Mathematical and computational modelling of spatio-temporal signalling in rod phototransduction

Abstract

Rod photoreceptors are activated by light through activation of a cascade that includes the G protein-coupled receptor rhodopsin, the G protein transducin, its effector cyclic guanosine monophosphate (cGMP) phosphodiesterase and the second messengers cGMP and Ca2+. Signalling is localised to the particular rod outer segment disc, which is activated by absorption of a single photon. Modelling of this cascade has previously been performed mostly by assumption of a well-stirred cytoplasm. We recently published the first fully spatially resolved model that captures the local nature of light activation. The model reduces the complex geometry of the cell to a simpler one using the mathematical theories of homogenisation and concentrated capacity. The model shows that, upon activation of a single rhodopsin, changes of the second messengers cGMP and Ca2+ are local about the particular activated disc. In the current work, the homogenised model is computationally compared with the full, non-homogenised one, set in the original geometry of the rod outer segment. It is found to have an accuracy of 0.03% compared with the full model in computing the integral response and a 5200-fold reduction in computation time. The model can reconstruct the radial time-profiles of cGMP and Ca2+ in the interdiscal spaces adjacent to the activated discs. Cellular electrical responses are localised near the activation sites, and multiple photons sufficiently far apart produce essentially independent responses. This leads to a computational analysis of the notion and estimate of 'spread' and the optimum distribution of activated sites that maximises the response. Biological insights arising from the spatio-temporal model include a quantification of how variability in the response to dim light is affected by the distance between the outer segment discs capturing photons. The model is thus a simulation tool for biologists to predict the effect of various factors influencing the timing, spread and control mechanisms of this G protein-coupled, receptor-mediated cascade. It permits ease of simulation experiments across a range of conditions, for example, clamping the concentration of calcium, with results matching analogous experimental results. In addition, the model accommodates differing geometries of rod outer segments from different vertebrate species. Thus it represents a building block towards a predictive model of visual transduction.