Modeling compartmentalization within intracellular signaling pathway

We present a novel approach to modeling receptor-activated signaling pathways that take into account the compartmentalization of receptors and their effectors, both on the cell surface and in dynamic intracellular vesicles called endosomes. The first building block of the model concerns compartment dynamics. It takes into account creation of de novo endosomes, i.e. endocytosis, and further recycling of endosomes to the cell surface or degradation, as well as fusion of endosomes via coagulation dynamics. The second building block concerns biochemical reactions on the cell surface and within intra-cellular compartments. Both building blocks are coupled by the transfer of molecules that occurs at each event that modifies the compartments. The model is formulated as a integro-partial differential equation, with transport and coagulation operators, and source terms, coupled to an integro-differential equation. In this work, we prove sufficient conditions to obtain exponential ergodicity for the size distribution of intracellular compartments. We further design a finite volume scheme to simulate our model. Finally, we show two application cases that show qualitative agreement with recently published data, proving that our model can help capture the spatio-temporal complexity of receptor-activated signaling pathway.