Neurons come in a variety of shapes and sizes, which impacts their ability to get excited. A common electrophysiological test of neuronal excitability is the measurement of input resistance. Input resistance is assessed by somatic current injection and serves to predict how easily neurons depolarize in response to synaptic current. Lower-resistance neurons are considered less excitable since larger synaptic currents are required to depolarize from rest to threshold, following Ohm’s law (voltage=current×resistance). Since measurements are performed at resting potentials, the primary determinant of conductance reporting input resistance is assumed to be membrane leak channels, although voltage-dependent channels and synaptic noise can also contribute to input resistance (Morales et al., 1987; Paré et al., 1998; Picton et al., 2018; Yuan et al., 2005).

In addition to electrical or chemical synaptic excitation, mixed electrical-chemical synapses form gap junctions and release glutamate to recruit neurons (Nagy et al., 2019). Gap junctions provide a rapid, reliable source of depolarizing current and can enhance glutamate release at co-active mixed synapses (Alcamí and Pereda, 2019; Connors, 2017). While higher-density electrical synapses would more easily excite target neurons, at resting potentials gap junctions also provide a source of leak that decreases input resistance and creates parallel paths for current spread (Marder et al., 2017). In addition, since electrophysiological assessments of connectivity often rely on spike-triggered averages to reveal postsynaptic potentials (Mendell and Henneman, 1968), it could be challenging to disentangle the contribution of monosynaptic currents from coupling potentials propagating indirectly through electrical synapses (García-Pérez et al., 2004; Korn et al., 1973). Consequently, the existence of mixed synapses has the potential to not only confound electrophysiological assessments of neuronal excitability, but also connectivity.

Here, we have explored this possibility within the spinal locomotor circuitry of larval zebrafish. Mixed synapses formed by reticulospinal and propriospinal interneurons provide sources of excitation during locomotion in larval zebrafish (Bhatt et al., 2007; Kimura et al., 2006; McLean et al., 2008; Menelaou and McLean, 2019; Pujala and Koyama, 2019; Wang and McLean, 2014). They also appear early in zebrafish embryos (Miller et al., 2015; Saint-Amant and Drapeau, 2001) and persist into adulthood (Pallucchi et al., 2022; Song et al., 2016). Thus, it is likely that gap junctions in mixed synapses impact electrophysiological assessments in zebrafish of all ages.

Our previous studies of spinal motor neurons in larval zebrafish have identified slow, intermediate, and fast motor units recruited during faster swimming in order of size and input resistance (Bello-Rojas et al., 2019; McLean et al., 2007; Menelaou and McLean, 2012). This observation in fish is consistent with the ‘size principle’ originally formulated in felines (Henneman et al., 1965) and more recently observed in flies (Azevedo et al., 2020). In this scenario, larger neurons are less excitable at rest due to a greater number of membrane leak channels. However, among populations of premotor spinal interneurons that regulate motor neuron recruitment, the relationship between size, input resistance, and recruitment order is more complicated. For instance, soma size (McLean et al., 2007) and input resistance (Menelaou and McLean, 2019) are not always predictive of interneuron recruitment order, ‘violating’ the biophysical predictions of the size principle.

Mixed synapses could explain these discrepancies, assuming input resistance measures reflect not only interneuron size but also the specificity and density of gap junctions. To test this idea, we explored potential links between size, excitability, and connectivity among molecularly defined premotor excitatory and inhibitory interneurons that coordinate the head-tail propagation and left-right alternation of cyclical body bends during swimming at different speeds (Figure 1a and b). The data set included unpublished recordings (n=46) and new analysis of published recordings from excitatory chx10-labeled V2a interneurons (Menelaou and McLean, 2019), and inhibitory dbx1-labeled V0d interneurons (Menelaou and McLean, 2019) and dmrt3a-labeled dI6 interneurons (Kishore et al., 2020).

Figure 1

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Analysis of two distinct morphological classes of excitatory V2a neurons with either descending (V2a-D) or bifurcating (V2a-B) axon trajectories revealed largely overlapping sizes, but distinct input resistance values (Figure 1c and d, left). For inhibitory dI6 and V0d interneurons the opposite was true—neurons had largely overlapping input resistances, but distinct sizes (Figure 1d, middle). Within V2a subtypes, we found no significant relationship between size and input resistance, although lower resistance V2a-B neurons were largest (Figure 1d, left). As a result, combining the two subtypes generated a significant relationship within the V2a population (ρ₍₂₄₈₎=–0.61, p<0.001, n=250), albeit a weaker one compared to motor neurons (Figure 1d, right). For dI6 neurons, there was an even weaker correlation and no significant correlation for V0d neurons (Figure 1d, middle). These observations suggest size and membrane leak channels are not the exclusive arbiters of input resistance among interneurons.

Next, if mixed synapses were contributing to measurements of input resistance, we would expect lower membrane time constants in lower resistance neurons (Getting, 1974). Theoretically, increases in size should not impact time constants, following τ=resistance×capacitance, however gap junctions can provide higher density leak conductances that impact membrane resistance more than capacitance. Consistent with this idea, membrane time constants were significantly correlated with input resistance within and between interneuron populations, reaching 25 ms in the highest resistance neurons (Figure 1e, left, middle). The same relationship is observed in motor neurons one synapse downstream (Wang and McLean, 2014), however, values never exceeded 5 ms (Figure 1e, right). Thus, membrane time constants better predict input resistance than soma size for motor neurons and interneurons, consistent with the idea that mixed synapse density is contributing to measurements of resting excitability.

To further test this idea, we examined cyclical excitatory drive during ‘fictive’ escape swimming in response to a brief electrical stimulus (Figure 1f), which includes mixed inputs from reticulospinal and propriospinal sources (Menelaou and McLean, 2019; Pujala and Koyama, 2019; Wang and McLean, 2014). As expected from components of swimming locomotor circuitry, all interneuron populations received oscillatory excitatory drive at a range of cyclical swimming frequencies (Figure 1h–j). Peaks in maximum oscillatory drive could occur at different frequencies among higher resistance interneurons—for example, at lower frequencies that occur near the end of the swim episode for V2a neurons (Figure 1h, top) or at higher frequencies near the beginning for V0d neurons (Figure 1j, top). This is consistent with differences in synaptic-specificity, rather than input resistance, dictating interneuron recruitment probability at different frequencies (Ampatzis et al., 2014).

Within and between interneuron populations, the lowest resistance neurons received the largest amount of excitatory current (Figure 1g). Analysis of V2a neurons revealed a significant correlation in bifurcating and morphologically unidentified V2a neurons that was not apparent in descending V2a neurons (Figure 1g, left). Similarly, there was a significant correlation in V0d neurons that was not observed in dI6 neurons (Figure 1g, middle). Notably, V0d neurons are recruited more reliably at higher frequencies compared to dI6 neurons, which operate over a broader frequency range (Kishore et al., 2020; Satou et al., 2020). Pooled excitatory and inhibitory interneuron analysis closely resembled the relationship between excitatory drive and input resistance observed in motor neurons (Kishore et al., 2014), where peak levels are higher commensurate with larger sizes (Figure 1g, right). These data suggest that higher-density mixed synapses to spinal neurons recruited preferentially during high frequency escape swimming contribute to lower input resistances.

To test this idea more directly, we performed a series of analyses on previous recordings of synaptic connectivity originating from V2a neurons recruited specifically at high swimming frequencies (Menelaou and McLean, 2019). We have previously shown that larger, lower resistance bifurcating V2a neurons form predominantly mixed synapses with interneurons and motor neurons, characterized by an early electrical component and a later glutamatergic component (Figure 2a), which are sensitive to the AMPA receptor blocker NBQX and the gap junction blocker 18-β-glycyrrhetinic acid (18-βGA), respectively (Menelaou and McLean, 2019). Higher resistance descending V2a neurons target the same neurons, but use predominantly glutamatergic synapses (Figure 1b), characterized by a faster, larger NBQX-sensitive component and a slower, lower amplitude 18-βGA-sensitive component most obvious during failures (Menelaou and McLean, 2019).

Figure 2

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If mixed synapses are contributing to input resistance, we would expect larger PSPs in lower resistance neurons. On the other hand, if membrane leak channels are the primary determinant of shunt, we would expect smaller PSPs. When we plotted the amplitude of the electrical component of mixed synapses against input resistance, we found a significant negative correlation—larger amplitude electrical excitatory postsynaptic potentials (eEPSPs) are observed in lower resistance neurons (Figure 2c and d). Higher-density eEPSPs to lower resistance neurons were also reflected in the ‘Ohmic’ current calculated using V=IR (Figure 2e), with individual values exceeding 100 pA. In addition, larger amplitude eEPSPs were linked to lower failure rates of the chemical component (Figure 2f). This is consistent with enhanced synchronous chemical excitation by depolarization spreading through the gap junctions of co-active mixed synapses (Liu et al., 2020; Pereda et al., 2004; Song et al., 2016). No link to failure rates was observed for purely chemical EPSPs (cEPSPs), despite a similar range of amplitudes (Figure 2g).

Next, we took advantage of the fact that descending V2a neurons can target the same interneurons and motor neurons with purely glutamatergic synapses to see if excitation from chemical EPSPs would be weaker in lower resistance neurons at rest, per the biophysical predictions of Ohm’s law. Consistent with previous studies (Burke, 1968; Mendell and Henneman, 1971), the amplitude of chemical EPSPs was positively correlated with input resistance (Figure 2h), giving the impression that lower resistance neurons are less excitable, despite increases in Ohmic current up to 100 pA that could accommodate for decreased excitability (Figure 2i). We also observed a positive correlation between chemical EPSP decay time constant and input resistance (Figure 2j), as expected if mixed synapses are contributing to resistance measures and impacting integrative properties.

Thus far, the data suggest that gap junctions within mixed synapses are contributing to measurements of resting excitability in the zebrafish spinal cord. If so, we would expect that input resistance measurements would be sensitive to 18-βGA. Analysis of resistances before and after application revealed increased values in small and large neurons (Figure 2k), consistent with the broad contribution of gap junctions to electrophysiological measurements of excitability. The impact on excitability was specific to electrical synapses, since blockade of AMPA receptors or both AMPA and NMDA receptors had no significant effect on input resistance (Figure 2l, left). Critically, the relative impact of gap junction blockade was greatest in the lowest resistance neurons (Figure 2l, right). This is consistent with measurements of excitatory currents (Figure 1g and h) and postsynaptic potentials (Figure 2d and e), and a larger contribution of mixed synapses to leak measurements in lower resistance neurons.

Finally, to verify if mixed synapse density alone could explain our experimental observations, we turned to a user-friendly computational model (NeuroSim5; see Materials and methods). Different-sized model somata received simulated cEPSPs from a single source with identical amplitudes and waveforms (Figure 3a and b), assuming synaptic scaling with size following τ=RC. However, individual electrical synapse conductances were weighted to achieve larger eEPSPs in larger neurons (Figure 3b), per our observations. To simulate different patterns of synaptic convergence from mixed sources related to size, the largest neurons received 100% of total inputs, while the smallest only 10% (Figure 3a). This approximates the tenfold difference in excitatory synapse number reported in larval zebrafish motor neurons (Bello-Rojas et al., 2019). By increasing the number of convergent sources, the model allowed us to explore both size-dependent and size-independent changes in resting excitability via increases in electrical synapse density.

Figure 3

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As expected, increases in the number of convergent sources of electrical synapses led to systematic decreases in measurements of input resistance using simulated current injection (Figure 3c), which were most obvious in the largest, lowest resistance neurons (Figure 3d,e). We observed systematic decreases not only in the amplitude (Figure 3c), but also the time constant (Figure 3f) of simulated chemical PSPs, increasing the dynamic range of integration. By varying the amount of convergent sources of electrical synapses, size and input resistance could be uncoupled (Figure 3d). This helps explain how interneurons can be the same size with different input resistances (Figure 1d, left) or different sizes but the same input resistances (Figure 1d, middle). If mixed synapses are often used in high-frequency swimming circuitry, then differences in convergence could also explain recruitment out of order based on size and input resistance (McLean et al., 2007; Menelaou and McLean, 2019)—higher density electrical synapses lower resistance at rest independent of size, but during activity provide stronger excitation to increase recruitment probability.

One consequence of increasing the convergence of different sources of electrical synapses is the creation of parallel paths for current to spread (Marder et al., 2017). To examine this more closely, we simulated targeted chemical inputs to neurons of different sizes at maximum electrical synapse convergence (Figure 3g, left) and measured the amplitude of the coupling potentials (Figure 3g, right). As expected, the amplitude of the direct chemical EPSP varied as a function of size and convergence ratio (Figure 3g), with current distributed predominantly to neurons sharing the most afferents (Figure 3h). The low pass filtering provided by electrical synapses generated slower coupling potentials that were orders of magnitude lower in amplitude (Figure 3g and h). Simulated coupling potentials resembled slower, lower amplitude 18-βGA-sensitive potentials observed during chemical failures (Figure 2b, bottom) and in unconnected pairs (Menelaou and McLean, 2019). We and others have argued these filtered potentials reflect indirect electrical continuity through gap junctions (García-Pérez et al., 2004; Korn et al., 1973), suggesting they more accurately reflect shared afferents than direct efferents.

Collectively, our findings suggest that mixed synapses contribute to excitability underestimations in zebrafish spinal cord and help reconcile reported violations of the size principle. We also find that mixed synapses can contribute to connectivity overestimations by acting as conduits for synaptic current and confirm coupling potentials are easily distinguished based on kinetics (García-Pérez et al., 2004; Menelaou and McLean, 2019). Studies of the premotor Ia reflex pathway in cats have revealed dual and single component EPSPs with different kinetics (Burke, 1968; Mendell and Henneman, 1971). These were attributed to filtering by motor neuron dendrites and differences in the density of leak channels (Gustafsson and Pinter, 1984; Rall et al., 1967), but could also reflect axon collaterals connecting motor neuron somata via mixed synapses. In mammals, mixed synapses are found in the spinal cord (Rash et al., 1996), Ia circuit function is disrupted in connexin36 mutants (Bautista et al., 2012), and larger, faster motor units receive denser connexin36 innervation from excitatory V0 interneurons (Recabal-Beyer et al., 2022). So, mixed synapses could also help reconcile conflicting observations related to size, synaptic drive, and neuronal excitability in mammalian spinal cord (Burke, 1981; Enoka and Stuart, 1984; Henneman, 1985).

More broadly, connexin36 and vesicular glutamate transporter co-localization are observed in a variety of brain circuits optimized for processing high-frequency information reliably at speed (Nagy et al., 2019). The use of electrical synapses likely expands neuronal integrative properties beyond what can be achieved by leak channels and size alone (Alcamí and Pereda, 2019; Galarreta and Hestrin, 2001). This would enable rate and/or timing codes to execute orderly patterns of recruitment among targeted ensembles of motor neurons and spinal interneurons using temporal summation (Wang and McLean, 2014), as observed in other sensory and motor circuits (Ainsworth et al., 2012; Sober et al., 2018). In this scenario, links between input resistance and recruitment order arise by gradations in mixed synapse density and convergence among various sized neurons. This could explain why the size principle best predicts function among motor neurons, which have the maximum capacity for synaptic convergence as the ‘final common path’ for all behavioral output (Sherrington, 1906).

All data generated or analyzed during this study are included in the manuscript and supporting files. Source data files are provided for Figures 1-3.

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Decision letter after peer review:

Thank you for submitting your article "Gap junctions impact synaptic integration and orderly recruitment in the zebrafish spinal cord" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, including Markus Meister as Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Richard Aldrich as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Alberto Pereda (Reviewer #2).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Consensus review:

This is a short but incisive report on the biophysical basis of the "size principle" – an old hypothesis to explain the orderly recruitment of interneurons and motorneurons according to the size of their motor pool. The conventional version of this idea assumes that neurons with different size motor pools receive synaptic inputs of similar magnitude but vary in membrane resistance and thus in excitability. In this study, the authors examine the contribution of electrical gap junctions to these recruitment phenomena in the spinal locomotor circuits in larval zebrafish. The paper is based on a re-analysis of a large electrophysiology dataset they acquired over many years. The authors show that the neurons with lower input resistance and faster time constant are likely to receive more electrical synaptic input, and that the abundance of electrical synapses plays a role in reducing the input resistance of these neurons. They further suggest that the electrical synapses prioritize their own signal based on the correlations they observed across cell types, which remains to be tested experimentally.

The following suggestions for revision include: improvements in readability; clarification of experimental results; the inclusion of some controls; and an expanded discussion.

General readability and figures:

1. Please spell out early on whether you are considering electrical synapses onto the motor neurons, or among the motor neurons, or both. The question arises already in the abstract. Obviously these scenarios predict different consequences.

2. Please include one or more equivalent circuit diagrams (ligand-gated conductances, driving forces, electrical coupling) to illustrate the postulated consequences of electrical synapses in different parts of the circuit.

3. Figure 1a: This is not helpful. Hard to spot any differences between the left and right panel. What is the significance of some leak channels being green and others white? Why are there no electrical junctions between neurons anywhere?

4. Please justify the use of log-log plots in the figures? Is there a theoretical basis for the linear data fits on log-log scales?

Clarification of results:

5. Line 82: Explain better how you separated electrical and chemical components of transmission. Is it assumed that the electrical input (membrane voltage) is the same whether or not the chemical transmission fails? If so is that justified? An equivalent circuit diagram might help. Also was the separation validated by pharmacology? Blockers are only mentioned in connection with Figure 3.

6. Line 105: What is "reliability"? What motivates this measure? Why does it have units of mV? Explain how this measure should depend on the biophysical parameters of electrical/chemical transmission. Presumably the effects will differ depending on whether the electrical synapses are onto or among the target neurons. Without such explanation it is hard to follow the claim in line 108.

7. Cell types: In all of the analyses, various cell types are collapsed together, raising the possibility that the observed trend arises from particular cell types that differ from the others. To exclude this possibility, the authors could colour-code each data point in the scatter plots based on the cell type (or the combination of the cell types for Figure 2 and 3). For statistical analyses, the authors could examine the contribution of both cell-type (or combination of cell types) and explanatory variable (input resistance for Figure 1, 2 and 3c, the amplitude of PSP for Figure 2a) at the same time using a generalized linear model. The introduction could say more about the cell types examined in this study (type 1 and 2 V2a cells and their differences and similarities). The discussion could address how the distribution of electrical synapses among different cell types might affect spinal circuits.

8. Electrical synapses prioritize their own signals: One of the major claims of the paper is that "stronger electrical synapses further prioritize their own signals by shunting other inputs and enhancing synchronous electrical inputs by lateral excitation". This claim seems to require further analysis. To directly demonstrate that electrical synapses shunt other inputs, one might show that other inputs get stronger after blocking the electrical synapse. Furthermore, it is confusing that the authors rely on Menelaou and McLean 2019 to support the claim of shunting because the connections examined in this paper come from the neurons (type I and II V2a neurons) that are active at the same time (during fast swim cycles). It would be more appropriate to examine how these electrical synapses impact the inputs from the neurons active during slow swim cycles.

Relation to prior work:

9. Line 15: "Our findings challenge the view that leak channels alone dictate input resistance and membrane time constant…." In addition to leak channels, it is well known that synaptic transmission affects input resistance and membrane time constant, in particular for inhibitory synapses. See for example D. Paré et al., Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo, J. Neurophysiol, 1998; Morales et al., J. Neurophys. 1987. The present results add the consequences of electrical coupling via mixed synapses to the established shunting by chemical synapses. The abstract and discussion should better reflect this state of understanding.

10. Line 102: "This potential shunting effect led us to examine the impact of larger electrical components of mixed PSPs on their own chemical components. In auditory and vestibular primary afferent circuits, electrical components propagate depolarizations in neighboring mixed synapses, enhancing chemical transmission at simultaneously active synapses (Alcami and Pereda, 2019)." A better reference for this phenomenon is Pereda et al., 2004 Brain Research Reviews (see Figure 4 and related text). Also, one could mention that this phenomenon was also found in invertebrates (Liu et al., Nature Comm., 2017).

11. Line 129: “Remarkably, dual electrical and chemical transmission has been observed between Ia primary sensory afferents and spinal motor neurons in adult cats (Curtis et al., 1979; Decima and Goldberg, 1976; Werman and Carlen, 1976), the origin circuit for the size principle.” These references did not show “dual electrical and chemical transmission between Ia primary sensory afferents and spinal motor neurons”, but rather the antidromic influence of motor neuron activity on presynaptic afferents. Coupling was discussed as a possible explanation along with other possibilities such as electrical field effects. Also, the Werman paper describes voltage-dependent properties of the Ia-evoked EPSP that deviates from their presumed reversal potential, but does not demonstrate its origin in electrical transmission. The presence of mixed synapses in the spinal cord of mammals was unequivocally demonstrated in Rash et al., PNAS, 1996.

12. Line 135: “The use of electrical synapses likely expands neuronal integrative properties …” Possibly cite prior demonstrations of this, e.g. Galarreta and Hestrin (2001), and Alcami and Pereda (2019).

13. It is worth considering the impact of cell morphology on the observations. For example a large dendritic tree can speed up the time constant (Rall, 1957 and 1962). The location of synaptic input also affects the time constant of postsynaptic potential (Rall, 1967). So the difference in the time constant of EPSP in Figure 2 could also arise from different locations of synapses along the dendritic tree.

Details:

14. Title suggestion: “Gap junction COUPLING impacts…”

15. Line 7. “Neuronal excitability is dictated by input resistance, which HAS MAINLY BEEN attributed to membrane leak channels.”

16. Line 10, “Moreover, differences in membrane time constants and temporal summation support greater densities of leak channels in larger neurons.”: Meaning of “support”? Maybe “suggest” or “imply”?

17. Line 13, “Stronger electrical synapses further prioritize their own…”: Perhaps replace “electrical synapses” with “electrical coupling”. Strong electrical coupling can be caused by stronger synapses or more synapses, something the present study cannot disambiguate. Check for similar instances elsewhere in the text. Also the reference for “further” here is unclear.

18. Line 14, “enhancing synchronous electrical inputs by lateral excitation”. Should this read “enhancing synchronous chemical transmission by lateral excitation”? The results and discussion talk about lateral excitation in the context of mixed electrical/chemical synapses.

19. Line 16, “that synaptic inputs not only contend with spinal neuron excitability, they contribute to it”: Meaning of “contend with”? “Synaptic input” is generally understood as “input current”. So synaptic input contributes to excitation, not to excitability.

20. Line 32, “motor neurons are still recruited by size thanks to the contribution of resistance to …” Does this argument assume that all the upstream neurons are active simultaneously? Is that justified?

21. Line 55, “…, it contributes to it.” Reference for the two “it”s?

22. Line 69, “not as predictive”: as what?

23. Line 70, “input resistance is not predictive of spinal interneuron recruitment order …”: This needs a bit more explanation for the non-expert, for example how this order relates to swimming frequency.

24. Line 79: “but that synaptic inputs contribute to input resistance …”. The results only show correlation, not causation, so “contribute” is not appropriate here.

25. Line 90: “If stronger electrical synapses contribute to leak current, we would expect…” This logic is unclear. As elsewhere the argument depends on whether the electrical synapses are onto or between target neurons. This reasoning would benefit from an equivalent circuit.

26. Line 92: “if soma size was the major source of leak current”. Perhaps better “major determinant”.

27. Line 314: “Before statistical analysis all data were tested for normality.” What was the outcome?

The following suggestions for revision include: improvements in readability; clarification of experimental results; the inclusion of some controls; and an expanded discussion.

We are grateful for the positive and rigorous review and the valuable suggestions for improvement. In response, we have completely re-written the manuscript to improve readability, clarify the experimental results and expand the discussion. We also include new simulation experiments to validate our experimental observations. We provide a point-by-point response below.

General readability and figures:

1. Please spell out early on whether you are considering electrical synapses onto the motor neurons, or among the motor neurons, or both. The question arises already in the abstract. Obviously these scenarios predict different consequences.

This is a very important point. We are talking about electrical synapses ‘onto’ motor neurons, which can serve as conduits to report coupling electrophysiologically ‘among’ motor neurons at rest, assuming they are in the same target pool. The manuscript has been substantially revised to take this head on. We hope the revisions to the text and the additional simulation experiments now make this clearer.

2. Please include one or more equivalent circuit diagrams (ligand-gated conductances, driving forces, electrical coupling) to illustrate the postulated consequences of electrical synapses in different parts of the circuit.

We now include simulations of conductances, driving forces and coupling that better illustrate the consequences of coupling in the circuit.

3. Figure 1a: This is not helpful. Hard to spot any differences between the left and right panel. What is the significance of some leak channels being green and others white? Why are there no electrical junctions between neurons anywhere?

This figure panel has been removed.

4. Please justify the use of log-log plots in the figures? Is there a theoretical basis for the linear data fits on log-log scales?

A log scale has been used historically with regression lines to illustrate trends related to input resistance. We now state in the methods (L391) that semi-log plots and linear fits were used to illustrate significant trends in the data per Burke (1968).

Clarification of results:

5. Line 82: Explain better how you separated electrical and chemical components of transmission. Is it assumed that the electrical input (membrane voltage) is the same whether or not the chemical transmission fails? If so is that justified? An equivalent circuit diagram might help. Also was the separation validated by pharmacology? Blockers are only mentioned in connection with Figure 3.

We have included more details on how we separated the fast electrical and chemical components of mixed transmission (L106), which are distinguished by their failure rates, latencies and pharmacology, per our previous publication (Figure 4a-c in Menelaou and McLean, 2019). The fast components are separated by about 1 ms, due to the delay for chemical transmission, so peak values of the fast electrical component are unlikely to be impacted significantly. This is also consistent with a lack of impact of NBQX or NMDA on the fast electrical component (Figure 4b in Menelaou and McLean, 2019).

6. Line 105: What is “reliability”? What motivates this measure? Why does it have units of mV? Explain how this measure should depend on the biophysical parameters of electrical/chemical transmission. Presumably the effects will differ depending on whether the electrical synapses are onto or among the target neurons. Without such explanation it is hard to follow the claim in line 108.

We apologize for the confusion. Reliability is the inverse of failure rate. We have now changed this to the more conventional ‘failure rate’ to avoid confusion. Since failure rates are linked to levels of presynaptic depolarization, we thought it would good to report. We interpreted this to mean that presynaptic terminals of large mixed synapses were more depolarized and thus more likely to release neurotransmitter, as proposed by Liu et al., 2017 and Pereda et al., 2004. We now make this more explicit in L123. More recent work has shown that injecting hyperpolarizing or depolarizing current in motor neurons can impact the amplitude of PSPs from excitatory interneurons, which is in line with this observation (Song et al., 2016). We now include this citation in L125. The units was a typo, thanks for catching this.

7. Cell types: In all of the analyses, various cell types are collapsed together, raising the possibility that the observed trend arises from particular cell types that differ from the others. To exclude this possibility, the authors could colour-code each data point in the scatter plots based on the cell type (or the combination of the cell types for Figure 2 and 3). For statistical analyses, the authors could examine the contribution of both cell-type (or combination of cell types) and explanatory variable (input resistance for Figure 1, 2 and 3c, the amplitude of PSP for Figure 2a) at the same time using a generalized linear model. The introduction could say more about the cell types examined in this study (type 1 and 2 V2a cells and their differences and similarities). The discussion could address how the distribution of electrical synapses among different cell types might affect spinal circuits.

We have now separated analysis based on cell type and updated Figure 1 with schematics to better outline the different cell types. We now include simulations address how the distribution of electrical synapses impacts spinal circuits.

8. Electrical synapses prioritize their own signals: One of the major claims of the paper is that “stronger electrical synapses further prioritize their own signals by shunting other inputs and enhancing synchronous electrical inputs by lateral excitation”. This claim seems to require further analysis. To directly demonstrate that electrical synapses shunt other inputs, one might show that other inputs get stronger after blocking the electrical synapse. Furthermore, it is confusing that the authors rely on Menelaou and McLean 2019 to support the claim of shunting because the connections examined in this paper come from the neurons (type I and II V2a neurons) that are active at the same time (during fast swim cycles). It would be more appropriate to examine how these electrical synapses impact the inputs from the neurons active during slow swim cycles.

We have backed off this claim. Instead, we focus on whether electrical synapses could provide the shunt normally attributed to leak channels at rest. Our simulation now takes on this issue without relying on citations to Menelaou and McLean, 2019. We agree that shunting would not occur between neurons active at the same time and have modified the text to clarify we are assessing the circuit at rest, not during activity.

Relation to prior work:

9. Line 15: “Our findings challenge the view that leak channels alone dictate input resistance and membrane time constant….” In addition to leak channels, it is well known that synaptic transmission affects input resistance and membrane time constant, in particular for inhibitory synapses. See for example D. Paré et al., Impact of spontaneous synaptic activity on the resting properties of cat neocortical pyramidal neurons in vivo, J. Neurophysiol, 1998; Morales et al., J. Neurophys. 1987. The present results add the consequences of electrical coupling via mixed synapses to the established shunting by chemical synapses. The abstract and discussion should better reflect this state of understanding.

During the re-write, this language has been edited out and we now include a sentence in L24 that includes references to synaptic activity and voltage-dependent conductances to input resistance.

10. Line 102: “This potential shunting effect led us to examine the impact of larger electrical components of mixed PSPs on their own chemical components. In auditory and vestibular primary afferent circuits, electrical components propagate depolarizations in neighboring mixed synapses, enhancing chemical transmission at simultaneously active synapses (Alcami and Pereda, 2019).” A better reference for this phenomenon is Pereda et al., 2004 Brain Research Reviews (see Figure 4 and related text). Also, one could mention that this phenomenon was also found in invertebrates (Liu et al., Nature Comm., 2017).

We have updated the references accordingly in L125.

11. Line 129: "Remarkably, dual electrical and chemical transmission has been observed between Ia primary sensory afferents and spinal motor neurons in adult cats (Curtis et al., 1979; Decima and Goldberg, 1976; Werman and Carlen, 1976), the origin circuit for the size principle." These references did not show "dual electrical and chemical transmission between Ia primary sensory afferents and spinal motor neurons", but rather the antidromic influence of motor neuron activity on presynaptic afferents. Coupling was discussed as a possible explanation along with other possibilities such as electrical field effects. Also, the Werman paper describes voltage-dependent properties of the Ia-evoked EPSP that deviates from their presumed reversal potential, but does not demonstrate its origin in electrical transmission. The presence of mixed synapses in the spinal cord of mammals was unequivocally demonstrated in Rash et al., PNAS, 1996.

We have updated the references accordingly in the revised discussion.

12. Line 135: "The use of electrical synapses likely expands neuronal integrative properties …" Possibly cite prior demonstrations of this, e.g. Galarreta and Hestrin (2001), and Alcami and Pereda (2019).

Done.

13. It is worth considering the impact of cell morphology on the observations. For example a large dendritic tree can speed up the time constant (Rall, 1957 and 1962). The location of synaptic input also affects the time constant of postsynaptic potential (Rall, 1967). So the difference in the time constant of EPSP in Figure 2 could also arise from different locations of synapses along the dendritic tree.

We now include a statement to this effect in L184, suggesting that our observations could also contribute to those attributed to compartmentalization in the past. We note that our model was able to achieve the same phenomena with neurons modeled as spheres. In the methods L415 we mention that compartments will likely enhance any filtering properties observed in the model.

15. Line 7. "Neuronal excitability is dictated by input resistance, which HAS MAINLY BEEN attributed to membrane leak channels."

During the re-write, this line was removed from the abstract. However the point is now made in the introduction in L24, including other contributors to input resistance.

16. Line 10, "Moreover, differences in membrane time constants and temporal summation support greater densities of leak channels in larger neurons.": Meaning of "support"? Maybe "suggest" or "imply"?

During the re-write, this line was edited out. We do not use support in this capacity anywhere now.

17. Line 13, "Stronger electrical synapses further prioritize their own…": Perhaps replace "electrical synapses" with "electrical coupling". Strong electrical coupling can be caused by stronger synapses or more synapses, something the present study cannot disambiguate. Check for similar instances elsewhere in the text. Also the reference for "further" here is unclear.

During the re-write, this sentence was removed. We now use ‘higher-density’ electrical synapses instead of stronger, where appropriate.

18. Line 14, "enhancing synchronous electrical inputs by lateral excitation". Should this read "enhancing synchronous chemical transmission by lateral excitation"? The results and discussion talk about lateral excitation in the context of mixed electrical/chemical synapses.

Yes, this is meant to refer to the chemical component of mixed synapses. We apologize for the lack of clarity here. The sentence in L123 has been modified to avoid confusion and cites references to mixed electrical/chemical synapses.

19. Line 16, "that synaptic inputs not only contend with spinal neuron excitability, they contribute to it": Meaning of "contend with"? "Synaptic input" is generally understood as "input current". So synaptic input contributes to excitation, not to excitability.

During the re-write, this line was removed.

20. Line 32, "motor neurons are still recruited by size thanks to the contribution of resistance to …" Does this argument assume that all the upstream neurons are active simultaneously? Is that justified?

During the re-write, this line was removed.

21. Line 55, "…, it contributes to it." Reference for the two "it"s?

During the re-write, this line was removed.

22. Line 69, "not as predictive": as what?

During the re-write, this line was removed.

23. Line 70, "input resistance is not predictive of spinal interneuron recruitment order …": This needs a bit more explanation for the non-expert, for example how this order relates to swimming frequency.

We apologize for the lack of clarity. During the re-write, this line and the associated experiments were removed. We have provided more details regarding ‘fictive’ escape swimming recordings in L85 and added a schematic to Figure 1.

24. Line 79: "but that synaptic inputs contribute to input resistance …". The results only show correlation, not causation, so "contribute" is not appropriate here.

This sentence has been edited during revisions.

25. Line 90: "If stronger electrical synapses contribute to leak current, we would expect…" This logic is unclear. As elsewhere the argument depends on whether the electrical synapses are onto or between target neurons. This reasoning would benefit from an equivalent circuit.

We apologize for the confusion and clarify the logic in L116. We also include a simulation that walks the reader more clearly through this reasoning and impact.

26. Line 92: "if soma size was the major source of leak current". Perhaps better "major determinant".

Changed, thanks.

27. Line 314: "Before statistical analysis all data were tested for normality." What was the outcome?

We have added the following to clarify in L428: “Before statistical analysis all data were tested for normality and were not normally distributed, so non-parametric tests were used.”

Author details

1. Evdokia Menelaou

   Department of Neurobiology, Northwestern University, Evanston, United States

   Contribution

   Formal analysis, Investigation, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

2. Sandeep Kishore

   Department of Neurobiology, Northwestern University, Evanston, United States

   Contribution

   Formal analysis, Investigation, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

3. David L McLean

   Department of Neurobiology, Northwestern University, Evanston, United States

   Contribution

   Conceptualization, Formal analysis, Supervision, Funding acquisition, Investigation, Visualization, Writing – original draft, Writing – review and editing

   For correspondence

   david-mclean@northwestern.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6337-2301

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