The reconstruction of synaptic conductance profiles is based on the current balance equation:(1)CdVmdt=gleak(Eleak−Vm(t))+gi(t)(Ei−Vm(t))+ge(t)(Ee−Vm(t))+Iinj(t)\begin{document}$$\displaystyle C\frac{dV_{m}}{dt}=g_{leak}\left (E_{leak}-V_{m}\left (t\right)\right)+g_{i}\left (t\right)\left (E_{i}-V_{m}\left (t\right)\right)+g_{e}\left (t\right)\left (E_{e}-V_{m}\left (t\right)\right)+I_{inj}\left (t\right)$$\end{document}

where C is the membrane capacitance, Vm\begin{document}$V_{m}$\end{document} is the membrane potential, gleak\begin{document}$g_{leak}$\end{document} and Eleak\begin{document}$E_{leak}$\end{document} are the conductance and the reversal potential of the leak current, respectively, git\begin{document}$g_{i}\left (t\right)$\end{document} and get\begin{document}$g_{e}\left (t\right)$\end{document} are inhibitory and excitatory conductances (subject to retrieval), Ei\begin{document}$E_{i}$\end{document} and Ee\begin{document}$E_{e}$\end{document} are reversal potentials of inhibitory and excitatory synaptic currents, and Iinjt\begin{document}$I_{inj}\left (t\right)$\end{document} is the injected current. We assume that the membrane potential of the cell is in instantaneous equilibrium (dVm/dt=0\begin{document}$dV_{m}/dt=0$\end{document}), which implies that the membrane time constant C/gleak\begin{document}$C/g_{leak}$\end{document} is much shorter than the time scale of the synaptic conductance variations. This assumption defines the time resolution of our method. For example, gleak/C\begin{document}$g_{leak}/C$\end{document} ratio in the respiratory interneurons was found to be in the range of 80–120 pS/pF (Koizumi and Smith, 2008), corresponding to the membrane time constant values of about 10 ms. Synaptic inputs originate from the periodically active network. The respiratory cycle period in our in situ rat brainstem-spinal cord preparation typically spans approximately 3–4 s (Figures 1 and 2), yielding a time resolution of roughly 1/300 of the period. This approach to determining time resolution can be similarly applied to other systems.

Another important assumption is that Equation (1) does not include voltage-dependent currents. This means that the equation is simplified to only consider the passive properties of the membrane, such as resistance and capacitance. To ensure that voltage-dependent currents are minimized during the recording, a hyperpolarizing current injection protocol is employed. This involves injecting a negative current into the neuron, which drives the membrane potential to a more negative value. In our test recordings, the membrane potential was typically held between –100 and –60 mV, and we primarily analyzed the data for these hyperpolarized voltages. At this hyperpolarized state, most voltage-gated ion channels are closed and do not significantly contribute to the neuronal current-voltage (I-V) relationships and affect interpretations of our conductance analyses. We note that there may be hyperpolarization-activated currents in the neurons studied, and in current-clamp recordings, non-linearity from such currents, such as h-currents, could introduce voltage-dependent changes in total conductance unrelated to synaptic inputs, potentially skewing the reconstruction. However, our data, as detailed below, consistently demonstrate linear I-V relationships across the voltage range tested for the set of neurons analyzed, indicating a minimal influence from such voltage-dependent currents.

The phase of the respiratory cycle was defined as a piece-wise linear function of time in the following way: φ(t)=(t−tk)/(tk+1−tk)\begin{document}$\varphi \left (t\right)=\left (t-t_{k}\right)/\left (t_{k+1}-t_{k}\, \right)$\end{document}, for times t\begin{document}$t$\end{document} between the time moments of two consecutive inspiratory phase onsets tk\begin{document}$t_{k}$\end{document} and tk+1\begin{document}$t_{k+1}$\end{document}. Our approach was based on the idea that in a network exhibiting periodic dynamics, the synaptic conductances depend on the cycle phase, so that gi,et=gi,e(φt)\begin{document}$g_{i,e}\left (t\right)=g_{i,e}\left (\varphi \left (t\right)\right)$\end{document}. That is, for a periodic system, specifying that synaptic conductance depends on phase is mathematically equivalent to saying that the conductance depends on time in a periodic manner, and thus, a phase-based representation—where conductances are expressed as functions of the cycle’s phase—is a justified and effective approach for capturing their behavior. The respiratory cycle was divided into 100 bins of phase values, and for each bin, the time moments {tik:φ(tki)∈[φi,φi+1]}\begin{document}$\left \{t_{ik}\colon \, \varphi \left (t_{ki}\right)\in \left [\varphi _{i},\varphi _{i+1}\right ]\right \}$\end{document} that correspond to phases in the bin were collected. For each phase bin i\begin{document}$i$\end{document} of the respiratory cycle, the relationship between the injected current Iinj(tik)\begin{document}$I_{inj}\left (t_{ik}\right)$\end{document} and the membrane potential Vm(tik)\begin{document}$V_{m}\left (t_{ik}\right)$\end{document}, where tk\begin{document}$t_{k}$\end{document} are the times that correspond to the phase bin, appears fairly linear (see Figure 1B, Figure 1—figure supplement 1). Therefore, by linear regression, we can find the slope and V\begin{document}$V$\end{document}-intercept of this dependence in the form:(2)Vm(tk)=V0(φ)+R(φ)⋅Iinj(tk)+δVm(tk)\begin{document}$$\displaystyle V_{m}\left (t_{k}\right)=V_{0}\left (\varphi \right)+R\left (\varphi \right)\cdot I_{inj}\left (t_{k}\right)+\delta V_{m}\left (t_{k}\right)$$\end{document}

where φ=(φi+φi+1)/2\begin{document}$\varphi =\left (\varphi _{i}+\varphi _{i+1}\right)/2$\end{document} is the center of the bin. The slope Rφ\begin{document}$R\left (\varphi \right)$\end{document} represents the total resistance, the intercept V0φ\begin{document}$V_{0}\left (\varphi \right)$\end{document} is the effective resting potential for the phase of the cycle φ\begin{document}$\varphi $\end{document}, and δVm(tk)\begin{document}$\delta V_{m}\left (t_{k}\right)$\end{document} are random fluctuations of the membrane voltage. Total conductance Gφ\begin{document}$G\left (\varphi \right)$\end{document} was calculated as the reciprocal of the total resistance, Gφ=1/Rφ\begin{document}$G\left (\varphi \right)=1/R\left (\varphi \right)$\end{document}. The total conductance has static (phase-independent) and dynamic (phase-dependent) components. The latter is assumed to be a sum of dynamic components of the inhibitory and excitatory synaptic conductances. Synaptic conductances can also have static components whose combination cannot be distinguished from a static conductance of any other nature. Accordingly, we can think of the total conductance as a superposition of inhibitory and excitatory conductances whose static components form a static component of the total conductance, and their dynamic components underlie dynamic changes in the total conductance. Hence, the total current can be thought as a combination of the inhibitory and excitatory currents:(3)G(φ)(Vm−V0(φ))=Gi(φ)(Vm−Ei)+Ge(φ)(Vm−Ee),\begin{document}$$\displaystyle G\left (\varphi \right)\left (V_{m}-V_{0}\left (\varphi \right)\right)=G_{i}\left (\varphi \right)\left (V_{m}-E_{i}\right)+G_{e}\left (\varphi \right)\left (V_{m}-E_{e}\right),$$\end{document}

where Gi(φ)\begin{document}$G_{i}\left (\varphi \right)$\end{document} and Ge(φ)\begin{document}$G_{e}\left (\varphi \right)$\end{document} are inhibitory and excitatory synaptic conductances, and Ei\begin{document}$E_{i}$\end{document} and Ee\begin{document}$E_{e}$\end{document} are corresponding reversal potentials. This equation must be fulfilled for any Vm\begin{document}$V_{m}$\end{document}, therefore,(4)G(φ)=Gi(φ)+Ge(φ),\begin{document}$$\displaystyle G\left (\varphi \right)=G_{i}\left (\varphi \right)+G_{e}\left (\varphi \right),$$\end{document}(5)G(φ)V0(φ)=Gi(φ)Ei+Ge(φ)Ee\begin{document}$$\displaystyle G\left (\varphi \right)V_{0}\left (\varphi \right)=G_{i}\left (\varphi \right)E_{i}+G_{e}\left (\varphi \right)E_{e}$$\end{document}

Solving this system of equations for the synaptic conductances yields(6)Gi(φ)=G(φ)(Ee−V0(φ))/(Ee−Ei),\begin{document}$$\displaystyle G_{i}\left (\varphi \right)=G\left (\varphi \right)\left (E_{e}-V_{0}\left (\varphi \right)\right)/\left (E_{e}-E_{i}\right),$$\end{document}(7)Ge(φ)=G(φ)(V0(φ)−Ei)/(Ee−Ei)\begin{document}$$\displaystyle G_{e}\left (\varphi \right)=G\left (\varphi \right)\left (V_{0}\left (\varphi \right)-E_{i}\right)/\left (E_{e}-E_{i}\right)$$\end{document}

To find the dynamic components of the synaptic conductances ΔGiφ\begin{document}$\mathrm{\Delta }G_{i}\left (\varphi \right)$\end{document} and ΔGeφ\begin{document}$\mathrm{\Delta }G_{e}\left (\varphi \right)$\end{document}, we subtract their minimal values over the respiratory cycle:(8)ΔGi(φ)=Gi(φ)−minφGi(φ),\begin{document}$$\displaystyle \mathrm{\Delta }G_{i}\left (\varphi \right)=G_{i}\left (\varphi \right)-\underset{\varphi }{\min } G_{i}\left (\varphi \right),$$\end{document}(9)ΔGe(φ)=Ge(φ)−minφGe(φ)\begin{document}$$\displaystyle \mathrm{\Delta }G_{e}\left (\varphi \right)=G_{e}\left (\varphi \right)-\underset{\varphi }{\min } G_{e}\left (\varphi \right)$$\end{document}

Finally, we can use the sum of the minimal values found as an estimate for the leak conductance:(10)gleak=minφGi(φ)+minφGe(φ)\begin{document}$$\displaystyle g_{leak}=\underset{\varphi }{\min } G_{i}\left (\varphi \right)+\underset{\varphi }{\min } G_{e}\left (\varphi \right)$$\end{document}

It is possible that during a certain part of the cycle, a neuron receives only one type of synaptic input, inhibitory or excitatory. Below is how this fact can be exploited for obtaining the estimates of reversal potentials for inhibition or excitation. For inhibition, after introducing(11)I0(φ)=−G(φ)V0(φ)\begin{document}$$\displaystyle I_{0}\left (\varphi \right)=-G\left (\varphi \right)V_{0}\left (\varphi \right)$$\end{document}

in (5) and combining (4) and (5), we get:(12)I0(φ)=−EiG(φ)−Ge(φ)(Ee−Ei)\begin{document}$$\displaystyle I_{0}\left (\varphi \right)=-E_{i}G\left (\varphi \right)-G_{e}\left (\varphi \right)\left (E_{e}-E_{i}\right)$$\end{document}

Since the total excitatory synaptic conductance Geφ\begin{document}$G_{e}\left (\varphi \right)$\end{document} is greater or equal to its static component Ge0=minφ⁡Ge(φ)\begin{document}$G_{e}^{0}=\underset{\mathrm{\varphi }}{\min } G_{e}\left (\varphi \right)$\end{document}, from (12) it follows that a straight line on the (G,I0)\begin{document}$\left (G,I_{0}\right)$\end{document}-plane described by(13)I0(φ)=−EiG(φ)−Ge0(Ee−Ei)\begin{document}$$\displaystyle I_{0}\left (\varphi \right)=-E_{i}G\left (\varphi \right)-G_{e}^{0}\left (E_{e}-E_{i}\right)$$\end{document}

serves as an upper boundary of the reconstructed trajectory {(G(φ),I0(φ)),φ∈[0,1]}\begin{document}$\left \{\left (G\left (\varphi \right),I_{0}\left (\varphi \right)\right),\, \varphi \in \left [0,1\right ]\right \}$\end{document}. If we suppose that the neuron receives only phase-dependent inhibition in a certain range of phase, i.e., the excitatory synaptic conductance is equal to its static component in this range, Geφ=Ge0\begin{document}$G_{e}\left (\varphi \right)=G_{e}^{0}$\end{document}, then the trajectory moves strictly along the line described by (13), which can be referred to as a zero excitation line. By identifying the upper portion of the trajectory with nearly linear behavior, we can perform linear regression of this portion to find its slope -Ei\begin{document}$-E_{i}$\end{document}, and thus estimate the reversal potential for inhibition (see Figure 1C). Similarly, for the phases of the cycle where only excitatory input is present, we can derive:(14)I0(φ)=−EeG(φ)+Gi0(Ee−Ei)\begin{document}$$\displaystyle I_{0}\left (\varphi \right)=-E_{e}G\left (\varphi \right)+G_{i}^{0}\left (E_{e}-E_{i}\right)$$\end{document}

where Gi0=minφ⁡Gi(φ)\begin{document}$G_{i}^{0}=\underset{\varphi }{\min } G_{i}\left (\varphi \right)$\end{document} is a static component of the inhibitory conductance and call it the zero inhibition line. The latter obviously serves as a lower boundary of the trajectory. Together, the zero excitation and zero inhibition lines form a wedge that bounds the trajectory, so hereinafter we refer to such plots as wedge diagrams (Figure 1C).

Interestingly, the linear upper boundary of the trajectory was seen in almost all recordings processed, implying that, first, during certain phase(s) of the respiratory cycle, the interneurons indeed receive only inhibitory input, and second, we could use the identified parameters of the zero-excitation line to measure the inhibitory reversal potential. The same approach might be applied for the determination of the reversal potential for excitation if there was a certain range of phases when a cell received the excitatory input only. Since Ε_e is expected to be close to 0 mV, this would be clearly identifiable by the presence of a nearly horizontal part of the curve serving as a lower boundary of the same. This kind of behavior was not found in most of the recordings, so, as commonly accepted, Ee\begin{document}$E_{e}$\end{document} was set to –10 mV in those cases. However, as we demonstrate below, variation of reversal potentials over a wide range of possible values does not affect the shape of synaptic conductance profiles qualitatively.

For our illustration of extracting synaptic conductances with the above approach, we targeted neurons in key interacting respiratory circuits located in discrete bilateral regions of the ventrolateral medulla, specifically in the preBötzinger complex (preBötC) region, which contains local excitatory and inhibitory circuit neurons critical for generating rhythmic inspiratory activity, and the adjacent more rostral Bötzinger complex (BötC) region (refer to Figure 2—figure supplement 1), containing neurons generating rhythmic expiratory activity that interact with preBötC circuits, including by inhibitory circuit connections (e.g. Lindsey et al., 2012; Smith et al., 2013; Molkov et al., 2017; Ausborn et al., 2018). Thus, targeting these regional microcircuits allowed us to test our methods for extracting various patterns of excitatory and inhibitory synaptic inputs in two functionally distinct microcircuits. Also, there are various electrophysiological phenotypes of respiratory neurons with different patterns of neuronal spiking activity during the respiratory cycle in these regions, thus providing a diversity of rhythmic neuronal types to correlate with synaptic input patterns from our analysis, which is useful for illustrating the utility of our techniques for delineating various functional synaptic interactions. We have used sharp microelectrode intracellular recordings in mature rat brainstem-spinal cord preparations in situ (see Materials and methods) for our analysis since this approach allowed us to readily record deep in the brainstem in these targeted regions from multiple neurons under current- and voltage-clamp with a single electrode. This provides complementary information to test the robustness of our approach, which should be insensitive to the mode of intracellular recording. Although our techniques can be applied to any type of rhythmic neuron, we specifically targeted and analyzed interneurons, verified by immunochemistry (as described below and in Material and methods), which are the most technically challenging to record from due to small neuronal sizes and potential recording instability, but are functionally critical for analyzing synaptic mechanisms of neural activity pattern generation. Thus, we could test how our technique performs for important neuronal populations under recording conditions that would likely be encountered for many rhythmic interneuronal circuits in nervous systems.

We have noted above and evaluated uncertainties concerned with synaptic reversal potentials and assumptions about the stability of the cellular properties and recordings on the inferred synaptic conductance profiles, but it is important to elaborate on certain points. We have used an experimental preparation and setup that provides optimal stability for sharp electrode intracellular recordings. We used strict criteria for assessing and accepting the quality and stability of the recordings. For the most part, our analysis results for a given neuron that meets our criteria were reproducible for different recording epochs and conditions. We also generated continuous error estimates for each example shown and confirmed the statistical significance of conductance values. Regarding stationarity, our results suggest that any differences between the inferred conductance profiles for different recording epochs and conditions in most cases were comparable to those between recordings obtained by current- and voltage-clamp protocols.

Most neurons that we have analyzed receive inhibition only during certain parts of the respiratory cycle, regardless of whether they are inspiratory or expiratory neuron types. This allowed retrieving their reversal potentials for inhibition using the approach described in Materials and methods. Interestingly, the inhibitory synaptic reversal potentials retrieved turned out to vary significantly among cells between –62 mv and –116 mV. The reversal potential estimates were in good correspondence with actual reversals of inhibitory events when a cell was hyperpolarized below the reversal potential. Therefore, regarding the analysis, the results were reliable. Nevertheless, on average, reversal potentials were much more negative than what would have been expected. It is well known that in intracellular recordings, the length constant of the neuron and the distance of the microelectrode from the synaptic inputs determine the measured reversal potential (Calvin, 1969; Spruston et al., 1993; Wehr and Zador, 2003). For the precise extraction of inhibitory and excitatory conductances from the total conductance, reversal potential values may be critical. The variability of the inhibitory reversal potential emphasizes the need to determine the reversal potential for each neuron separately. Otherwise, a wrong inhibitory reversible potential value used for the reconstruction may lead to incorrect conductance profiles. For example, a large positive bias in the inhibitory reversal potential will have the effect that a part of the inhibitory conductance may be mislabeled as excitatory conductance and, therefore, show a pattern of concurrent inhibition and excitation. Our method for the estimation of inhibitory reversible potential appeared very reliable when compared to the experimental estimates of the inhibitory reversal potential and essentially excluded the occurrence of this excitatory conductance artifact.

The absolute values of inhibitory and excitatory conductance calculated by the analysis are contaminated with an error depending on the length constant of the neuron and the distance of the microelectrode from the synaptic inputs (Calvin, 1969; Wehr and Zador, 2003). Importantly, Wehr and Zador, 2003 show that the estimate of the timing of synaptic conductances is reliable and not influenced by the length constant of the neuron. Therefore, the conductance profiles extracted with our analysis are qualitatively reliable, and the overall time course of inhibitory and excitatory conductances reflects the overall inhibitory and excitatory inputs to the different electrophysiological classes of active neurons analyzed.

Our analysis revealed different sets of inhibitory and excitatory synaptic conductances that are characteristic of the different populations of respiratory neurons. Indeed, our results suggest that phasic excitatory and inhibitory synaptic inputs that result from network interactions of these respiratory neuron populations shape membrane potential trajectories and spiking patterns of the neurons throughout the respiratory cycle. What can we learn from these results about the organization and operation of the underlying pattern generation networks?

We have suggested circuit motifs that are consistent with the patterns of synaptic inputs to the various neurons, and which also account for our immuno-histochemical identification of inhibitory neurons as subpopulations of most of the electrophysiological types. However, these circuit elements do not explain the overall dynamical operation of the circuits, particularly how the rhythm and the orderly generation of the multiple activity phases occurs. A more comprehensive synthesis of circuit interactions as illustrated below, and ultimately computational simulation studies (e.g. Lindsey et al., 2012; Molkov et al., 2017), are required. In Figure 4—figure supplement 1, we illustrate the construction of a combinatorial circuit schematic of the functional connectivity from the neuronal population interactions suggested by our collection of circuit motifs.

Previously, computational models for core circuits of the respiratory CPG, including interacting microcircuits in the preBötC and BötC regions, have proposed a network organization with respiratory neuron population interactions that are capable from simulation studies with models incorporating circuit architectures (e.g. Figure 4—figure supplement 1B) and neuronal and synaptic biophysical properties to generate a realistic respiratory rhythm and the three-phase rhythmic pattern of neuron and neuronal population activity (Lindsey et al., 2012; Molkov et al., 2017; Rubin et al., 2009; Rybak et al., 2007). These include the model proposed by Smith et al., 2007 based on regional circuit mapping and electrophysiological studies with the mature rat in situ experimental preparation used in the present studies. Despite its plausibility, this and other models remain speculative because the experimental evidence for functional connectivity is mostly indirect.

Our cellular-based analysis provides a way of untangling functional connections within the respiratory CPG and testing computational models. By assuming the origin of these inputs according to the phase in which they occur, we can draw conclusions on the functional connections between the key respiratory neuron populations recorded here. Our synaptic conductance profiles are consistent with multiple features of the network architecture and interactions proposed by Smith et al., 2007 as illustrated in Figure 4—figure supplement 1B, which was suggested to be a minimal and sufficient circuit configuration to explain how the three-phase rhythmic respiratory pattern, including activity patterns of key interneuron populations in the medulla, can be generated. As reconstructed from our synaptic conductance profiles and collection of circuit motifs, there are new features in our more elaborate circuit connectome in the new combinatorial circuit schematic in Figure 4—figure supplement 1A as noted in the supplemental figure legend. There are likely additional connectivity features that remain to be uncovered as the catalogue of intracellular recording data and inferred functional interactions is expanded from further studies. We note that the profiles of neuronal synaptic interactions that we consider are specific for the in situ reduced rat brainstem-spinal cord system, which has proven to be an important model system for understanding the operation of core CPG respiratory circuits in the medulla and pontine reticular formation that are operational in our experimental set-up (Paton et al., 2022), but cannot account for the supra-brainstem and peripheral circuit inputs in the nervous system in vivo (e.g. Lindsey et al., 2012; Smith et al., 2013; Paton et al., 2022). Our objective here was to illustrate how our techniques can delineate the functional circuit interactions in an established core set of circuits in the respiratory CPG as an example of the utility of our approach that can be generally applied to rhythmic neural circuits as discussed below.

Our method for extracting and separating phasic patterns of inhibitory and excitatory synaptic conductances from single neuronal intracellular recordings is broadly applicable to rhythmic circuits, which are ubiquitous in nervous systems. Our approach involves phase-based analysis, where the network activity cycle is divided into activity phases to capture dynamic changes of synaptic input conductances throughout the activity cycle. This approach is relevant for any circuits with repetitive activity cycles, such as rhythmic CPG motor networks (e.g. Calabrese and Marder, 2025) and circuits generating cortical rhythms (Yuste et al., 2005). The method is based on the general mathematical framework presented, involving current balance equations and linear regression to separate excitatory and inhibitory conductances, and therefore is applicable to different rhythmic neuron types and circuits and is suitable for diverse experimental setups. By providing high-resolution temporal profiles of synaptic inputs and outputs (below, based on neuronal spiking patterns), this method enables researchers to infer the functional connectivity and dynamic interactions within any rhythmically active network.

Applying this method, as we have illustrated for respiratory circuits, to other rhythmic networks such as locomotor or cortical circuits, including sensory processing networks, follows a similar process for extracting neuronal excitatory and inhibitory inputs during different oscillatory phases of endogenous or sensory-driven periodic activity. This allows for the inference of functional synaptic input connections for any targeted neuron populations based on the timing and strength of the extracted synaptic inputs. In this context, functional populations are defined as groups of neurons with similar firing patterns with respect to the cycle phase. If the synaptic conductance profile of a recorded neuron contains a component that mirrors the firing pattern of a specific population, it can be inferred that there is a functional connection from that population to the recorded neuron. Similarly, in sensory processing networks, it can reveal how sensory inputs are synaptically integrated in neurons by examining synaptic conductance patterns in response, for example, to repetitive stimuli.

The approach that we have described is versatile since it is compatible with various recording protocols, such as current-clamp and voltage-clamp, and different modes of intracellular recording (sharp electrode or whole-cell patch clamp). We note that our approach to defining functional connectivity does not provide information on the locations of the sources of the synaptic inputs, although we can infer spiking patterns of the source neurons from the temporal features of the synaptic conductance profiles. These profiles represent the total synaptic inputs that can arise from many neurons, possibly with short- and long-range axonal projections to a given neuron. The capability of our approach to read out the total synaptic conductance and separate the excitatory and inhibitory components from all sources at high temporal resolution is a strength of our approach. These inferred neuronal population connections from the electrophysiological analyses provided by our technique can be further mapped and corroborated with other functional and anatomical approaches.

In summary, the versatility of our technique lies in its foundation on basic electrophysiological principles and adaptability to different rhythmic activities, making it a powerful tool for investigating a wide range of rhythmically active neuronal networks and potentially offering insights into their functional organization and dynamic operations.

All animal procedures were approved by the Animal Care and Use Committee of the National Institute of Neurological Disorders and Stroke (Animal Study Proposal #1154–21).

Experiments were performed using the in situ arterially perfused brainstem-spinal cord preparations from mature (3–4-wk-old) rats (Paton, 1996; Paton et al., 2022) following experimental procedures described in detail in Smith et al., 2007 and modified as described below to provide optimal conditions for intracellular recording. Briefly, preheparinized (1000 units, given intraperitoneally) rats (Sprague-Dawley, 45–70 g; male) were anaesthetized deeply with 5% isoflurane, and the portion of the body caudal to the diaphragm was removed. The head and thorax were immersed in ice-chilled carbogenated Ringer solution, and the brain was decerebrated at a precollicular level. The descending aorta, phrenic nerve, central vagus, and hypoglossal nerves were surgically isolated. The dorsal brainstem was exposed by craniotomy and cerebellectomy. To achieve the mechanical stability necessary for intracellular recordings, the great veins and heart were removed. The preparation was transferred to a recording chamber, and the descending aorta was cannulated with a double-lumen catheter for perfusion and recording of perfusion pressure with a pressure transducer. A hydraulic damping Windkessel chamber was used in the perfusion circuit immediately downstream from the output of the roller pump (Watson-Marlow, Wilmington, MA) to eliminate peristaltic flow pulsations that affect the stability of the sharp electrode intracellular recordings.

The perfusate contained the following in distilled water: magnesium sulphate (MgSO4–1.25 mM), potassium phosphate (KH₂PO₄–1.25 mM), potassium chloride (KCl–5.0 mM), sodium bicarbonate (NaHCO₃–25 mM), sodium chloride (NaCl–125 mM), calcium chloride (CaCl₂–2.5 mM), dextrose (10 mM), and polyethylene glycol (0.1785 mM). Vecuronium bromide was added to the perfusate to block neuromuscular transmission (4 µg/ml; SUN Pharmaceutical Industries, Bryan, USA). The perfusate was gassed with 95% O₂-5% CO₂ and maintained at 31 °C. Vasopressin (200–400 pM as required; APP Pharmaceuticals, East Schaumburg, USA) was added to the perfusate to raise and maintain perfusion pressure at 70–80 mmHg. Unless stated, all chemicals were from Sigma.

Efferent activity of the phrenic (PN) and central vagus (VN) nerves was recorded simultaneously with glass suction electrodes and their activities were amplified, filtered (0.3–6.0 KHz), rectified, and integrated (50 ms time constant). Sharp microelectrode somatic intracellular recordings were made in the preBötC and BötC regions. The brainstem was mapped by recording population activity of neurons in the medulla oblongata with an extracellular electrode (5–10 MOhm) prior to intracellular recording. The position of the electrode was monitored by software that kept track of the micromanipulator mechanical coordinates. Once the region of the preBötC or BötC was identified by rhythmic inspiratory/expiratory population activity, coordinates were saved, and in some cases, the brainstem surface was marked with pontamine sky blue dye. Intracellular recordings were made with fine-tipped glass microelectrodes (45–70 MOhm) pulled from borosilicate glass capillaries. The microelectrodes for intracellular recording were driven into the recording site by a combination DC motor-driven micromanipulator with an integrated piezotranslator (PM10-1, Marzhauser Wetzlar, Germany), allowing high stepping speeds for cell penetration. A dual current clamp-voltage clamp amplifier (SEC-05X, NPI, Tamm, Germany) was used to amplify the signals in bridge and discontinuous current clamp (DCC) recording modes. Discontinuous single electrode voltage clamp (SEVC) recordings were obtained by exploiting the high switching frequencies and electrode capacity compensation of the SEC-05X system, allowing high-fidelity SEVC recordings with the high-resistance sharp microelectrodes used. The microelectrodes were filled with a solution of 2 M potassium acetate (KAc) and 0.1 M potassium chloride (KCl), and 4% neurobiotin. During recordings, some neurons were labeled by ionophoresis of neurobiotin into the cell. All recordings were digitized via a CED 1401-plus multi-channel interface and acquired (6–12 kHz digitization rates) using CED Spike 2 software.

Transected brain stem was fixed in 4% buffered (0.1 M phosphate buffer) paraformaldehyde for 24 hr at 4 °C, cryoprotected at 4 °C in 30% sucrose, and subsequently coronally sectioned (30 µm thick) on a freezing microtome. All the floating sections were preincubated for 1 h with 10% donkey serum in PBS and subsequently incubated for 48–72 hr at room temperature with primary antibodies: Rabbit anti-Glycine antibody (1:5000; Immunosolution), rabbit anti-GABA antibody (1:1000; Millipore-Sigma), and goat anti-ChAT antibody (1:500; Chemicon). Labeling for neuronal ChAT expression was used to label motoneurons of the nucleus ambiguous to verify the region where the neurons were recorded and to confirm that the recordings were obtained from non-motoneurons. Floating sections were incubated for 2 hr at room temperature with a mixture of donkey anti-rabbit IgG conjugated with Cy5 and donkey anti-goat IgG conjugated with Cy3 (1:500; Jackson ImmunoResearch). For fluorescence labeling of neurons filled with neurobiotin during electrophysiological recording, slices were incubated with Alexa Fluor 488-Avidin D (1:500, Invitrogen). Tissue was mounted on slides and covered with antifading medium. Confocal images were obtained with a laser-scanning microscope (LSM 510 Meta, Zeiss). Alexa Fluor 488, Cy3, and Texas Red or Cy5 were detected at 488, 543, and 633 nm emission wavelengths, respectively. Images were acquired and processed with the Zeiss Zen software and presented as single optical sections selected from serial optical sections (Z-stacks).