Modeling diffusion in a signal transduction pathway: The use of virtual volumes in p systems

In living cells, the diffusion of molecules is fundamental for the proper functioning of many intracellular processes and for their correct response to external or internal signaling. In this paper, we consider the diffusion of a pivotal protein involved in bacterial chemotaxis, and show how to model and simulate the formation of concentration gradients of this protein along the bacterial cell. For this purpose, we exploit the framework of P systems to represent the partition of the bacterial volume into separate but communicating virtual volumes, and make use of communication rules to mimic the diffusive events. We simulate this system by means of the multivolume stochastic simulation algorithm τ-DPP, and present the effects of different diffusion coefficients and of a varying number of virtual volumes over the response of the chemotactic pathway.