Inference technique for the synaptic conductances in rhythmically active networks and application to respiratory central pattern generation circuits

Reviewer #1 (Public review):

Summary:

The paper develops a phase method to obtain the excitatory and inhibitory afferents to certain neuron populations in the brainstem. The inferred contributions are then compared to the results of voltage clamp and current clamp experiments measuring the synaptic contributions to post-I, aug-E, and ramp-I neurons.

Strengths:

The electrophysiology part of the paper is sound and reports novel features with respect to earlier work by JC Smith et al 2012, Paton et al 2022 (and others) who have mapped circuits of the respiratory central pattern generator. Measurements on ramp-I neurons, late-I neurons, and two types of post-I neurons in Figure 2 besides measurements of synaptic inputs to these neurons in Figure 5 are to my knowledge new.

Weaknesses:

The phase method for inferring synaptic conductances fails to convince. The method rests on many layers of assumptions and the inferred connections in Figure 4 remain speculative. To be convincing, such a method ought to be tested first on a model CPG with known connectivity to assess how good it is at inferring known connections back from the analysis of spatio-temporal oscillations. For biological data, once the network connectivity has been inferred as claimed, the straightforward validation is to reconstruct the experimental oscillations (Figure 2) noting that Rybak et al (Rybak, Paton Schwaber J. Neurophysiol. 77, 1994 (1997)) have already derived models for the respiratory neurons.

The transformation from time to phase space, unlike in the Kuramoto model, is not justified here (Line 94) and is wrong. The underpinning idea that "the synaptic conductances depend on the cycle phase and not on time explicitly" is flawed because synapses have characteristic decay times and delays to response which remain fixed when the period of network oscillations increases. Synaptic properties depend on time and not on phase in the network. One major consequence relevant to the present identification of excitatory or inhibitory behaviour, is that it cannot account for change in the behaviour of inhibitory synapses - from inhibitory to excitatory action - when the inhibitory decay time becomes commensurable to the period of network oscillations (Wang & Buzsaki Journal of Neuroscience 16, 6402 (1996), van Vreeswijk et al. J. Comp. Neuroscience 1,313 (1994), Borgers and Kopell Neural Comput. 15, 2003). In addition, even small delays in the inhibitory synapse response relative to the pre-synaptic action potential also produce in-phase synchronization (Chauhan et al., Sci. Rep. 8, 11431 (2018); Borgers and Kopell, Neural Comput. 15, 509 (2003)). The present assumptions are way too simplistic because you cannot account for these commensurability effects with a single parameter like the network phase. There is therefore little confidence that this model can reliably distinguish excitatory from inhibitory synapses when their dynamic properties are not properly taken into account.

Line 82, Equation 1 makes extremely crude assumptions that the displacement current (CdV/dt) is negligible and that the ion channel currents are all negligible. Vm(t) is also not defined. The assumption that the activation/inactivation times of all ion channels are small compared to the 10-20ms decay time of synaptic currents is not true in general. Same for the displacement current. The leak conductance is typically g~0.05-0.09ms/cm^2 while C~1uF/cm^2. Therefore the ratio C/g leak is in the 10-20ms range - the same as the typical docking neurotransmitter time in synapses.

Models of brainstem CPG circuits have been known to exist for decades: JC Smith et al 2012, Paton et al 2022, Bellingham Clin. Exp. Pharm. And Physiol. 25, 847 (1998); Rubin et al., J. Neurophysiol. 101, 2146 (2009) among others. The present paper does not discuss existing knowledge on respiratory networks and gives the impression of reinventing the wheel from scratch. How will this paper add to existing knowledge?

Reviewer #2 (Public review):

Summary:

By measuring intracellular changes in membrane voltage from a single neuron of the medulla the authors describe a method for determining the balance of excitatory and inhibitory synaptic drive onto a single neuron within this important brain region.

Strengths:

This approach could be valuable in describing the microcircuits that generate rhythms within this respiratory control centre. This method could more generally be used to enable microcircuits to be studied without the need for time-consuming anatomical tracing or other more involved electrophysiological techniques.

Weaknesses:

This approach involves assuming the reversal potential that is associated with the different permeant ions that underlie the excitation and inhibition as well as the application of Ohms law to estimate the contribution of excitation and inhibitory conductance. My first concern is that this approach relies on a linear I-V relationship between the measured voltage and the estimated reversal potential. However, open rectification is a feature of any I-V relationship generated by asymmetric distributions of ions (see the GHK current equation) and will therefore be a particular issue for the inhibition resulting from asymmetrical Cl- ion gradients across GABA-A receptors. The mixed cation conductance that underlies most synaptic excitation will also generate a non-linear I-V relationship due to the inward rectification associated with the polyamine block of AMPA receptors. Could the authors please speculate what impact these non-linearities could have on results obtained using their approach?

This approach has similarities to earlier studies undertaken in the visual cortex that estimated the excitatory and inhibitory synaptic conductance changes that contributed to membrane voltage changes during receptive field stimulation. However, these approaches also involved the recording of transmembrane current changes during visual stimulation that were undertaken in voltage-clamp at various command voltages to estimate the underlying conductance changes. Molkov et al have attempted to essentially deconvolve the underlying conductance changes without this information and I am concerned that this simply may not be possible. The current balance equation (1) cited in this study is based on the parallel conductance model developed by Hodgkin & Huxley. However, one key element of the HH equations is the inclusion of an estimate of the capacitive current generated due to the change in voltage across the membrane capacitance. I would always consider this to be the most important motivation for the development of the voltage-clamp technique in the 1930's. Indeed, without subtraction of the membrane capacitance, it is not possible to isolate the transmembrane current in the way that previous studies have done. In the current study, I feel it is important that the voltage change due to capacitive currents is taken into consideration in some way before the contribution of the underlying conductance changes are inferred.

Studies using acute slicing preparations to examine circuit effects have often been limited to the study of small microcircuits - especially feedforward and feedback interneuron circuits. It is widely accepted that any information gained from this approach will always be compromised by the absence of patterned afferent input from outside the brain region being studied. In this study, descending control from the Pons and the neocortex will not be contributing much to the synaptic drive and ascending information from respiratory muscles will also be absent completely. This may not have been such a major concern if this study was limited to demonstrating the feasibility of a methodological approach. However, this limitation does need to be considered when using an approach of this type to speculate on the prevalence of specific circuit motifs within the medulla (Figure 4). Therefore, I would argue that some discussion of this limitation should be included in this manuscript.