Biophysical mechanisms in the mammalian respiratory oscillator re-examined with a new data-driven computational model

An autorhythmic population of excitatory neurons in the brainstem pre-Bötzinger complex is a critical component of the mammalian respiratory oscillator. Two intrinsic neuronal biophysical mechanisms—a persistent sodium current (INaP) and a calcium-activated non-selective cationic current (ICAN)—were proposed to individually or in combination generate cellular- and circuit-level oscillations, but their roles are debated without resolution. We re-examined these roles in a model of a synaptically connected population of excitatory neurons with ICAN and INaP. This model robustly reproduces experimental data showing that rhythm generation can be independent of ICAN activation, which determines population activity amplitude. This occurs when ICAN is primarily activated by neuronal calcium fluxes driven by synaptic mechanisms. Rhythm depends critically on INaP in a subpopulation forming the rhythmogenic kernel. The model explains how the rhythm and amplitude of respiratory oscillations involve distinct biophysical mechanisms.


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Defining cellular and circuit mechanisms generating the vital rhythm of breathing in mammals 30 remains a fundamental unsolved problem of wide-spread interest in neurophysiology (Richter 31 & Smith, 2014;Del Negro et al., 2018), with potentially far-reaching implications for 32 2 understanding mechanisms of oscillatory circuit activity and rhythmic motor pattern generation 33 in neural systems (Marder & Calabrese, 1996;Buzsaki, 2006;Grillner, 2006;Kiehn, 2006). 34 The brainstem pre-Bötzinger complex (pre-BötC) region (Smith et al., 1991)  From these previous analyses, involvement of two possible cellular-level biophysical 50 mechanisms have been proposed. One based on a slowly inactivating persistent sodium current 51 ( ) (Butera et al., 1999a), and the other on a calcium-activated non-selective cation current 52 ( ) coupled to intracellular calcium ( ) dynamics (for reviews see (Rybak et al., 2014;53 Del Negro et al., 2010), or a combination of both mechanisms (Jasinski et al., 2013). Despite 54 the extensive experimental and theoretical investigations of these sodium-and calcium-based 55 mechanisms, the actual roles of , and the critical source(s) of transients in the 56 pre-BötC are still unresolved. Furthermore, in pre-BötC circuits the process of rhythm 57 generation must be associated with an amplitude of circuit activity sufficient to drive 58 downstream circuits to produce adequate inspiratory motor output. Biophysical mechanisms 59 involved in generating the amplitude of pre-BötC circuit activity have also not been 60 established. 61 is proposed to mediate an essential oscillatory burst-generating mechanism since 62 pharmacologically inhibiting abolishes intrinsic neuronal rhythmic bursting as well as 63 pre-BötC circuit inspiratory activity and rhythmic inspiratory motor output in vitro. Theoretical 64 models of cellular and circuit activity based on -dependent bursting mechanisms closely 3 reproduce experimental observations such as voltage-dependent frequency control, spike-66 frequency adaptation during bursts, and pattern formation of inspiratory motor output (Butera 67 et al., 1999b;Pierrefiche et al., 2004;Smith et al., 2007). This indicates the plausibility of -68 dependent rhythm generation. 69 In the pre-BötC, was originally postulated to underlie intrinsic pacemaker-like 70 oscillatory bursting at the cellular level and contribute to circuit-level rhythm generation, since 71 intrinsic bursting in a subset of neurons in vitro was found to be terminated by the inhibitor 72 flufenamic acid (FFA) . Furthermore, inhibition of in the pre-BötC 73 reduces the amplitude of the rhythmic depolarization (inspiratory drive potential) driving 74 neuronal bursting and can eliminate inspiratory motor activity in vitro (Pace et al., 2007). propagated to the soma (Mironov 2008  , and the Na + /K + pump (Jasinski et al., 2013). Surprisingly, 94 pharmacological inhibition of /TRPM4 has recently been shown to produce large 95 reductions in the amplitude of pre-BötC inspiratory neuron population activity without 96 significant perturbations of inspiratory rhythm (Koizumi et al., 2018 (Koizumi et al., 2018) has demonstrated that pharmacological 122 inhibition of /TRPM4 in the pre-BötC in slices from in vitro neonatal mouse/rat slice 123 preparations, strongly reduces the amplitude of (or completely eliminates) the inspiratory 124 hypoglossal (XII) motor output, as well as the amplitude of pre-BötC excitatory circuit activity 125 that is highly correlated with the decline of XII activity, while having little effect on inspiratory 126 burst frequency. Here, we systematically examine the relationship between conductance 127 ( ̅ ) on amplitude and frequency of circuit activity for voltage-gated ( ) and synaptically 128 activated sources ( ) of intracellular calcium. We found that that reduction of ̅ drives 129 opposing effects on circuit activity amplitude and frequency that are dependent on the source 130 of intracellular calcium transients (Fig. 1). In the network, where calcium influx is 131 5 generated exclusively from voltage-gated calcium channels, increasing ̅ has no effect on 132 amplitude but increases the frequency of network oscillations (Fig. 1A, C, D). Conversely, in 133 the network where calcium influx is generated exclusively by excitatory synaptic input, 134 increasing ̅ strongly increases the amplitude and slightly decreases the oscillation 135 frequency (Fig. 1B, C

Effects of Subthreshold Activation of on Network Frequency 146
In -dependent bursting neurons in the pre-BötC, bursting frequency depends on their 147 6 excitability (i.e., baseline membrane potential) which can be controlled in different ways, e.g. 148 by directly injecting a depolarizing current (Smith et al., 1991) or varying the conductance 149 and/or reversal potentials of some ionic channels (Butera et al., 1999a). Due to their relatively 150 short duty cycle, the bursting frequency in these neurons is largely determined by the interburst 151 interval, defined as the time between the end of one burst and the start of the next. During the 152 burst, slowly inactivates resulting in burst termination and abrupt hyperpolarization of the 153 membrane. The interburst interval is then determined by the amount of time required for 154 to recover from inactivation and return the membrane potential back to the threshold for burst 155 initiation. This process is governed by the kinetics of inactivation gating variable ℎ . 156 Higher neuronal excitability reduces the value of ℎ required to initiate bursting. 157 Consequently, the time required to reach this value is decreased, which results in a shorter 158 interburst interval and increased frequency. 159 To understand how changing ̅ affects network bursting frequency we quantified 160 the values of ℎ averaged over all pacemaker neurons immediately preceding each network 161 burst and, also, the average values between the bursts in the and networks ( Fig.  162 2). In the network, as modeled remains residually activated between the bursts thus 163 creating the background calcium concentration which partially activates . Therefore, 164 between the bursts functions as a depolarizing leak current. Consistently, we found that 165 in the network increasing ̅ increases ( Fig. 2A) progressively depolarizing the 166 network, which reduces the ℎ threshold for burst initiation (Fig. 2B) and, thus, increases 167 network frequency (Fig. 1D). 168 In the model the intracellular calcium depletes entirely during the interburst 169 interval. Consequently, increasing ̅ has no effect on ( Fig

Robustness of Amplitude and Frequency Effects 243
We also examined if the effects are conserved in both the and networks over 244 a range of network parameters. To test this, we investigated the dependence of network activity 245 amplitude and frequency on ̅ and average synaptic weight for and networks 246 with high ( 1) and low ( 0.05) connection probabilities, and high ( 247 0.1 , 0.1), medium ( 0.01 , 0.01) and low ( 0.001 , 248 0.005) strengths of calcium sources (Figures 5 and 6). We found that changing the synaptic 249 connection probability and changing the strength of the calcium sources has no effect on the To summarize, in the model, increasing ̅ increases frequency, through 256 increased excitability but has no effect on amplitude. In contrast, in the model, 257 increasing ̅ slightly decreases frequency and increases amplitude. In this case, increasing 258 ̅ acts as a mechanism to increase the inspiratory drive potential and recruit previously 259 If the calcium influx is exclusively voltage-gated, our model predicts that blockade will 287 14 have no effect on amplitude but reduce the frequency. In contrast, if the calcium source is 288 exclusively synaptically gated, our model predicts that blocking will strongly reduce the 289 amplitude and slightly increase the frequency. Therefore, a multi-fold decrease in amplitude, 290 seen experimentally, is consistent with the synaptically driven calcium influx mechanisms, 291 while constant bursting frequency may be due to calcium influx through both voltage-and 292 synaptically gated channels. Following predictions above, to reproduce experimental data, we 293 incorporated both mechanisms in the model and inferred their individual contributions by 294 finding the best fit. We found that the best match is observed (Fig. 7) if synaptically mediated 295 and voltage gated calcium influxes comprise about 95% and 5% of the total calcium influx,  We investigated the sensitivity of intrinsic bursting in our model to and calcium channel 316 blockade (Fig. 8). Intrinsic bursting was identified in neurons by zeroing the synaptic weights 317 to simulate synaptic blockade. and blockade was simulated by setting ̄ and ̄ 318 to 0. We found that after decoupling the network ( 0) a subset of neurons remained 319 rhythmically active (7%) and that these were all neurons with a high conductance. In these 320 rhythmically active neurons, bursting was abolished in all neurons by blockade. Our simulations have shown that the primary role of is amplitude but not oscillation 341 frequency modulation with little or no effect on network activity frequency. Here we examined 342 the neurons that remain active and maintain rhythm after blockade (Fig. 9). We found that 343 the neurons that remain active are primarily neurons with the highest ̅ and that bursting in 344 these neurons is dependent on . Some variability exists and neurons with relatively low 345 ̅ value can remain active due to synaptic interactions while a neuron with a slightly higher 346 are correlated with circuit activity as a whole, as the experimental data suggest. We compared 364 the network activity characterized by the average intracellular calcium concentration and the 365 network firing. We found that for a single network burst, the average intracellular calcium 366 concentration and network firing are highly correlated (Fig. 10A). 367 We also compared intracellular calcium transients and spiking frequency in individual 368 pacemaker and follower neurons (Fig. 10B) We examined the relationship between connection probability and the change in during 394 simulated blockade (Fig. 11). We found that the has no effect on the relationship 395 between amplitude, frequency or calcium transients at the network level provided that the 396 synaptic strength remains constant ( • • ) (Fig. 11A, B). Additionally, 397 regardless of , the network activity amplitude and average intracellular calcium 398 concentration are highly correlated.
does however affects the change in the peak in 399 individual neurons. In a network with a high connection probability ( 1) the synaptic 400 current/calcium transient is nearly identical for all neurons and therefore the change in 401 during blockade is approximately the same for each neuron (Fig. 11C). In a sparsely 402 connected network the synaptic current and calcium influx are more variable and reflect the 403 heterogeneity in spiking frequency of the pre-synaptic neurons (Fig. 11D). Interestingly, in a 404 network with low connection probability ( 0.1), the peak transient in some 405 neurons increases when is blocked (Fig. 11E). pre-BötC neurons are experimentally supported (Mironov, 2008;Pace et al., 2007), however 489 the mechanism of burst termination remains unclear. Again, the computational group-490 pacemaker models that have been explored ) rely on as yet unproven 491 mechanisms for burst termination, and in some cases lack key biophysical features of the pre-492 BötC neurons such as voltage-dependent frequency control and expression of . 493 In our model, we showed that blockade of either or synaptic interactions produce 494 qualitatively equivalent effects on network population activity amplitude and frequency when 495 the calcium transients are primarily generated from synaptic sources (Fig.4). Consequently, our 496 model predicts that blockade of or synaptic interactions in the isolated pre-BötC in vitro 497 will produce comparable effects on amplitude and frequency. This is the case as Johnson et al. 498 (1994) showed that gradual blockade of synaptic interactions by low calcium solution 499 significantly decreases network activity amplitude while having little effect of frequency, 500 similar to the experiments where the channel TRPM4 is blocked with 9-phenanthrol 501 (Koizumi et al., 2018). 502 Overall, our new model simulations for the isolated pre-BötC excitatory network 503 suggest that the role of /TRPM4 activation is to amplify excitatory synaptic drive in 504 generating the amplitude of inspiratory population activity, independent of the biophysical 505 mechanism generating inspiratory rhythm. We note that the recent experiments have also 506 shown that in the more intact brainstem respiratory network that ordinarily generates patterns 507 of inspiratory and expiratory activity, endogenous activation of /TRPM4 appears to 508 augment the amplitude of both inspiratory and expiratory population activity, and hence these 509 channels are fundamentally involved in inspiratory-expiratory pattern formation (Koizumi et 510 al., 2018). 511 512

Calcium Transients as Correlates of Activity 513
Neuronal calcium transients can arise from voltage-gated calcium sources, driven by 514 action potentials, and serve as correlates of neuronal activity. We analyzed the correlation 515 between calcium transients and inspiratory activity of individual inspiratory neurons as well as 516 the entire network, particularly since dynamic calcium imaging has been utilized to assess 517 24 activity of individual and populations of pre-BötC excitatory neurons in vitro during 518 pharmacological inhibition of /TRPM4 (Koizumi et al., 2018). In our model, most of the 519 calcium influx is synaptically-triggered and may occur within a given neuron in the absence of 520 action potentials. We show that intracellular calcium transients are highly correlated with 521 network and cellular activity. This is true across individual neuron bursts and when comparing 522 changes in peak values of neuronal firing and intracellular calcium transients across the 523 duration of an blockade simulation. The correlation at the onset of bursting in pacemaker 524 neurons are an exception. In these neurons, the correlations between the intracellular calcium 525 concentration and the instantaneous firing rate across a single burst are not apparent at the onset 526 of this burst. This is because pacemaker neurons start spiking before the rest of the network, 527 which precedes synaptically triggered calcium influx. 528 Additionally, we examined the relative change in the peak calcium transients in single 529 neurons as a function of conductance. We show that in a subset of neurons the peak 530 calcium transient increases with reduced . This result is surprising but is supported by the 531 recent calcium imaging data (Koizumi et al., 2018). This occurs in neurons that receive most 532 of their synaptic input from pacemaker neurons and our analyses suggest this is possible in 533 sparse networks, i.e. with relatively low connection probability. In pacemaker neurons, 534 blockade leads to a reduction of their excitability resulting in an increased value of 535 inactivation gating variable at the burst onset. Thus, during the burst, the peak action potential 536 frequency and the synaptic output from these neurons is increased with blockade. 537 Consequently, neurons that receive synaptic input from pacemaker neurons will see an increase 538 in their peak calcium transients. In most neurons, however, synaptic input is received primarily 539 from follower neurons. Since blockade de-recruits follower neurons, the synaptic input 540 and subsequent calcium influx in most decreases. Therefore, our model predicts that in a sparse 541 network, blocking results in very diverse responses at the cellular level with overall 542 tendency to reduce intracellular calcium transients such that the amplitude of these transients 543 averaged over the entire population decreases during blockade while their frequency is 544 unchanged. This is consistent with the experimental calcium imaging data (Koizumi et  Metabotropic glutamate receptors (mGluR) indirectly activate ion channels through G-576 protein mediated signaling cascades. Group 1 mGluRs which include mGluR1 and mGluR5 577 are typically located on post-synaptic terminals (Shigemoto et al., 1997) and activation of group 578 1 mGluRs is commonly associated with calcium influx through calcium permeable channels 579 (Berg et al., 2007;Endoh, 2004;Mironov, 2008) and calcium release from intracellular calcium 580 stores (Pace et al., 2007). 581 In the pre-BötC, mGluR1/5 are thought to contribute to calcium influx by triggering the 582 release of calcium from intracellular stores (Pace et al., 2007) and/or the activation of the 583 transient receptor potential C3 (TRPC3) channel (Ben-Mabrouk & Tryba, 2010). Blockade of 584 mGluR1/5 reduces the inspiratory drive potential in pre-BötC neurons and reduces XII motor 585 output (Pace et al., 2007) which is consistent with the effects of /TRPM4 blockade (Pace 586 et al., 2007). TRPC3 is a calcium permeable channel (Thebault et al., 2005) that is associated 587 with calcium signaling (Hartmann et al., 2011), store-operated calcium entry (Kwan et al., 588 2004), and synaptic transmission (Hartmann et al., 2011). TRPC3 is activated by diacylglycerol 589 (DAG) (Clapham, 2003) which is formed after synaptic activation of mGluR1/5. TRPC3 is 590 highly expressed in the pre-BötC and was hypothesized to underlie activation in the pre-591 BötC In the pre-BötC, the effect of TRPC3 blockade by 3-pyrazole on network amplitude is 598 remarkably similar to blockade of TRPM4 (Koizumi et al., 2018). This suggests that the 599 /TRPM4 activation may be dependent on/coupled to TRPC3. A possible explanation is 600 that TRPC3 mediates synaptically-triggered calcium entry. It is also likely that TRPC3 plays a 601 role in maintaining background calcium concentration levels. We tested this hypothesis by 602 simulating the blockade of synaptically-triggered calcium influx while simultaneously 603 lowering the background calcium concentration (Fig. 12). These simulations generated large 604 reductions in activity amplitude with no effect on frequency which are consistent with data 605 from experiments where TRPC3 is blocked using 3-pyrazole (Koizumi et al., 2018). This 606 indirectly suggests that TRPC3 is critical for synaptically-triggered calcium entry and 607 subsequent activation. Biophysical mechanisms generating rhythmic burstlets and the large amplitude inspiratory 654 population bursts in the burstlet theory are unknown. We have identified a major Ca 2+ -655 dependent conductance mechanism for inspiratory burst amplitude (pattern) generation and 656 show theoretically how this mechanism may be coupled to excitatory synaptic interactions and 657 is independent of the rhythm-generating mechanism. We also note that a basic property of 658 is its ability to generate subthreshold oscillations and promote burst synchronization (Butera et 659 al., 1999b;Bacak et al., 2016). However, in contrast to our proposal for the mechanisms 660 operating in the kernel rhythm-generating subpopulation, with its favorable voltage-661 dependent and kinetic autorhythmic properties-is not proposed to be a basic biophysical 662 mechanism for rhythm generation in the burstlet theory (Del Negro et al., 2018). 663 We emphasize that the above discussions regarding the role of pertain to the 664 isolated pre-BötC including in more mature rodent experimental preparations in situ where 665 29 inspiratory rhythm generation has also been shown to be dependent on (Smith et al., 2007). 666 The analysis is more complex when the pre-BötC is embedded within interacting respiratory 667 circuits in the  700   where  is the membrane capacitance,  , ,  ,  ,  ,  and  are ionic  701 currents through sodium, potassium, leak, persistent sodium, calcium activated non-selective 702 cation, voltage-gated calcium, and synaptic channels, respectively. Description of these 703 currents, synaptic interactions, and parameter values are taken from (Jasinski et al., 2013 corresponding parameter values, were derived from previous models (see (Jasinski et