Numerical Modelling of C. elegans L1 Aggregation

摘要

We attempt to explain the aggregation behavior of starvedC. elegansL1s (Artyukhin et al., 2015) by a variation of the Keller-Segel chemotaxis model (1970). Each worm releases a diffusible, unstable attractant. The worms chemotax towards the attractant. By using a continuous density function to approximate the spatial distribution of worms, behavior may be described by a nonlinear system of partial differential equations. To determine whether such a model can account forC. elegansL1 behavior, we solve this PDE system numerically. In the original Keller-Segel model, density is unbounded, leading to unrealistic results. We modified the model in such a way as to limit the maximum density. We also developed numerical methods designed to work well near equilibrium. With these changes our model can reproduce some but not all aspects of the behavior.