Fig. 3.
Forward crawling survival times are well captured by noise-induced transitions in the model phase dynamics. (A) The distribution of survival times measured from worm data. We measure the probability that a worm’s trajectory, which is in the neighborhood of the forward attractor at time t, has not crossed to negative phase velocity by time t + τ. The decay is exponential, with a mean time 〈τ〉 = 16.3 ± 0.3 s. (B) The predicted mean time 〈τ〉theory as a function of the noise level. We scale the strength of the noise σ2 by a factor 1/β and solve Eqs. 3 and 4 for many noise realizations. The noise at β = 1 corresponds to the strength derived from actual worm motion and the average survival time at the measured noise level (〈τ〉theory = 15.7 ± 1.3 s) is in close agreement with worm data. In the low-noise limit (β≫1) we find 1/〈τ〉theory ∝ exp(-βE) (blue line), analogous to the Arrhenius temperature dependence of chemical reaction rates. Inset shows the region near β = 1 and the red point marks the measured 1/〈τ〉data. The red error bar denotes the bootstrap error in the noise strength, β = 1 ± 0.05.