ElegansBot: Development of equation of motion deciphering locomotion including omega turns of Caenorhabditis elegans

Reviewer #1 (Public Review):

Summary:
This work describes a simple mechanical model of worm locomotion, using a series of rigid segments connected by damped torsional springs and immersed in a viscous fluid. It uses this model to simulate forward crawling movement, as well as omega turns.

Strengths:
The primary strength is in applying a biomechanical model to omega-turn behaviors. The biomechanics of nematode turning behaviors are relatively less well described and understood than forward crawling. The model itself may be a useful implementation to other researchers, particularly owing to its simplicity.

Weaknesses:
The strength of the model presented in this work relative to prior approaches is not well supported, and in general, the paper would be improved with a better description of the broader context of existing modeling literature related to undulatory locomotion. This paper claims to improve on previous approaches to taking body shapes as inputs. However, the sole nematode model cited aims to do something different, and arguably more significant, which is to use experimentally derived parameters to model both the neural circuits that induce locomotion as well as the biomechanics and to subsequently compare the model to experimental data. Other modeling approaches do take experimental body kinematics as inputs and use them to produce force fields, however, they are not cited or discussed. Finally, the overall novelty of the approach is questionable. A functionally similar approach was developed in 2012 to describe worm locomotion in lattices (Majmudar, 2012, Roy. Soc. Int.), which is not discussed and would provide an interesting comparison and needed context.

The idea of applying biomechanical models to describe omega turns in C. elegans is a good one, however, the kinematic basis of the model as used in this paper (the authors do note that the control angle could be connected to a neural model, but don't do so in this work) limits the generation of neuromechanical control hypotheses. The model may provide insights into the biomechanics of such behaviors, however, the results described are very minimal and are purely qualitative. Overall, direct comparisons to the experiments are lacking or unclear. Furthermore, the paper claims the value of the model is to produce the force fields from a given body shape, but the force fields from omega turns are only pictured qualitatively. No comparison is made to other behaviors (the force experienced during crawling relative to turning for example might be interesting to consider) and the dependence of the behavior on the model parameters is not explored (for example, how does the omega turn change as the drag coefficients are changed). If the purpose of this paper is to recapitulate the swim-to-crawl transition with a simple model, and then apply the model to new behaviors, a more detailed analysis of the behavior of the model variables and their dependence on the variables would make for a stronger result. In some sense, because the model takes kinematics as an input and uses previously established techniques to model mechanics, it is unsurprising that it can reproduce experimentally observed kinematics, however, the forces calculated and the variation of parameters could be of interest.

Relatedly, a justification of why the drag coefficients had to be changed by a factor of 100 should be explored. Plate conditions are difficult to replicate and the rheology of plates likely depends on a number of factors, but is for example, changes in hydration level likely to produce a 100-fold change in drag? or something more interesting/subtle within the model producing the discrepancy?

Finally, the language used to distinguish different modeling approaches was often unclear. For example, it was unclear in what sense the model presented in Boyle, 2012 was a "kinetic model" and in many situations, it appeared that the term kinematic might have been more appropriate. Other phrases like "frictional forces caused by the tension of its muscles" were unclear at first glance, and might benefit from revision and more canonical usage of terms.

Reviewer #2 (Public Review):

Summary:
Developing a mechanical model of C. elegans is difficult to do from basic principles because it moves at a low (but not very small) Reynolds number, is itself visco-elastic, and often is measured moving at a solid/liquid interface. The ElegansBot is a good first step at a kinetic model that reproduces a wide range of C. elegans motiliy behavior.

Strengths:
The model is general due to its simplicity and likely useful for various undulatory movements. The model reproduces experimental movement data using realistic physical parameters (e.g. drags, forces, etc). The model is predictive (semi?) as shown in the liquid-to-solid gait transition. The model is straightforward in implementation and so likely is adaptable to modification and addition of control circuits.

Weaknesses:
Since the inputs to the model are the actual shape changes in time, parameterized as angles (or curvature), the ability of the model to reproduce a realistic facsimile of C. elegans motion is not really a huge surprise.

The authors do not include some important physical parameters in the model and should explain in the text these assumptions. 1) The cuticle stiffness is significant and has been measured [1]. 2) The body of C. elegans is under high hydrostatic pressure which adds an additional stiffness [2]. 3) The visco-elasticity of C. elegans body has been measured. [3]

There is only a very brief mention of proprioception. The lack of inclusion of proprioception in the model should be mentioned and referenced in more detail in my opinion.

These are just suggested references. There may be more relevant ones available.

1. Rahimi M, Sohrabi S, Murphy CT. Novel elasticity measurements reveal C. elegans cuticle stiffens with age and in a long-lived mutant. Biophys J. 2022 Feb 15;121(4):515-524. doi: 10.1016/j.bpj.2022.01.013. Epub 2022 Jan 19. PMID: 35065051; PMCID: PMC8874029.

2. Park SJ, Goodman MB, Pruitt BL. Analysis of nematode mechanics by piezoresistive displacement clamp. Proc Natl Acad Sci U S A. 2007 Oct 30;104(44):17376-81. doi: 10.1073/pnas.0702138104. Epub 2007 Oct 25. PMID: 17962419; PMCID: PMC2077264.

3. Backholm M, Ryu WS, Dalnoki-Veress K. Viscoelastic properties of the nematode Caenorhabditis elegans, a self-similar, shear-thinning worm. Proc Natl Acad Sci U S A. 2013 Mar 19;110(12):4528-33. doi: 10.1073/pnas.1219965110. Epub 2013 Mar 4. PMID: 23460699; PMCID: PMC3607018.

Reviewer #3 (Public Review):

Summary:
A mechanical model is used with input force patterns to generate output curvature patterns, corresponding to a number of different locomotion behaviors in C. elegans

Strengths:
The use of a mechanical model to study a variety of locomotor sequences and the grounding in empirical data are strengths. The matching of speeds (though qualitative and shown only on agar) is a strength.

Weaknesses:
What is the relation between input and output data? How does the input-output relation depend on the parameters of the model? What biological questions are addressed and can significant model predictions be made?