Individual-based models for the functional impact of signalling proteins spatial distribution and diffusion heterogeneity

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. Di erent 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 di erent degrees of freedom, and di use either in the plasma membrane that is bidimensional interface, or in the cytoplasm which is tridimensional medium. Within these very di usion 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. Di usion and reaction between simulated molecules are reproduced based on biophysically accurate stochastic processes. Such granularity allows for the reproduction of heterogeneous spatial distributions and di usion of signalling proteins as observed in biology, and the investigation of their e ect on the functioning of a simulated signalling pathway. First, we explored the e ect of xed heterogeneous receptor distributions on the extracellular ligand-receptor binding process. In simulation, receptors in clusters presented a decreased apparent a nity 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 rst 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 modi ed 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 di usion : restricted zones of low-di usivity were introduced. When receptors and their substrate were co-clustered, an ampli cation e ect was observed. When only receptors were clustered, the response was attenuated as observed with xed receptor distributions.