A comparative study of stochastic and deterministic simulation methods for transport-diffusion systems

Abstract: The growth of tissues and organs in plants is governed by the morphogen auxin coupled with the membrane protein PIN, which together generate patterns that guide development. Systems of this kind have been studied extensively in experiments and computational system biology models. This thesis builds on that work by introducing a stochastic version of these models to examine differences between stochastic and deterministic behaviours of the patterning process. Stochastic simulations are found to exhibit a more dynamic behaviour while deterministic simulations produce patterns that are more sensitive to the underlying cell grid arrangement. The minimum distance between auxin concentration peaks also depends on the cell grid, but is found to be conserved between simulation types. The difference between stochastic and deterministic simulations is significant under certain conditions, and future research should evaluate the system conditions before utilising deterministic algorithms when stochastic simulations might model the system more accurately.