Robustness of respiratory rhythm generation across dynamic regimes
[['A variety of neuronal circuits , including a range of brainstem and spinal cord central pattern generators ( CPGs ) in many species , exhibit rhythmic activity patterns .', 'In many CPGs , these patterns consist of sequential activations of different neuronal populations that interact through synaptic connections [1 , 2] .', 'Significant effort has gone into exploring , using experimental and theoretical methods , the extent to which the intrinsic bursting or pacemaking capabilities of neurons within these populations are responsible for the existence of the network rhythms in which they participate .', 'For example , experimental studies have established the existence of intrinsically bursting neurons in the respiratory pre-Bötzinger complex ( preBötC ) , the inspiratory oscillator within the mammalian brainstem [3] , and certain experimental manipulations of burst-supporting conductances in these neurons have eliminated respiratory rhythms [4–7] .', 'Although these and a wide range of other investigations have explored burst generation mechanisms in respiratory preBötC neurons and have debated the role of this burst generation capability in respiratory rhythms across a variety of conditions [8 , 9] , these studies have not answered a key question: What happens to this intrinsic bursting when the intrinsically burst-capable neurons are embedded within the full network with which they interact synaptically ?', 'In fact , it remains unknown whether the intrinsic bursting capabilities of subsets of preBötC neurons affect the dynamics that these neurons actually exhibit once they are embedded within a synaptically interconnected respiratory circuit and how this bursting capability contributes to the properties of the circuit’s rhythmic outputs .', 'These issues relate to the broader concept of robustness .', 'Respiration is critical for survival in mammalian species; respiratory rhythms within individuals must be produced across variations in environmental conditions , metabolic demands , and physiological states , and this persistence must occur across individuals despite their phenotypic heterogeneity .', 'Robustness of a dynamical output such as a respiratory rhythm refers to the maintenance of that pattern of output across conditions or , in a modeling context , across changes in the model parameters or features that represent these conditions .', 'An even stronger form of robustness can arise in which not only the output pattern but also the dynamical mechanisms that give rise to that pattern are preserved .', 'Past experimental and computational work has revealed significant robustness of rhythmicity in the stomatogastric ganglion CPG , which generates certain digestive rhythms in crustacean species , with respect to changes in extrinsic factors such as temperature as well as intrinsic factors such as conductances of ionic currents [10–12] .', 'In this study , we use highly reduced models of the respiratory CPG , composed of a small number of units representing important neuron populations [13] , to highlight some key ideas relating to robustness of rhythmic outputs across parameter variations , including changes that would induce a switch in intrinsic dynamics if applied to isolated preBötC neurons .', 'The model network generates a three-phase respiratory rhythm and includes inspiratory neurons that abruptly activate at the onset of inspiration , with gradually declining input; a post-inspiratory component that strongly activates at the inspiratory-to-expiratory transition and then gradually diminishes its activity; and a component with activity that represents a later expiratory phase , gradually augmenting after the main post-inspiratory activity surge [14 , 15] .', 'We model the burst-capable neurons in the respiratory network using differential equations that incorporate a representation of the persistent sodium current , which supports an established oscillatory burst generating mechanism and has been well documented in these neurons experimentally [6 , 16–18] .', 'Basic principles of dynamical systems theory imply , however , that any alternative mechanisms providing a similar voltage-dependence of activity and autorhythmic capability would yield similar results [19] , and hence the ideas that we illustrate are not dependent on a specific bursting mechanism .', 'In particular , our key finding is that network rhythmicity extends smoothly and robustly across different dynamical regimes of the intrinsically burst-capable neurons in the network .', 'Within the multi-phase rhythmic outputs that emerge , these neurons’ outputs can become dominated by network influences .', 'While network rhythms exhibit similar features whether the tuning of these neurons renders them intrinsically burst-capable or not , the maintenance of output function across different tunings of intrinsic dynamics yields a broadened dynamic range of network output properties .'], ['We simulated a highly reduced rhythm-generating network model consisting of ordinary differential equations representing coupled neuronal units .', 'We based our network connectivity on published models for the generation of rhythmic activity patterns in respiratory circuits [5] and we tuned the network to produce rhythmic outputs that are qualitatively similar to the experimentally observed tri-phasic rhythmic respiratory pattern , including the inspiratory ( I ) , the post-I expiratory , and the subsequent augmenting-expiratory ( aug-E ) stages .', 'The circuit depicted ( Fig 1 ) consists of a preBötC excitatory ( glutamatergic ) unit ( often referred to as pre-I/I because its firing occurs before and during the I phase , but abbreviated as pre-I throughout this work ) representing rhythmogenic neurons in the preBötC , a brainstem region that can exhibit intrinsic oscillatory dynamics and drives I activity , along with inhibitory units named after the timing within the respiratory cycle at which their activity occurs ( early-I , post-I and aug-E ) .', 'Among these , it is thought that critical subpopulations of post-I and aug-E inhibitory neurons in respiratory CPG circuits reside in the BötC region adjacent to the preBötC [5 , 8] , and these inhibitory neurons have been shown to provide strong inhibition to the preBötC to regulate inspiratory rhythmicity [20] .', 'In some simulations , as noted in the corresponding text , we also included a unit representing the recently identified glutamatergic post-inhibitory complex ( PiCo ) [21] .', 'Within this framework , we tuned the parameters in the equations for each unit to represent a distinct activity profile experimentally identified to arise in a corresponding subpopulation of respiratory neurons during the respiratory cycle [5] .', 'In each of these populations , neurons become active and fall silent in a synchronized way but need not spike in synchrony , and hence we omitted spiking currents in our model units .', 'Within the respiratory rhythm-generating circuit , some members of the pre-I population in the preBötC have been found to be capable of producing rhythmic bursting activity even when isolated from synaptic inputs , at least over some range of constant input currents or extracellular potassium concentrations [3 , 22 , 23] .', 'We simulate the conditional bursting property of pre-I neurons by endowing the pre-I unit’s voltage equation with a persistent sodium current , INaP , which is an established feature of preBötC excitatory neurons [6 , 16 , 18] and provides a voltage-controlled relaxation-oscillator type of rhythmic oscillation .', 'In the reduced modeling framework , the dynamics produced by the pre-I unit can be understood by using a phase plane representation .', 'The phase plane shows values of voltage , Vpre−I , and INaP inactivation , hpre−I , along with these variables’ nullclines , which are curves along which dVpre−I/dt = 0 or dhpre−I/dt = 0 , respectively ( Fig 2A ) .', 'Nullcline intersections correspond to fixed points , or combinations of Vpre−I , hpre−I for which the unit is at equilibrium .', 'Fixed points may be asymptotically stable , stable , or unstable; in the last case , if we choose a starting point for ( Vpre−I , hpre−I ) at random , then we expect these quantities to stay away from the fixed point as time evolves .', 'Because the tonic excitatory drive to the pre-I unit affects dVpre−I/dt , the Vpre−I-nullcline’s position and shape depend on the strength of this drive , denoted by c11 .', 'Generally , increases in c11 cause nullcline alterations that promote elevations in voltage ( Fig 2A ) .', 'More specifically , for relatively low values of c11 , the unit’s Vpre−I-nullcline is cubic or N-shaped and features an asymptotically stable fixed point on its hyperpolarized ( or left ) branch , corresponding to a quiescent state .', 'As c11 is increased , the Vpre−I-nullcline changes , causing the location of its intersection with the h p r e I-nullcline to change as well .', 'As a result , the fixed point crosses to the middle branch and a bifurcation occurs ( an Andronov-Hopf , or A-H , bifurcation with a canard explosion [24] ) that destabilizes the fixed point , after which the unit will , in isolation from synaptic inputs from other units , produce relaxation oscillations .', 'In this regime , the unit is intrinsically rhythmic , and this rhythmicity depends on INaP .', 'Finally , with additional increases in c11 , the Vpre−I nullcline switches from cubic to monotonically increasing and another ( A-H ) bifurcation occurs , producing the loss of oscillations and the restabilization of the fixed point , now at a depolarized voltage , corresponding to a tonically activated state ( Fig 2 ) .', 'In this regime , the excitatory drive to the unit keeps voltage high enough that INaP deinactivation is limited , including in the tonically activated state .', 'Note that the actual numerical values of c11 used here are given in arbitrary units .', 'Once this pre-I unit is embedded within the full respiratory network ( as shown in Fig 1 , but without the PiCo ) , its intrinsic properties are masked , or superseded by the network dynamics .', 'There are multiple manifestations of this form of masking .', 'First , at the low end of the c11 range over which the isolated pre-I unit generates oscillations , the coupled network does not produce oscillatory dynamics but rather settles into a tonic activity regime in which the post-I unit maintains a steady elevated activation level while the pre-I and early-I units exhibit low activation levels .', 'Second , the ranges of periods and amplitudes that the pre-I unit exhibits during its intrinsic oscillations differ from those that it produces when operating within the oscillatory dynamics of the full network ( Fig 3 ) .', 'The sensitivity of the pre-I oscillation period and amplitude to changes in c11 is also altered by the embedding .', 'Interestingly , the activity pattern of the synaptically connected respiratory network remains remarkably similar regardless of whether c11 is tuned to yield oscillatory or tonic pre-I dynamics in isolation .', 'These network activity patterns are shown in Fig 4A and 4B for representative c11 values , one per regime of intrinsic pre-I dynamics , in terms of nondimensional variables ( scaled between 0 and 1 , with the same scaling used across all c11 ) representing the output of the pre-I , early-I , post-I , and aug-E units that comprise the network , when PiCo is silent .', 'In both cases , pre-I and to a lesser extent early-I output slowly ramps up before pre-I and early-I activity levels surge together , corresponding to the onset of inspiration .', 'Pre-I and early-I then gradually decline before an abrupt take-over by post-I unit activity and corresponding inhibition of the two I units , marking the phase switch to expiration .', 'After this switch , post-I output declines , disinhibiting aug-E , the output of which ramps up , yielding what is known as the late-expiratory or E-2 phase , with aug-E output exceeding and inhibiting but not completely suppressing post-I .', 'This similarity in the pattern of network dynamics across different pre-I unit tunings represents another form of masking , since the intrinsic tuning of the pre-I unit dynamics becomes hidden and cannot be deduced from observation of the network activity pattern .', 'A comparison between the examples shown reveals that the periods of the outputs generated for these parameter values do differ .', 'We will next explore frequency responses to parameter changes across the two regimes of pre-I intrinsic dynamics , and later we will consider network dynamics when PiCo activity is included ( Fig 4C and 4D ) .', 'In the model that we are considering , we use a persistent sodium current , INaP , to allow the possibility of intrinsic rhythmicity in our pre-I unit .', 'In experiments , addition of the INaP blocker riluzole to the perfusate of an in situ rat preparation that preserved the intact respiratory network yielded little change in respiratory period but caused the output of the phrenic nerve , which corresponds to the excitatory output from the inspiratory neurons in the respiratory circuit , to decrease in amplitude [5] .', 'This decrease occurred roughly linearly with riluzole concentration , reaching about 1/3 of the original amplitude with the maximal riluzole dose applied .', 'We tested the dependence of the period of our network rhythm ( T ) , the duration of its inspiratory ( TI ) and expiratory ( TE ) phases , and the amplitude of the pre-I unit’s output on the strength of INaP , represented by its maximal conductance gNaP , exc .', 'Moreover , we evaluated this dependence over a range of values of the pre-I tonic drive parameter c11 spanning across regimes of both oscillatory and tonic pre-I intrinsic dynamics .', 'Note that the value of c11 at which the pre-I unit’s intrinsic dynamics changes from oscillatory to tonic depends on gNaP , exc .', 'Since this transition occurs at an A-H bifurcation as shown in Fig 2B , we used the continuation capabilities of XPPAUT [25] to follow this bifurcation in the two parameters ( gNaP , exc , c11 ) , thereby generating a transition curve .', 'This curve appears in red in all panels of Fig 5 .', 'We found that the quantitative properties of the network rhythm did depend on both gNaP , exc and c11 ( Fig 5 ) .', 'For example , T was sensitive to gNaP , exc over a range of c11 values but less so for sufficiently large c11 , possibly because units other than pre-I exerted more control over network timing for large c11 values associated with tonic intrinsic pre-I dynamics ( Fig 2 ) .', 'A sufficient reduction of gNaP , exc prevented network output of a rhythmic pattern for most of the range of c11 considered because pre-I became unable to activate , although for c11 sufficiently large , rhythmic outputs persisted down to gNaP , exc = 0 nS , despite the lack of intrinsic pre-I rhythmicity at this c11 level .', 'Wider ranges of T , TI , and TE values could occur for relatively small ( i . e . , relatively negative ) c11 than for large c11 ( Fig 5A , 5C and 5D ) , while amplitude changed more with gNaP , exc when c11 was large ( i . e . , near 0 or positive , Fig 5B ) , due to the wider range of gNaP , exc values preserving rhythmicity .', 'Importantly , however , when gNaP , exc and c11 were varied from one side of the oscillatory-tonic transition curve ( red curves in Fig 5 ) to the other , the transition in pre-I intrinsic dynamics caused absolutely no associated jump or shift in the quantitative properties of the network rhythm ( Fig 5 ) .', 'In other words , the patterns of changes in period , amplitude , TI , and TE with respect to gNaP , exc and c11 continue uninterrupted across this transition curve .', 'Finally , we compared the dependence of the model on gNaP , exc to that found experimentally [5] .', 'We found that over a range of c11 values straddling 0 ( c11 ∈ [−0 . 006 , 0 . 004] ) , we could select a range of gNaP , exc values ( gNaP , exc ∈ [1 . 7 nS , 4 . 1 nS] ) such that when gNaP , exc was reduced through this range , the model provided an excellent agreement with the experimentally observed [5] invariance of period and 2/3 drop in amplitude of inspiratory output ( blue boxes , Fig 5A and 5B; amplitude range approximately 0 . 23 to 0 . 75 ) .', 'In fact , there was some decrease in TI over this range ( Fig 5C ) , but it was compensated by an increase in TE ( Fig 5D ) to yield little net change in T ( Fig 5A ) .', 'Although the network’s rhythmic activity pattern is similar for both oscillatory and tonic intrinsic preBötC unit dynamics , it remains possible that this intrinsic tuning could affect the detailed dynamical mechanisms by which this pattern is produced , potentially leading to different dynamics in response to certain inputs or perturbations .', 'Since we use model units with dynamics that can be visualized in the phase plane to model each population in the network , we can represent the network oscillation mechanisms geometrically and compare them between the two cases .', 'To do so , although the full network model consists of an eight-dimensional dynamical system , we consider the network outputs projected to various two-dimensional phase planes , each defined using the two variables for one specific unit ( Figs 6 and 7 ) .', 'Within these phase planes , we plot the nullclines , or curves of zero rate of change , for each of these two variables .', 'Since each unit’s voltage equation depends on the outputs of the other units that are coupled to it synaptically , the location of each projected voltage nullcline varies with the activity of each presynaptic unit .', 'We plot the nullclines at several key moments within a network activity cycle that are particularly helpful for understanding the network dynamics .', 'We also plot the projection of the network output trajectory to each phase plane .', 'Because voltage changes much more rapidly than the persistent sodium inactivation variable , these trajectory projections generally lie on appropriate voltage nullclines except during brief excursions when the network output rapidly changes , which occur in the transitions between inspiratory and expiratory phases .', 'Note that we omit the early-I unit from this discussion , because it always settles to a stable fixed point corresponding to the level of input that it receives , and it lacks the auto-rhythmic capability needed to initiate a transition to the I phase .', 'The phase plane for the pre-I unit shows that even if the pre-I unit is tuned to be intrinsically oscillatory , at the moment when it receives its maximal level of inhibition , which occurs at the onset of post-I activity ( black square in Fig 6A ) , the unit cannot activate through INaP deinactivation alone , because its voltage- or Vpre−I-nullcline ( leftmost blue curve , Fig 6A ) intersects the hpre−I-nullcline ( red curve ) in a stable fixed point at large hpre−I , corresponding to stable quiescence .', 'When inhibition to the pre-I is at its peak , Vpost−I is at its maximum ( black square in Fig 6C ) , while Vaug−E is hyperpolarized due to the strong inhibition that the aug-E unit receives from post-I ( black square in Fig 6D ) .', 'As can be seen in Fig 6C and 6D , during the ensuing post-I phase , Vpost−I gradually decreases , which occurs due to an inhibitory input from the aug-E unit ( which is already present—although very weak—near the onset of the expiratory phase in our model tuning; see Fig 4 ) , and Vaug−E gradually increases ( Fig 6C and 6D arrows ) ; together , these changes form a self-reinforcing feedback loop .', 'As a result , the inhibitory output from the post-I unit drops , the Vpre−I-nullcline position changes , and the value of Vpre−I increases correspondingly while hpre−I continues to deinactivate ( Fig 6A , arrow ) .', 'A key moment in the respiratory cycle is the transition from expiration to inspiration .', 'From the phase plane in Fig 2 , recall that when the pre-I unit is tuned to be intrinsically oscillatory , the Vpre−I-nullcline has a cubic shape whether it receives any inhibition or not .', 'In a phase plane with a cubic voltage nullcline , a unit transitions from the hyperpolarized phase to the depolarized phase when its voltage rises above the left fold or knee of its voltage nullcline , corresponding to sufficient INaP deinactivation relative to the level and time course of input that the unit receives .', 'Because the inhibition from post-I to pre-I is stronger than the inhibition from aug-E to pre-I , it follows that the inhibition to pre-I declines over the course of expiration .', 'This decline allows the pre-I unit to reach its curve of knees once Vpost−I is sufficiently reduced .', 'This event is illustrated in Fig 6A , where the Vpre−I-nullcline is shown at the moment ( marked with a black circle ) when Vpre−I reaches this curve of knees ( grey curve ) , allowing the transition to inspiration to commence ( see also black circles and corresponding voltage nullclines in Fig 6C and 6D ) .', 'Another view of this transition is provided by plotting the total level of inhibition to the pre-I unit versus hpre−I ( Fig 6B ) .', 'The ( Vpre−I , hpre−I ) coordinates of both the knee itself ( dashed blue curve ) and the fixed point ( dashed green curve ) , where the Vpre−I and hpre−I nullclines intersect , depend on this inhibition level .', 'The projection of the trajectory would tend to the curve of fixed points if inhibition were held fixed , preventing the onset of inspiration .', 'But the gradual decrease of total inhibition to pre-I carries the trajectory across the curve of knees , allowing Vpre−I to rapidly increase and inspiration to begin .', 'During the subsequent inspiratory phase , the pre-I unit progresses along the right branch of its uninhibited voltage nullcline as INaP inactivates ( rightmost blue curve , Fig 6A; see also sharp rise in pre-I output in Fig 4 ) , while the post-I and aug-E units become strongly inhibited and jump to corresponding inhibited voltage nullclines at hyperpolarized voltages ( Fig 6C and 6D ) .', 'Finally , once Vpre−I becomes close enough to its synaptic threshold ( black vertical line , Fig 6A ) , the inhibition to post-I and aug-E weakens , allowing both of their nullclines to shift to depolarized voltages .', 'Both units attempt to activate but post-I wins , yielding a transient spike and subsequent hyperpolarization of the aug-E unit and the transition to expiration , which completes the respiratory cycle .', 'Note that the only possible moment in this process when the intrinsic oscillation capability of the pre-I unit could have mattered was at the onset of inspiration , which depends on the cubic shape of the Vpre−I-nullcline .', 'Yet examining similar phase plane representations when the pre-I unit is tuned to be intrinsically tonic shows that even in this tuning , the Vpre−I-nullcline is still cubic at the moment of onset of inspiration and the mechanism underlying the transition to inspiration is the same as in the oscillatory tuning case ( Fig 7A and 7B ) .', 'That is , even though in the absence of inhibition the Vpre−I-nullcline becomes monotonic in this tuning , sufficiently strong inhibition can yield a prolonged quiescent period with enhanced INaP deinactivation , corresponding to a cubic Vpre−I-nullcline .', 'When the inhibition to the pre-I unit starts to decay after a period of strong inhibition during expiration , the deinactivation of INaP can allow the pre-I unit to cross its inhibition-induced knee curve and activate .', 'This mechanism is robust; the Vpre−I-nullcline has a cubic shape , with a corresponding left knee , over a wide range of inhibition levels to the pre-I unit ( dashed blue curve , Fig 7B ) .', 'Not surprisingly , we observed that the phase plane projections for the post-I and aug-E units are qualitatively identical between the two pre-I unit tunings as well .', 'The fact that the same dynamical mechanisms underlie network rhythmicity across parameter tunings explains the insensitivity of output period , phase durations , and amplitude to the switch in intrinsic preBötC dynamics as gnap and c11 are varied ( Fig 5 ) .', 'Similarly , we can expect the changes of the network rhythm properties with variations in other network parameters to be independent of intrinsic preBötC tuning .', 'Although we already explored variations in c11 , we first plotted period ( T ) and inspiratory ( TI ) and expiratory ( TE ) phase durations versus c11 for comparison with effects of other parameter variations ( Fig 8A ) .', 'As seen previously ( Fig 5 ) , there was no abrupt change as the preBötC tuning switched from intrinsically oscillatory to intrinsically tonic .', 'The period T decreased as c11 increased , via a shortening of TE as also observed experimentally with preBötC stimulation ( e . g . , [26] ) , from a maximum of just over 7 seconds to a minimum of about 3 seconds .', 'Next , since the role of inhibition in respiratory rhythmicity has received significant recent attention [8 , 20 , 26–29] , we considered the effects of varying the strength of the inhibition from the post-I to the pre-I unit , b31 .', 'This parameter variation produced similar effects whether the pre-I unit was tuned to be intrinsically oscillatory ( Fig 8B ) or tonic ( Fig 8C ) : increases in b31 produced increases in overall period , largely via increases in TE but with a small accompanying increase in TI , again yielding a range of periods between about 3 and 7 seconds .', 'The stronger maximal inhibition allowed faster deinactivation of INaP , represented by a faster increase in hpre−I , than with weaker inhibition and therefore allowed the pre-I unit to cross its curve of left knees and activate at a larger inhibition level than previously ( dashed black curves , Figs 6B and 7B ) .', 'Nonetheless , the amount of time for inhibition to decay from its larger maximum value enough to allow the trajectory to hit the curve of left knees and initiate inspiration was still longer than the escape time with weaker inhibition , leading to an overall longer TE .', 'The stronger INaP deinactivaton represented by the larger value of hpre−I at the onset of inspiration in this case yielded the small increase in inspiratory duration TI .', 'Similarly , reducing b31 allowed an earlier crossing of the pre-I curve of left knees to initiate inspiration and a shorter TE ( dotted black curve , Figs 6B and 7B ) .', 'After these manipulations of parameters associated with the pre-I unit , we varied the drive levels to the other units in the network , one by one , to analyze their abilities to tune network oscillation frequency .', 'In all three cases , these parameter changes produced qualitatively similar results across both tunings of the pre-I unit ( Fig 9 ) .', 'Increases in the drive to the early-I unit , c12 , caused decreases in network period via decreases in TE .', 'In contrast , increases in c13 ( post-I drive ) and c14 ( aug-E drive ) both increased T , again via changes in TE .', 'Interestingly , the period was much more sensitive to c14 than to c13 ( also consistent with previous modeling [13] ) .', 'This sensitivity emerged because in the baseline tuning , the aug-E unit activation was much more modest than the post-I activation , with the aug-E output much farther from maximal .', 'Thus , changes in drive to aug-E influenced the inhibition level to the pre-I unit more than changes in drive to post-I .', 'Finally , because the baseline period was shorter for the intrinsically tonic than the intrinsically oscillatory pre-I tuning , the range of periods in all cases extended to larger values , producing a wider overall range , for the oscillatory regime .', 'Recent experiments considered perturbations of respiratory rhythms resulting from microinjection of GABAA receptor and glycine receptor antagonists into the preBötC or the BötC of rats to disrupt post-synaptic inhibition [29] .', 'The former manipulation led to a decrease in respiratory period and amplitude , as measured by integrated phrenic nerve activity .', 'In an in situ rat brainstem-spinal cord perfused preparation , sufficient blockade of inhibition to the preBötC completely disrupted the respiratory rhythm .', 'Sufficient blockade of inhibition to the BötC , where the subpopulations of post-I and aug-E inhibitory neurons providing input to preBötC circuits are thought to reside [8 , 20 , 29] , also perturbed respiratory rhythms , in both in vivo and in situ experiments .', 'In contrast to the experiments on the preBötC , however , this manipulation increased respiratory period while decreasing the amplitude of phrenic nerve outputs .', 'In some cases , rhythmic activity was completely suppressed with block of inhibition in the BötC .', 'Responses of our model to reductions in inhibition were similar , but not identical , to the experimental findings .', 'Our results agreed completely with the experimental findings [29] associated with reduction of inhibition to the pre-I and early-I units of the preBötC , both for intrinsically oscillatory and for intrinsically tonically active pre-I tunings .', 'Indeed , in both cases , period was approximately halved and amplitude , measured in terms of inspiratory output , dropped by about 40% ( Fig 10A and 10B ) , quantitatively consistent with the experimental results .', 'As observed in vivo , the drop in period included shortening of both TI and , especially , TE .', 'The reduction in TE was clearly expected based on the lessened ability of the expiratory units to suppress the inspiratory units , while the decrease of TI resulted from the fact that inspiratory onset occurred with less deinactivation of INaP , yielding a shorter time needed for INaP inactivation to occur ( Fig 11 ) .', 'The production of a rhythmic output failed at a higher remaining fraction of inhibition when the pre-I unit was intrinsically tonic than when it was oscillatory , because the pre-I and early-I units became tonically active within the network with less of a loss of inhibition than in the former case .', 'When we decreased inhibition to the post-I and aug-E units , corresponding to experimental perturbations of synaptic inhibition in the BötC , the network did not exhibit an appreciable change in inspiratory output amplitude .', 'When the pre-I unit was intrinsically oscillatory , output period was relatively insensitive to the inhibition level to the BötC within the range over which rhythmicity persisted , although it did increase by about 20% ( Fig 10C ) .', 'With a reduction of inhibition of only about 10% , output rhythmicity was lost .', 'An intrinsically tonic tuning of the pre-I unit provided more robustness to the stronger inhibition from expiratory units that resulted from a decrease in inhibition to the BötC , such that network rhythmicity persisted down to about 65% of normal inhibition levels .', 'Moreover , network period increased by almost 50% over this range of inhibition levels , due to the same effect that was observed to be dominant experimentally , namely an increase in TE , consistent with the mechanism of network rhythmogenesis ( Fig 10D ) .', 'This comparison with experimental results supports the idea that an intrinsically tonic tuning of pre-I neurons may be more consistent with experimental observations than an intrinsically pacemaking tuning , since the tonic tuning provides more robustness against decreased inhibition in the BötC [29] .', 'Recently , a glutamatergic post-inspiratory complex ( PiCo ) including neurons with intrinsic oscillatory capabilities has been identified [21] .', 'As its name suggests , PiCo neurons activate during the post-inspiratory phase .', 'The timing of PiCo activation shifts to inspiration when the inhibition that it normally receives during the I phase is blocked , suggesting that the PiCo receives excitatory inputs from glutamatergic inspiratory neurons .', 'To explore its possible role , we incorporated an intrinsically oscillatory PiCo unit into our model network , sending excitation to the post-I unit , excited by the pre-I unit , and , like the post-I inhibitory unit , inhibited by the early-I and aug-E units .', 'We modeled the PiCo as an intrinsically oscillatory unit [21] , with a voltage equation including the same formulation of INaP used in the pre-I unit and , for simplicity , with the same persistent sodium and leak conductances as the pre-I unit as well .', 'The inclusion of the PiCo did not qualitatively alter network activity patterns: the PiCo remained suppressed by inhibition from early-I during i
['Introduction', 'Results', 'Discussion', 'Methods']
['A central issue in the study of the neural generation of respiratory rhythms is the role of the intrinsic pacemaking capabilities that some respiratory neurons exhibit .', 'The debate on this issue has occurred in parallel to investigations of interactions among respiratory network neurons and how these contribute to respiratory behavior .', 'In this computational study , we demonstrate how these two issues are inextricably linked .', 'We use simulations and dynamical systems analysis to show that once a conditional respiratory pacemaker , which can be tuned across oscillatory and non-oscillatory dynamic regimes in isolation , is embedded into a respiratory network , its dynamics become masked: the network exhibits similar dynamical properties regardless of the conditional pacemaker node’s tuning , and that node’s outputs are dominated by network influences .', 'Furthermore , the outputs of the respiratory central pattern generator as a whole are invariant to these changes of dynamical properties , which ensures flexible and robust performance over a wide dynamic range .']
['Breathing movements in mammals are generated by brainstem respiratory central pattern generator ( CPG ) networks , which incorporate an excitatory oscillator located in the pre-Bötzinger Complex ( preBötC ) that can exhibit autorhythmic behavior .', 'To understand how these autorhythmic properties impact CPG network dynamical performance , we performed computational studies with an established modeling framework to systematically analyze network behavior when the preBötC excitatory neurons’ intrinsic dynamics are tuned to operate in autorhythmic versus non-autorhythmic regimes .', 'Both of these regimes enable rhythmic activity of the CPG network , and we show that the rhythm and its responses to various manipulations are preserved across the tunings of intrinsic properties of the preBötC component .', 'Correspondingly , the emergence of behaviorally appropriate rhythmic patterns of network activity is maintained across preBötC regimes , accompanied by an expansion of the ranges of network output frequencies and amplitudes beyond those attainable with either preBötC regime alone .', 'These results lead to the novel conclusion and concept that the dynamical operation of the CPG is functionally highly robust with respect to the rhythmogenic state of the preBötC excitatory circuits , which could represent a key property for preserved respiratory function across varying conditions and demands on network performance .']
['knees', 'medicine and health sciences', 'legs', 'neural networks', 'population dynamics', 'membrane potential', 'electrophysiology', 'neuroscience', 'systems science', 'mathematics', 'network analysis', 'body limbs', 'population biology', 'neuronal tuning', 'computer and information sciences', 'musculoskeletal system', 'animal cells', 'dynamical systems', 'cellular neuroscience', 'cell biology', 'anatomy', 'physiology', 'neurons', 'biology and life sciences', 'cellular types', 'physical sciences']