  We present a new modeling approach for G protein coupled receptors signaling
systems, that take into account the compartmentalization of receptors and their
effectors, both at plasma membrane and in dynamic intra-cellular vesicles
called endosomes. The first building block of the model is about compartment
dynamics. It takes into account creation of de-novo endosomes, i.e.
endocytosis, recycling of endosomes back to plasma membrane, degradation
through transfer into lysosomes as well as endosomes fusion through coagulation
dynamics. The second building block is biochemical reactions into each
compartments and the transfer of molecules between the dynamical compartments.
In this work, we prove sufficient conditions to obtain exponentially ergodicity
for the size distribution of intracellular compartments. We futher design a
finite volume scheme to simulate our model and show two application cases for
receptor trafficking and spatially biased second effector signaling.
