Signalling pathways allow cells to perceive and exchange information under the form of chemical signals. Such a signal generates a response of the cell through the crucial stages of reception and transduction. Different types of protein interact in a structured manner as a cascade of reactions that relay the signal from the exterior to the interior of the cell, notably through the membrane. Signalling proteins are restricted to compartments with different degrees of freedom, and diffuse either in the plasma membrane that is bidimensional interface, or in the cytoplasm which is tridimensional medium. Within these very diffusion spaces, the spatial distributions of signalling proteins are heterogeneous. The mathematical models of signalling pathways dynamics, however, classically assume that signalling proteins are distributed homogeneously. We developed computational models of biochemical reactions between populations of molecules where the state and the position of each molecule are tracked. Diffusion and reaction between simulated molecules are reproduced based on biophysically accurate stochastic processes. Such granularity allows for the reproduction of heterogeneous spatial distributions and diffusion of signalling proteins as observed in biology, and the investigation of their effect on the functioning of a simulated signalling pathway. First, we explored the effect of fixed heterogeneous receptor distributions on the extracellular ligand-receptor binding process. In simulation, receptors in clusters presented a decreased apparent affinity compared to the situation where they were distributed homogeneously. Clustering induced a redistribution of binding events that favored rebinding at short time scales at the expense of first passage binding events. Secondly, we explored the transduction stage between receptors and their membrane-bound signalling substrate at the membrane level. Clustering induced a decrease in response as well, and modified the structure of the dose-response relationship. Finally, we implemented a dynamical clustering mechanism in simulation, and reproduced the transduction stage on a membrane presenting non-homogeneous diffusion: restricted zones of low-diffusivity were introduced. When receptors and their substrate were co-clustered, an amplification effect was observed. When only receptors were clustered, the response was attenuated as observed with fixed receptor distributions.
Individual-based models for the functional impact of signalling proteins spatial distribution and diffusion heterogeneity