Spatiotemporal Feedback and Network Structure Drive and Encode Caenorhabditis elegans Locomotion
Using a computational model of the Caenorhabditis elegans connectome dynamics, we show that proprioceptive feedback is necessary for sustained dynamic responses to external input. This is consistent with the lack of biophysical evidence for a central pattern generator, and recent experimental evidence that proprioception drives locomotion. The low-dimensional functional response of the Caenorhabditis elegans network of neurons to proprioception-like feedback is optimized by input of specific spatial wavelengths which correspond to the spatial scale of real body shape dynamics. Furthermore, we find that the motor subcircuit of the network is responsible for regulating this response, in agreement with experimental expectations. To explore how the connectomic dynamics produces the observed two-mode, oscillatory limit cycle behavior from a static fixed point, we probe the fixed point’s low-dimensional structure using Dynamic Mode Decomposition. This reveals that the nonlinear network dynamics encode six clusters of dynamic modes, with timescales spanning three orders of magnitude. Two of these six dynamic mode clusters correspond to previously-discovered behavioral modes related to locomotion. These dynamic modes and their timescales are encoded by the network’s degree distribution and specific connectivity. This suggests that behavioral dynamics are partially encoded within the connectome itself, the connectivity of which facilitates proprioceptive control.
Fig 2. The raster plot at left plots shows a single trial of neuron voltage responses to a random impulse.
The nonlinear network dynamics encode six clusters of dynamic modes with timescales spanning three orders of magnitude. In the right panel we plot a subset of the dynamic modes which we extract from these dynamics (the ϕ vectors calculated from Eq 14). The modes shown are those with the slowest timescales, later referred to as Modes 4, 5 and 6. One can see the modal dynamics within the raster plot (e.g. one can see traces of the “slow” and “slower” modes, each decaying at a different rate).