From head to tail: a neuromechanical model of forward locomotion in Caenorhabditis elegans

Because we know the neural network structure and because it produces well-defined dynamic behavior (sinusoidal movements), Caenorhabditis elegans is probably the best organism to study the link between the structure of neural network and the dynamics generated from the neural network.

This paper models not only the neural dynamics, but also the physical dynamics of the muscles and sensory signals. The unknown parameters are found

The behaviour of the models match not only the speed of the worm but also the overall qualitative kinematics of for- ward movement.

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We have demonstrated that a model of the head motor neuron circuit with SMD and RMD alone is sufficient to gener- ate oscillations that can drive dorsoventral undulations in the head and neck. Analysis of the variations in the ensemble of sol- utions revealed two possible mechanisms: an intrinsic network oscillator and an oscillator driven by stretch-receptor feedback with information about the length of the region posterior to cumulative dorsoventral speed bend magnitude the SMD motoneuron. Furthermore, the coexistence of both mechanisms in the worm would be feasible.

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We highlight here the most substan- tive differences between these two previous models and the one proposed here. First, in previous models, the circuit responsible for oscillations included a broad range of head interneurons and motor neurons. In the Sakata and Shingai model [54], these classes include AIB, AIZ, AVB, AVK, RIA, RIB, RIC, RIG, RIS, RIV, RMD, RME, SAA, SMB and SMD. In the Karbowski et al. model [49], the neurons were ident- ified more abstractly as one of several possible head interneurons subsets, including AIZ, AIA, AWA and AIZ or RIB, RIG, URY and RIB, SAA and head motor neurons including one of either SMB or SMD, and RME. By contrast, in the current model we demonstrate that a minimal set of head motor neurons (specifically SMD and RME) are suffi- cient to generate oscillations. Second, in the previous models the stretch-receptor feedback into the head inter- neurons was postulated to come from SAA and was thus modelled to receive stretch information from the head pos- ture. By contrast, the current model postulates that stretch receptor feedback from SMD is sufficient to drive oscillations in the head using postural information from regions in the head and posterior to the head. Third, in the previous models the oscillations in the head circuit were imposed on downstream premotor command interneurons (e.g. AVB and PVC), which were then communicated to VNC motor neurons. However, the activity of these neurons has since been demonstrated not to correlate with locomotion undula- tions [27,29]. By contrast, in the current model, we demonstrate that the oscillations in the head motor neurons can be propagated to the VNC motor neurons through stretch-receptor feedback. Finally, in previous models, the parameters of the head circuit were hand-designed to gener- ate oscillations. In the current model, we do not assume that oscillations can only be generated in the head; oscillations in the head emerge from the evolutionary optimization process given the neuroanatomical constraints.

Discussion questions