A toy computational model of evolution of directed motility

Nonequilibrium systems dissipate energy and hence break time-reversal symmetry. As a result, a polarization vector in such systems is allowed to couple to the system's velocity vector. Thus, one expects that, generically, a polarized nonequilibrium system would exhibit directed motion along the polarization direction. However, the coupling between polarization and motion may be very weak. Here we conduct a computational experiment with a model of a 1-d gas of active agents (motors) in an enclosure (cell) with polarized mechanical properties to demonstrate that (1) generic values of the parameters of the system, indeed, result in a weak directed motion, and (2) a biological evolution-inspired genetic algorithm can strongly amplify the polarization-velocity coupling in relatively few generations. This toy model suggests that directed motility (e.g., chemotaxis) may be present generically in the context of living cells, and evolution may only need to amplify the taxis speed instead of performing a much harder task of evolving the taxis from scratch.