Mathematical Analysis and Simulations of the Neural Circuit for Locomotion in Lampreys

We analyze the dynamics of the neural circuit of the lamprey central pattern generator. This analysis provides insight into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behavior regimes (characterized by phase and amplitude relationships between oscillators) of forward or backward swimming, and turning, can be controlled using the neural connection strengths and external inputs.

Figure 1

The lamprey CPG circuit. The solid lines and the dashed lines denote intrasegment and intersegment connections, respectively.

Figure 2

Simulations. (a) Membrane potentials of $\mathbf{E}$ population on either side of one segment during forward swimming and turning. Turning is induced by an additional constant input to one side only, starting at the time indicated by the dashed line. (b) $\mathbf{C}$ slightly phase leads $\mathbf{E}$ during forward swimming. (c),(d) Waveform of $\mathbf{E}$ along the body in forward and backward swimming, at consecutive times increasing in the direction indicated by the arrows, in the translational invariant model. The switch from forward to backward swimming is achieved by increasing the strength of $\mathsf{H}$ and $\mathsf{Q}$. (e) Oscillation waveforms (note different amplitudes) in body segments at head, tail, and center of the body, without translational invariance. (f) Forward and backward swimming from different initial conditions, with the same connection strengths and inputs.