Author response:
The following is the authors’ response to the original reviews.
Reviewer #1 (Public review):
Summary:
The authors aim to explore the effects of the electrogenic sodium-potassium pump (Na+/K+-ATPase) on the computational properties of highly active spiking neurons, using the weakly-electric fish electrocyte as a model system. Their work highlights how the pump's electrogenicity, while essential for maintaining ionic gradients, introduces challenges in neuronal firing stability and signal processing, especially in cells that fire at high rates. The study identifies compensatory mechanisms that cells might use to counteract these effects, and speculates on the role of voltage dependence in the pump's behavior, suggesting that Na+/K+-ATPase could be a factor in neuronal dysfunctions and diseases
Strengths:
(1) The study explores a less-examined aspect of neural dynamics-the effects of (Na+/K+-ATPase) electrogenicity. It offers a new perspective by highlighting the pump's role not only in ion homeostasis but also in its potential influence on neural computation.
(2) The mathematical modeling used is a significant strength, providing a clear and controlled framework to explore the effects of the Na+/K+-ATPase on spiking cells. This approach allows for the systematic testing of different conditions and behaviors that might be difficult to observe directly in biological experiments.
(3) The study proposes several interesting compensatory mechanisms, such as sodium leak channels and extracellular potassium buffering, which provide useful theoretical frameworks for understanding how neurons maintain firing rate control despite the pump's effects.
Weaknesses:
(1) While the modeling approach provides valuable insights, the lack of experimental data to validate the model's predictions weakens the overall conclusions.
(2) The proposed compensatory mechanisms are discussed primarily in theoretical terms without providing quantitative estimates of their impact on the neuron's metabolic cost or other physiological parameters.
We thank the reviewer for their concise and accurate summary and appreciate the constructive feedback on the article’s strengths and weaknesses. Experimental work is beyond the scope of our modeling-based study. However, we would like our work to serve as a framework for future experimental studies into the role of the electrogenic pump current (and its possible compensatory currents) in disease, and its role in evolution of highly specialized excitable cells (such as electrocytes).
Quantitative estimates of metabolic costs in this study are limited to the ATP that is required to fuel the pump. By integrating the net pump current over time and dividing by one elemental charge, one can find the rate of ATP that is consumed by the Na+/K+pump for either compensatory mechanism. The difference in net pump current is thus proportional to ATP consumption, which allows for a direct comparison of the cost efficiency of the Na+/K+ pump for each proposed compensatory mechanism. The Na+/K+ pump is, however, not the only ATP-consuming element in the electrocyte, and some of the compensatory mechanisms induce other costs related to cell
‘housekeeping’ or presynaptic processes. We now added a section in the appendix titled
‘Considerations on metabolic costs of compensatory mechanisms’ (section 11.4), where we provide ballpark estimates for the influence of the compensatory mechanisms on the total metabolic costs of the cell and membrane space occupation. Although we argue that according these estimates, the impact of discussed compensatory mechanisms could be significant, due to the absence of more detailed experimental quantification, a plausible quantitative cost approximation on the whole cell level remains beyond the scope of this article.
Reviewer #1 (Recommendations for the authors):
(1) For the f-I curves in Figures 1 and 6, the firing rate increases as the input current increases. I am curious to know: (a) whether the amplitudes of the action potentials (APs) vary with increased input current; (b) whether the waveform of APs (such as in Fig. 1I) transitions into smaller amplitude oscillations at higher input currents; and (c) if the waveform does change at higher input currents, how do the "current contributions," "current," and "ion exchanges per action potential" in Figures 1HJ and 6AB respond?
To fully answer these questions, we added a supplemental figure with accompanied text in section 11.1 (Fig. A1). We also added a reference to this figure in the main text (section 4.1). Here, it is shown that, as previously illustrated in [1], AP amplitude decreases when the input current increases (Fig. A1 A, left). This effect remains upon addition of either a pump with constant pump rate and co-expressed sodium leak channels (Fig. A1 A, center), or a voltage-dependent pump (Fig. A1 A, right). Interestingly, even though the shape of the current contributions (Fig. A1 B) and the APs (Fig. A1 C) look very different for low (Fig. A1 C, top) and high inputs (Fig. A1 C, bottom), the total sodium and potassium displacement per AP, and thus the pump rate, is roughly the same (Fig. A1 D). Under the assumption that voltage-gated sodium channel (NaV) expression is adjusted to facilitate fixed-AP amplitudes, however, (as in [1]) more NaV channels would be expressed in fish with higher synaptic drives. This would then result in an additional sodium influx per AP and result in higher energetic requirements per AP for electrocytes with higher firing rates (also shown in [1]).
(2) Could the authors clarify what the vertical dashed line represents in Figures 1B and 1F? Does it correspond to an input current of 0.63uA?
(Reviewer comment refers to Fig. 1C and 1F in new version): Yes, it corresponds to the input current that is also used in figures 1D and 1G. We clarified this by adding an additional tick label on the x-axis in 1F. The current input of 0.63uA was chosen as a representative input for this cell as follows: we first modeled an electrocyte with a periodic synaptic drive as in [1]. The frequency of this drive was set to 400 Hz, which is an intermediate value in the range of reported EODfs (and thus presumably pacemaker firing rates) of 200-600Hz [2]. Then, acetylcholine receptor currents IAChRNa and IAChRNa were summed and averaged to obtain the average input current of 0.63uA. This is now also explained in new Methods section 6.2.1.
(3) What input current was used for Figures 1H, 1I, and 1J?
Response: In a physiological setting, where the electrocyte is electrochemically coupled to the pacemaker nucleus, stimulation of the electrocyte occurs through neurotransmitter release in the synaptic cleft, which then leads to the opening of acetylcholine receptor channels. As figures 1H-J concern different ion fluxes, we aimed to also include currents stemming from acetylcholine receptor channels. We therefore did not stimulate the electrocyte with a constant input current as in Fig. 1C and F, but simulated elevated constant neurotransmitter levels in the synaptic cleft, which then leads to elevated acetylcholine receptor currents. In the model, this neurotransmitter level, or ‘synaptic drive’ is represented by parameter synclamp. A physiologically relevant value for synclamp was deduced by averaging the synaptic drive during a 400 Hz pacemaker stimulus. This is now also explained in new Methods section 6.2.1.
(4) In Figure 4A, there is a slight delay between the PN spikes (driver) and the EO (receiver), and no EO spikes occur without PN spikes. However, the firing rate of EO (receiver) appears to decrease before the chirp initiations in Fig 4B; and this delay seems to disappear in Fig 4C. Could the authors explain these observations?
As shown in the bottom right of figure 4A, when plotting the instantaneous firing rate as one over the inter-spike-interval (1/ISI), the firing rate of a cell is only plotted at the end of every ISI. Therefore, even though the PN drives the electrocyte and thus spikes earlier in time than the electrocyte, when it initiates chirps, these will only be plotted as an instantaneous firing rate at the end of the chirp. If the electrocyte fires spontaneously within this chirp, its instantaneous firing rate will appear earlier in time than the initiation of the chirp of the PN. The PN did, however, initiate the chirp before that and causality between the PN and electrocyte is not disturbed.
(5) Regarding Figure 6, could the authors specify the input current used in Figures 6A and 6B?
Figure 6A and 6B have the same synaptic drive as Fig. 1 H, I and J (synclamp=0.13).
(6) In Section 6, I would recommend that the authors provide a table of parameters and their corresponding values for clarity.
Thank you for your suggestion. We now reorganized the method section and added two tables with parameters for clarity. Table 1 (see Methods 6.1) includes all parameters that differ from the parameters reported in [1], and parameters that arise from the additionally modeled equations to simulate ion concentration dynamics and pump. We also added the parameters used to simulate the different stimulus protocols (and corresponding tuned parameters) that are presented in the article in Table 2 (see Methods 6.2).
Reviewer #2 (Public review):
Summary:
The paper 'The electrogenicity of the Na+/K+-ATPase poses challenges for computation in highly active spiking cells' by Weerdmeester, Schleimer, and Schreiber uses computational models to present the biological constraints under which electrocytes-specialized highly active cells that facilitate electro-sensing in weakly electric fish-may operate. The authors suggest potential solutions these cells could employ to circumvent these constraints.
Electrocytes are highly active or spiking (greater than 300Hz) for sustained periods (for minutes to hours), and such activity is possible due to an influx of sodium and efflux of potassium ions into these cells for each spike. This ion imbalance must be restored after each spike, which in electrocytes, as with many other biological cells, is facilitated by the Na-K pumps at the expense of biological energy, i.e., ATP molecules. For each ATP molecule the pump uses, three positively charged sodium ions from the intracellular space are exchanged for two positively charged potassium ions from the extracellular volume. This creates a net efflux of positive ions into the extracellular space, resulting in hyperpolarized potentials for the cell over time. This does not pose an issue in most cells since the firing rate is much slower, and other compensatory mechanisms and other pumps can effectively restore the ion imbalances. In electrocytes of weakly electric fish, however, that operate under very different circumstances, the firing rate is exceptionally high. On top of this, these cells are also involved in critical communication and survival behaviors, emphasizing their reliable functioning.
In a computation model, the authors test four increasingly complex solutions to the problem of counteracting the hyperpolarized states that occur due to continuous NaK pump action to sustain baseline activity. First, they propose a solution for a well-matched Na leak channel that operates in conjunction with the NaK pump, counteracting the hyperpolarizing states naturally. Additionally, their model shows that when such an orchestrated Na leak current is not included, quick changes in the firing rates could have unexpected side effects. Secondly, they study the implication of this cell in the context of chirps - a means of communication between individual fishes. Here, an upstream pacemaking neuron entrains the electrocyte to spike, which ceases to produce a so-called chirp - a brief pause in the sustained activity of the electrocytes. In their model, the authors show that it is necessary to include the extracellular potassium buffer to have a reliable chirp signal. Thirdly, they tested another means of communication in which there was a sudden increase in the firing rate of the electrocyte followed by a decay to the baseline. For reliable occurrence of this, they emphasize that a strong synaptic connection between the pacemaker neuron and the electrocyte is warranted. Finally, since these cells are energy-intensive, they hypothesize that electrocytes may have energyefficient action potentials, for which their NaK pumps may be sensitive to the membrane voltages and perform course correction rapidly.
Strengths:
The authors extend an existing electrocyte model (Joos et al., 2018) based on the classical Hodgkin and Huxley conductance-based models of Na and K currents to include the dynamics of the NaK pump. The authors estimate the pump's properties based on reasonable assumptions related to the leak potential. Their proposed solutions are valid and may be employed by weakly electric fish. The authors explore theoretical solutions that compound and suggest that all these solutions must be simultaneously active for the survival and behavior of the fish. This work provides a good starting point for exploring and testing in in vivo experiments which of these proposed solutions the fish use and their relative importance.
Weaknesses:
The modeling work makes assumptions and simplifications that should be listed explicitly. For example, it assumes only potassium ions constitute the leak current, which may not be true as other ions (chloride and calcium) may also cross the cell membrane. This implies that the leak channels' reversal potential may differ from that of potassium. Additionally, the spikes are composed of sodium and potassium currents only and no other ion type (no calcium). Further, these ion channels are static and do not undergo any post-translational modifications. For instance, a sodium-dependent potassium pump could fine-tune the potassium leak currents and modulate the spike amplitude (Markham et al., 2013).
This model considers only NaK pumps. In many cell types, several other ion pumps/exchangers/symporters are simultaneously present and actively participate in restoring the ion gradients. It may be true that only NaK pumps are expressed in the weakly electric fish Eigenmannia virescens. This limits the generalizability of the results to other cell types. While this does not invalidate the results of the present study, biological processes may find many other solutions to address the non-electroneutral nature of the NaK pump. For example, each spike could include a small calcium ion influx that could be buffered or extracted via a sodium-calcium exchanger.
Finally, including testable hypotheses for these computational models would strengthen this work.
We thank the reviewer for the detailed summary and the identified weaknesses according to which we improved our article. Our model assumptions and simplifications are now mentioned in more detail in the introduction of the article (section 3), and justified in the Methods (section 6.1).
Furthermore, we added a discussion section (section 5.1) where we outline the conditions under which the present study can be extended to other cell types. We now also state more clearly that the pump current will be present for any excitable cell with significant sodium flux (assuming that the NaK pump carries out the majority of its active transport), but that compensatory mechanisms (if employed at all in a particular cell) could also be implemented via other ionic currents and transporters. We furthermore now highlight the testable hypotheses that we put forward with our computational study on the weakly electric fish electrocyte more explicitly in the first paragraph of the discussion.
Reviewer #2 (Recommendations for the authors):
Main text
Please explicitly state this model's assumptions in the introduction and elaborate on them in the discussion if necessary. For example, some assumptions that I find relevant to mention are: - The Na and K channels are classic HH conductance-based channels, with no post-translational modifications or beta subunit modifications as seen in other high-frequency firing cells (10.1523/JNEUROSCI.23-12-04899.2003).
Neither calcium nor chloride ions are considered in the spike generation. Nor are Na-dependent K channels (10.1152/jn.00875.2012).
Only the Na-K pump (and not the Na-Ca exchanger, Ca-pump, or Cl pumps) is modeled,
Calmodulin, which can buffer calcium, is highly expressed in electric eels, but it is not considered. If some of these assumptions have valid justifications in weakly electric fish electrocytes, please state so with the citations. I recognize that including these in your models is beyond the scope of the current paper.
We thank the reviewer for pointing out this issue. We now specified in the introduction that the model only contains sodium and potassium ions and only classic HH conductance-based channels. We there also explicitly specify the details on the Na+/K+-ATPase: it is the only active transporter in this model, thus solely responsible for maintaining ionic homeostasis; its activity is only modulated by intracellular sodium and extracellular potassium concentrations. In the discussion (6.1), we now elaborate on how ion-channel-related aspects (i.e., the addition of resurgent Na+ or Na+ -dependent K+ channels), additional ion fluxes (including some not relevant for the electrocyte but for other excitable cells), and additional active transporters and pumps would influence the results presented in the article.
In addition, there might be other factors that the authors and the reviewers have yet to consider. The model is a specific case study about the weakly electric fish electrocyte with high-frequency firing. It is almost guaranteed that biology will find other compensatory ways in different cell types, systems, and species (auditory nerve, for example). Given this, it would be prudent to use phrases such as 'this model suggests,' 'perhaps,' 'could,' 'may,' and 'eludes to,' etc., to accommodate other possible solutions to ion homeostasis in rapidly spiking neurons. The solutions the authors are proposing are some of many.
We rephrased some of the statements to highlight more the hypothetical nature of the compensatory mechanisms in specific cells and to draw attention to the fact that there can be many more such factors. This fact is now also explicitly mentioned in discussion section 5.2.
Figures
Some of my comments on the figures are stylistic, others are to improve clarity, and some are critical for accuracy.
The research problem concerns weakly electric fish E. virescens. I suggest introducing a picture of an electric fish in the beginning (such as that in Figure 3, but not exactly; see specific comments on this fish figure) along with a schema of the research question.
We agree, and added an overview schema in Fig. 1A.
Font sizes change between the panels in all the figures. Please maintain consistency. The figure panel titles and axis labels should start with a capital letter.
Thank you for pointing this out, both issues have been resolved in the new version of the article.
Figure 1:
Please rearrange the figure - BCFG belong together and should appear in the same order. The x-axis labels could be better placed.
Consider using fewer pump current f-I curves (B, D, E, F). Five is sufficient to make the point. Having 10 curves adds to the clutter. The placement of the color bar could be better. Similarly, the placement of the panel titles 'without co-expression' and 'with co-expression' and the panel labeling (BCFG) makes it confusing. The panel labels should be above the panel title.
Response (C, D, F, G in new version): We improved the layout of figure 1. Panels B, C, F, G are now C, D, F, G. We opted to include panel E before panels F and G, because it shows the coexpression mechanism before its effect on the tuning curve. We did move the colorbar, added x-axis labels to B and C, and adjusted the location of the panel labels for clarity. We also plotted fewer pump currents.
B, F: What does the dashed line indicate?
Response (C, F in new version): The dashed line indicates the input current that was used in figures 1D and 1G. We now clarified this by adding this value on the x-axis.
C: Any reason not to show the lower firing rates?
Response (B in new version): In the previous version of the article, pump currents were estimated for electrocytes that were stimulated with the mean synaptic drive that stems from periodic stimulation in the 200-600 Hz regime. We now extended the range of synaptic inputs to obtain lower (and higher) firing rates. The linear relationship between firing rate and pump current also holds for these additional firing rates.
D: There is no difference between the curves at the top and the bottom. One fills the area between the curve and the zero line; the other shows the curve itself. Please use only one of the two representations.
Response (panel I in new version): In the previous version, the difference between the plots was that one showed the absolute values of the currents (the curves), and the other plot showed the contributions of the currents to the total (area between the curves). We now only depict the current contributions.
The I and H orders can be swapped.
Thank you, they are now swapped.
The colors used for Na and K are very dull (light blue and pink).
We now use darker colors in the new version of the article.
Figure 2:
Please verify that without the synaptic input perturbations (i.e., baseline in A, D), the firing rate (B, E) and pump current (C, F) converge to the baseline. There is a noticeable drift (downward for firing rate and upward for pump currents) at the 10-second time point.
Thanks to you noticing, we identified a version mismatch in the code that estimates the pump current required for ionic homeostasis (see Methods 6.1.2). We have now corrected the code and made sure to start the simulation in the steady state so that there is no drift at baseline firing. We also used this corrected code to present tuned parameters for different stimulus protocols in Table 2 (Methods 6.2).
Figure 3:
A. The dipole orientation with respect to the fish in panel B needs to be corrected. Consider removing this as this work is not about the dipole.
This panel has been removed.
B. This figure has already been overused in multiple papers; please redraw it. Localized expressions of different pumps and ion channels are present within each electrocyte, which generates the dipole. Either show this correctly or don't at all (the subfigure pointed out by the red arrow).
This panel has been moved to Fig. 1A. We opted to remove the localized expressions.
C and D belong together; please place them next to each other. Consider introducing panel D first since it follows a similar protocol to the last figure.
Response (A in new version): Panel placement has been adjusted. We opted to maintain the order to maintain the flow of the text, but we do now combine them in one panel.
E and F are very similar in that they are swapped on the x and y axes. Either that or I have severely misunderstood something, in which case it needs to be shown better.
Response (B and C in new version): We adjusted the placement of these panels. They are not the same, panel B shows the mean of physiological periodic inputs, and figure C shows that when this mean is fed to the electrocyte, it also induces tonic firing. The range of mean currents that result from periodic synaptic stimulation in the physiological regime (panel B, y-axis) is now indicated in panel C by a grey box along the x-axis.
G. Why show the lines with double arrow ends? The curves are diverging - that's enough.
Good point, we updated this panel accordingly (now panel D).
Figure 4
Please verify the time units in these plots. Something seems amiss. B and D lower plots-perhaps this is seconds? B could use an inset box/ background gray color (t1, t2) indicating the plots of the C panel (left, right). Likewise, for D (t1, t2), connect to E (left, right).
You are right, the x-axes were supposed to be in seconds, we updated this. We indicated the relations between D-C and D-E by gray backgrounds and by adding the corresponding panel label on the x-axis.
A: Indicate the perturbation in the schematic, i.e., extracellular K buffer.
The perturbation is now indicated.
D: Even with the extracellular K buffer, there is a decay (slower than in B) of the pump current over time. Please verify (you do not have to show in your paper) that this decay saturates.
After the ten chirps are initiated, pacemaker firing goes back to baseline. In both cases (panel B and panel D), the pump current goes back to baseline after some time. With extracellular potassium buffering, this happens more slowly due to a decreased reaction speed of the pump to changes in firing rate (in comparison to the case without extracellular potassium buffer).
The decrease in reaction speed however merely delays the effects of changes in firing rates on the pump current in time. Therefore, even with an extracellular potassium buffer, when more chirps are initiated in a short period of time, the pump current can still decrease to an extent that impairs entrainment. Using the same protocol as in panel B and D, we increased the number of chirps and found that with an extracellular potassium buffer, a maximum of 13 chirps could be encoded without entrainment failure (as opposed to 2 chirps without the buffer as shown in panel B).
Figure 5
Please verify the time units in these plots, as for Figure 4. B and E lower plots-perhaps this is seconds? B could use an inset box/ background gray color (t1, t2) indicating the plots of the panels C and D. Likewise, for E (t1, t2), connect to F and G.
The time axis in this figure was indeed also in seconds, which we corrected here. The relations between plots B-C/D and E-F/G are now indicated through gray backgrounds and corresponding panel references on the x-axis.
A: Indicate the perturbation in the schematic, i.e., the synapse's strength. There is no need to include the arrow or to mention freq. rise. The placement of the time scale can be misinterpreted as a current clamp. Instead, plot it as a zoomed inset.
The arrow is removed and we now also show a zoomed inset. Also, the perturbation is now indicated.
E: Verify that the pump current in the strong synapse case already starts at 1.25
We verified this and noticed that the pump current in the strong synapse case is indeed lower than that in the weak synapse case. This is because to ensure a fair comparison for this stimulation protocol, voltage-gated sodium channel conductance was tuned to maintain a spike amplitude of 13 mV in both cases (see Methods 6.2). In this case, a weak synapse leads to a lower influx of sodium via AChR channels, but a higher influx via voltage-gated sodium channels. The total sodium influx in this case is larger than that for a stronger synapse with relatively less voltage-gated sodium currents, and thus a larger pump current. In the previous version of the article, this was wrongly commented on in the figure captions, and we removed the erroneous statement.
This is not critical, but because the R-value here can be obtained as a continuous value, it would be appropriate to show it for the whole duration of the weak and strong synapses in B and E. Maybe consider including a schema that shows how R is calculated in panel A.The caption has a typo, 'during frequency rises before (D) and after (E)'. It should be before C) and after (D) instead.
The caption typo has been corrected. The R-value for the whole duration of the weak and strong synapses in B and E is 1.000. This is because the R-value is the variance of all phase relations between the PN and the electrocyte, and for the entire duration of the stimulus protocol, there are only a few outliers in phase relations at the maxima of the frequency rises. We decided to include this R-value to show that in general, synchronization between the PN and the electrocyte is very stable. The schema that explains how R is calculated has not been included in favor of not overcrowding the figure. We did add a reference in the figure caption to the methods section in which the calculation of R is explained.
Figure 6:
A: The top and bottom plots are redundant. Use one of the two. They show the same thing. It may be better to plot Na, K, pump, and net currents on the top panels and the Na leak, which is of smaller magnitude, in a different panel.
We now only show current contributions.
B: Please change the color schema. It is barely visible on my prints.
D: Pump current, instantaneous case, is barely visible
Color schemes were adjusted.
Figure A1: It's all good.
Methods:
Please provide some internal citations for where specific equations were used in the results/figures. You do this for sections 6.2.3, referencing Figure 5 (c,d,e,g), and 6.2.4, referencing Fig 5 C-E.
There are now internal references in each methods section to where in the figures they were used. We also included a table with stimulus parameters for each figure with a stimulus protocol (Table 2).
Also, the methods could be ordered in the same order as the results are presented. Please consider if some details in the methods could be moved to the appendix.
The ordering of the methods has now been changed to separately explain the model expansions (6.1) and the stimulus protocols (6.2). Both sections are in corresponding order of the figures presented in the article. We opted to maintain all details in the methods.
6.1.1 Please cite 26 after the first line. Where was this used? In Figure 3C, 4, 5?
We added the citation. The effects of co-expressed leak channels are shown in Fig. 1 EG, and were used to compensate for pump currents at baseline firing in figures 1 D, H-J (left, with pump), 2, 4, 5, and 6 A-B (left), C (top). This is now also added to the text for clarity.
Traditionally (Hodgkin, A. L. and Huxley, A. F. (1952). J. Physiol. (Lond.), 117:500-544. Table 3; & Hodgkin, A. L. and Huxley, A. F. (1952). J. Physiol. (Lond.), 116:473-496 Table 5 and the paragraph around it), leak potential is set such that it accounts for all leak from all ions. While in your work, this potential is equal to the reversal of potassium - it need not be so in the animal. There may be leaks from other ions as well, particularly sodium and chloride. Please verify that assuming the leak reversal is the same as that of potassium (Ek, in Equation 3) does not lead to having to model Na leak currents separately.
In the original model [1], it was assumed that the reversal potential of the leak was the same as that of potassium, which contains the implicit assumption that only potassium ions contribute to the leak. In our article, we also assume that sodium ions contribute to the leak. This can be modeled by adjusting the leak reversal potential accordingly, or by adding an additional leak current that solely models the sodium leak. We opted for the latter in order to track all sodium and potassium ions separately so that ion concentration dynamics could also be modeled properly. Chloride ions were neglected in this study; in our model they do not contribute to the leak. If one were to also model chloride currents and chloride concentration dynamics, it would be beneficial to model these as an additional separate leak current.
The notation of I_pump_0 needs to be more convenient. Please consider another notation instead of the _0 (pump at baseline). Similarly for [Na+]_in_0 [Na+]_out_0 and [K+]_in_0 and [K+]_out_0
We changed the notation for baseline similarly to [3], with ‘0’ as a superscript instead of a subscript.
Equation 11: Please mention why AChRs do not let calcium ions through. Please cite a justification for this. If this is an assumption of the model, please state this explicitly.
The AChR channels that were found in the E. virescence electrocytes are muscle-type acetylcholine nicotinic receptors [4], which are non-selective cation channels that could indeed support calcium flux [5]. No calcium currents were, however, modeled in the original electrocyte model [1], presumably due to the lack of significant contributions of calcium currents or extracellular calcium concentrations to electrocyte action potentials of a similar weakly electric electrogenic wave-type fish Sternopygus macrurus [6].
Due to the lack of calcium currents in the original electrocyte model, and due to the limitation of this study to sodium and potassium ions, we chose not to include calcium currents stemming from AChR channels. This assumption is now explicitly stated in Methods 6.1.
Equation 12, V_in, where the intracellular volume. If possible, avoid the notation of 'V' - you already use a small v for membrane potential.
We changed the notation for volume to ‘ω’ similarly to [3]. As we previously used ω as a notation for the firing rate, we changed the notation for firing rate to ‘r’.
Equation 17: Does this have any assumptions? Would the I_AchRNa, and thus Sum(mean(I_Na))) not change depending on the synaptic drive?
The assumptions of this equations are the following (now also mentioned in Methods 6.1.2):
The sum of all sodium currents also includes sodium currents through acetylcholine channels (I_AChRNa).
All active sodium transport (from intra- to extracellular space) is carried out by the Na+/K+-ATPase, and active sodium transport through additional transporters and pumps is negligible.
The time-average of sodium currents is either taken in a tonic firing regime where the timeinterval that is averaged over is a multiple of the spiking period, nT, or if it is taken for a more variable firing regime, the size of the averaging window should be sufficiently large to properly sample all firing statistics.
Under these assumptions, Eq. 17 can be used to compute suitable pump currents for different synaptic drives (as Sum(mean(I_Na))) and thus I_pump0 indeed change with the synaptic drive, see Table 2 in Methods 6.2).
6.2: Please rewrite the first sentence of this paragraph.
The first sentence of this paragraph, which has been moved to section 6.2.2 for improved structuring of the text, has been rewritten.
6.2.1: The text section could use a rewrite.
Please elaborate on what t_p is. If it is not time, please do not use 't.' What is p here? What are the units of the equation (22), t_p < 0.05 (?)
This section has now also been moved to 6.2.2. It has been rewritten to improve clarity and t_p has been renamed to t_pn (as it does reflect time, which is now better explained). The units have now also been added to the equation (which is now Eq. 26).
6.2.4: Please rewrite this.
This section has been rewritten (and has been moved to section 6.1.4).
Bibliography
Some references are omitted (left anonymous) or inconsistent on multiple occasions.
Thank you for pointing this out! It is now rectified.
References used for author response
(1) Joos B, Markham MR, Lewis JE, Morris CE. A model for studying the energetics of sustained high frequency firing. PLOS ONE. 2018 Apr;13:e0196508.
(2) Hopkins CD. Electric communication: Functions in the social behavior of eigenmannia virescens. Behaviour. 1974;50(3-4):270–304.
(3) Hübel N, Dahlem MA. Dynamics from seconds to hours in hodgkin-huxley model with time-dependent ion concentrations and buer reservoirs. PLoS computational biology.ff2014;10(12):e1003941.
(4) BanY, Smith BE, Markham MR. A highly polarized excitable cell separates sodium channels from sodium-activated potassium channels by more than a millimeter. Journal of neurophysiology. 2015; 114(1):520–30.
(5) Vernino S, Rogers M, Radcliffe KA, Dani JA. Quantitative measurement of calcium flux through muscle and neuronal nicotinic acetylcholine receptors. Journal of Neuroscience. 1994;14(9):5514-5524.
(6) Ferrari M, Zakon H. Conductances contributing to the action potential of sternopygus electro-cytes. Journal of Comparative Physiology A. 1993;173:281–92.
