An inspiration-off attractor supports the robust and flexible control of breathing

An inspiration-off attractor supports the robust and flexible control of breathing | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results An inspiration-off attractor supports the robust and flexible control of breathing View ORCID Profile Nicholas E. Bush , View ORCID Profile Luiz M. Oliveira , View ORCID Profile Zachary T. Glovak , View ORCID Profile Jan-Marino Ramirez doi: https://doi.org/10.1101/2025.09.23.678177 Nicholas E. Bush 1 Norcliffe Foundation Center for Integrative Brain Research, Seattle Children’s Research Institute ; Seattle, WA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Nicholas E. Bush For correspondence: nicholas.bush{at}seattlechildrens.org Luiz M. Oliveira 1 Norcliffe Foundation Center for Integrative Brain Research, Seattle Children’s Research Institute ; Seattle, WA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Luiz M. Oliveira Zachary T. Glovak 1 Norcliffe Foundation Center for Integrative Brain Research, Seattle Children’s Research Institute ; Seattle, WA, USA 2 Behavioral Phenotyping Core, Seattle Children’s Research Institute ; Seattle, WA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Zachary T. Glovak Jan-Marino Ramirez 1 Norcliffe Foundation Center for Integrative Brain Research, Seattle Children’s Research Institute ; Seattle, WA, USA 3 Neurological Surgery, University of Washington ; Seattle, WA, USA 4 Pediatrics, University of Washington ; Seattle, WA, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jan-Marino Ramirez Abstract Full Text Info/History Metrics Supplementary material Preview PDF Summary Breathing is a fundamental motor rhythm necessary to sustain life. The rhythm and pattern of breathing arises from the coordination of a bilaterally symmetric, rostro-caudally extended column of heterogeneous neural populations in the medulla called the Ventral Respiratory Column (VRC). By recording from the extent of the VRC using Neuropixels during optogenetic and physiological manipulations, and projecting the population activity into a dynamical latent space, we find that GABAergic lung-stretch feedback circuits promote rhythmic population activity by creating a temporary stable fixed point in the latent state that terminates diaphragmatic contraction. Stimulation of GABAergic circuits either intrinsic to the VRC (VRC GABA ) or via afferent pathways from GABAergic neurons of the Nucleus of the Solitary Tract (NTS GABA ) advance or delay breathing when activated with specific respiratory phase through temporary stabilization of this fixed point. Lastly, we show that activation of glutamatergic signaling opposes the effects of inhibitory signaling by destabilizing this expiratory fixed point to promote rapid inspiration. Together, we decompose the functional impact of different respiratory control subpopulations to reveal an integrated network level mechanism for respiratory control in vivo . Introduction Rhythmicity is both ubiquitous and varied in nervous systems. Rhythmic activity occurs at multiple mechanistic, temporal, and functional levels; from molecules to brain-wide networks, from milliseconds to months, and from stereotyped motor patterns to cognition 2 – 8 . Consequently, the fundamental questions of how these rhythms are generated and maintained, and how they functionally contribute to an organism’s fitness remains a subject of intense interest. Of these rhythms, the respiratory rhythm is particularly vital. It sustains physiological function and life 9 , 10 , responds to homeostatic demands and threats like obstruction or irritants 11 – 14 , serves as a medium for communication 15 , 16 , and influences our cognitive and emotional state 17 – 20 . The respiratory rhythm and pattern is generated in a rostro-caudally extended, bilaterally synchronized column in the ventrolateral medulla called the Ventral Respiratory Column (VRC) 21 – 25 . Central among the VRC structures is the preBötzinger Complex (preBötC), which is intrinsically rhythmic in slices 26 – 30 and exerts exquisite control over breathing rhythm and pattern in vivo 31 – 34 . In addition, the components of the VRC are strongly connected within itself, its contralateral counterpart, and myriad other medullary and extra medullary brain regions 35 , 36 . The ability to isolate rhythmogenic networks and preserve rhythmogenesis in the absence of sensory feedback 37 has led to the concept of central pattern generators as the key driver of rhythmic behaviors. In some reduced preparations, (e.g., the in vitro medullary slice preparation of a core respiratory, the preBötzinger Complex (preBötC)) 27 , intrinsic cellular excitability and/or recurrent excitatory signaling are sufficient for generating rhythms 28 , 38 – 43 . In the intact animal, however, recurrent excitatory, inhibitory, and neuromodulatory circuits composed of diverse cell classes with complex connectivity patterns across anatomically distributed brain regions 36 , 44 – 48 coalesce to generate robust, yet flexible motor outputs. Importantly, fundamental attributes of the respiratory rhythm are vastly different in vivo and in vitro, emphasizing the potential for fundamentally different effective mechanisms to maintain rhythmic activity. For example, the frequency of the generated rhythm is an order of magnitude slower in vitro and neural activity becomes essentially silent immediately after termination of inspiration 49 , which is not the case in vivo 50 . This leads to the important and largely unresolved question as to how interactions between core rhythmogenic kernels integrate into distributed networks in vivo to maintain and control rhythmic functions 48 . Sensory feedback via incoming projections is a critical component of the respiratory rhythm in vivo . Inhibitory circuits, particularly those that relay mechanoreceptive feedback about lung stretch 51 – 53 , have been implicated as instrumental in other motor rhythms 54 , 55 , and as a key fast-feedback mechanism which can both depress and accelerate breathing rates on short time scales (within one breath) 49 , 56 . However, it remains unknown if inhibitory pathways downstream of lung afferents are indeed capable of bidirectional respiratory control 13 , 57 , 58 . Further, little is known about how excitatory and inhibitory signaling affects on-going distributed neural population dynamics in the respiratory brain centers in vivo . Recently, we performed large scale recordings along the extent of the VRC in vivo using Neuropixels. By analyzing the simultaneous activity of hundreds of neurons in a low-dimensional, latent projection 59 , 60 , we showed that the population dynamics of the VRC follow rotational latent trajectories constrained by limit-cycle attractor dynamics 50 . Interestingly, we observed that the trajectories of the neural population activity were characterized by a consistent feature. At the end of each inspiration, the neural state accelerated towards a consistent point in the latent space as if the network state was being pushed into an attractive well. We hypothesize that this acceleration is instrumental in setting the respiratory rate, and is triggered by timed, phasic inhibition. We further hypothesize that inhibitory populations in a restricted part of the Nucleus of the Solitary Tract at the level of the Area Postrema (NTS - second order lung stretch relay neurons, i.e. pump cells 61 , 62 ) could elicit both bidirectional breathing rate modulation and trigger the characteristic acceleration of the latent trajectory. Here, we test these hypotheses by performing high-density neural recordings with Neuropixels from the extent of the VRC during direct activation of either inhibitory signaling in the contralateral VRC (VRC GABA ), inhibitory NTS (NTS GABA ) populations, or the endogenous lung stretch feedback circuit via the physiological lung stretch defense reflex (Hering-Breuer reflex 63 ). We show that precisely timed phasic optogenetic stimulation of VRC GABA or NTS GABA neurons elicited bidirectional control of respiratory rate, confirming the sufficiency of afferent feedback to both depress and accelerate breathing. Further, all three manipulations caused latent trajectories to accelerate to the same fixed point, effectively “short-cutting” the eupneic limit cycle. This fixed point coincided with the neural state at the offset of inspiration. Importantly, activation of the NTS GABA populations exhibits an exquisite sub-phase specificity of effects observed in the pattern of respiratory rate changes, single neuron firing rates, and latent trajectories that contrasted with the activation of VRC GABA . These data highlight that activating inhibitory inputs projecting to the VRC is quantitatively and functionally distinct from activating inhibitory neurons within the VRC itself, despite the apparent similarities of their effects on respiration. Importantly, we show that direct activation of VRC inhibition exhibits inspiration promoting effects not present when stimulating the afferent input. That is, local inhibition in the VRC keeps the network state poised on the edge of an inspiration, while incoming inhibition from NTS GABA forces the state away from the expiration/inspiration transition. We further contrast the differential effects of inhibitory neurons with the results obtained by the direct activation of excitatory, Vglut2 + neurons in the VRC (VRC VGLUT2 ). This caused expected amplitude and respiratory rate increases 31 , 49 and coincided with a repulsion of latent trajectories from the inspiratory-off fixed point. Subsequently, latent neural trajectories were not short-cut; rather, trajectory speed increased, representing a qualitatively different network mechanism contributing to respiratory rhythmogenesis. Lastly, we develop a data-driven, generative dynamical model 64 , 65 that reveals that inhibitory and excitatory stimulations can be interpreted as uniform vector fields perturbing the on-going eupneic limit cycle. Importantly, these generative models extrapolate to predict experimental data not present in the fitting procedure (e.g., bidirectional respiratory control and reset curves), as well as a relationship with stimulus amplitude described elsewhere 25 . Excitation and inhibition emerge to be diametrically opposed in this dynamic representation, and stabilize or destabilize, respectively, the inspiratory-off fixed point. Consistent with the quantitative difference between direct or indirect inhibition of the VRC, we further distinguish the resultant stimulus vector fields that emerge during VRC GABA and NTS GABA stimulations. This distinction identifies inspiration promoting components of inhibitory signaling within the VRC. Together, these data support and expand the classical inspiratory off-switch hypothesis 56 , 66 with cell-type specific manipulations and neural population recordings at single cell resolution. This hypothesis states that the normal breathing rhythm is governed by a lung-volume set point that triggers a reset of the inspiratory cycle when reached. We show that activation of putative pump cells is sufficient for this behavior and results in reset curves consistent with an inspiratory-off switch. Importantly, we offer a reframing of this hypothesis from the view of dynamical systems. The core rhythm and pattern generating circuitry in the VRC can be represented as a low-dimensional limit cycle. When inspired air generates sufficient lung stretch that is relayed by afferents, the VRC network state is forced toward a more stabilized inspiratory off fixed point. Upon ceasing inspiratory effort, the lung stretch signal diminishes and inspiration promoting mechanisms prevail to initiate the next breath. However, if lung stretch remains high (as it does during triggering of the Hering-Breuer reflex), the inspiratory-off point remains stable, preventing or slowing respiration. This inspiratory-off switch/attractor hypothesis is corroborated by experimental evidence that respiratory rates decrease, and motor amplitudes increase, when vagal afferents are removed 49 , 67 . Results Activating inhibitory populations in the Nucleus of the Solitary Tract drives phase-dependent changes in breathing distinct from activation of excitatory and inhibitory neurons in the VRC To test the effects on the VRC neural dynamics of perturbing constituent components of the brainstem respiratory neural circuitry, we inserted Neuropixel 1.0 probes along the length of the left VRC 50 of urethane anesthetized mice while optogenetically stimulating inhibitory (Vgat + ) neurons or excitatory (Vglut2 + ) neurons of the contralateral (right) VRC (VRC GABA , VRC VGLUT2 respectively, or Vgat + neurons of the Nucleus of the Solitary Tract (putative pump cells, NTS GABA ). To target VRC GABA neurons, we generated Vgat Cre ;Ai32 (n=8) or Vglut2 Cre ;Ai32 (n=7) crosses and acutely inserted a 200 μm optical fiber over VRC ( Figure 1A , Supplemental Figure 1 ). To target NTS GABA neurons, we injected Cre-dependent ChRmine bilaterally into the NTS of Vgat Cre mice (n=9). ChRmine-oScarlet was well expressed in the NTS ( Supplemental Figure 1D ); some animals were only transfected unilaterally, but similar physiological responses were observed, thus bilateral/unilaterally transfected mice were pooled. Download figure Open in new tab Figure 1: Activation of ventral and dorsal medullary groups differentially affect breathing. (A) Experimental schematic (B) Example integrated diaphragm traces during optogenetic stimulation. Shaded region is laser on. Color indicates wavelength used (blue:473nm, red:635nm). (C) Mean (+/- S.E.M.) respiratory rate during before and during optogenetic stimulation during activation of different populations. Dots are individual animals. Solid lines indicate bilateral transfection/stimulation. (Paired t-test two-sided, VRC VGLUT2 n=5, p=0.036; VRC GABA n=6,p=0.004; NTS GABA n=7, p=0.006) (D) Latency (mean +/- S.E.M.) from laser offset to onset of first post-stimulation breath. (Kruskal-Wallis test H=10.2, dof=2,p=0.006; *p<0.05 Holm-Bonferroni corrected) Dots are individual animals. (E) Number of transfected neurons in the NTS as a function of bregma. Black line is mean (shaded region +/- S.E.M.), colored lines are individual animals. Atlas images adapted from 1 In agreement with previous reports, activating VRC VGLUT2 neurons with 2s of constant laser illumination increased respiratory rate, while activating inhibitory neurons in the VRC or the NTS decreased or abolished breathing (VRC GABA or VRC VGLUT2 ) 473nm, 8-10mW; NTS GABA 635nm, 15-20mW) 13 , 58 ( Figure 1B , C). Activation of NTS GABA slightly decreased, and activation of VRC VGLUT2 increased, heart rate ( Supplemental Figure 2B ). Interestingly, the latency to the first breath after cessation of stimulation was shorter when stimulating VRC GABA populations compared to either VRC VGLUT2 or NTS GABA populations (Kruskal-Wallis test p<0.006). ( Figure 1D , E). We next replicate the phase specific effects of stimulating VRC inhibitory or excitatory populations 49 , and tested if stimulation of NTS GABA populations exhibit the effect on breathing as stimulating directly VRC GABA neurons. As expected, activation of VRC VGLUT2 neurons during inspiration does not change respiratory rate, but increases diaphragm EMG amplitude; and stimulation during expiration increases respiratory rate ( Figure 2A , D; Supplemental Figure 2A ). Conversely, stimulation of VRC GABA and NTS GABA neurons during expiration slows respiratory rate, while stimulation during inspiration increases respiratory rate ( Figure 2B , C, D). We observed a reduction in diaphragm amplitude during inspiratory stimulation of both populations, while we only observed a reduction in amplitude during expiratory stimulations during activation of NTS GABA populations ( Supplemental Figure 2A ). Download figure Open in new tab Figure 2: Stimulation of inhibitory NTS neurons exerts phase dependent control of respiratory rate. (A-C) Example integrated diaphragm EMG during laser stimulation of medullary cell types triggered by inspiration (top) or expiration (bottom). Color indicates laser wavelength. (D) Respiratory rate compared to baseline during phase triggered stimulation. (red: inspiration trigger, blue: expiration trigger). (Two-sided one-sample t-test; VRC VGLUT2 n=5, p insp =0.48, p exp =0.016; VRC GABA n=6, p insp =0.017, p exp =3.7E-4; NTS GABA n=7, p insp =0.018, p exp =0.017) (E) Phase reset driven by 50ms laser pulses. Color represents stimulated population. Horizontal dashed line represents no change in rhythm, diagonal dashed line indicates theoretical limit on phase advance (i.e., immediate activation of next breath). Vertical lines represent average phase at which diaphragm features occur. (F) Timing of the phase reset curve intercept with 1 (no change in respiratory rate) relative to the peak or end of the diaphragm EMG signal. Color represents stimulated population. (Two-sided one sample t-test; VRC GABA n=6, p peak =0.01, p end =0.69; NTS GABA n=6, p peak =0.14, p end =0.003). Marker indicates unilateral (crosses) or bilateral (circles) transfection/stimulation. In all panels, bars/shaded regions are mean +/- S.E.M Lastly, we presented brief, 50ms pulse laser stimulations (n=75) at random times throughout the phase to observe how momentary activation of these populations perturbs ongoing respiratory rhythms. We compute the reset curves ( Figure 2E ). Stimulation of VRC VGLUT2 neurons advances respiratory phase (curve below 1), specifically when activated during expiratory time (i.e., after the end of the diaphragm EMG activity). Stimulation of VRC GABA advances respiratory phase if stimulating during inspiration and delays respiratory phase if stimulated during expiration. Interestingly, Stimulation of NTS GABA population advances respiratory phase specifically during the first half of the inspiration, i.e., when the diaphragm amplitude is increasing. Otherwise, activation of these populations delays phase. To quantify this difference between activating VRC GABA and NTS GABA populations, we compute the point at which each animal’s phase reset curve crosses one and find that the intercept is at the end of the diaphragm activity for VRC GABA stimulations, but at the peak of the diaphragm for NTS GABA stimulation ( Figure 2E , F). Activation of NTS GABA populations selectively inhibits inspiratory VRC neural activity We next asked how activation of these respiratory circuit components drives changes in the activity of recorded VRC populations. These stimulations are targeted to either contralateral (VRC GABA or VRC VGLUT2 ) or input (NTS GABA ) populations. We analyzed single units recorded from the VRC during the 2s continuous laser stimulations described above. After spike sorting and quality control steps, we categorized single units by their phasic activation patterns as inspiratory, expiratory, or tonic (see methods). Example raster plots showing a subsample of the recorded population before, during, and after optogenetic stimulation show diverse, stimulus specific changes in single unit activity ( Figure 3A-C ). We compare the firing rate in baseline control conditions against stimulation to see how much each unit is activated/inhibited as a result of stimulating our targeted populations ( Figure 3D-F ). While there is diversity in firing rate changes in all respiratory populations as a response to all stimulus conditions, we find that activating VRC GABA neurons on average drastically inhibits all neuron types and most neurons in the VRC ( Figure 3D , E top). Conversely, activation of VRC VGLUT2 increases the firing rate of most neurons on average ( Figure 3D , E bottom). Interestingly, activation of NTS GABA populations on average does not change the firing rates of expiratory neurons ( Figure 3D , E middle, F top), and only minorly decreases firing of tonic neurons ( Figure 3D , E middle, F bottom). Strikingly, these data suggest a functional specificity of activity of NTS GABA populations to selectively decrease inspiratory activity without altering other respiratory population dynamics. Download figure Open in new tab Figure 3: NTS GABA populations selectively inhibit inspiratory neurons. (A-C). Example breathing and activity of example single units of tonic, inspiratory, and expiratory (10 per category, each row is a unit) in the VRC during optogenetic stimulation. (D) Average firing rate (spikes/s) of each unit during baseline control versus during 2s laser stimulations. Each dot is a unit. Note the symmetric logarithmic scale. Black dashed diagonal is unity, and grey dashed lines indicate 2x or 0.5x firing rate during laser stimulus. (E) Cumulative distributions of firing rate ratios (stim vs control). X-axis is log scaled. All comparisons are p<0.05 except expiratory units during NTS GABA stimulation (Wilcoxon signed rank test, control vs stimulus average firing rate). Right shifted curves indicate increases in firing rates during stimulations. (F) same curves as E, but phasic unit types are plotted together across stimulated populations. Color indicates stimulated population. Activating inhibitory circuits shortcuts rotational population dynamics towards inspiration off Recently, we showed that rotational latent dynamics underlie VRC population dynamics 50 . Further, we showed that these rotations targeted an attractive-like region (potential well) that represents the offset of inspiration. Here, we use neuronal subtype specific stimulations to test the hypothesis that activation of inhibitory circuits triggers an acceleration of the latent state towards that inspiration-off target to organize the respiratory rhythm. In addition, we tested a complimentary hypothesis that activation of VRC VGLUT2 populations drives the latent state away from the inspiration-off target. Indeed, we observe that activation of both VRC GABA and NTS GABA populations during inspiration drives the network preemptively towards the inspiration-off target, while activation during expiration clamps the network in that potential well ( Figure 4A , B middle, right, Supplemental videos 1-2). Activating VRC VGLUT2 populations does not alter the rotation but does increase trajectory speed ( Figure 4A , B left, Supplemental Figure 3 , Supplemental Video 3). NTS GABA stimulation most dramatically reduces trajectory speed during pre-inspiration and inspiration ( Supplemental Figure 3C, D ), emphasizing the selective inhibition of expiratory dynamics. We next examine the trajectories during and after the randomly timed, 50ms laser pulses. Agreeing with the phase trigged stimulus results, activating both VRC GABA and NTS GABA populations drives the network directly toward the inspiration-off target, while activating VRC VGLUT2 populations drives the network along its current trajectory. We quantify the degree of convergence of the trajectories by measuring the dispersion of the two-d latent trajectories 25ms after the offset of the stimulus pulse (i.e., to address the question how similar the network states are shortly after the stimulus, see Methods). Activating VRC VGLUT2 populations does not reduce the dispersion compared to randomly selected states during baseline, while activating either inhibitory population does. Similarly, we compute the distance from the post-stimulation state to the inspiration-off point observed during baseline breathing and observe VRC VGLUT2 pushes the network away from the inspiration-off state toward inspiration peak, while both inhibitory populations push the network toward inspiration-off ( Figure 4E , Supplemental Figure 4A ). Lastly, we compute this distance as a function of post stimulus time ( Figure 4F ), and of latent state dimensionality ( Supplemental Figure 4 ). Interestingly, VRC GABA converges to the inspiration-off target more quickly and diverges more rapidly than the NTS GABA stimulations, suggesting an underlying difference in how these populations affect VRC dynamics. Download figure Open in new tab Figure 4: Inhibitory stimulations drive VRC populations dynamics towards inspiration off. (A) Latent dynamic trajectories during inspiration and (B) expiration triggered stimulations of medullary populations for three example recordings. Blue-white-red gradient shows normal latent trajectory (color mapped to respiratory phase), black lines indicated trajectory during unstimulated periods, blue/red lines indicate trajectories during stimulated periods corresponding to laser wavelength used to stimulate respective opsins. One stimulation replicate is shown (inspiration triggered: 15s, expiration triggered: 2s). (C) Randomly timed, 50ms pulse stimulations (75 pulses) of each medullary population. Red-white-blue gradient lines indicate normal trajectory, blue/red lines indicate trajectory during stimulation as in A. Black lines indicated trajectory for 25ms after end of stimulation. Grey dots indicate latent state 25ms after end of stimulation. (D) Dispersion (i.e., trace of the covariance matrix) of two-dimensional latent state a t=25ms post-stimulation, compared to a sample of randomly chosen points in the baseline period. Each dot is a recording. (Paired t-test two-sided, VRC VGLUT2 n=7, p=0.24; VRC GABA n=8,**p=0.006; NTS GABA n=7, ***p=8.3E-4). (E) Distance between average two-dimensional latent state at inspiration offset compared to 25ms post-stimulation. Random shuffled control as in D. (Paired t-test two-sided, VRC VGLUT2 n=7, p=0.014; VRC GABA n=8,p=0.0014; NTS GABA n=7, p=2.7E-5). (F) Distance to the inspiration off average latent state as in E, for all post-stimulation time delays. Dashed line indicates random shuffled controls. Lines, shaded regions are mean +/- S.E.M. Neural population dynamics during lung stretch reflex suggests inspiratory-expiratory competition mechanism The Hering-Breuer inflation reflex 63 , 68 is characterized by the rapid and robust lung-stretch induced apnea, often caused by exogenous increases in positive airway pressure. This reflex critically protects against damage to the lung due to over inflation. The Neuropixel recordings allow us to determine how triggering this reflex altered neural activity in the VRC populations. We present positive airway pressure (15cm H 2 O) briefly by closing an exhaust valve in the airway line, diverting presented airflow into a water column for 2 or 5 seconds ( Figure 5A ). This causes a decrease or cessation of inspiration, and concomitant changes in VRC neural activity ( Figure 5B , C, Supplemental Figure 5C ). Inspirations that break through the inflation stimulation are shorter than control (Wilcoxon signed-rank test p=3.0E-5, Figure 5D , E). We compare the breath-cycle averaged firing rates of respiratory neurons between control and Hering-Breuer stimulation. Inspiratory neurons unsurprisingly have shorter durations of activations during stimulation ( Figure 5F , G). The reduction in both phase-normalized inspiratory firing rates ( Figure 5H ) and average firing rate ( Figure 5I ), is likely due specifically to a reduction in the inspiration time; computing only the firing rate during inspiration reveals an average increase in inspiration-specific firing rate ( Supplemental Figure 5E , F). This indicates that inspiratory neurons fire more spikes per inspiration, but over fewer inspirations with shorter inspiratory times. Interestingly, some expiratory neurons lose the gradual decrement over the expiratory phase that leads towards inspiration ( Figure 5F-H ) and transition to quiescence more rapidly during the transition into inspiration ( Figure 5G , H), signifying a more abrupt state transition. The firing rate of expiratory neurons does not change on average, matching what was seen in direct activation of NTS GABA populations. There is no striking anatomical specificity to changes in neural activity ( Supplemental Figure 5A-D ) suggesting that the Hering-Breuer affect the entire VRC network. Download figure Open in new tab Figure 5: Activation of airway protective Hering-Breuer reflex selectively reduces firing of inspiratory neurons and alters population activity (A) Schematic for triggering positive airway pressure. (B) Example integrated diaphragm EMG and selection of tonic, expiratory, and inspiratory single units during positive airway pressure. (C) Respiratory rate during 2s and 5s positive airway pressure presentation. (n=16). (D) Normalized, breath-triggered average integrated diaphragm EMG for normal breaths (black) and “break-through” breaths during lung inflation (magenta).(E) Average inspiration duration (Wilcoxon signed rank test, n=16,p=3.0E-5). Color as in D. (F) Breath-triggered average firing rates for example single units during baseline (black) and during lung inflation (magenta). (G). As in F, but averaged over all neurons of a given respiratory category in and example recording. (H) Phase normalized, breath triggered average firing rates for all units across all recordings. Color as in G. Shaded region is mean +/-S.E.M.(I) Firing rate of each unit of a given category in baseline control against during Hering-Breuer stimulation (lung inflation). Note the symmetric logarithmic scale. Black dashed diagonal is unity, and grey dashed lines indicate 2x or 0.5x firing rate during lung inflation stimulus. (J) Cumulative distributions of firing rate ratios (stimulation vs control) (Wilcoxon signed rank test firing rate control vs firing rate during lung inflation insp: Wilcoxon=137,470, ***p=6.4E-48, n=1,064; exp: Wilcoxon=79,908, p=0.43, n=576; tonic: Wilcoxon=976,308, ***p=1.0E-12,n=2,177). (K) Average firing rates for given category (indicated by color as in I) of units in the 50ms before the onset of inspiration (indicated in inset) during baseline control and Hering-Breuer stimulation. Firing rates are a normalized percentage of mean firing rate in baseline control period. (Two-sided paired t-test t insp =-5.1,***p insp=4.9E-7; t exp =-4.9, ***pexp=1.0E-6; ttonic=1.5, ptonic=0.14) (L) Breath-triggered ratio of expiratory/inspiratory unit firing rates (top) or vice versa (bottom) for all units pooled across recordings during baseline control (black) and lung inflation (magenta). (M) Ratio of firing rates of expiratory neurons to inspiratory neurons 10ms before and after onset of inspiration. Dots/thin lines are individual recordings, thick banded lines are means +/- S.E.M. In all panels, shaded regions are mean +/- 95%CI unless otherwise noted. To further characterize how lung inflation changes the neuronal network activity during the transition into inspiration, we compute the firing rate of each neuron type (inspiratory, expiratory, and tonic) in the 50ms before the onset of inspiration. Both inspiratory and expiratory neurons show higher firing rates in this period during the lung inflation stimulation compared to control ( Figure 5K , two-sided paired t-test p insp =4.9E-7 p exp =1.0E-6). Lastly, we compare the ratio of inspiratory to expiratory firing rates, pooled across all neurons and recordings. Interestingly, we find that the inspiration on transition occurs when the inspiratory/expiratory firing rate ratio is one in both control and stimulated conditions ( Figure 5K , M), irrespective of the observation that the absolute firing rates are higher. Lung-inflation induced latent dynamics resemble direct stimulation of inhibitory populations We next examined the low-dimensional latent state dynamics of the VRC population during Hering-Breuer reflex activation evoked by lung inflation stimuli. Presentation of positive pressure causes that latent state to arrest at a single point in the latent space ( Figure 6A , Supplemental Video 4). This arrest is exemplified by a reduction in latent trajectory speed ( Figure 6B ) that matches well the arrest observed when we stimulated either the VRC GABA or NTS GABA populations directly. ( Figure 6C , D, also compare to Figure 4B ). In addition, trajectory speed during inspiration onset is higher during Hering-Breuer break through breaths ( Supplemental Figure 5G ). The lung inflation stimulation converges the latent state toward the inspiration-off attractive target ( Figure 6E , F) as in the stimulation of inhibitory populations. Lastly, we asked if the single neuron activity observed during lung-inflation stimulations resembled the single neuron activity observed during the 2s optogenetic stimuli applied previously ( Figure 6G ). We compute the difference and Pearson correlation of the mean square-root transformed firing rates between the two stimulation paradigms. The difference indicates if the average firing rates are similar across conditions, and the Pearson correlation indicates if individual units are modulated similarly across the different conditions. While VRC VGLUT2 and VRC GABA showed higher and lower average firing rates than the lung inflation stimulation, respectively for all respiratory neuron types, NTS GABA stimulation matched the average firing rates well ( Figure 6H ). Interestingly, the correlation of the inspiratory neurons during NTS GABA stimulation was strikingly lower than expiratory or tonic populations, while that of the inspiratory neurons during VRC GABA stimulation was high, suggesting incomplete mimicry of the physiological stimulus with this circuit specific activation, despite a strong match in the physiology. Download figure Open in new tab Figure 6: Lung inflation drives latent dynamics towards inspiration off attractor similar to activation of inhibitory circuits. (A) Example diaphragm EMG (top), first 3 PCs (grayscale), and latent trajectory speed (blue-yellow gradient, scale arbitrary, not shared with PCs) during a 2s lung inflation. (B) Trajectory speed of leading 3 dimensions for all recordings during 2s laser stimulations (color indicates targeted population), or 5s Hering-Breuer stimulation (magenta). Shaded regions are mean +/- S.E.M. (C). Percent change in trajectory speed in the period (1,2)s during stimulation compared to the period (-2,-1)s before onset of stimulation. One-way ANOVA (F=25.5, DF=3,DF=40,p=2.2E-9; Tukey-HSD post-hoc test ***p<0.001). (D) Example two-dimensional latent trajectories during baseline (red-white-blue gradient lines colored by phase) and during one 5s lung inflation stimulation (magenta). (E) Distance between average two-dimensional latent state at inspiration offset compared to random shuffled points (Random) or 1s after lung inflation onset (HB). Dots, thin lines are recordings. Color indicates optogenetically targeted population in other experiments. Linear mixed effects model DF1=2,DF2=19; F population = 9.14, p=1.6E-3; F HBstim =56.33,***p=4.3E-7; F interaction =1.4,p=0.27. (F) As in E, but comparing the dispersion (i.e., trace of the covariance matrix) of two-dimensional latent state a 1s after lung inflation onset. Linear mixed effects model DF1=2,DF2=19; F population = 2.14, p=0.145; F HBstim =56.2,***p=4.3E-7; F interaction =1.98,p=0.15). (G) Firing rate of individual units during lung inflation stimulation (x-axis) and during 2s optogenetic hold stimulation (y-axis), stratified by stimulated population and respiratory neuron type. Note the square root scaled axis. Black dashed diagonal is unity, and grey dashed lines indicate 2x or 0.5x firing rate during optogenetic stimulation compared to lung inflation stimulation. (H) Comparison of firing rates of subpopulations during different stimulus modalities. X-axis shows difference of the means of square root firing rates between optogenetic and lung inflation stimuli. Zero indicates similar firing rates in both conditions; positive values indicate higher firing rates during opto-genetic stimulus. Y-axis and marker size show correlation ( ρ ) between the firing rates of the two modalities. Color shows optogenetically targeted population, marker shape indicates respiratory category. Activation of brainstem subpopulations are transient forces applied to ongoing dynamic landscapes We previously reported that explicitly incorporating dynamics into our latent state models reveals a limit cycle underlying VRC population dynamics that is highly consistent across animals 50 . This limit cycle was well recovered with a recurrent switching linear dynamical system (rSLDS) 64 with two partitions of the latent state (that correspond to inspiration and expiration) and two continuous latent dimensions 50 . Analyses of the latent state above suggest that inhibitory stimulations push the network state back down to the inspiratory off attractor. We test that hypothesis explicitly by incorporating a dependence of the two-dimensional latent state x t on an external input u t (see Methods), where u t is the presence of the laser pulse. We fit the latent state to the baseline (no stimulus) period and periods of stimulation with short (10ms, 50ms) laser pulses. This estimates the latent dynamics, from which we can predict the integrated diaphragmatic activity as a function of that latent state ( Figure 7A , B). This fitting also estimates the imposed effect of the optogenetic stimulation on the dynamics ( Figure 7B , C, Supplemental Videos 5,6). The learned stimulus effect manifests as two uniform vector fields partitioned by the same partitions learned by the dynamics (i.e., respiratory phase). By increasing the stimulus effect post-hoc, we can elicit qualitative changes in the limit cycle such that the limit cycle disappears ( Figure 7B ). We first examine the learned stimulus fields. By computing the norm of the stimulus vectors, we find that the VRC VGLUT2 stimulus has a stronger effect during expiration, VRC GABA has a stronger effect during inspiration, and NTS GABA has a similar strength during both states ( Figure 7D ). We next compare the learned inspiratory stimulus direction with the slow eigenvector of the expiratory dynamics. The slow expiratory eigenvector resembles the direction through which the latent state evolves as it transitions into inspiration ( Figure 7C ). The cosine similarity of the inspiratory stimulus field with the expiratory slow dynamics is large and positive for VRC VGLUT2 stimulation, indicating the stimulus pushes the network along the existing dynamics ( Figure 7E , Supplemental Figure 6 ). The stimulus opposes (i.e., large and negative) the normal dynamics during VRC GABA stimulation, and is more diffuse compared to NTS GABA stimulations. These results are consistent with the experimental observations in Figure 4 . Download figure Open in new tab Figure 7: Activation of subpopulations drive generalizable changes to latent dynamics. (A) Example fitting of piecewise latent dynamical system (rSLDS). Example rasters/integrated diaphragm as in Figure 3A . rSLDS model is fit only to spiking observations during baseline, 10ms, and 50ms laser pulses. Fitted latent dynamics are regressed against observed integrated diaphragm to map simulated diaphragm from two-dimensional latent state. (B) Simulated latent dynamics from data in A, varying strength of simulated stimulus. Red and blue streamlines are underlying piecewise dynamical system, black lines are example latent evolutions for 5s. Red, blue markers are fixed points of inspiratory/expiratory partitions of latent state, respectively. Circle is stable node, triangle is saddle. (C) Red and blue arrows represent the learned effect of optogenetic stimulation on the latent dynamics, as they affect the inspiratory/expiratory partitions respectively. Light blue arrows show the two eigenvectors of the expiratory partition in B. (D) Norm of the stimulus (i.e., stimulus strength) as it affects the dynamics of inspiratory or expiratory partitions, stratified by stimulated populations. Each connected pair of dots is one recording. (E) Cosine similarity (i.e. dot product of normed vectors) comparing the direction of the slow expiratory eigenvector with the direction of the inspiratory stimulus field. Each dot is a recording. Shuffle compares learned stimulus with eigenvectors from other recordings. (F) Example generalization of learned stimulus effect to recapitulate phase-dependent effects on respiratory rate in a simulated NTS GABA recording, simulated entirely from learned dynamics. Gray trace is simulated diaphragm, shaded red regions are triggered stimulations(G) Example generalization of varying stimulus strength in a simulated NTS GABA recording, gradually decreasing and abolishing respiration. Brown, grey traces are simulated latent, black trace is simulated diaphragm. Red line is duration of applied stimulation. (H) Quantification of results in G with high-density parameter sweep. Dot size and color indicate amplitude of simulated diaphragm during inspirations. In all panels, bars are mean +/- 95%CI. We next asked if applying this learned stimulus field could generalize to other types of stimulus patterns that were not part of the fitting procedure. We applied phasic simulated NTS GABA stimulations and found that indeed, inspiratory triggered stimulations increase simulated respiratory rate, and vice versa ( Figure 7F ). We then simulated long stimulus holds for a range of amplitudes ( Figure 7G , H) and found that both simulated respiratory rate and amplitude decrease gradually as a function of stimulus strength until it is abolished. This amplitude sweep was not collected here for direct comparison, but matches published data in 25 . Dynamic motifs generalize across stimulus types to predict neural activity and physiological behavior Strikingly, we observed that the learned stimulus fields are qualitatively similar within a given experimental stimulus (e.g., VRC GABA stimulus fields oppose the slow expiratory dynamics ( Figure 7E ). We asked if we could apply arbitrary stimulus fields that are defined based only on the observed dynamics without fitting the stimulus directly. If so, we could, for example, artificially apply stimulation of all three experimental populations in the same experimental recording. We generated three prototypical stimulus fields: VRC VGLUT2 -like VRC GABA -like, and NTS GABA -like ( Figure 8A ). These were defined as being: inline with slow expiratory eigenvector only during expiration, opposed to the expiratory eigenvector only during inspiration, and opposed to the expiratory eigenvector over the whole space, respectively (see Methods). Thus, we fit the dynamics only to the baseline recording, computed and applied these stimulus fields for each recording, and simulated diaphragmatic activity through our regression model. Strikingly, we could well recreate many of the observed experimental phenomena: reset curves as created with 50ms stimulations ( Figure 8AB ), phase dependent modulation ( Figure 8C , D, Supplemental Figure 6C, E ), rebound latency (Supplemental Figure 6D), and stimulus amplitude dependence ( Figure 8E, F ). A notable difference is that large stimulus simulation of VRC VGLUT2 -like fields caused a reduction or cessation of respiratory rate. We expect his was due to a limitation of the piecewise linear model; the state would become restricted to the inspiratory region of the latent space, which was often a stable spiral and would subsequently fail to reach the expiratory region. Together these results present a predictive, network-level control mechanism for respiratory neural dynamics by which subpopulations exert specific influences on the dynamic landscape to reshape respiratory rhythms. Download figure Open in new tab Figure 8: Experimental stimulation of specific subpopulations is recapitulated by parametric, unlearned perturbations of underlying dynamical systems. Simulated stimulations are indicated by green. (A) Latent dynamics are fit without inclusion of optogenetic stimulation. (Left) Dynamics for an example recording (red/blue streamlines, fixed points as in 7B) and (right) the three candidate stimulus fields (black arrows). Direction of stimulus field is always aligned to slow expiratory eigenvector; same direction for VRC VGLUT2 -like, opposite direction for inhibitory-like. (bottom) Simulated phase reset curves for application of these stimulus fields (50ms stimulation). Reset curves as in Figure 2E . Stimulus amplitude is set to 4. (B) Average reset curves applying the three stimulus fields in A to all recordings. Shaded region is mean +/- 95%CI. All simulated fields generalize to all recordings, regardless of animal genotype recorded; n=19 per group. (C) Example simulated phasic stimulation using an NTS GABA -like (i.e., uniform) stimulus field. (D) Change in simulated respiration rate for the three stimulus fields applied during inspiration or expiration (each marker is a recording, crosses are omitted from statistics as outliers, two outlier points of Δ Resp.Rate >400% are omitted). Stimulus amplitude is set at 4. (One sample Wilcoxon signed rank test **p<0.01,***p<0.001, see source data for p-values). Bars are median +/- 95%CI (E) Example varying strength of NTS GABA -like stimulus for held period. Brown, grey traces are simulated latent, black trace is simulated diaphragm. Top gray line is duration of applied stimulation. (F) Average simulated respiratory rate as a function of supplied stimulus amplitude for the three stimulus types (color as in B, n= 19 per stimulus application). Shaded regions are mean +/-S.E.M. Methods Animals All procedures were approved by the Seattle Children’s Research Institute Institutional Animal Care and Use Committee. Male and female mice aged 9-24 weeks were used. For targeting of VRC VGLUT2 and VRC GABA populations, homozygous Vglut2 Cre (Jax #028863) and Vgat Cre (Jax# 016962) were crossed with homozygous Ai32 mice (Jax# 012569) allowing Cre-dependent expression of a channelrhodopsin-2/EYFP fusion (ChR2(H134R)/EYFP). Surgery To target NTS GABA populations, we injected AAV8-nEF-Con/Foff 2.0-ChRmine-oScarlet (30 nL; 137161-AAV8) into the NTS at the level of the Area Postrema (7.56 mm caudal from Bregma, ±0.5 mm lateral from the midline and 3.9 mm below the dura mater) of Vgat Cre (Jax# 016962) mice. Anesthesia was induced with 3% isoflurane and maintained at 1.5%. Body temperature was maintained at 37°C with a recirculating heated waterbed (Adroit medical). Peri-operative Ketoprofen (5 mg/kg sc.) was administered. Scalp fur was shaved and the scalp was sterilized with isopropyl alcohol and betadine prior to incision. The skull was cleared and a midline craniotomy extending over the left and right NTS was drilled (± 0.7 mm from the midline). Virus was loaded into a glass pipette attached to a Nanoject 2 (Drummond Scientific), and the pipette was targeted to the left NTS. After cranial injection, the pipette remained in place for ∼5 minutes prior to removal of the pipette and targeting of the right NTS. Skin was then sutured over the craniotomies and mice were allowed to recover. Ketoprofen (5 mg/kg sc.) was administered for two consecutive days after the surgery. Virus was allowed to transfect for 10-28 days prior to recordings. in vivo Neuropixel recordings Recording preparations are modified from 50 , see that reference for further details. Anesthesia was induced at 3% isoflurane and urethane (1.5 g/kg) was administered intraperitoneally (IP) before removing animals from isoflurane. Animals were placed on a feedback controlled heating bed (FHC 40-90-8D) to maintain body temperature at 37°C throughout the experiment. Two stainless steel EMG wires (AM systems 0.005 inch diameter) were inserted into the right diaphragm, and two were inserted to record electrocardiogram (one lead over the heart and one in the left intraperitoneal space). EMG wires were secured in the skin with cyanoacrylate (Krazy Glue). EMG signal was amplified (10,000x), hardware filtered (100-5,000 Hz, AM-Systems 1700), and digitized at 10Khz (NI PXIe-8381). Diaphragm EMG was hardware rectified and integrated (custom) to be used for closed-loop online triggering of optical stimulation. (N.B. This rectified and integrated signal was not used in downstream analyses – see Preprocessing). Scalp fur was removed with depilatory cream (Nair). The mouse was then placed in a stereotaxic frame (Stoelting), affixed with earbars, and the skull was leveled. The scalp and skin overlying the rostral neck were removed, and neck muscles were dissected to allow visualization of the foramen magnum and the first cervical vertebra. A stainless steel headplate (custom) was cemented to the skull with UV cure cement (Pulpdent Embrace Wetbond). A small craniotomy was opened over the right cortex, and a bare silver ground wire 0.005in (AM systems) soldered to a gold pin (AM systems) was inserted overlying the dura and secured with cyanoacrylate (Krazy Glue) as a ground. In experiments in VRC GABA or VRC VGLUT2 stimulations, a ∼0.5mm craniotomy was drilled over the right VRC (1.25 mm lateral, 6.84mm caudal from bregma) and overlying dura was carefully removed. The animal was then transferred to a custom head-fixing apparatus. A 3D printed nose cone was placed over the animal’s snout, and 100% O 2 was supplied. If labored breathing was observed, atropine (0.1mg/kg) was administered to alleviate mucous buildup. The dura overlying the left caudal brainstem surface was cut, and the brainstem surface was kept hydrated with PBS. For recordings in VRC GABA or VRC VGLUT2 experiments, the optical fiber (200 μ m diameter, 0.22NA ThorLabs) was calibrated and then targeted above the right VRC (1.25mm lateral, 6.84mm caudal from bregma, 5.3mm ventral from bregma). In NTS GABA experiments with animals expressing virally mediated, red-shifted ChRmine opsins bilaterally in the NTS, the optic fiber (400 μ m diameter, 0.22NA, Doric) was placed on the surface of the skull overlying the NTS (midline, 7.2mm caudal from bregma). Neuropixels 1.0 probes coated in DiI (Thermofisher V22885) were then targeted to the left VRC (1.25 mm lateral, 4.8mm ventral from the intersection of the parietal and occipital bones at midline (see 50 for details). The probe was then inserted ∼3.5mm rostrally from the caudal brainstem surface at 10 μ m/s (Scientifica PatchStar). The probe was then retracted 100 μ m to reduce tissue distortion and allowed to settle for 15 minutes before recording. 10-15 minutes of baseline neural and respiratory activity were recorded before optical stimulation protocols. Stimulation Protocols All experimental hardware was controlled with custom python and Arduino software ( https://github.com/nbush257/pyExpControl ). Red (635nm) or blue (473nm) lasers (Cobalt MLD 635/473) were driven with an analog voltage (0-1v) calibrated to output either: 635nm light 20mW at the tip outside the skull (400 μ m diameter fiber) or 473nm light 8-10mW at the tip ∼300 μ m above the VRC (200 μ m fiber). A 2 millisecond sigmoidal ramp was added to the start and end of each pulse to minimize light artifacts on neural recordings. The following stimulus paradigms were applied:1) Hold stimulus: 5-15 repetitions of 2s illumination interleaved with 20s inter-trial interval. 2) Pulse stimulus: 50 repetitions of 10ms and 50 repetitions of 50ms pulses with 3s inter-trial interval. 3) 10 Repetitions of 10 seconds long inspiratory triggered stimulations. 4) 10 Repetitions of 2-4 seconds long expiratory triggered stimulations. Phasic (i.e., inspiratory and expiratory) triggered stimulations were performed by applying a hysteresis trigger to the hardware integrated diaphragm. During inspiratory stimulation, a positive threshold crossing turned on the laser and a negative crossing of the signal at 90% of the rising threshold turned off the laser. Expiratory stimulations used the same logic and thresholds, only the laser control was inverted (i.e., laser off when integrated diaphragm was above threshold, laser on when integrated diaphragm was below 90% threshold). Prior to recordings, the experimenter set the threshold manually with the light path interrupted (to not alter respiratory behavior which could alter the threshold choice) such that the threshold was as low as possible while maintaining phasic activation and avoiding constant illumination. To perform positive pressure experiments triggering the Hering-Breuer reflex, nose cone gas outlet was connected to a T-junction where one line led into a 15cm water column and the other to a constitutively open solenoid valve. To apply positive pressure, the solenoid valve was closed, forcing exhaust gas into the water column. Histology After recording, the animal was euthanized, perfused with phosphate-buffered saline followed by 4% PFA, and the brain was removed. The brain was then fixed overnight in 4% PFA, in 15% sucrose for 24 h and finally 30% sucrose. The brain was embedded in embedding medium (NEG-50) and frozen at −80 °C. Then 25-μm sagittal or coronal sections were collected and imaged (Olympus BX61VS) at 4x-10x magnification. Recording location was identified by the DiI fluorescent track and optical fiber placement confirmed by tissue damage. To minimize potential bias in the quantification, all photomicrography and cell counting were performed by a single researcher blinded to the experimental conditions. Cell counts were obtained using ImageJ software (version 1.41; National Institutes of Health). For each mouse, one-in-two coronal series of 25-µm brain sections was analyzed, resulting in sections spaced 50 µm apart. First, section alignment across brains was performed relative to a reference section of the nucleus of the solitary tract (NTS), which is anatomically bordered dorsally by the area postrema, laterally by the spinal trigeminal nucleus, and ventrally by the dorsal motor nucleus of the vagus (DMV). For sagittal sections, all brain slices were analyzed to identify the Neuropixel probe trajectory and optic fiber placement. Sections were mounted onto slides in phosphate buffer (PB) solution in rostrocaudal sequential order. After drying, they were cover slipped with DAPI-Fluoromount (0100-20; SouthernBiotech) and sealed with nail polish. The neuroanatomical nomenclature used in the experiments followed the atlas of Paxinos and Franklin (2012). Preprocessing Preprocessing of physiological and neural data was performed with custom python software available at https://github.com/nbush257/cibrrig . After recording, raw diaphragm EMG was rectified, median filtered, and EKG artifact was removed using custom removal methods. Breaths were then detected using scipy.find_peaks from the resulting timeseries. Neural data were preprocessed using spikeinterface 69 . Briefly, neural traces were destriped: traces were highpass filtered (250Hz), phase shifted, noise channels were removed, spatial high-pass filtered (local median subtraction), and optogenetic-induced artifacts were removed. Recordings were then motion corrected and spike sorted with Kilosort 4 70 . Only units that passed the following quality control metrics were marked as acceptable and included in downstream analyses (noise cutoff < 0.1, sliding refractory period 40.0 μ V, number of spikes > 500, presence ratio>0.8; for details see https://spikeinterface.readthedocs.io/en/stable/modules/qualitymetrics.html ). For ease of reuse, extracted data were saved according to International Brain Lab Open Neurophysiology Environment conventions (ONE https://github.com/int-brain-lab/ONE ). Physiology analysis Respiratory rates were computed during the stimulation period and compared to the equivalent length control period immediately preceding each stimulation. Relative changes in respiratory rate were computed as for all i stimulations. Similarly for diaphragm amplitude. Reset curves were created by computing the time from each 50ms pulse stimulus to the previous t pre and the next breath t next onset, and the average respiratory period . Then we compute normalized values: and . We quantify the intersection ( reset intercept ) of the phase reset curve with the y = 1 line by first smoothing the reset curve with a second order Savitsky – Golay filter with a window size of 21, then finding the normalized stimulus phase at which that smooth reset curve crosses y = 1. We then subtract the normalized phase time to the diaphragm peak, and the diaphragm offset (end). We compute respiratory phase as in 50 such that respiratory phase ϕ is defined on [− π , π ]; ϕ = 0 is defined as the onset of an inspiration (i.e., diaphragm activation), and ϕ = π is the offset of an inspiration (diaphragm inactivation). We set the sample immediately following ϕ = π to − π . Lastly, we linearly interpolate between [− π , 0) as expiration, and [0, π ]as inspiration. Single unit analyses We restrict all analyses to units that passed quality control (see above Preprocessing). The response of each neuron as a function of phase is computed where dt is the time step of the ϕ signal (1ms) and ϕ is binned at a resolution . of We define the respiratory modulation and preferred respiratory phase as the vector mean of the phasic histogram from 71 where the normalized length of the vector is the respiratory modulation ∈ [0,1] and the angle is the preferred phase ∈ [− π , π ]. Units with a respiratory modulation <0.2 were classified as tonic, all others as phasic. Phasic units were classified as inspiratory if the preferred phase was ≥ 0, otherwise expiratory. To compare firing rates between the two stimulus conditions (Hering-Breuer (HB) and opto-hold), we first take the square root transform of the mean firing rate of each unit in the stimulus period to transform the firing rate distributions before computing the correlation ρ . We also compute the difference in the mean square root firing rates: , where is the mean firing rate of unit i for that stimulus across repetitions, to estimate the difference in firing rates on average between the two stimulus conditions. Principal Components Projections We project the simultaneously recorded neural data into a low dimensional projection as previously 50 . Briefly, we first compute the binned spike counts for each unit in 5ms bins in the last 5 minutes of the baseline recording. The binned spike counts were smoothed with a gaussian kernel ( σ = 10 ms ) and square root transformed before applying PCA. In downstream analyses, we truncate the projection to a specific number of leading dimensions. We compute instantaneous trajectory speed as the Euclidean distance between two subsequent points ( dt = 5 ms ) in that truncated projection in time. We then compute the post-stimulus point as the point in the latent space at a given time after the offset of the stimulus, for each stimulus repetition i . To compute dispersion (i.e., how far apart are the post-stimulus points), we create a matrix of all stimulus points (# projection dimensions X # stimulus repetitions), compute its covariance matrix Σ, then compute Tr (Σ). We compute the distance to inspiration-off by first computing the mean point in the latent space where respiratory phase is immediately after the offset of inspiration in the last 100 second window of the baseline recording (i.e., no stimulus). We compute the mean Euclidean distance to all post stimulus points as the mean distance to I-off. All computations are performed in the truncated low-dimensional space indicated. Random shuffled controls were computed by choosing 100 uniformly distributed random points from the last 100 seconds of the baseline window to be the stimulus offset times. Because there is a delay between closing of the valve and buildup of pressure in the lung, we consider the post-stim time to be 2.5 seconds after the valve closing. Dynamical modeling To account for temporal structure when fitting a latent representation of the neural population activity, we fit recurrent switching linear dynamical systems models (rSLDS) 64 as in 50 . Briefly, the rSLDS model fits a low dimensional continuous latent state x t where x t ∈ R d . The rSLDS also partitions the space such that the state of the model can be in any of k discrete states z k , and the discrete state z t is a function of the continuous state x t . These partitions are each governed by separate linear dynamical systems subject to external inputs u t such that the continuous state follows: Where the fitted parameters are: A k , the dynamics matrix, V k the control matrix applied to the input u t , and b k the offset vector, all associated with discrete state k . w t is a noise term which we set to zero during simulation due to the observed stereotypy of the neural activity. We choose k = 2, d = 2, dt = 10 ms as we previously report this simple system to be sufficient to model these populations 50 . u t is one dimensional and binary; it takes a value of 1 when the optogenetic laser is on, 0 otherwise. Thus V k is a d dimensional vector. For analyses in Figure 7 where we analyze the learned stimulus field V k , we fit jointly { A k , b k , V k } during the last 5 minutes of the baseline period and the brief pulse stimulations only (50 repetitions each of 10ms and 50ms optogenetic stimuli). In analyses in Figure 8 where we impose arbitrary V k , we fit only { A k , b k } during the last 5 minutes of the baseline period (i.e., fit without optogenetic stimulus). While u t is {0,1} during fitting, the term V k u t , the effective stimulus field during the k th discrete state is uniform over the k th partition, and differs in magnitude and direction for each discrete state. We restrict all subsequent analyses only for recordings that exhibited limit cycle dynamics (n=16 for joint fitting of all parameters, n=18 for fitting baseline only). Importantly, we showed previously that when limit cycle dynamics were observed, the two discrete states z k corresponded to inspiration and expiration. We compute the stimulus strength for a given phase as the norm of the real components of each V k . Next we compute the eigenvectors of the dynamics matrices A k and determine slow and fast eigen vectors for each discrete state by the magnitude of the eigenvalue. To determine how aligned the dynamics matrices A k were with the stimulus vector V k , we compute the real component of the dot product between the normed eigenvectors and the normed stimulus vectors for each discrete state. Of particular importance was the slow expiratory eigenvector as it corresponded to the steady progression during expiration towards the next breath. After fitting { A k , b k } and optionally V k , we could simulate latent states x ^ by initializing at x ^ = (0,0) and following the latent state forward in time as it reached the limit cycle attractor according to the state update rule. Then, simulated integrated diaphragm traces were generated by first fitting a nonlinear support vector regression (SVR) with the fitted 2D latent state x as input and the observed integrated diaphragm trace as the target followed by applying that SVR to x ^. We simulated optogenetic stimulation by multiplying V k (either fitted from data or arbitrarily applied) by a chosen scaler multiplier that represented the stimulus amplitude. We performed simulated phasic triggered simulations by setting a threshold on the simulated integrated diaphragm above (or below) which we multiply V k by some constant. We further controlled whether phasic stimulation occurred during the first (i.e., rising) or latter (i.e., falling) part of the inspiration, given the sub-phase specificity of NTS GABA effects on breathing. We manually examined a variety of arbitrary stimulus fields V (e.g, uniform across all directions, piecewise uniform, sinks, sources). We chose three simple stimulus fields that qualitatively matched the effects of the optogenetic stimulation observed in experiment: VRC VGLUT2 -like, VRC GABA -like, NTS GABA -like. VRC VGLUT2 -like was uniform in the direction of the slow expiratory eigenvector (constructive) with a sigmoidal decay in amplitude at the boundary of the inspiratory/expiratory partition. VRC GABA -like was the mirror of VRC VGLUT2 -like (opposed to the slow expiratory eigenvector). NTS GABA -like was also opposed to the expiratory eigenvector but constant amplitude over the entire space. The choice of a sigmoidal decay and the parameter of the decay was chosen manually that qualitatively matched observed data. To make stimulus amplitudes approximately comparable across recordings, stimulus amplitudes were scaled by the mean speed of the latent trajectory. Note that the amplitude scaling in the different fitting procedures (with or without including stimulus observations) are not comparable due to the explicit fitting of V k in the former case. In some analyses, outlier data points were omitted after visual inspection showed that, for some recordings, the applied stimulus showed unexpected divergence or convergence to fixed points. These points are shown in figures, but excluded from statistical analyses. Statistics Statistical analyses were computed using custom python software using statsmodels and pingouin. Analysis software is available at https://github.com/nbush257/VLAD . Software and data availability All analysis software and documentation will be available on GitHub at https://github.com/nbush257/inspiration-off-attractor . Preprocessing software is available at https://github.com/nbush257/cibrrig , and experimental control software is available at https://github.com/nbush257/pyexpcontrol . Extracted data (spike data, physiology, events) in ONE format will be hosted upon publication. Raw electrophysiological data are available upon reasonable request. Discussion Overview Here we provide a data-driven, low dimensional dynamical systems framework for flexible respiratory control in vivo informed by high-spatiotemporal resolution neural recordings and causal manipulations of identified respiratory control circuit sub-populations. These results further the inspiration-off switch mechanism as a central respiratory pacing mechanism in vivo as originally proposed by systems-level approaches. In these original investigations of the inspiratory-off switch mechanism 53 , 56 , 72 , 73 , the primary read-out has been gross physiological activity (i.e., EMG, airflow, nerve recordings, few single units) which represents the integrated output of a complex, heterogeneous, and spatially distributed neuronal network. These approaches allowed limited insights into the underlying neural mechanisms, and much of the support for these models was primarily inferred from computational biophysical simulations 74 – 76 . Here, we leverage comprehensive, high-resolution electrophysiological recordings with Neuropixels and the optogenetic manipulation of genetically defined neuronal subtype to unveil the neuronal network dynamics underlying flexible respiratory control. This “inspiratory-off attractor” model provides further evidence for, and follows in spirit from, the classical inspiratory off-switch model in that timed phasic inhibition from mechano-sensory feedback resets the respiratory cycle to set breathing frequencies. It further augments the model in that it generalizes to predict bidirectional respiratory control from inhibitory populations, to account for manipulations of excitatory populations, and to predict the activity of the entirety of VRC neural populations. This is especially powerful as this generalization held even for predictive models fit without observations of stimulations. Although, the simultaneous high-resolution recordings from large populations of distinct, genetically defined neuronal subtypes and their phase-specific selective manipulations constitute a fundamental departure from the previous, traditional in vivo studies, the present study clearly builds on important insights that were gained by many of these original studies. Here we show that breathing phase can be both advanced and delayed as a result of well-timed activity of inhibitory neurons in the NTS. Our experiments build on prior investigations of inhibitory cells in this region of the NTS, “pump cells”, that have been shown to receive direct innervation from slowly adapting lung mechanoreceptors 61 , 77 , 78 . These populations have been well implicated as respiratory interrupting, direct bidirectional control via optogenetics has not yet been shown. Indeed, because respiratory rhythmic activity can be maintained in vitro without this off-switch mechanism, there has been considerable uncertainty and confusion in the field surrounding the role and importance of the off-switch mechanism as proposed for the in vivo network. Some work speculated that the burst-termination as seen in vitro may reflect a “fail-safe” mode that could play a role in gasping but not eupneic breathing 79 . It is known that in the absence of vagal inputs, respiration slows and diaphragmatic amplitude increases dramatically 67 . Normal rates and amplitudes can be recovered by direct stimulation of the remaining vagal nerves 72 or by direct stimulation of inhibitory neurons of the preBötC 49 . Whether activation of the NTS GABA populations in conditions of vagotomy are sufficient to recover qualitatively normal respiration is yet unknown, but an important next step. We speculate that the diverse molecular and anatomical targets of the vagi into the NTS make this plausible, but unlikely to be the sole circuit involved. For example our study did not address the role of the Kolliker-Fuse as an important contributor to the inspiratory off-switch. There are likely multiple pathways that can evoke identical, subtly different, or entirely different mechanisms that result in a similar physiological output, emphasizing the need for detailed and comprehensive neural recordings to disentangle. Indeed, our data here show similarity between physiological responses NTS GABA stim and lung-inflation but subtly different effects on the VRC (namely, a subpopulation of inspiratory VRC neurons that are unaffected in lung-inflation). We expect that emerging techniques to target sub-populations based on more granular cell marker will provide critical insights into the mechanisms that govern the generation of breathing in the largely intact animal 80 – 82 . Subphase specificity of respiratory modulation by different sources of VRC inhibition Interestingly, we find that activating NTS GABA populations plays a significant role in inspiratory rhythmogenesis in vivo by specifically advancing the respiratory phase during the rising half of the inspiration while delaying phase in the second half of inspiration. This contrasts with direct stimulation of VRC GABA populations which advances phase throughout inspiration. We interpret this as having two critical implications. Firstly, this agrees with the accepted role of the NTS GABA population as relaying lung volume for the purpose of pacing via feedback inhibition and volutrauma protection. But, NTS GABA neurons also amplified the re-afferent representation of lung volume, and the inspiration is terminated once this lung state representation reaches a threshold. Subsequently, amplification of this signal during early inspiration will pre-emptively trigger that reset. In contrast, amplification of the re-afferent signal in the latter half of inspiration will relay a lung-state representation that is larger than normal (as in a sigh), or in the inter-breath interval, a lung that is overfull (as in the Hering-Breuer reflex) and delay respiratory phase. Secondly, the fact that activating re-afferent circuitry during the latter half of inspiration delays respiration implies a role for inhibitory signaling in the VRC as rhythm advancing separate from mechanosensory feedback. Taken with the observation that latency to next breath after stimulation (i.e. rebound latency) is shorter for direct VRC GABA stimulation than for NTS GABA , we conclude that inhibitory signaling within the VRC concurrently prepares for an inspiration while also opposing its execution. The dynamical systems modeling results adds further evidence for this functional separability of inhibition. We showed that NTS GABA like effects could be recreated by opposing the phase advancing dynamics ( Figure 8 ) while VRC GABA like effects were matched by opposing phase advance only during inspiratory dynamics. Consequently, during VRC GABA -like stimulation, the model systems are held at the edge of the transition into inspiration. This implies that VRC GABA stimulation, but not NTS GABA stimulation, prepares the dynamics to transition into inspiration. Moreover, VRC GABA stimulation concurrently reduced the activity of expiratory unit activity ( Figure 3F ), while NTS GABA did not ( Figure 3F ). It is important to note that these data do not reveal if it is specifically inhibitory, expiratory neurons that are inhibited here, we have previously shown that expiratory neurons are more likely inhibitory in vivo 50 . Our data are consistent with the notion that the VRC GABA stimulation disinhibits the phase advancing components of the respiratory network that is absent during NTS GABA stimulations. The separability of these inspiratory phase promoting and phase advancing components of inhibitory signaling suggests that purely excitatory mechanisms of rhythm generation, while well established as being sufficient for in vitro rhythms 41 , 43 , 83 , are likely less important during eupneic breathing in vivo . In vitro respiratory rhythms rely on recurrent excitability within the preBötC and are terminated by intrinsic cellular mechanisms and local interactions 38 . Our results offer an integrated view of the rhythmogenic process in vivo which relies on the dynamic, well-timed activation of inhibitory neurons to coordinate inspiratory motor commands with proprioceptive inputs derived from lung-afferents via the NTS. Further investigations will be important to unravel exactly what sub-circuits and cell-types might be involved in the phase promoting aspects of VRC inhibition. In addition, we found that for our generative dynamical model to consistently recreate respiratory rate increases during inspiratory stimuli for the NTS GABA -like stimuli, we had to restrict stimulation to the rising phase of the diaphragm ( Supplemental Figure 6C ). This explains the difference in these results and recent reports in which inspiration timed NTS GABA stimulations resulted in respiratory slowing 58 . In those results, the phasic stimulations were long enough to potentially continue during expiration. Antagonistic control of inspiratory transitions by expiratory/inspiratory balance The Hering-Breuer reflex has been described for over a century 63 , and the responses of single neurons of various subregions of the VRC have been well characterized 51 , 57 , 62 , 84 – 89 . However, the coordinated changes in activity that arise in these distributed neural populations of the VRC during specific activation of transcriptionally defined respiratory populations has not been investigated. Interestingly, we observe that during lung inflation, expiratory neural activity remains high until a breath is triggered ( Figure 5G , K); contrasting the observation that expiratory neural activity decays in advance of the increase in inspiratory populations ( Figure 5G ). The lung inflation keeps expiratory tone high, which in turn putatively inhibits inspiratory tone. Simultaneously, inspiratory tone increases over time, likely due to a combination of intrinsic excitability 90 , 91 and tonic excitatory input 92 . Whether and when the inspiratory tone overcomes this balance will likely be specific to the sensory input and internal state of the animal. Lung inflation opposes inspiratory tone and recruits expiratory neurons, and the inspiratory drive to overcome that expiratory “barrier” is increased. This “stiffening” of the transition to inspiration is supported by the observation of a coordinated increase in both inspiratory and expiratory firing rates just before inspiration ( Figure 5K ), with the absence of a change in the ratios of firing ( Figure 5M ). Further supporting this is the change in inspiratory dynamics during lung inflation. Inspiratory neural activity is higher ( Supplemental Figure 5F ), inspirations are shorter ( Figure 5E ), and neural trajectories during inspiration are faster ( Supplemental Figure 5G ). In other systems (e.g., arm movement 93 and fish locomotion 94 ), a similar mechanism of antagonistic control is a common strategy for fine-tuned control. Balance in two opposing forces results in stability, while imbalance moves the state with more precision than without antagonistic control. It is important to note the (expected) lack of a perfect match between neural activity during Hering-Breuer reflex responses and stimulation of either NTS GABA or VRC GABA populations ( Figure 6H ). This indicates that the optogenetic stimulus cannot completely mimic the lung inflation stimulus at the detailed level of neural populations. The lung-inflation stimulation will specifically activate an endogenous inflation protection circuit, which will include activation of rapidly adapting stretch receptors (RARs) 95 , 96 and the pons 73 . Conversely, the optogenetic stimulations will likely activate off-target circuits which may be involved in other aspects of respiratory control, or other, non-respiratory functions 97 . The strong match in the breathing data for both stimulus types without the perfect match of the neural data is a warning that behavioral/gross physiological readouts are not complete, and limits how much certainty can be said without comprehensive examination of the neural activity. Contrasting dynamic motifs to modulate neural rhythms Our data show that stimulation of VRC VGLUT2 , VRC GABA, or NTS GABA populations can differentially increase respiratory rate if done with precise timing. By interrogating latent population dynamics, we uncover that the neural mechanism by which this respiratory rate increase occurs is strikingly different. The inspiration-off target is a critical feature in this dynamic landscape. Neural trajectories are attracted to, and dwell in, this region. Activation of VRC VGLUT2 populations speeds up neural trajectories by pushing them away from the inspiratory off target (i.e. destabilizing); conversely, activation of either inhibitory population temporarily increases the attractiveness of that region (i.e., stabilizing). In this way, VRC VGLUT2 populations increase respiratory rate by increasing trajectory speeds, most strongly in between inspirations, while inhibitory stimulations “short cut” the latent trajectory. This perturbation of the dynamic landscape is further supported when the latent dynamics are modeled explicitly and the impact of driving input or constituent subcircuits can be mapped directly onto vector fields with those behaviors that act on the neural dynamics. Importantly, in the transgenic (VRC GABA or VRC VGLUT2 ) mice, we stimulate not only local VRC neurons, but also glutamatergic or GABAergic inputs, and therefore are activating broadband excitatory and inhibitory inputs to the region. We show here that lung stretch inputs are sufficient to drive the network back to the inspiration off attractor and likely play a primary role in shaping the normal eupneic dynamics. However, further experiments are required to delineate circuit, region, or input cell type specific roles in sculpting or modulating those dynamics. In particular, we hypothesize that glutamatergic inputs from NMB + RTN neurons may play a primary role in destabilizing the inspiratory off attractor, particularly that inhibiting and removing these populations drastically reduces the regularity and rate of the inspiratory rhythm in vivo 12 . Notably, VRC GABA stimulation more quickly and directly drove the dynamics to the inspiration off target than did NTS GABA stimulations. This agrees with our targeting of the NTS GABA neurons that are presumptive secondary afferents receiving input from the SARs and affect breathing potentially via a multi-synaptic pathway 57 , 98 , 99 . Recent compelling work has implicated local inhibition of NTS Phox2B neurons 58 , but they do not rule out the function of additional collateral projections. Other possible mechanisms for these slower perturbation responses may include slower intrinsic dynamics of NTS GABA cells, smaller post-synaptic effects, or lower levels of transfection in viral approaches compared to transgenic. Conclusion The conceptual model for respiratory control as presented here provides a differentiated view of the rhythmogenic process in which inhibitory and excitatory mechanisms play opposing roles in the coordination of the respiratory cycle via dynamic control of the stability of an inspiratory off attractor. Further, this control is in large part dictated by mechanoreceptive inputs from lung afferents. However, our study also raises important questions that remain unanswered. First, how is the lung stretch set point determined? What exogenous or endogenous subcircuits within the medulla, pons and other areas of the brain can manipulate that set point? What are the contributions of various inspiration promoting mechanisms to the destabilization of the inspiratory-off fixed point? We speculate that excitatory chemo-sensitive inputs from the carotid bodies and the RTN/pFRG are also critically involved. Lastly, how do other inspiration terminating mechanisms (e.g., those triggered by irritants or e.g. during speech/vocalization 13 , 100 , 15 ) or slowing mechanisms 19 affect VRC latent dynamics? Together these data emphasize the role of inhibitory re-afferent feedback in shaping the normal ongoing dynamics of diverse respiratory motor control populations that govern breathing. Viewing the activity of neural populations in a low-dimensional dynamic space allows us to decompose the impact of manipulating cell-type specific subcircuits and inputs into the respiratory control circuitry. This has been used to great effect in other motor and behavioral settings 101 , 102 , offering an exciting and powerful way to dissect neural circuits in exquisite detail beyond observing motor output (e.g., breathing behavior). When combined with perturbation of intersectionally defined cell-type and projection specific populations 45 , 46 , 103 , we can begin to disambiguate the functional role of neural populations that may have overlapping or indistinguishable impact on respiratory output. Declaration of interests The authors declare no competing interests. Declaration of generative AI and AI-assisted technologies in the manuscript preparation process During the preparation of this work the author(s) used GitHub Copilot in order to aid writing of analysis software. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the published article. Supplemental Figures Download figure Open in new tab Supplemental Figure 1: (A) Example histology and summary (B) of optic fiber locations for VRC GABA (dark red) and VRC VGLUT2 (dark blue). (D) Change in respiratory rate as a function of fiber placement for 2s hold stimulations. Horizontal lines are mean of each animal, vertical lines are S.E.M., dots are individual stimulations. (Mixed linear model VRC VGLUT2 z=-0.430 coeff 95%CI= [-0.061,0.039], p=0.667, n=5, VRC VGAT z=0.759 coeff 95%CI= [-0.079,0.179], p=0.448, n=6) (D) number of cells transfected with ChRmine in NTS GABA animals as a function of bregma. Black line is average, shaded region is S.E.M, colored lines are individual animals (n=7). Abbreviations: Amb, ambiguus nu; 6Cb, 6th cerebellar lobule; 7Cb, 7th cerebellar lobule; 8Cb, 8th cerebellar lobule; Cu, cuneate nu; LR4V, lateral recess of 4 th ventricle; LRt, lateral reticular nu; LSO, lateral superior olive; Mo5, motor trigeminal nu; psf, posterior superior fissure; ppf, prepyramidal fissure; RPO, rostral periolivary region; RRF, retrorubral field; SNR, substantia nigra reticular; VII, facial nu; VIIn, facial nerve. Download figure Open in new tab Supplemental Figure 2: Physiological effects of optogenetic and physiological stimulations. (A) Change in diaphragm EMG amplitude (as % of baseline) for phasic-triggered optogenetic stimulations, stratified by targeted population. (One sample t-test VRC VGLUT2 n=5, p insp =0.04, p exp =0.17; VRC GABA n=6, p insp =0.007, p exp =0.09; NTS GABA n=5, p insp =0.028, p exp =0.046). (B) Change in heart rate (beats per minute) during 2s hold optogenetic stimulations, stratified by targeted genotype (Two way paired t-test pre stimulus compared to during stimulus VRC VGLUT2 n=5, p insp =0.007; VRC GABA n=5, p insp =0.054; NTS GABA n=7, p=0.01). (C) Respiratory rate before (control) and during Hering-Breuer stimulation (lung inflation) held for 2s or 5s (row) and stratified by optogenetic target (columns). Three-way ANOVA (stimulus,target,duration). significant main effect of stimulus p stimulus =2.19E-15,F stimulus =124.1 and target p target =2.2E-7, F target =20.8, but not duration p duration =0.55,F target 0.35; no significant interaction effects see supplemental table 1 ) Bars are mean +/- S.E.M. View this table: View inline View popup Download powerpoint Supplemental Table 1: Hering-Breuer ANOVA table Download figure Open in new tab Supplemental Figure 3: Change in trajectory speed during optogenetic stimulation of different target populations. (A-C) Phase averaged trajectory speed during phasic-triggered stimulations. Shaded regions are mean +/- 95% C.I. VRC VGLUT2 n=5, VRC GABA n=6, NTS GABA n = 4. (D) Phase averaged trajectory speeds for 2s hold stimulations. Shaded regions are mean +/- S.E.M. VRC VGLUT2 n=5, VRC GABA n=6, NTS GABA n = 5. Download figure Open in new tab Supplemental Figure 4: Convergence of latent trajectories after short optogenetic pulses. (A) Histogram of the values of phase from baseline average trajectory nearest to the average latent state during Hering-Breuer stimulation (HB), 25ms after brief 50ms optogenetic pulse (50ms) or random shuffled control points (random) aggregated across recordings. Rows stratified by optogenetically targeted population. (B) Dispersion and (C) distance to inspiration-off point of post-stimulus latent state 25ms after brief 50ms optogenetic pulse (solid line) or random baseline control points (dashed line) computed for increasing included dimensions of the latent state. Shaded regions are mean +/- S.E.M. (D) Dispersion and (E) Distance to inspiration off point as a function of both time after stimulation (x-axis) and number of dimensions included in latent state (y-axis) for 50ms optogenetic pulses, averaged across recordings. White dots indicate minimum along y-axis. VRC VGLUT2 n=5, VRC GABA n=6, NTS GABA n = 5. Download figure Open in new tab Supplemental Figure 5: Changes in neural dynamics during Hering-Breuer stimulation. (A-C) Percent change in firing rate for (A) inspiratory (B) expiratory and (C) tonic neurons averaged in 100 μ m bins as a function of inferred anterior posterior location relative to the caudal border of the facial nucleus (VII). (D) Number of units in each bin – fewer units near anterior/posterior extents contributes to nosy estimates of changes in firing rate. (E) Firing rate in baseline control (x-axis) vs Hering-Breuer stimulation(y-axis), but excluding time and spikes observed outside of preferred phase (i.e., inspiratory neuron firing rate is computed for spikes only in inspiration, and normalized only for inspiratory time). Each dot is a unit. (F) Cumulative distribution of firing rate ratios. Right shifted means neurons fire faster during Hering-Breuer stimulation (p insp =2.3E-39 W insp =150,296; p exp =0.039,W exp =74,336). (G) PCA trajectory speed aligned to (top) breath onset and (bottom) breath offset during baseline control (black) and break through breaths in Hering-Breuer stimulation (magenta). Shaded region is mean +/- S.E.M. Download figure Open in new tab Supplemental Figure 6: rSLDS simulations (A) Cosine similarity of learned inspiratory stimulus vectors with fast expiratory eigenvectors as in Figure 7E . (B) Cosine similarity of inspiratory (top) and expiratory (bottom) stimulus vectors with both slow and fast expiratory eigenvectors (includes data in Figure 7E and Supplemental Figure 5A ). Dot size indicates norm of stimulus field. Lines indicate stimulus vectors from the same recording. Color signifies experimentally targeted populations. (C) Change in simulated respiratory rate during NTS GABA -like, inspiratory-triggered stimulations restricting stimulation to either the rising or falling period of the simulated diaphragm contraction, or to both periods. (one sample Wilcoxon signed rank test: p rising =6.5E-4, W rising =0, N rising =16;p falling =1.6E-4, W falling =10, N falling =19,p both =5.2E-4, W both =15, N both =19.) (D) Latency from offset of stimulus until next simulated breath onset for the three stimulus types (Friedman test dof=2, Q=17.1, p=1.8E-4, post-hoc test Holm-Bonferroni corrected *p<0.05). (E) Change in simulated diaphragm amplitude (as % of baseline) for phasic-triggered simulated stimulations, stratified by stimulus type. (One sample Wilcoxon, outliers as crosses defined from C, *** p<0.001, see supplemental table 2 for statistics). In all panels bars are median +/- 95% CI (outliers included), crosses indicate outliers. View this table: View inline View popup Download powerpoint Supplemental Table 2: Phasic NTS GABA -like simulated stimulations statistics Supplemental Videos Supplemental Videos 1-3 Effects of stimulation of VRC GABA , NTS GABA , and VRC VGLUT2 (Supplemental videos 1,2,3 respectively) on diaphragm activity (top, yellow), single unit activity (middle, white), and two dimensional PCA projection (bottom). Hold stimulations and inspiratory triggered stimulations are shown sequentially. Optogenetic activation is shown as a solid colored line above the diaphragm trace (color indicates applied laser color specific for appropriate expressed opsin). Light cyan traces in PCA projection are past, unshown activity, yellow traces are unstimulated trajectory, laser colored traces (blue or red) are trajectories during stimulation. Supplemental video 4 Effects of Hering-Breuer stimulation on diaphragm activity (top, yellow), single unit activity (middle, white), and two dimensional PCA projection (bottom) for the same recording as in Supplemental video 1. Positive pressure is shown as a solid magenta line above the diaphragm trace. Light cyan traces in PCA projection are past, unshown activity, yellow traces are unstimulated trajectory, magenta traces are trajectories during stimulation. Supplemental Videos 5,6 Simulated rSLDS model dynamics (two dimensional, two state) from example VRC GABA and NTS GABA recordings with fitted stimulus fields (Supplemental videos 5,6 respectively). Ramping stimulus amplitude and pulses of various durations are shown. Stimulus amplitude is shown top in yellow. Background color indicates vector field speed; apparent discontinuity in speed is the boundary between partitions of the latent state governed by the individual discrete states. Green dot and trail indicates simulated latent dynamical model with initial state (0,0). Acknowledgements We thank the National Institutes of Health for funding: NIH R01 HL144801, R01 HL126523, and R01 HL151389 to J.M.R, NIH F32HL159904 to N.E.B. We thank the Behavioral Phenotyping Core (RRID:SCR_026371) at Seattle Children’s Research Institute for its assistance with the completion of neural recordings. We thank Research Scientific Computing at Seattle Children’s Research Institute for providing HPC resources that have contributed to the research results reported within this paper. Funder Information Declared National Heart Lung and Blood Institute , R01 HL144801 , R01 HL126523 , R01 HL151389 , F32HL159904 References 1. Paxinos , G. , and Franklin , K.B. ( 2019 ). Paxinos and Franklin’s the mouse brain in stereotaxic coordinates ( Academic press ). 2. ↵ Buzsáki , G. ( 2006 ). Rhythms of the Brain ( Oxford university press ). 3. Marder , E. , and Calabrese , R.L . ( 1996 ). Principles of rhythmic motor pattern generation . Physiological Reviews 76 , 687 – 717 . doi: 10.1152/physrev.1996.76.3.687 . OpenUrl CrossRef PubMed Web of Science 4. Lubenov , E.V. , and Siapas , A.G . ( 2009 ). Hippocampal theta oscillations are travelling waves . Nature 459 , 534 – 539 . doi: 10.1038/nature08010 . OpenUrl CrossRef PubMed Web of Science 5. Fernandez-Ruiz , A. , Sirota , A. , Lopes-Dos-Santos , V. , and Dupret , D . ( 2023 ). Over and above frequency: Gamma oscillations as units of neural circuit operations . Neuron 111 , 936 – 953 . doi: 10.1016/j.neuron.2023.02.026 . OpenUrl CrossRef PubMed 6. Takahashi , J.S . ( 2017 ). Transcriptional architecture of the mammalian circadian clock . Nature Reviews Genetics 18 , 164 – 179 . doi: 10.1038/nrg.2016.150 . OpenUrl CrossRef PubMed 7. Mizuseki , K. , Sirota , A. , Pastalkova , E. , and Buzsáki , G . ( 2009 ). Theta Oscillations Provide Temporal Windows for Local Circuit Computation in the Entorhinal-Hippocampal Loop . Neuron 64 , 267 – 280 . doi: 10.1016/j.neuron.2009.08.037 . OpenUrl CrossRef PubMed Web of Science 8. ↵ Buzsaki , G. , and Draguhn , A . ( 2004 ). Neuronal oscillations in cortical networks . Science 304 , 1926 – 1929 . OpenUrl Abstract / FREE Full Text 9. ↵ Del Negro , C.A. , Funk , G.D. , and Feldman , J.L . ( 2018 ). Breathing matters . Nature Reviews Neuroscience 19 , 351 – 367 . doi: 10.1038/s41583-018-0003-6 . OpenUrl CrossRef PubMed 10. ↵ Ramirez , J.-M. , and Baertsch , N.A . ( 2018 ). The Dynamic Basis of Respiratory Rhythm Generation: One Breath at a Time . Annual Review of Neuroscience 41 , 475 – 499 . doi: 10.1146/annurev-neuro-080317-061756 . OpenUrl CrossRef PubMed 11. ↵ Stornetta , R.L. , Moreira , T.S. , Takakura , A.C. , Kang , B.J. , Chang , D.A. , West , G.H. , Brunet , J.F. , Mulkey , D.K. , Bayliss , D.A. , and Guyenet , P.G . ( 2006 ). Expression of Phox2b by brainstem neurons involved in chemosensory integration in the adult rat . Journal of Neuroscience 26 , 10305 – 10314 . doi: 10.1523/JNEUROSCI.2917-06.2006 . OpenUrl Abstract / FREE Full Text 12. ↵ Souza , G.M.P.R. , Stornetta , D.S. , Shi , Y. , Lim , E. , Berry , F.E. , Bayliss , D.A. , and Abbott , S.B.G . ( 2023 ). Neuromedin B-expressing neurons in the retrotrapezoid nucleus regulate respiratory homeostasis and promote stable breathing in adult mice . Journal of Neuroscience 43 , JN–RM– 0386–0323 . doi: 10.1523/jneurosci.0386-23.2023 . OpenUrl CrossRef 13. ↵ Gannot , N. , Li , X. , Phillips , C.D. , Ozel , A.B. , Uchima Koecklin , K.H. , Lloyd , J.P. , Zhang , L. , Emery , K. , Stern , T. , Li , J.Z. , and Li , P . ( 2024 ). A vagal–brainstem interoceptive circuit for cough-like defensive behaviors in mice . Nature Neuroscience . doi: 10.1038/s41593-024-01712-5 . OpenUrl CrossRef 14. ↵ Taylor-Clark , T.E . ( 2015 ). Peripheral neural circuitry in cough . Current Opinion in Pharmacology 22 , 9 – 17 . doi: 10.1016/j.coph.2015.02.001 . OpenUrl CrossRef PubMed 15. ↵ Park , J. , Choi , S. , Takatoh , J. , Zhao , S. , Harrahill , A. , Han , B.-X. , and Wang , F . ( 2024 ). Brainstem control of vocalization and its coordination with respiration . Science 383 , eadi8081 . doi: 10.1126/science.adi8081 . OpenUrl CrossRef 16. ↵ Wei , X.P. , Collie , M. , Dempsey , B. , Fortin , G. , and Yackle , K . ( 2022 ). A novel reticular node in the brainstem synchronizes neonatal mouse crying with breathing . Neuron 110 , 644 – 657 . e646. OpenUrl PubMed 17. ↵ Ashhad , S. , Kam , K. , Del Negro , C.A. , and Feldman , J.L . ( 2022 ). Breathing Rhythm and Pattern and Their Influence on Emotion . Annual Review of Neuroscience 45 , 223 – 247 . doi: 10.1146/annurev-neuro-090121-014424 . OpenUrl CrossRef PubMed 18. Vlemincx , E. , Severs , L. , and Ramirez , J.-M . ( 2022 ). The psychophysiology of the sigh: II: The sigh from the psychological perspective . Biological Psychology 173 , 108386 . doi: 10.1016/j.biopsycho.2022.108386 . OpenUrl CrossRef 19. ↵ Jhang , J. , Liu , S. , O’Keefe , D.D. , and Han , S. ( 2023 ). A top-down slow breathing circuit that alleviates negative affect . bioRxiv , 2023.2002.2025.529925 . doi: 10.1101/2023.02.25.529925 . OpenUrl Abstract / FREE Full Text 20. ↵ Yackle , K. , and Do , J . ( 2025 ). The multifunctionality of the brainstem breathing control circuit . Current Opinion in Neurobiology 90 , 102974 . doi: 10.1016/j.conb.2025.102974 . OpenUrl CrossRef PubMed 21. ↵ Smith , J.C. , Abdala , A.P.L. , Borgmann , A. , Rybak , I.A. , and Paton , J.F.R . ( 2013 ). Brainstem respiratory networks: Building blocks and microcircuits . Trends in Neurosciences 36 , 152 – 162 . doi: 10.1016/j.tins.2012.11.004 . OpenUrl CrossRef PubMed Web of Science 22. Wu , J. , Capelli , P. , Bouvier , J. , Goulding , M. , Arber , S. , and Fortin , G . ( 2017 ). A V0 core neuronal circuit for inspiration . Nature Communications 8 , 544 – 544 . doi: 10.1038/s41467-017-00589-2 . OpenUrl CrossRef PubMed 23. Baertsch , N.A. , Severs , L.J. , Anderson , T.M. , and Ramirez , J.M . ( 2019 ). A spatially dynamic network underlies the generation of inspiratory behaviors . Proceedings of the National Academy of Sciences 116 , 7493 – 7502 . doi: 10.1073/pnas.1900523116 . OpenUrl Abstract / FREE Full Text 24. Guyenet , P.G. , and Bayliss , D.A . ( 2015 ). Neural Control of Breathing and CO2 Homeostasis . Neuron 87 , 946 – 961 . doi: 10.1016/j.neuron.2015.08.001 . OpenUrl CrossRef PubMed 25. ↵ Ausborn , J. , Koizumi , H. , Barnett , W.H. , John , T.T. , Zhang , R. , Molkov , Y.I. , Smith , J.C. , and Rybak , I.A . ( 2018 ). Organization of the core respiratory network: Insights from optogenetic and modeling studies . PLOS Computational Biology 14 , e1006148 . doi: 10.1371/journal.pcbi.1006148 . OpenUrl CrossRef PubMed 26. ↵ Koizumi , H. , and Smith , J.C . ( 2008 ). Persistent Na+ and K+-dominated leak currents contribute to respiratory rhythm generation in the pre-Bötzinger complex in vitro . Journal of Neuroscience 28 , 1773 – 1785 . doi: 10.1523/JNEUROSCI.3916-07.2008 . OpenUrl Abstract / FREE Full Text 27. ↵ Smith , J.C. , Ellenberger , H.H. , Ballanyi , K. , Richter , D.W. , and Feldman , J.L . ( 1991 ). Pre-Bötzinger complex: A brainstem region that may generate respiratory rhythm in mammals . Science 254 , 726 – 729 . doi: 10.1126/science.1683005 . OpenUrl Abstract / FREE Full Text 28. ↵ Lieske , S.P. , Thoby-Brisson , M. , Telgkamp , P. , and Ramirez , J.M . ( 2000 ). Reconfiguration of the neural network controlling multiple breathing patterns: Eupnea, sighs and gasps . Nature Neuroscience 3 , 600 – 607 . doi: 10.1038/75776 . OpenUrl CrossRef PubMed Web of Science 29. Ramirez , J.M. , Schwarzacher , S.W. , Pierrefiche , O. , Olivera , B.M. , and Richter , D.W . ( 1998 ). Selective lesioning of the cat pre-Botzinger complex in vivo eliminates breathing but not gasping . Journal of Physiology 507 , 895 – 907 . doi: 10.1111/j.1469-7793.1998.895bs.x . OpenUrl CrossRef PubMed Web of Science 30. ↵ Carroll , M.S. , and Ramirez , J.-M . ( 2012 ). Cycle-by-cycle assembly of respiratory network activity is dynamic and stochastic . Journal of Neurophysiology 109 , 296 – 305 . doi: 10.1152/jn.00830.2011 . OpenUrl CrossRef PubMed 31. ↵ Cui , Y. , Kam , K. , Sherman , D. , Janczewski , W.A. , Zheng , Y. , and Feldman , J.L . ( 2016 ). Defining preBötzinger Complex Rhythm- and Pattern-Generating Neural Microcircuits In Vivo . Neuron 91 , 602 – 614 . doi: 10.1016/j.neuron.2016.07.003 . OpenUrl CrossRef PubMed 32. Sherman , D. , Worrell , J.W. , Cui , Y. , and Feldman , J.L . ( 2015 ). Optogenetic perturbation of preBötzinger complex inhibitory neurons modulates respiratory pattern . Nature Neuroscience 18 , 408 – 416 . doi: 10.1038/nn.3938 . OpenUrl CrossRef PubMed 33. Gray , P.A. , Janczewski , W.A. , Mellen , N. , McCrimmon , D.R. , and Feldman , J.L . ( 2001 ). Normal breathing requires preBötzinger complex neurokinin-1 receptor-expressing neurons . Nature Neuroscience 4 , 927 – 930 . doi: 10.1038/nn0901-927 . OpenUrl CrossRef PubMed Web of Science 34. ↵ Tan , W. , Janczewski , W.A. , Yang , P. , Shao , X.M. , Callaway , E.M. , and Feldman , J.L . ( 2008 ). Silencing preBötzinger Complex somatostatin-expressing neurons induces persistent apnea in awake rat . Nature Neuroscience 11 , 538 – 540 . doi: 10.1038/nn.2104 . OpenUrl CrossRef PubMed Web of Science 35. ↵ Yang , C.F. , and Feldman , J.L . ( 2018 ). Efferent projections of excitatory and inhibitory preBötzinger Complex neurons . Journal of Comparative Neurology 526 , 1389 – 1402 . doi: 10.1002/cne.24415 . OpenUrl CrossRef PubMed 36. ↵ Yang , C.F. , Kim , E.J. , Callaway , E.M. , and Feldman , J.L . ( 2020 ). Monosynaptic Projections to Excitatory and Inhibitory preBötzinger Complex Neurons . Frontiers in Neuroanatomy 0 , 58 – 58 . doi: 10.3389/FNANA.2020.00058 . OpenUrl CrossRef 37. ↵ Brown , T.G . ( 1911 ). The intrinsic factors in the act of progression in the mammal . Proceedings of the Royal Society of London. Series B, containing papers of a biological character 84 , 308 – 319 . OpenUrl CrossRef 38. ↵ Ashhad , S. , and Feldman , J.L . ( 2020 ). Emergent Elements of Inspiratory Rhythmogenesis: Network Synchronization and Synchrony Propagation . Neuron 106 , 482 – 497 .e484. doi: 10.1016/j.neuron.2020.02.005 . OpenUrl CrossRef PubMed 39. Koch , H. , Zanella , S. , Elsen , G.E. , Smith , L. , Doi , A. , Garcia , A.J. , Wei , A.D. , Xun , R. , Kirsch , S. , Gomez , C.M. , et al. ( 2013 ). Stable respiratory activity requires both P/Q-type and N-type voltage-gated calcium channels . Journal of Neuroscience 33 , 3633 – 3645 . doi: 10.1523/JNEUROSCI.6390-11.2013 . OpenUrl Abstract / FREE Full Text 40. Ramirez , J.M. , and Viemari , J.C . ( 2005 ). Determinants of inspiratory activity . Respiratory Physiology and Neurobiology 147 , 145 – 157 . doi: 10.1016/j.resp.2005.05.003 . OpenUrl CrossRef PubMed Web of Science 41. ↵ Kam , K. , Worrell , J.W. , Ventalon , C. , Emiliani , V. , and Feldman , J.L . ( 2013 ). Emergence of population bursts from simultaneous activation of small subsets of preBötzinger complex inspiratory neurons . Journal of Neuroscience 33 , 3332 – 3338 . doi: 10.1523/JNEUROSCI.4574-12.2013 . OpenUrl Abstract / FREE Full Text 42. Tryba , A.K. , and Ramirez , J.M . ( 2004 ). Background sodium current stabilizes bursting in respiratory pacemaker neurons . Journal of Neurobiology 60 , 481 – 489 . doi: 10.1002/neu.20050 . OpenUrl CrossRef PubMed Web of Science 43. ↵ Phillips , R.S. , and Baertsch , N.A . ( 2024 ). Interdependence of cellular and network properties in respiratory rhythm generation . Proceedings of the National Academy of Sciences 121 . doi: 10.1073/pnas.2318757121 . OpenUrl CrossRef 44. ↵ Moreira , T.S. , Takakura , A.C. , Falquetto , B. , Ramirez , J.-M. , Oliveira , L.M. , Silva , P.E. , and Araujo , E.V . ( 2025 ). Neuroanatomical and neurochemical organization of brainstem and forebrain circuits involved in breathing regulation . Journal of Neurophysiology 133 , 1116 – 1137 . doi: 10.1152/jn.00475.2024 . OpenUrl CrossRef PubMed 45. ↵ Krohn , F. , Novello , M. , Van Der Giessen , R.S. , De Zeeuw , C.I. , Pel , J.J. , and Bosman , L.W. ( 2023 ). The integrated brain network that controls respiration . eLife 12 . doi: 10.7554/elife.83654 . OpenUrl CrossRef 46. ↵ Yackle , K . ( 2023 ). Transformation of Our Understanding of Breathing Control by Molecular Tools . Annual Review of Physiology 85 , 93 – 113 . doi: 10.1146/annurev-physiol-021522-094142 . OpenUrl CrossRef PubMed 47. Ray , R.S. , Corcoran , A.E. , Brust , R.D. , Kim , J.C. , Richerson , G.B. , Nattie , E. , and Dymecki , S.M . ( 2011 ). Impaired Respiratory and Body Temperature Control Upon Acute Serotonergic Neuron Inhibition . Science 333 , 637 – 642 . doi: 10.1126/science.1205295 . OpenUrl Abstract / FREE Full Text 48. ↵ Richter , D.W. , and Smith , J.C . ( 2014 ). Respiratory Rhythm Generation In Vivo . Physiology 29 , 58 – 71 . doi: 10.1152/physiol.00035.2013 . OpenUrl CrossRef PubMed 49. ↵ Baertsch , N.A. , Baertsch , H.C. , and Ramirez , J.M . ( 2018 ). The interdependence of excitation and inhibition for the control of dynamic breathing rhythms . Nature Communications 9 , 843 – 843 . doi: 10.1038/s41467-018-03223-x . OpenUrl CrossRef PubMed 50. ↵ Bush , N.E. , and Ramirez , J.-M . ( 2024 ). Latent neural population dynamics underlying breathing, opioid-induced respiratory depression and gasping . Nature Neuroscience 27 , 259 – 271 . doi: 10.1038/s41593-023-01520-3 . OpenUrl CrossRef PubMed 51. ↵ Bonham , A.C. , and McCrimmon , D.R . ( 1990 ). Neurones in a discrete region of the nucleus tractus solitarius are required for the Breuer-Hering reflex in rat . The Journal of Physiology 427 , 261 – 280 . doi: 10.1113/jphysiol.1990.sp018171 . OpenUrl CrossRef PubMed Web of Science 52. Nonomura , K. , Woo , S.H. , Chang , R.B. , Gillich , A. , Qiu , Z. , Francisco , A.G. , Ranade , S.S. , Liberles , S.D. , and Patapoutian , A . ( 2017 ). Piezo2 senses airway stretch and mediates lung inflation-induced apnoea . Nature 541 , 176 – 181 . doi: 10.1038/nature20793 . OpenUrl CrossRef PubMed 53. ↵ St.-John , W.M. ( 1998 ). Neurogenesis of patterns of automatic ventilatory activity . Progress in Neurobiology 56 , 97 – 117 . doi: 10.1016/S0301-0082(98)00031-8 . OpenUrl CrossRef PubMed Web of Science 54. ↵ Takatoh , J. , Prevosto , V. , Thompson , P. , Lu , J. , Chung , L. , Harrahill , A. , Li , S. , Zhao , S. , He , Z. , and Golomb , D . ( 2022 ). The whisking oscillator circuit . Nature 609 , 560 – 568 . OpenUrl PubMed 55. ↵ Marder , E. , and Bucher , D . ( 2001 ). Central pattern generators and the control of rhythmic movements . Current Biology 11 , R986 – R996 . doi: 10.1016/s0960-9822(01)00581-4 . OpenUrl CrossRef PubMed Web of Science 56. ↵ Clark , F.J. , and Von Euler , C. ( 1972 ). On the regulation of depth and rate of breathing . The Journal of Physiology 222 , 267 – 295 . doi: 10.1113/jphysiol.1972.sp009797 . OpenUrl CrossRef PubMed Web of Science 57. ↵ Moreira , T.S. , Takakura , A.C. , Colombari , E. , West , G.H. , and Guyenet , P.G . ( 2007 ). Inhibitory input from slowly adapting lung stretch receptors to retrotrapezoid nucleus chemoreceptors . The Journal of Physiology 580 , 285 – 300 . doi: 10.1113/jphysiol.2006.125336 . OpenUrl CrossRef PubMed Web of Science 58. ↵ Deng , T. , Jing , X. , Shao , L. , Wang , Y. , Fu , C. , Yu , H. , Wang , X. , Zhao , X. , Kong , F. , Ji , Y. , et al. ( 2025 ). A Molecularly Defined Medullary Network for Control of Respiratory Homeostasis . Advanced Science . doi: 10.1002/advs.202412822 . OpenUrl CrossRef 59. ↵ Perich , M.G. , Narain , D. , and Gallego , J.A . ( 2025 ). A neural manifold view of the brain . Nature Neuroscience 28 , 1582 – 1597 . doi: 10.1038/s41593-025-02031-z . OpenUrl CrossRef 60. ↵ Lindén , H. , Petersen , P.C. , Vestergaard , M. , and Berg , R.W . ( 2022 ). Movement is governed by rotational neural dynamics in spinal motor networks . Nature 610 , 526 – 531 . doi: 10.1038/s41586-022-05293-w . OpenUrl CrossRef PubMed 61. ↵ Ezure , K. , and Tanaka , I . ( 2004 ). GABA, in some cases together with glycine, is used as the inhibitory transmitter by pump cells in the Hering-Breuer reflex pathway of the rat . Neuroscience 127 , 409 – 417 . doi: 10.1016/j.neuroscience.2004.05.032 . OpenUrl CrossRef PubMed Web of Science 62. ↵ Ezure , K. , and Tanaka , I . ( 1996 ). Pump neurons of the nucleus of the solitary tract project widely to the medulla . Neuroscience Letters 215 , 123 – 126 . doi: 10.1016/0304-3940(96)12968-2 . OpenUrl CrossRef PubMed Web of Science 63. ↵ Breuer , J. ( 1868 ). Die Selbststeuerung der Athmung durch den Nervus vagus . 64. ↵ Linderman , S. , Johnson , M. , Miller , A. , Adams , R. , Blei , D. , and Paninski , L . ( 2017 ). Bayesian learning and inference in recurrent switching linear dynamical systems . ( PMLR ), pp. 914 – 922 . 65. ↵ Nair , A. , Karigo , T. , Yang , B. , Ganguli , S. , Schnitzer , M.J. , Linderman , S.W. , Anderson , D.J. , and Kennedy , A . ( 2023 ). An approximate line attractor in the hypothalamus encodes an aggressive state . Cell 186 , 178 – 193 .e115. doi: 10.1016/j.cell.2022.11.027 . OpenUrl CrossRef PubMed 66. ↵ Dutschmann , M. , and Herbert , H . ( 2006 ). The Kölliker-Fuse nucleus gates the postinspiratory phase of the respiratory cycle to control inspiratory off-switch and upper airway resistance in rat . European Journal of Neuroscience 24 , 1071 – 1084 . doi: 10.1111/j.1460-9568.2006.04981.x . OpenUrl CrossRef PubMed Web of Science 67. ↵ Lumsden , T . ( 1923 ). Observations on the respiratory centres in the cat . The Journal of physiology 57 , 153 . OpenUrl CrossRef PubMed Web of Science 68. ↵ Nonomura , K. , Woo , S.-H. , Chang , R.B. , Gillich , A. , Qiu , Z. , Francisco , A.G. , Ranade , S.S. , Liberles , S.D. , and Patapoutian , A . ( 2017 ). Piezo2 senses airway stretch and mediates lung inflation-induced apnoea . Nature 541 , 176 – 181 . doi: 10.1038/nature20793 . OpenUrl CrossRef PubMed 69. ↵ Buccino , A.P. , Hurwitz , C.L. , Garcia , S. , Magland , J. , Siegle , J.H. , Hurwitz , R. , and Hennig , M.H . ( 2020 ). SpikeInterface, a unified framework for spike sorting . eLife 9 . doi: 10.7554/elife.61834 . OpenUrl CrossRef 70. ↵ Pachitariu , M. , Sridhar , S. , Pennington , J. , and Stringer , C . ( 2024 ). Spike sorting with Kilosort4 . Nature Methods 21 , 914 – 921 . doi: 10.1038/s41592-024-02232-7 . OpenUrl CrossRef PubMed 71. ↵ Mazurek , M. , Kager , M. , and Van Hooser , S.D. ( 2014 ). Robust quantification of orientation selectivity and direction selectivity . Frontiers in Neural Circuits 8 . doi: 10.3389/fncir.2014.00092 . OpenUrl CrossRef PubMed 72. ↵ Boyd , T. , and Maaske , C . ( 1939 ). Vagal inhibition of inspiration, and accompanying changes of respiratory rhythm . Journal of Neurophysiology 2 , 533 – 542 . OpenUrl Web of Science 73. ↵ Dutschmann , M. , and Dick , T.E . ( 2012 ). Pontine mechanisms of respiratory control . Comprehensive Physiology 2 , 2443 – 2469 . doi: 10.1002/cphy.c100015 . OpenUrl CrossRef PubMed 74. ↵ Ogilvie , M.D. , Gottschalk , A. , Anders , K. , Richter , D.W. , and Pack , A.I . ( 1992 ). A network model of respiratory rhythmogenesis. American Journal of Physiology-Regulatory , Integrative and Comparative Physiology 263 , R962 – R975 . doi: 10.1152/ajpregu.1992.263.4.r962 . OpenUrl CrossRef 75. Rybak , I.A. , Shevtsova , N.A. , Paton , J.F.R. , Dick , T.E. , St.-John , W.M. , Mörschel , M. , and Dutschmann , M. ( 2004 ). Modeling the ponto-medullary respiratory network . Respiratory Physiology & Neurobiology 143 , 307 – 319 . doi: 10.1016/j.resp.2004.03.020 . OpenUrl CrossRef PubMed Web of Science 76. ↵ Smith , J.C. , Abdala , A.P.L. , Koizumi , H. , Rybak , I.A. , and Paton , J.F.R . ( 2007 ). Spatial and functional architecture of the mammalian brain stem respiratory network: A hierarchy of three oscillatory mechanisms . Journal of Neurophysiology 98 , 3370 – 3387 . doi: 10.1152/jn.00985.2007 . OpenUrl CrossRef PubMed Web of Science 77. ↵ Mazzone , S.B. , and Undem , B.J . ( 2016 ). Vagal Afferent Innervation of the Airways in Health and Disease . Physiological Reviews 96 , 975 – 1024 . doi: 10.1152/physrev.00039.2015 . OpenUrl CrossRef PubMed 78. ↵ Kubin , L. , Alheid , G.F. , Zuperku , E.J. , and McCrimmon , D.R . ( 2006 ). Central pathways of pulmonary and lower airway vagal afferents . Journal of Applied Physiology 101 , 618 – 627 . doi: 10.1152/japplphysiol.00252.2006 . OpenUrl CrossRef PubMed 79. ↵ St John , W.M. ( 2009 ). Noeud vital for breathing in the brainstem: gasping—yes, eupnoea— doubtful . Philosophical Transactions of the Royal Society B: Biological Sciences 364 , 2625 – 2633 . doi: 10.1098/rstb.2009.0080 . OpenUrl CrossRef PubMed 80. ↵ Qian , Y. , Li , J. , Zhao , S. , Matthews , E.A. , Adoff , M. , Zhong , W. , An , X. , Yeo , M. , Park , C. , Yang , X. , et al. ( 2022 ). Programmable RNA sensing for cell monitoring and manipulation . Nature 610 , 713 – 721 . doi: 10.1038/s41586-022-05280-1 . OpenUrl CrossRef PubMed 81. Jiang , K. , Koob , J. , Chen , X.D. , Krajeski , R.N. , Zhang , Y. , Volf , V. , Zhou , W. , Sgrizzi , S.R. , Villiger , L. , Gootenberg , J.S. , et al. ( 2023 ). Programmable eukaryotic protein synthesis with RNA sensors by harnessing ADAR . Nature Biotechnology 41 , 698 – 707 . doi: 10.1038/s41587-022-01534-5 . OpenUrl CrossRef 82. ↵ Zhang , M. , Pan , X. , Jung , W. , Halpern , A.R. , Eichhorn , S.W. , Lei , Z. , Cohen , L. , Smith , K.A. , Tasic , B. , Yao , Z. , et al. ( 2023 ). Molecularly defined and spatially resolved cell atlas of the whole mouse brain . Nature 624 , 343 – 354 . doi: 10.1038/s41586-023-06808-9 . OpenUrl CrossRef PubMed 83. ↵ Anderson , T.M. , Garcia , A.J. , Baertsch , N.A. , Pollak , J. , Bloom , J.C. , Wei , A.D. , Rai , K.G. , and Ramirez , J.M . ( 2016 ). A novel excitatory network for the control of breathing . Nature 536 , 76 – 80 . doi: 10.1038/nature18944 . OpenUrl CrossRef PubMed 84. ↵ Segers , L.S. , Nuding , S.C. , Dick , T.E. , Shannon , R. , Baekey , D.M. , Solomon , I.C. , Morris , K.F. , and Lindsey , B.G . ( 2008 ). Functional connectivity in the pontomedullary respiratory network . Journal of Neurophysiology 100 , 1749 – 1769 . doi: 10.1152/jn.90414.2008 . OpenUrl CrossRef PubMed Web of Science 85. Segers , L.S. , Nuding , S.C. , Vovk , A. , Pitts , T. , Baekey , D.M. , O’Connor , R. , Morris , K.F. , Lindsey , B.G. , Shannon , R. , and Bolser , D.C . ( 2012 ). Discharge identity of medullary inspiratory neurons is altered during repetitive fictive cough . Frontiers in Physiology 3 JUN, 223–223 . doi: 10.3389/fphys.2012.00223 . OpenUrl CrossRef 86. Shannon , R. , Baekey , D.M. , Morris , K.F. , Li , Z. , and Lindsey , B.G . ( 2000 ). Functional connectivity among ventrolateral medullary respiratory neurones and responses during fictive cough in the cat . Journal of Physiology 525 , 207 – 224 . doi: 10.1111/j.1469-7793.2000.00207.x . OpenUrl CrossRef PubMed Web of Science 87. Nuding , S.C. , Segers , L.S. , Iceman , K.E. , O’Connor , R. , Dean , J.B. , Valarezo , P.A. , Shuman , D. , Solomon , I.C. , Bolser , D.C. , Morris , K.F. , and Lindsey , B.G . ( 2024 ). Hypoxia evokes a sequence of raphe-pontomedullary network operations for inspiratory drive amplification and gasping . Journal of Neurophysiology . doi: 10.1152/jn.00032.2024 . OpenUrl CrossRef 88. Ezure , K. , and Tanaka , I . ( 2000 ). Lung inflation inhibits rapidly adapting receptor relay neurons in the rat . NeuroReport 11 . 89. ↵ Takakura , A.C. , Moreira , T.S. , West , G.H. , Gwilt , J.M. , Colombari , E. , Stornetta , R.L. , and Guyenet , P.G . ( 2007 ). GABAergic Pump Cells of Solitary Tract Nucleus Innervate Retrotrapezoid Nucleus Chemoreceptors . Journal of Neurophysiology 98 , 374 – 381 . doi: 10.1152/jn.00322.2007 . OpenUrl CrossRef PubMed 90. ↵ Phillips , R.S. , and Rubin , J.E . ( 2019 ). Effects of persistent sodium current blockade in respiratory circuits depend on the pharmacological mechanism of action and network dynamics . PLOS Computational Biology 15 , e1006938 . doi: 10.1371/journal.pcbi.1006938 . OpenUrl CrossRef PubMed 91. ↵ Del Negro , C.A. , Koshiya , N. , Butera , R.J. , and Smith , J.C . ( 2002 ). Persistent Sodium Current, Membrane Properties and Bursting Behavior of Pre-Bötzinger Complex Inspiratory Neurons In Vitro . Journal of Neurophysiology 88 , 2242 – 2250 . doi: 10.1152/jn.00081.2002 . OpenUrl CrossRef PubMed Web of Science 92. ↵ Tryba , A.K. , Peña , F. , and Ramirez , J.M . ( 2003 ). Stabilization of bursting in respiratory pacemaker neurons . Journal of Neuroscience 23 , 3538 – 3546 . doi: 10.1523/jneurosci.23-08-03538.2003 . OpenUrl Abstract / FREE Full Text 93. ↵ Gribble , P.L. , Mullin , L.I. , Cothros , N. , and Mattar , A . ( 2003 ). Role of Cocontraction in Arm Movement Accuracy . Journal of Neurophysiology 89 , 2396 – 2405 . doi: 10.1152/jn.01020.2002 . OpenUrl CrossRef PubMed Web of Science 94. ↵ Ruiz-Torres , R. , Curet , O.M. , Lauder , G.V. , and Maciver , M.A . ( 2014 ). Kinematics of the ribbon fin in hovering and swimming of the electric ghost knifefish . Journal of Experimental Biology 217 , 3765 – 3766 . doi: 10.1242/jeb.113670 . OpenUrl FREE Full Text 95. ↵ Pack , A.I. , and Delaney , R.G . ( 1983 ). Response of pulmonary rapidly adapting receptors during lung inflation . Journal of Applied Physiology 55 , 955 – 963 . doi: 10.1152/jappl.1983.55.3.955 . OpenUrl CrossRef PubMed Web of Science 96. ↵ Yu , J . ( 2021 ). A historical perspective of pulmonary rapidly adapting receptors . Respiratory Physiology & Neurobiology 287 , 103595 . doi: 10.1016/j.resp.2020.103595 . OpenUrl CrossRef PubMed 97. ↵ Ran , C. , Boettcher , J.C. , Kaye , J.A. , Gallori , C.E. , and Liberles , S.D . ( 2022 ). A brainstem map for visceral sensations . Nature 609 , 320 – 326 . doi: 10.1038/s41586-022-05139-5 . OpenUrl CrossRef PubMed 98. ↵ Kawai , Y . ( 2018 ). Differential Ascending Projections From the Male Rat Caudal Nucleus of the Tractus Solitarius: An Interface Between Local Microcircuits and Global Macrocircuits . Frontiers in Neuroanatomy 12 . doi: 10.3389/fnana.2018.00063 . OpenUrl CrossRef PubMed 99. ↵ Oliveira , L.M. , Takakura , A.C. , and Moreira , T.S . ( 2021 ). Forebrain and Hindbrain Projecting-neurons Target the Post-inspiratory Complex Cholinergic Neurons . Neuroscience 476 , 102 – 115 . doi: 10.1016/j.neuroscience.2021.09.015 . OpenUrl CrossRef PubMed 100. ↵ Callado Pérez , A. , Demers , M. , Fassihi , A. , Moore , J.D. , Kleinfeld , D. , and Deschênes , M. ( 2023 ). A brainstem circuit for the expression of defensive facial reactions in rat . Current Biology 33 , 4030 – 4035 .e4033. doi: 10.1016/j.cub.2023.08.041 . OpenUrl CrossRef 101. ↵ Sadtler , P.T. , Quick , K.M. , Golub , M.D. , Chase , S.M. , Ryu , S.I. , Tyler-Kabara , E.C. , Yu , B.M. , and Batista , A.P . ( 2014 ). Neural constraints on learning . Nature 512 , 423 – 426 . doi: 10.1038/nature13665 . OpenUrl CrossRef PubMed 102. ↵ Vinograd , A. , Nair , A. , Kim , J.H. , Linderman , S.W. , and Anderson , D.J . ( 2024 ). Causal evidence of a line attractor encoding an affective state . Nature 634 , 910 – 918 . doi: 10.1038/s41586-024-07915-x . OpenUrl CrossRef 103. ↵ Alheid , G.F. , and McCrimmon , D.R . ( 2008 ). The chemical neuroanatomy of breathing . Respiratory Physiology and Neurobiology 164 , 3 – 11 . doi: 10.1016/j.resp.2008.07.014 . OpenUrl CrossRef PubMed Web of Science View the discussion thread. Back to top Previous Next Posted September 25, 2025. Download PDF Supplementary Material Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. You are going to email the following An inspiration-off attractor supports the robust and flexible control of breathing Message Subject (Your Name) has forwarded a page to you from bioRxiv Message Body (Your Name) thought you would like to see this page from the bioRxiv website. Your Personal Message CAPTCHA This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. Share An inspiration-off attractor supports the robust and flexible control of breathing Nicholas E. Bush , Luiz M. Oliveira , Zachary T. Glovak , Jan-Marino Ramirez bioRxiv 2025.09.23.678177; doi: https://doi.org/10.1101/2025.09.23.678177 Share This Article: Copy Citation Tools An inspiration-off attractor supports the robust and flexible control of breathing Nicholas E. 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