Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.
Keywords: Calcium dynamics; Diffusion; Enzyme kinetics; Second messengers; Signaling pathways; Stochastic simulation.
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