Modelling chemical signalling cascades as stochastic reaction diffusion systems

Abstract

The main objective of this work lies on the development and application of methods for the analysis of stochastic effects in spatially extended chemical signalling cascades. The chemical master equation is used as a starting point for a stochastic description. The introduction of a functional integral representation allows for the precise derivation of chemical rate equations from the stochastic formulation. Moreover this method is used to demonstrate that chemical noise can have counterintuitive effects; for instance it may enhance a signal. If a description of diffusion is included in the chemical master equation, it serves as a starting point for numerical Monte Carlo simulations. The comparison of several Monte Carlo algorithms reveals that the not very well know Logarithmic Classes algorithm is the most efficient algorithm. We combine this stochastic algorithm with two different ways for representing spatial geometries. The resulting Transformed Grid and Finite Volume Monte Carlo method enable the simulation of arbitrary reaction diffusion systems in arbitrary geometries. The developped algorithms are used in two different projects. In the first project it is investigated whether chemical wave fronts provide a reliable mechanism for propagating a signal over large distances, if one accounts for chemical and spatial noise. A bistable model for the lateral spreading of phosphorylation of epidermal growth factor (EGF) receptors is used as an example. This system possesses two stable, steady states A and B, in which either almost none or almost all of the receptors are phosphorylated. Chemical noise may lead to the spontaneous switching from state A to state B with the phosphorylation being spread as a chemical wave front. These wave fronts propagate with constant velocity even if parts of the reaction medium are occluded by obstacles. At biologically plausible values for the obstacle density the front roughens as it propagates through the medium. This makes a temporally exact propagation of the signal almost impossible. - In a second project the Monte Carlo methods are used in order to analyse a minimal, generic model for gradient sensing in Dictyostelium discoideum. It is shown that our model adapts perfectly to uniform stimuli and that it maps linear stimulus gradients on to the intracellular side.