Mathematical Modeling of the Rod Phototransduction Process

Rod photoreceptors are capable of responding to very dim light, thus allowing for night vision. The phototransduction process in rods is a quite well known phenomenon and thus it can be considered as a paradigm of cell signalling mechanisms. Despite a quite deep understanding of the underlying biochemical processes and the availability of measured ranges for all the involved physical parameters, a model able to capture the intricate diffusion processes arising inside the rod cell was not available in the literature. In fact, only simple well stirred models, considering the concentration of the involved species as uniform inside the cell, have been proposed and used by biologists for the interpretation of the experimental measurements. As a matter of fact, due to the intricate cell structure and the photon absorption mechanism, the diffusion processes inside the cell turn out to be crucial for a correct understanding of the cell operation. To this end, a spatially fully resolved model of the rod cell has been proposed, taking into account all the diffusion processes arising inside the rod. The complexity due to the intricate rod cell structure was greatly reduced by using the mathematical techniques of homogenization and concentration of capacity, yielding a model described by coupled partial differential equations of parabolic type, with non-linear source terms, set into simple homogeneous domains. A finite element formulation of the proposed model was then developed, supplying numerical results well reproducing the available experimental results. Once validated, the model was used for performing virtual experiments, not possible in vivo, and testing new hypotheses, providing insights about unknown and debated aspects of the rod phototransduction phenomenon.