Discussions on simulating the worm's crawling by means of command neurons, motor neurons and muscle cells

[raminmh]

In a series of documents, I will discuss the role of the command-neurons, different types of motor neurons and their connectivity with the body-wall muscle cells. The ultimate goal is to derive a valid assumption on how the crawling happens in C. elegans and accordingly, simulate the response of the worm to a tap or touch stimulus in C302 and Sibernetics. My justifications will be based on the connectome dataset provided for the adult hermaphrodite by the WormWiring [1]. I will be investigating various neural circuits consisting of command neurons such as AVB and AVA, together with B-type, A-type, D-type and AS motor neurons including their connectivity to the muscles. The first discussion will be on a neural circuit comprised of AVB and B-type motor neurons. I will then discuss D-type and AS motor neurons within the next discussion. Afterwards, I will include the body-wall muscles into the neural circuit and discuss in details the propagation of an AVB-excitation into the motor neurons and muscle cells. I will finally repeat such analyses with AVA command neuron and A-type motor neurons and explain the neural circuit's architecture.
We then simulate our hypotheses in C302 and perform a parameter optimization based on our findings.

1) On the importance of the command neuron AVB and B-type motor-neurons in the worm’s crawling:

AVB command neuron together with B-type motor neurons function in the deriving the forward locomotion. There are seven dorsal and eleven ventral B-type motor neurons spread over the body of the worm. Considering a neural circuit, shown in Figure 1A and 1B, consist of only AVBL/R and all the B-type motor-neurons on the dorsal and ventral sides, one can highlight some attractive fundamental architectural design properties within the circuit:

• AVBL/R synapse onto all B-type motor neurons with an average number of 10 connections to the dorsal and 8 connections to the ventral motor neurons. Among the motor neurons VB2 is getting the highest number of gap-junctions which can be an indicator of the importance of the VB2 in signaling. Many motor neurons receive a similar number of connections form AVB (with the assumption of the equally distributed weights of each synaptic connection). This presumably implies that the objective of AVB can be in the initiation of a forward-locomotion action as well as equal distribution of the forward-command for several motor-neurons.

Figure 1. AVB and B-type motor neurons neural circuit. A) AVBR\L and dorsal motor neuron neural circuit. Green lines are bidirectional gap junctions. Blue arrows represent excitatory synapses. Numbers on each line/arrow represent the number of synaptic connection between neurons. (Note that for instance 4/3, stands for 4 connections from AVBL and 3 connections from AVBR.) B) AVBR\L and ventral motor neuron neural circuit. C) Worm's muscles [2].

• By looking at the sequential lateral connections among dorsal B-type motor-neurons, one can observe that DB1, DB2 and DB3 are strongly coupled through their gap-junctions while weakening their correlation rate with the rest of the synced motor-neurons DB4, DB5, DB6 and DB7, through a weak gap-junction between DB3 and DB4. This can potentially indicate that the activity of the dorsal B-type motor-neurons can be decoupled where the neurons 1 to 3 can be responsible for exciting part-A muscle cells shown in figure 1C, and the rest being responsible for the stimulation of the muscles depicted in part-B.

• Such property holds for the ventral B-type motor neurons as well. Neurons VB2 and VB3 are strongly coupled while they get gradually decoupled to the rest of the motor neurons by means of the weak connections among VB3, VB4 and VB5. Therefore, we assume that the first group including VB1 to VB4 excites part-A muscles cells and second group including VB5 to VB11 excites part-B of the body-wall muscles.

• Hypothesis 1: Like many other biological optimal networks such as beta cell hubs in islet functional architecture [3], I assume there exist hub neurons within the network of motor neurons in the C. elegans connectome which distribute commands within the network. This is explainable by looking at the connections from AVB to the motor neurons where the first group of motor neurons and specially their hubs (DB1 and VB2) are getting stimulated the most and in the next group DB7 and VB11 gets the most number of connections. The hypothesis can be further supported by an analysis on the connectivity of the motor neurons and muscle cells which will be included within the next discussions.

Such property has been observed also within the D-type dorsal and ventral motor neurons which will be explained in the next discussion.

References:
[1] wormwiring, http://wormwiring.org/hermaphrodite/herm.php
[2] wormbrowser, http://browser.openworm.org
[3] Johnston, Natalie R., et al. "Beta cell hubs dictate pancreatic islet responses to glucose." Cell Metabolism 24.3 (2016): 389-401.

[slarson]

Relevant: http://www.jneurosci.org/content/33/15/6380#sec-13

I'd suggest that these hypotheses can have tests built around them via c302 models to explore their implications.

[raminmh]

2) Proprioception in motor neurons is key for generating the forward locomotion

Even when all the command interneurons were knocked out, C. elegans was able to generate the crawling [1]. This suggests the significant role of motor neurons in propagation of the bending waves.

In general, rhythmic behavior is exhibited in animals thanks to the existence of neural circuits named as central pattern generator (CPG) [2]. There can be groups of CPG networks distributing rhythmic activities in an organism. CPG networks therefore should get coordinated with each other. Usually a sensory feedback mechanism exists for such coordination [3, 4, 5].

In C. elegans however, such sensory feedback does not exist due to lack of advanced sensory neurons. Accordingly, one argument suggests that the proprioceptive property can be "economically" exhibited by means of individual motor neurons [6, 8]. Electron microscopy illustrated that particularly cholinergic motor neurons (e.g. B-type), induce asynaptic processes all along the posterior without synaptic connections [6, 8]. Such mechanisms have been hypothesized as a proprioception process.
It has been also seen that the mechanical load from different environments (e.g. water or soil), changes the gait (e.g. swimming or crawling) [7], suggesting an unknown proprioception mechanism [8].

Wen et al. in [8], conducted wonderful experiments on quantification of proprioception in the B-type motor neurons of C. elegans.

• By employing microfluidic devices and in vivo optical neurophysiology, they showed that [8]: “proprioceptive coupling between adjacent body segments constitutes the trigger that derives the bending wave propagation from head to tail.”
• They showed that the posterior body parts are forced to bend shortly after the neighborhood anterior bending, in the same direction.
• They quantified the spatial and temporal kinetics of the proprioceptive coupling localized to the B-type motor neurons.
• They have also demonstrated [8]: “Proprioception in the C. elegans motor circuit, beyond simply explaining the propagation of an undulatory wave from head to tail, also provides a quantitative explanation for gait adaptation to external load.”

Figure 1. (Taken from [8]) Symbolic representation of connections from DB and VB motor neurons to some muscle cells through their neuromuscular junctions (Triangles) and their axons along the body of the worm. The asynaptic process shown in the figure illustrates the potential proprioceptive effect of the B-type motor neurons by means of their axons. Axons of the anterior DB motor neurons extend along the body of the worm to the posterior side making it possible to propagate a bending wave [8].

According to such findings, I believe for modeling the crawling of C. elegans, in our neuron or muscle model one should properly include the biomechanics of the undulatory movement in order to include the proprioception mechanisms.
Axons of the B-type motor neurons overlap each other along the body from head to tail. While some of them getting activated, they can communicate with their naighbors from the anterior side to the posterior side. Such overlapping structure together with gap junctions between motor neurons (discussed in the first document) might presumably be the way a wave propagates from neuron to neuron.
One possible way to include proprioception can be the establishment of hypothetical synapse-like actuators from anterior DB motor neurons along their axons to the muscle segments to which they face and to the neurons they overlap.

We will try this soon together with David! @lungd

References:
[1] T. Kawano, M.D. Po, S. Gao, G. Leung, W.S. Ryu, M. Zhen, An imbalancing act: gap junctions reduce the backward motor circuit activity to bias C. elegans for forward locomotion, Neuron, 72 (2011), pp. 572–586.
[2] T.G. Brown, The intrinsic factors in the act of progression in the mammal, Proc. R. Soc. Lond. B Biol. Sci., 84 (1911), pp. 308–319.
[3] O.J. Mullins, J.T. Hackett, J.T. Buchanan, W.O. Friesen
Neuronal control of swimming behavior: comparison of vertebrate and invertebrate model systems, Prog. Neurobiol., 93 (2011), pp. 244–269.
[4] X. Yu, W.O. Friesen, Entrainment of leech swimming activity by the ventral stretch receptor, J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol., 190 (2004), pp. 939–949.
[5] K.G. Pearson, Generating the walking gait: role of sensory feedback, Prog. Brain Res., 143 (2004), pp. 123–129.
[6] J.G. White, E. Southgate, J.N. Thomson, S. Brenner, The structure of the nervous system of the nematode Caenorhabditis elegans, Philos. Trans. R. Soc. Lond. B Biol. Sci., 314 (1986), pp. 1–340.
[7] J.H. Boyle, S. Berri, N. Cohen, Gait modulation in C. elegans: An integrated neuromechanical model, Front. Comput. Neurosci., 6 (2012), p. 10
[8] Wen, Quan, Michelle D. Po, Elizabeth Hulme, Sway Chen, Xinyu Liu, Sen Wai Kwok, Marc Gershow et al. "Proprioceptive coupling within motor neurons drives C. elegans forward locomotion." Neuron 76, no. 4 (2012): 750-761.

[raminmh]

This recent article could be insightful for studying the proprioceptive coupling.

A new computational method for a model of C. elegans biomechanics: Insights into elasticity and locomotion performance

Netta Cohen, Thomas Ranner

https://arxiv.org/abs/1702.04988

[slarson]

Sub-roadmap for the nervous system simulation

1. Achieve a targetted output from the nervous system model in whatever means possible
   1. We consider this phase to be the "engineering phase" where we are willing to make compromises on biological realism within certain boundaries. We do want to use an accurate quantity of neurons and we want to have the connections be real and we want to use ion channel based dynamics for the neurons. We want to include synaptic connections and gap junction connections. We want to have excitatory and inhibitory connections that are driven by neurotransmitter receptor dynamics. Initially we will work with single compartmental neurons, but we will also want to explore using the multi-compartmental version of the nervous system model soon after. We want to reuse as much of the knowledge as possible that we have incorporated into PyOpenWorm
   2. Specifically, we have found from our work with Sibernetic that a sinusoidal input to the dorsal muscles and a second sinusoid shifted by 90 degrees to the ventral muscles is sufficient to produce appropriate swimming and crawling behavior. The exact quantities to target are (Fang-Yen 2010): . Thus we are trying to see an activation pattern result in the muscles that is sustainable.
   3. By "whatever means possible" that means we are working with the free parameters of the C. elegans nervous system to try different values within parameter space that achieves a network, that when simulated over time, produces that pattern on the muscle cells in an ongoing fashion. This includes using some values that are unrealistically homogenous or within unrealistic ranges. The purpose in this first pass is not to have exactly correct values but to have the correct output with the real connectome composed of at least a majority of the neurons involved
2. As we are exploring parameter space on the way to reaching this targetted output, we are keeping a list of assumptions and non-biogically chosen parameters for the nervous system.
3. Upon achieving the desired level of performance, we go back to the list of assumptions, and we explore replacing the unrealistic values with the realistic ones one by one while still constraining the model to continue to maintain the target performance.
   1. In this phase we are now in a space where we begin to explore and hypothesize about the functional role of various biological features and parameters (role of certain neuron classes, role of certain subcircuits, role of particular ion channels, role of particular connections) as we add them back in.