of 0.75) can be calculated from the viscosity values, falling well within the range observed for the n-alkanes and chloroalkanes, as well as aqueous solution with high solutes concentration\u003csup\u003e39\u003c/sup\u003e. We theorized that the sensitivity of the calculated model parameters to observable bulk viscosity represents a qualitative description of local viscosity fluctuations due to anchored proteins on the membrane surfaces, increased local friction with the solvent and variabilities in the membrane internal viscosity due to variations in lipids concentration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eCharacteristics of local fluctuations.\u003c/b\u003e The spatial dependence of the decay rate \u003cem\u003eΓ\u003c/em\u003e shows excess mobility in addition to the underlying \u003cem\u003eq\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e-dependent undulation dynamics. To quantify these deviations we used the approach established by Nagao and collaborators\u003csup\u003e13,21\u003c/sup\u003e where the excess motion is described as local shape and thickness fluctuations with peristaltic and protrusion motions, see Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e in Methods. The intent is to describe the trend of the relaxation rate by Lorentz functions, using the previous peak model analysis used for photosynthetic cells\u003csup\u003e1\u003c/sup\u003e based on simulation results for thickness fluctuations\u003csup\u003e21\u003c/sup\u003e and protein-induced deformations in lipid bilayers\u003csup\u003e20,40\u003c/sup\u003e. There are two strong deviations identifiable, one in the small to intermediate \u003cem\u003eq\u003c/em\u003e-range where we sample distances proportional to the center-to-center bilayer distance, and another deviation in the high \u003cem\u003eq\u003c/em\u003e-regime at distances in the range of a single membrane thickness. In the past, similar excess dynamics have been attributed to swelling of the membrane pair, \u003cem\u003ee.g.\u003c/em\u003e, thickness fluctuations, bilayer-bilayer interactions, and dynamics due to protrusion and diffusion of proteins at the membrane surface. The decay rate \u003cem\u003eΓ\u003c/em\u003e experimentally obtained fit was separated again, for the purpose of this study, in two \u003cem\u003eq\u003c/em\u003e-regimes: a high \u003cem\u003eq\u003c/em\u003e-regime\u0026thinsp;\u0026ge;\u0026thinsp;0.07\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e (red data in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) and a small \u003cem\u003eq\u003c/em\u003e-regime\u0026thinsp;\u0026le;\u0026thinsp;0.07\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e (black data in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) and two Lorentzian were used for the analysis of the two \u003cem\u003eq\u003c/em\u003e-regimes. The best fit was obtained by Lorentzian functions having the peak center situated around the same position as the first and the last observable SANS correlation peaks: \u003cem\u003eq\u003c/em\u003e\u0026thinsp;~\u0026thinsp;0.027\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e and \u003cem\u003eq\u003c/em\u003e\u0026thinsp;~\u0026thinsp;0.11\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e. This is a clear indication of excess dynamics occurring at length scales corresponding to both: bilayer periodicity and single membrane thickness. The calculated parameters from the Lorentz fit are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe large difference observed in the decay rate of the local fluctuations, \u003cem\u003eA\u003c/em\u003e\u0026middot;\u003cem\u003eq\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e, between small and high \u003cem\u003eq\u003c/em\u003e-regime is a good indication of the underlaying dynamical process. In the small \u003cem\u003eq\u003c/em\u003e-regime the faster decay rate points toward longer relaxation times and slower motions. These slow motions can be attributed to progressive swelling of the thylakoid pair stack as well and to adjacent bilayer repulsive interactions. The photosynthetic membrane pair is a living structure, and a certain amount of flexibility is needed to adjust to the active photosynthetic process. The swelling of the thylakoid pair happens within the restricted space of the chloroplast, up to the point where is contracted by the adjacent bilayer swelling. Although we lack a more discrete refinement of \u003cem\u003eΓ vs q\u003c/em\u003e dependence, as well as values at the very low \u003cem\u003eq\u003c/em\u003e, we can still formulate some hypothesis on a reasonable behavior for living photosynthetic membranes under restricted spatial architecture within chloroplasts.\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\u003e\u003cb\u003eCharacteristics of local thickness fluctuations.\u003c/b\u003e \u003cem\u003eA\u003c/em\u003e\u0026thinsp;=\u0026thinsp;damping frequency of the peristaltic mode, \u003cem\u003eξ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;the peristaltic mode amplitude, \u003cem\u003eq\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;the peak maximum position, local length scale of thickness fluctuations. The product \u003cem\u003eA\u003c/em\u003e\u0026middot;\u003cem\u003eq\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e describes the decay rate of the local fluctuations. *\u003cem\u003eNote that the parameters are calculated for each peak displayed in\u003c/em\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e \u003cem\u003eusing the intercept value y\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u0026thinsp;Γ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e\u003cem\u003e/q\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e\u0026thinsp;\u003cem\u003e=\u0026thinsp;0.89 of the two Lorentzian.\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" 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=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSample\u003c/p\u003e \u003cp\u003ename\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eΓ\u003csub\u003eZG\u003c/sub\u003e/q\u003csup\u003e3\u003c/sup\u003e (\u0026Aring;\u003csup\u003e3\u003c/sup\u003e/ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eq\u003csub\u003e0\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eA\u003c/p\u003e \u003cp\u003e(\u0026Aring;\u003csup\u003e3\u003c/sup\u003e/ns)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eξ\u003c/p\u003e \u003cp\u003e(\u0026Aring;)\u003c/p\u003e\u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA*q\u003csub\u003e0\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e x 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(ns\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eχ\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePeak1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.24\u0026thinsp;\u0026plusmn;\u0026thinsp;0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;2.5E-4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e0.045\u0026thinsp;\u0026plusmn;\u0026thinsp;0.0004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.4E-4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePeak2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e \u003cp\u003e0.89\u0026thinsp;\u0026plusmn;\u0026thinsp;0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.109\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e \u003cp\u003e0.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e \u003cp\u003e1.74\u0026thinsp;\u0026plusmn;\u0026thinsp;0.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWith increasing distance from the marked high \u003cem\u003eq\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.11\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;50\u0026Aring;) to the marked low \u003cem\u003eq\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.027\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;250\u0026Aring;), the field of view changes from the local single membrane leaflet to center-to-center distance of adjacent bilayer membrane-pair stack. The thermal fluctuations can induce collisions between neighboring membranes. These collisions give rise to repulsive bilayer-bilayer interactions caused by the reduction of entropy, called Helfrich steric repulsion\u003csup\u003e41\u003c/sup\u003e. Experimental work on lamellar microemulsion of sodium dodecyl sulfate (SDS) of Safinya \u003cem\u003eet al\u003c/em\u003e.,\u003csup\u003e42\u003c/sup\u003e showed that for intermembrane distances between ~\u0026thinsp;40\u0026Aring; and ~\u0026thinsp;170\u0026Aring; Helfrich steric interaction is the dominant interaction. The \u003cem\u003eq-\u003c/em\u003ewindow that NSE was able to sample during the measurements on \u003cem\u003eLemna minor\u003c/em\u003e 0.04\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e \u0026lt; \u003cem\u003eq\u003c/em\u003e \u0026lt; 0.13\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e with corresponding distances of 157\u0026Aring; \u0026lt; \u003cem\u003ed\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;48\u0026Aring; sits within the exact region of steric repulsion described above. In the high \u003cem\u003eq\u003c/em\u003e-regime, however, the larger decay rate \u003cem\u003eA\u003c/em\u003e\u0026middot;\u003cem\u003eq\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e (38-fold faster), points toward much faster motions. The sole existence of an observable deviation at higher q (distances in the range of a single membrane thickness, ~ 50\u0026Aring;), points toward short-range dynamics due perhaps to protrusion and diffusion of large proteins anchored on the surface of the single leaflet membrane, that contaminate the observed NSE relaxation time window. Future planned experiments at extended \u003cem\u003eq\u003c/em\u003e-range with the characteristic dynamical trends combined with a thorough analysis of the SANS correlations peaks under variable illumination conditions are planned and will expand further our understating of these photosynthetic membranes dynamics over an extended \u003cem\u003eq\u003c/em\u003e-scale.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e \u003cb\u003eSample preparation and setup\u003c/b\u003e. \u003cem\u003eLemna minor\u003c/em\u003e (6-DW138, purchased from the Rutgers Duckweed Stock Cooperative, Rutgers State University New Jersey, New Brunswick, NJ, USA) was grown in H\u003csub\u003e2\u003c/sub\u003eO-based medium (3.2 g/L Schenk and Hildebrandt Basal Salt Mixture at pH4.2, Millipore Sigma, USA) at 24\u0026deg;C and 100 \u0026micro;E light intensity with a 12h/12h day/night cycle. Before the NSE experiment, the plants were transferred to D\u003csub\u003e2\u003c/sub\u003eO and equilibrated overnight. The plants were combined in a final sample batch before the NSE experiment, and the duckweeds were gently harvested and placed in NSE quartz cells of 4mm thickness as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the final step pure D\u003csub\u003e2\u003c/sub\u003eO was added as solvent and couple of hours of equilibration were allowed for D\u003csub\u003e2\u003c/sub\u003eO exchange to improve the contrast. Two identical samples were prepared consecutively and used during the NSE measurements to make sure the plants are alive, and the thylakoids are functionally intact.\u003c/p\u003e \u003cp\u003e \u003cb\u003eNSE experiment and data reduction.\u003c/b\u003e To investigate the collective dynamics we used SNS-NSE, the NSE spectrometer at the Spallation Neutron Source\u003csup\u003e43,44\u003c/sup\u003e, Oak Ridge National Laboratory. Measurements were carried out in 4mm-path quartz cells at 20\u0026deg;C. The NSE data acquisition setup included a combination of incident wavelengths of 8\u0026Aring; and 11\u0026Aring;, accessing a dynamical range of 0.1\u0026thinsp;\u0026le;\u0026thinsp;\u003cem\u003eτ\u003c/em\u003e\u003csub\u003emax\u003c/sub\u003e\u0026thinsp;\u0026le;\u0026thinsp;130ns Fourier time for different momentum transfers. Five solid angles between 0.035\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e and 0.12\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e, as minimum momentum transfer, were set to cover most of the correlation peaks observed in the SANS experiment, Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe characteristic peaks observable on the SANS scattering curve are originating from the periodic thylakoid membrane structure. This has been demonstrated through a series of experiments following the isolation protocol of thylakoid membranes from intact leaves\u003csup\u003e45\u003c/sup\u003e which preserves the diffraction features. Ideally, the correlation peak at ~\u0026thinsp;0.027\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e, which relates to the first order Bragg peak of the periodic membrane system would be at the center of the NSE study, but this falls outside the \u003cem\u003eq\u003c/em\u003e-range of the SNS-NSE spectrometer for the 8\u0026Aring; and 11\u0026Aring; incident wavelengths where the neutron flux is statistically acceptable. Therefore, as a compromise between neutron flux, reliable statistics, and beam-time availability, the next Bragg peaks in the \u003cem\u003eLemna minor\u003c/em\u003e diffraction pattern were selected (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). Graphite foil and Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e were used as a standard elastic reference and pure D\u003csub\u003e2\u003c/sub\u003eO as solvent. The entire experiment was ~\u0026thinsp;130 hours, with a change of sample in between, to provide fresh \u003cem\u003eLemna minor\u003c/em\u003e plants. The NSE raw data from the two \u003cem\u003eLemna minor\u003c/em\u003e samples were combined and reduced using \u003cem\u003eDrSpine\u003c/em\u003e SNS-NSE reduction software\u003csup\u003e46\u003c/sup\u003e. The reduced data populated a \u003cem\u003eQ-\u003c/em\u003e\u0026amp;\u003cem\u003e-tau\u003c/em\u003e space histogram displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, with ten momentum transfers collected with good statistics, for a different number of Fourier times as allowed by the time-of-flight nature of the SNS-NSE data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eNSE data analysis.\u003c/b\u003e The intermediate scattering functions obtained from the NSE data reduction were fitted at first by a stretched exponential function with a stretching exponent of 2/3 predicted by Zilman \u0026amp; Granek\u003csup\u003e18,19\u003c/sup\u003e for single membrane using the python package \u003cem\u003ePySEN\u003c/em\u003e\u003csup\u003e47\u003c/sup\u003e developed by P. Zolnierczuk for the SNS-NSE data analysis:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\frac{\\text{S}(\\text{q},\\text{t})}{\\text{S}(\\text{q},0)}=\\text{exp}\\left[-{\\left({\\Gamma }\\text{t}\\right)}^{2/3}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewere \u003cem\u003eΓ\u003c/em\u003e is the relaxation rate.\u003c/p\u003e \u003cp\u003eUsing this initial approach for fitting the NSE data any additional diffusion contributions and intermembrane interactions are neglected. The Zilman \u0026amp; Granek\u003csup\u003e18,19\u003c/sup\u003e model explains the dependence of the relaxation rate \u003cem\u003eΓ\u003c/em\u003e with \u003cem\u003eq\u003c/em\u003e\u003csup\u003e3\u003c/sup\u003e for systems where the hydrodynamic interactions dominate and the wavelengths are shorter than the characteristic correlation length, in our case \u003cem\u003e1/q\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u0026lt;\u0026thinsp;inter-thylakoidal distance:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${{\\Gamma }}_{\\text{Z}\\text{G}}=\\text{0.025}{\\alpha }\\sqrt{\\frac{{\\text{k}}_{\\text{B}}\\text{T}}{\\stackrel{\\sim}{{\\kappa }}}}\\cdot \\frac{{\\text{k}}_{\\text{B}}\\text{T}}{{{\\eta }}_{\\text{D}2\\text{O}}}\\cdot {\\text{q}}^{3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere: \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e is the decay rate due to bending fluctuations, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{\\kappa }\\)\u003c/span\u003e\u003c/span\u003e is the effective bending modulus, \u003cem\u003eα\u003c/em\u003e is an angle factor\u0026thinsp;=\u0026thinsp;1 for NSE, \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e\u003cem\u003eT\u003c/em\u003e is the thermal energy, and \u003cem\u003eη\u003c/em\u003e\u003csub\u003eD2O\u003c/sub\u003e is the viscosity of the D\u003csub\u003e2\u003c/sub\u003eO solvent at \u003cem\u003eT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20\u0026deg;C.\u003c/p\u003e \u003cp\u003eTo assess the characteristics of thickness and local fluctuations we apply further the model used by Nagao M., 2009\u003csup\u003e21\u003c/sup\u003e in which shape fluctuations are taken into account together with bending fluctuations using a well-known analogy with the shape fluctuations of droplet micro-emulsions\u003csup\u003e48\u003c/sup\u003e:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\frac{{\\Gamma }}{{\\text{q}}^{3}}=\\frac{{{\\Gamma }}_{\\text{Z}\\text{G}}}{{\\text{q}}^{3}}+\\frac{\\text{A}}{1+{\\left(\\text{q}-{\\text{q}}_{0}\\right)}^{2}\\cdot {{\\xi }}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere: \u003cem\u003eΓ\u003c/em\u003e is the effective relaxation rate due to both bending motions, \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eZG\u003c/sub\u003e, and local thickness fluctuations, \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eTF\u003c/sub\u003e, with \u003cem\u003eA\u003c/em\u003e the damping frequency of the peristaltic mode, \u003cem\u003eA\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eΓ\u003c/em\u003e\u003csub\u003eTF\u003c/sub\u003e/\u003cem\u003eq\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e\u003csup\u003e3\u003c/sup\u003e, \u003cem\u003eξ\u003c/em\u003e is the mode amplitude and \u003cem\u003eq\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the membrane thickness at which the excess motions associated with local shape fluctuations are observed\u003csup\u003e48\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn the final step the data were treated using the dynamics structure factor for a stack of oriented lamellar phases at the length scale of the intermembrane distance, as opposed to single membrane dynamics\u003csup\u003e34,35\u003c/sup\u003e. This model implemented in \u003cem\u003eJscatter\u003c/em\u003e software\u003csup\u003e36,37\u003c/sup\u003e allows the evaluation of membrane curvature elasticity, bending elastic modulus \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\kappa\\)\u003c/span\u003e\u003c/span\u003e, compression modulus, and the dissipation related to the viscosity of the solvent according to Eq.\u0026nbsp;16 in Mihailescu \u003cem\u003eet al\u003c/em\u003e.,\u003csup\u003e34\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eAuthor Contributions Statement\u003c/h2\u003e \u003cp\u003eL.-R.S. developed and performed the experiment, methodology, data reduction and analysis, wrote the original draft, reviewed, and introduced co-authors editing; prepare the manuscript for submission. G.N. grew the plants and help with sample preparation and experiment setup. B.R.E. provided the original duck weed specimens. C.-H. L. helped with data error calculations. All authors reviewed and edited the manuscript.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eL.-R.S. developed and performed the experiment, methodology, data reduction and analysis, wrote the original draft, reviewed, and introduced co-authors editing; prepare the manuscript for submission. G.N. grew the plants and help with sample preparation and experiment setup. B.R.E. provided the original duck weed specimens. C.-H. L. helped with data error calculations. All authors reviewed and edited the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eNeutron beam time for this research at ORNL\u0026rsquo;s Spallation Neutron Source was allocated through the ScientificUser Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. SANS data were previouslyobtained using resources at the High Flux Isotope Reactor sponsored by the Scientific User Facilities Division,Office of Basic Energy Sciences and by the Office of Biological and Environmental Research, U.S. Department ofEnergy. The authors acknowledge Dr. K. Weiss for biochemistry lab support.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets used and analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eNotice\u003c/strong\u003e: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/doe-public-access-plan).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eStingaciu, L.-R. \u003cem\u003eet al.\u003c/em\u003e Revealing the Dynamics of Thylakoid Membranes in Living Cyanobacterial Cells. Sci. Rep. 6, 19627 (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eStingaciu, L.-R., O\u0026rsquo;Neill, H. M., Liberton, M., Pakrasi, H. B. \u0026amp; Urban, V. S. Influence of Chemically Disrupted Photosynthesis on Cyanobacterial Thylakoid Dynamics in Synechocystis sp. PCC 6803. Sci. Rep. 9, (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllen, J. F. \u0026amp; Forsberg, J. Molecular recognition in thylakoid structure and function. Trends in Plant Science vol. 6 317\u0026ndash;326 (2001).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMust\u0026aacute;rdy, L., Buttle, K., Steinbach, G. \u0026amp; Garab, G. The three-dimensional network of the thylakoid membranes in plants: Quasihelical model of the granum-stroma assembly. Plant Cell vol. 20 2552\u0026ndash;2557 (2008).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePosselt, D. \u003cem\u003eet al.\u003c/em\u003e Small-angle neutron scattering study of the ultrastructure of chloroplast thylakoid membranes - Periodicity and structural flexibility of the stroma lamellae. in \u003cem\u003eBiochimica et Biophysica Acta - Bioenergetics\u003c/em\u003e vol. 1817 1220\u0026ndash;1228 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Uuml;nnep, R. \u003cem\u003eet al.\u003c/em\u003e Thylakoid membrane reorganizations revealed by small-angle neutron scattering of Monstera deliciosa leaves associated with non-photochemical quenching: Membrane reorganizations in vivo and NPQ. Open Biol. (2020) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1098/rsob.200144rsob200144\u003c/span\u003e\u003cspan address=\"10.1098/rsob.200144rsob200144\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagy, G. \u003cem\u003eet al.\u003c/em\u003e Kinetics of structural reorganizations in multilamellar photosynthetic membranes monitored by small-angle neutron scattering. Eur. Phys. J. E 36, (2013).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagy, G. \u003cem\u003eet al.\u003c/em\u003e Dynamic properties of photosystem II membranes at physiological temperatures characterized by elastic incoherent neutron scattering. Increased flexibility associated with the inactivation of the oxygen evolving complex. Photosynth. Res. 111, 113\u0026ndash;124 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagy, G. \u003cem\u003eet al.\u003c/em\u003e Chloroplast remodeling during state transitions in Chlamydomonas reinhardtii as revealed by noninvasive techniques in vivo. \u003cem\u003eProc. Natl. Acad. Sci. U. S. A.\u003c/em\u003e (2014) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1073/pnas.1322494111\u003c/span\u003e\u003cspan address=\"10.1073/pnas.1322494111\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Uuml;nnep, R. \u003cem\u003eet al.\u003c/em\u003e Low-pH induced reversible reorganizations of chloroplast thylakoid membranes \u0026mdash; As revealed by small-angle neutron scattering. Biochim. Biophys. Acta - Bioenerg. (2017) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.bbabio.2017.02.010\u003c/span\u003e\u003cspan address=\"10.1016/j.bbabio.2017.02.010\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Uuml;nnep, R. \u003cem\u003eet al.\u003c/em\u003e Thylakoid membrane reorganizations revealed by small-angle neutron scattering of Monstera deliciosa leaves associated with non-photochemical quenching. Open Biol. (2020) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1098/rsob.200144\u003c/span\u003e\u003cspan address=\"10.1098/rsob.200144\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagao, M., Kelley, E. G., Ashkar, R., Bradbury, R. \u0026amp; Butler, P. D. Probing elastic and viscous properties of phospholipid bilayers using neutron spin echo spectroscopy. J. Phys. Chem. Lett. (2017) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1021/acs.jpclett.7b01830\u003c/span\u003e\u003cspan address=\"10.1021/acs.jpclett.7b01830\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWoodka, A. C., Butler, P. D., Porcar, L., Farago, B. \u0026amp; Nagao, M. Lipid bilayers and membrane dynamics: Insight into thickness fluctuations. Phys. Rev. Lett. (2012) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1103/PhysRevLett.109.058102\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevLett.109.058102\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYi, Z., Nagao, M. \u0026amp; Bossev, D. P. Bending elasticity of saturated and monounsaturated phospholipid membranes studied by the neutron spin echo technique. J. Phys. Condens. Matter (2009) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1088/0953-8984/21/15/155104\u003c/span\u003e\u003cspan address=\"10.1088/0953-8984/21/15/155104\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagao, M. Temperature and scattering contrast dependencies of thickness fluctuations in surfactant membranes. J. Chem. Phys. (2011) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1063/1.3625434\u003c/span\u003e\u003cspan address=\"10.1063/1.3625434\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNickels, J. D. \u003cem\u003eet al.\u003c/em\u003e Bacillus subtilis Lipid Extract, A Branched-Chain Fatty Acid Model Membrane. J. Phys. Chem. Lett. (2017) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1021/acs.jpclett.7b01877\u003c/span\u003e\u003cspan address=\"10.1021/acs.jpclett.7b01877\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGupta, S. \u003cem\u003eet al.\u003c/em\u003e Dynamics of Phospholipid Membranes beyond Thermal Undulations. J. Phys. Chem. Lett. (2018) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1021/acs.jpclett.8b01008\u003c/span\u003e\u003cspan address=\"10.1021/acs.jpclett.8b01008\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZilman, A. G. \u0026amp; Granek, R. Undulations and dynamic structure factor of membranes. Phys. Rev. Lett. 77, 4788\u0026ndash;4791 (1996).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZilman, A. G. \u0026amp; Granek, R. Membrane dynamics and structure factor. Chem. Phys. 284, 195\u0026ndash;204 (2002).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWatson, M. C. \u0026amp; Brown, F. L. H. Interpreting membrane scattering experiments at the mesoscale: The contribution of dissipation within the bilayer. Biophys. J. (2010) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.bpj.2009.11.026\u003c/span\u003e\u003cspan address=\"10.1016/j.bpj.2009.11.026\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNagao, M. Observation of local thickness fluctuations in surfactant membranes using neutron spin echo. Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys. (2009) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1103/PhysRevE.80.031606\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevE.80.031606\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAshkar, R. \u003cem\u003eet al.\u003c/em\u003e Tuning Membrane Thickness Fluctuations in Model Lipid Bilayers. Biophys. J. (2015) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.bpj.2015.05.033\u003c/span\u003e\u003cspan address=\"10.1016/j.bpj.2015.05.033\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMihailescu, M. \u003cem\u003eet al.\u003c/em\u003e Neutron spin-echo investigation of the microemulsion dynamics in bicontinuous, lamellar and droplet phases. Appl. Phys. A Mater. Sci. Process. 74, (2002).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIqbal, J., Javed, A. \u0026amp; Baig, M. A. Growth and nutrient removal efficiency of duckweed (lemna minor) from synthetic and dumpsite leachate under artificial and natural conditions. PLoS One 14, (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePaolacci, S., Stejskal, V. \u0026amp; Jansen, M. A. K. Estimation of the potential of Lemna minor for effluent remediation in integrated multi-trophic aquaculture using newly developed synthetic aquaculture wastewater. Aquac. Int. 29, 2101\u0026ndash;2118 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhao, X. \u003cem\u003eet al.\u003c/em\u003e Enzymatic saccharification of duckweed (Lemna minor) biomass without thermophysical pretreatment. Biomass and Bioenergy 47, 354\u0026ndash;361 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDemann, J. \u003cem\u003eet al.\u003c/em\u003e Nutritional Value of Duckweed as Protein Feed for Broiler Chickens\u0026mdash;Digestibility of Crude Protein, Amino Acids and Phosphorus. Animals 13, 130 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAli, S. \u003cem\u003eet al.\u003c/em\u003e Application of floating aquatic plants in phytoremediation of heavy metals polluted water: A review. Sustain. 12, (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCope; B. T.; Bose; S..; Crespi; H. L.; Katz; J. J. Growth of Lemna in H2O-D2O mixtures: Enhancement by kinetin. Bot. Gaz. 126, 214\u0026ndash;221 (1965).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEvans, B. R., Foston, M., O\u0026rsquo;Neill, H. M., Reeves, D., Rempe, C., McGrath, K., Ragauskas, A. J., and Davison, B. H. Production of Deuterated Biomass by Cultivation of Lemna minor (duckweed) in D2O. Planta 249, 1465\u0026ndash;1475 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCooke, R. J., Grego, S., Olivier, J., Davies, D. D. The effect of deuterium oxide on protein turnover in Lemna minor. Planta 146, 229\u0026ndash;236 (1979).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTat, VT; Lee, Y. Spatiotemporal study of galactolipid biosynthesis in duckweed with mass spectrometry imaging and in vivo isotope labeling. Plant Cell Physiol. (2024) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1093/pcp/pcae032\u003c/span\u003e\u003cspan address=\"10.1093/pcp/pcae032\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYi, Z., Nagao, M. \u0026amp; Bossev, D. P. Bending elasticity of saturated and monounsaturated phospholipid membranes studied by the neutron spin echo technique. J. Phys. Condens. Matter 21, 155104 (2009).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMihailescu, M. \u003cem\u003eet al.\u003c/em\u003e Neutron scattering study on the structure and dynamics of oriented lamellar phase microemulsions. Phys. Rev. E 66, (2002).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHolderer, O. \u003cem\u003eet al.\u003c/em\u003e Dynamic properties of microemulsions modified with homopolymers and diblock copolymers: The determination of bending moduli and renormalization effects. J. Chem. Phys. 122, (2005).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBiehl, R. Jscatter, a Program for Evaluation and Analysis of Experimental Data.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRalf Biehl. Jscatter, a program for evaluation and analysis of experimental data. PLoS One.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMihailescu, M. \u003cem\u003eet al.\u003c/em\u003e Dynamics of bicontinuous microemulsion phases with and without amphiphilic block-copolymers. J. Chem. Phys. 115, 9563\u0026ndash;9577 (2001).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ehttps://\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003een.wikipedia.org/wiki/List_of_viscosities\u003c/span\u003e\u003cspan address=\"http://en.wikipedia.org/wiki/List_of_viscosities\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrannigan, G. \u0026amp; and F. L. Brown. A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayers. (2006).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHelfrich, W. Steric Interaction of Fluid Membranes in Multilayer Systems. Zeitschrift f\u0026uuml;r Naturforsch. A 33, 305\u0026ndash;315 (1978).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSafinya, C. R. \u003cem\u003eet al.\u003c/em\u003e Steric Interactions in a Model Multimembrane System: A Synchrotron X-Ray Study. Phys. Rev. Lett. 57, 2718\u0026ndash;2721 (1986).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOhl, M. \u003cem\u003eet al.\u003c/em\u003e The high-resolution neutron spin-echo spectrometer for the SNS with τ\u0026thinsp;\u0026ge;\u0026thinsp;1 \u0026micro;s. in Physica B: Condensed Matter (2004). doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.physb.2004.04.014\u003c/span\u003e\u003cspan address=\"10.1016/j.physb.2004.04.014\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eK\u0026auml;mmerling, P. \u003cem\u003eet al.\u003c/em\u003e SNS-NSE control and data acquisition system for the neutron spin echo spectrometer at the spallation neutron source. in \u003cem\u003eSEI 2013\u0026thinsp;\u0026ndash;\u0026thinsp;104. Tagung der Studiengruppe Elektronische Instrumentierung im Fruhjahr 2013\u003c/em\u003e (2013).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u0026Uuml;nnep, R. \u003cem\u003eet al.\u003c/em\u003e The ultrastructure and flexibility of thylakoid membranes in leaves and isolated chloroplasts as revealed by small-angle neutron scattering. Biochim. Biophys. Acta - Bioenerg. (2014) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.bbabio.2014.01.017\u003c/span\u003e\u003cspan address=\"10.1016/j.bbabio.2014.01.017\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZolnierczuk, P. A. \u003cem\u003eet al.\u003c/em\u003e Efficient data extraction from neutron time-of-flight spin-echo raw data. J. Appl. Crystallogr. 52, 1022\u0026ndash;1034 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZolnierczuk, P. \u003cem\u003ePySEN: A Python Package for Aiding Experiments at the SNS Neutron Spin Echo Spectrometer\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2172/1987766\u003c/span\u003e\u003cspan address=\"10.2172/1987766\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2023) doi:10.2172/1987766.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMilner, S. T. \u0026amp; Safran, S. A. Dynamical fluctuations of droplet microemulsions and vesicles. Phys. Rev. A 36, 4371\u0026ndash;4379 (1987).\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-4437351/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4437351/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe study is the first known exploration of photosynthetic membranes dynamics in living plants by high resolution inelastic neutron scattering spectroscopy. We characterized \u003cem\u003ein vivo\u003c/em\u003e thylakoid membranes mobility in \u003cem\u003eLemna minor\u003c/em\u003e plants. Excess dynamics at length scales corresponding to both the membrane stacks and membrane thickness were observed and described by classical biophysical models to assess the undulation modes, the rigidity of the membranes, and how the structural variations affect the observed dynamics. The stacks of thylakoids in \u003cem\u003eLemna minor\u003c/em\u003e are rigid systems with an apparent bending coefficient in the upper range observed for surfactant membranes, while the single thylakoid leaflet is very flexible situated well within the bi-continuous surfactant phases dynamics. These observations further our understanding of the relationship between photosynthesis and the cellular architecture, while simultaneously opening more questions and the need for further investigations at extended \u003cem\u003eq\u003c/em\u003e-and-time regimes.\u003c/p\u003e","manuscriptTitle":"Neutrons reveal the dynamics of leaf thylakoids in living plants","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-03 17:20:54","doi":"10.21203/rs.3.rs-4437351/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-08T05:28:21+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-30T17:06:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-26T09:54:12+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"78818602585681317833191917010630569509","date":"2024-06-24T09:24:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-05T17:54:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"244234386172938531794915819054479548222","date":"2024-05-26T09:30:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"56493315724511398415411209418872032471","date":"2024-05-22T16:41:58+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-05-22T16:37:04+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-22T12:56:12+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-05-22T12:32:09+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-22T03:08:16+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-05-17T14:30:19+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":"ef669e10-817e-46b1-84ab-a56b1fb4def3","owner":[],"postedDate":"June 3rd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":32698103,"name":"Biological sciences/Biological techniques"},{"id":32698104,"name":"Biological sciences/Biophysics"},{"id":32698105,"name":"Biological sciences/Plant sciences"},{"id":32698106,"name":"Physical sciences/Physics"},{"id":32698107,"name":"Physical sciences/Physics/Applied physics"},{"id":32698108,"name":"Physical sciences/Physics/Biological physics"}],"tags":[],"updatedAt":"2025-11-10T16:04:10+00:00","versionOfRecord":{"articleIdentity":"rs-4437351","link":"https://doi.org/10.1038/s41598-025-22747-z","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-11-05 15:57:25","publishedOnDateReadable":"November 5th, 2025"},"versionCreatedAt":"2024-06-03 17:20:54","video":"","vorDoi":"10.1038/s41598-025-22747-z","vorDoiUrl":"https://doi.org/10.1038/s41598-025-22747-z","workflowStages":[]},"version":"v1","identity":"rs-4437351","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4437351","identity":"rs-4437351","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}