Fig. 5.
The changes in the stochastic dynamical system, Eqs. 3 and 4, as a consequence of increasing time away from food (A, B) and with genetic perturbations (C, D). (A) The mean deterministic force F(ϕ,ω) along escape trajectories derived from wild-type worms in early (black), middle (red), and late (blue) epochs. Units are cycles/s2 and differences among the three 700 s epochs are relatively small. Within each epoch we fit the stochastic model and generate N = 104 trajectories with initial conditions in the forward crawling attractor. As before, we evolve each trajectory until a phase reversal. The escape trajectories are aligned to the moment of the reversal (t = 0) and errors denote standard errors in the mean. (B) The mean noise amplitude σ2(ϕ,ω) along escape trajectories in early, middle and late epochs. Units are cycles2/s3. The mean noise amplitude systematically decreases resulting in longer times within the forward crawling state. (C, D) The mean deterministic force and noise amplitude derived from a goa-1 mutant during the early 700 s epoch. For comparison we also show the wild-type (N2) dynamics from the same early epoch. Befitting the general nature of the goa-1 gene, the mutant dynamics reveal substantial changes to both the deterministic force and the noise.