From single neurons to behavior in the jellyfish Aurelia aurita

Essential revisions:

The full reviewer comments are provided and should be fully addressed, but as a guide to the revision, we emphasize a few points brought out in these reviews.

1) In the comparison of uniform MNN versus von Mises MNN, it will strengthen the paper significantly if the authors provide a superposition of the kind of experimental cuts Romanes conducted on the two models to see if/how they survive conduction around these interdigitating barriers.

We tested both the radial and the circular cutting experiments performed by Romanes in the two types of networks (von Mises and uniform). We find that the through-conducting property is preserved even for severe cuts. We added one subsection and two new figures (Figures 7 and 8) to the Results which describe these simulations.

2) There are published figures of Aurelia nerve nets using immunohistochemical techniques (both MNN and DNN) (Figure 5 in Biological Bulletin 226: 29-40 (2014)) where information could be gleaned regarding neurite orientation and density for comparison with the models and the resulting estimates.

We added two paragraphs to the Discussion, highlighting that our model suggests a low density of the DNN, since this is beneficial for efficient turning. Consistent with this, the immunohistochemical staining experiments displayed in Satterlie and Eichinger, 2014, find a much lower DNN than MNN neuron density. We further incorporated the experimental finding of general radial bias in the DNN neurite orientation, and find that a radial bias leads to a slightly lower propagation speed (see Figure 20 in the revised manuscript). We have attempted to estimate the neuron densities of the MNN and DNN from Figure 3 in Satterlie and Eichinger, 2014. Direct extrapolation to adult medusa sizes as considered in our manuscript leads, however, to excessively large neuron numbers. We discuss this in more detail in our response below.

3) The manuscript itself must be improved to make it more accessible to the research communities working on underwater locomotion and behavior, and to broaden the impact of this work beyond the computational neuroscience community.

To improve the accessibility of our manuscript and broaden its appeal beyond the computational neuroscience community, we added an introductory figure including a schematic overview of our model to the beginning of the manuscript (Figure 1 in the revised manuscript). We also added another subsection to the Introduction describing in more detail previous approaches towards modeling of underwater locomotion and summarizing what is known about jellyfish swimming. We also expanded our account of previous work on fluidstructure interactions and vortex ring dynamics in the Results section of the manuscript.

Reviewer #1:

This is an interesting manuscript that uses modeling of established properties of neurons and neuronal connections to examine the connection between neuronal conduction and behavior, including biomechanics. Modeling is an appropriate way to approach this problem due to difficulties in making multiple recording from scyphozoan neurons. Also, Aurelia is a good choice since it has been used for behavioral and neurobiological projects since the time of Romanes.

We thank the reviewer for his careful reviewing of our manuscript and his inspiring and encouraging suggestions. In the following we address his comments one by one.

The writing is clear and concise, and the figures are appropriate. I am not a modeler, so I have mostly minor comments on the manuscript, with a few major comments.

In the comparison of uniform MNN versus von Mises MNN, I would like to have seen a superposition of the kind of experimental cuts Romanes conducted on the two models to see if they would survive conduction around these interdigitating barriers.

Following the suggestion of the referee, we tested both the radial and the circular cutting experiments performed by Romanes in both von Mises and uniform networks. In agreement with the experiments the simulations show that conduction survives even for severe cuts. There is no qualitative difference between von Mises and uniform networks. We describe our simulations and our findings in the newly added subsection “Cutting experiments" in the Results section of the revised manuscript. It includes two new figures, Figures 7 and 8 and two additional animations.

Also, there are published figures of Aurelia nerve nets using immunohistochemical techniques (both MNN and DNN) where information could be gleaned regarding neurite orientation and density for comparison with the models and the resulting estimates.

We added two paragraphs in the Discussion comparing the results of Satterlie and Eichinger, 2014, on neuron orientation and density with our model. Since Satterlie and Eichinger discovered a general radial bias in the neurite orientation of DNN neurons we tested if this bias has a similar effect on the propagation speed as our von Mises model of the MNN. We find that a radial bias implemented with a von Mises distribution leads to a slightly slower propagation speed (Figure 20 in the revised manuscript). We discuss this in the Discussion section as well. We also highlight that the lower density of the DNN in comparison to the MNN allows the jellyfish to better steer its swimming motion, since a lower density leads to a slower conduction speed. This means that the delays between MNN and DNN can be larger. We were, however, unable to obtain a reliable estimate for the total number of neurons in DNN and MNN networks for the medusa sizes used in our manuscript. Concretely, we attempted to estimate the neuron density of the MNN using Figure 3A in Satterlie and Eichinger, 2014. A very coarse (lower) estimate of 25 neurites in the shown area of about 0.025 mm2 leads to a density of 100,000 neurons per cm2, which would result in an excessively large number of neurons in adult medusa. In the literature we found that for Hydra the total number of neurons was estimated as 5600 (Bode et al., 1973). For Cubozoa, the neuron number in the ring nerve was estimated to lie between 8500 and 17,000 (Garm et al., 2007). A partial remedy could follow from taking into account that the MNN neurites are longer than the side length of the area shown in Figure 3 of Satterlie and Eichinger, 2014. Then a single neurite contributes to the density by crossing several areas as the one shown. But to compute the resulting density we need to assume a typical neurite length, which is unknown in Figure 3A and may vary with medusa size, which is not given in the article. Further, we identify about 25 somas in Figure 3B of Satterlie and Eichinger, 2014, which would again result in an excessively large number of neurons for the DNN in adult medusa. Taken together, it is unclear to us if and how the observed neuron densities in Figure 3 from Satterlie and Eichinger can be extrapolated to the medusa sizes considered in our manuscript. Therefore, we think that a quantitative comparison is not adequate at this point.

Not applicable to this manuscript: I would like to encourage the authors to use their models to investigate conduction in colonial nerve nets of anthozoan corals since Horridge and Anderson found that there were species-specific differences with some exhibiting through-conduction of polyp withdrawal while others had a restricted area of polyp withdrawal. Of the latter, some exhibited incremental conduction while other exhibited decremental conduction. Modeling could elucidate properties of nerve nets that might produce these differences (it would also be a further test of the models).

Thank you very much for highlighting this interesting possible further application and test of our modeling approach to us.

Reviewer #2:

The paper proposes a computational model of jellyfish that integrates multiple scales from single-neuron activity to neuronal networks to muscle activation and fluid-structure interaction all coupled together to produce locomotion and behavior. The modeling is impressive! I find the results on the effect of the size of the neural network on the travel distance and direction of locomotion very interesting, as well as the results on how the interplay between DNN and MNN could produce turning behavior. However, I have a few comments and suggestions for improving the manuscript.

1) After reading the manuscript, I remained unsure what are the mathematical differences between the MNN and the DNN models and how the two networks are coupled together. I suggest that the authors use a schematic figure that clearly shows the different components of the model and how they are all coupled together. The schematic should be placed in the main document, upfront, not at the end of the manuscript in the Materials and methods section. For inspiration on how to produce such a schematic, consult the animal locomotion literature. For example, see Figure 2 of Dickinson's 2000 Science paper "how animals move: an integrative view" and elaborate on the different components of the nervous system of the jellyfish, how it couples to the musculoskeletal system and to the external fluid environment.

Following your suggestion we have added a new schematic figure to the Introduction of the manuscript (Figure 1 in the revised manuscript). In this schematic figure, we explain the extent of the two nerve nets, how they are coupled to the rhopalia and which muscle groups they innervate. Inspired by your comment we have also added an explanation of the DNN setup in the Results subsection “The Mechanism of Turning" such that the reader does not have to go back and forth between Results and Materials and methods to understand the setup.

2) The coupling between the multiple scales from single neuron all the way to biomechanics and behavior is impressive. The power of such mathematical model lies in the ability to use it to make predictions and testable hypotheses on how behavior is enacted at the physiological level, which the authors touch upon in the Results section. However, the literate review in the Introduction is heavily biased towards describing the jellyfish nervous system, and refers to behavior very briefly, if at all. In fact, the literature review on jellyfish turning behavior is introduced in the Results section, which in my opinion is not effective. I suggest that all relevant background information, including jellyfish behavior be introduced in the Introduction, together with clearly stating existing or new hypotheses and research questions, such as "how do jellyfish turn away to avoid undesired stimuli", this is only mentioned at the end of the Results section.

Following your suggestion, we added the subsection “The Hydrodynamics of Swimming" on previous studies of jellyfish swimming and turning to the Introduction. This subsection more comprehensively reviews the literature on jellyfish swimming in both experimental and theoretical studies and highlights current open questions.

3) From a biomechanics standpoint, mathematical models have been developed by Lisa Fauci, Eric Tytell, and collaborators in the context anguilliform swimming, where muscle activation is coupled to fluid-structure interactions to produce swimming behavior, with body undulations not prescribed a priori, but emerging from the coupling between the internal dynamics (muscle activation) and fluid-structure interactions. To me, the novelty of the present work is in modeling the neural network itself. However, I feel that it is important for the authors to acknowledge the work done in the aquatic locomotion community on related problems, such as in the context of undulatory swimming. This should be done in the Introduction section. In the least, such connection will serve to attract wider audience to this work.

In the newly added subsection “The Hydrodynamics of Swimming" of the Introduction we acknowledge the work of the aquatic locomotion community, in particular the work by Fauci and Tytell and we discuss how our study relates to it.

4) Figure 7 is supposed to "validate" or "benchmark" the model against experimental study. I suggest that the authors show the experimental results from Figure 2 of McHenry and Jed, 2003, in Figure 7. On the same note, I'm also almost confident that many groups have worked on fluid-structure interaction simulations showing the vortex ring around a symmetric jellyfish. I suggest that the authors properly reference this body of literature, and use it to both benchmark their flow simulation results and to distinguish their model from existing models that assume prescribed bell deformations.

We included the results from McHenry and Jed, 2003, into our Figure 10 and expanded the comparison in the results. We now also show that the agreement between the recorded data and our simulations can be improved by changing parameters of the jellyfish model's geometry. We more comprehensively discuss the potentials and shortcomings of our 2D simulation in this context and compare it with other jellyfish simulations. Furthermore we expanded our description of the simulated swimming motion to better compare our results to other simulations and recordings of jellyfish swimming.

In sum, I think the mathematical model and the main results are potentially exciting, but the manuscript itself could be improved to make them more accessible to the research communities working on underwater locomotion and behavior, and to broaden the impact of this work beyond the computational neuroscience community.

Thank you again for your helpful comments. We have carefully addressed them and improved the manuscript, in particular with respect to the listed points.