Statistics of cellular signal transduction as a race to the nucleus by multiple random walkers in compartment/phosphorylation space

Abstract

Cellular signal transduction often involves a reaction network of phosphorylation and transport events arranged with a ladder topology. If we keep track of the location of the phosphate groups describing an abstract state space, a simple model of signal transduction involving enzymes can be mapped on to a problem of how multiple biased random walkers compete to reach their target in the nucleus yielding a signal. Here, the first passage time probability and the survival probability for multiple walkers can be used to characterize the response of the network. The statistics of the first passage through the network has an asymmetric distribution with a long tail arising from the hierarchical structure of the network. This distribution implies a significant difference between the mean and the most probable signal transduction time. The response patterns for various external inputs generated by our model agree with recent experiments. In addition, the model predicts that there is an optimal phosphorylation enzyme concentration for rapid signal transduction.stochastic biology ͉ first passage time ͉ NFAT A chieving a quantitative understanding of the reaction networks that transduce cellular signals is one of the major challenges in biology. Signaling networks are found in a diverse set of organisms, ranging from prokaryotes to eukaryotes, and provide mechanisms for fundamental processes such as generegulatory control and cellular communication. Qualitative descriptions of the biomolecular components and mechanisms of cellular signaling have greatly improved our understanding of how cells function and have given insights into how to intervene therapeutically when such signals are miscommunicated. Experimental advances now allow quantitative studies of signal transduction and thereby inspire theoretical treatments. Many networks of nonlinear reactions exhibit interesting behavioral features as ultrasensitivity, adaption, robustness, and discrete ''all-or-none'' response, which have been quantitatively explored (1-8).A commonly occurring network topology is the reaction ladder network. This network may be viewed as a generalization of multiple-site phosphorylation͞dephosphorylation cascades, such as the pathway governing nuclear factor activation of T cells (NFAT), which regulates the response of T cells to antigen signaling (9-13). To stimulate T cells, NFAT must be transported to the nucleus. This transition occurs in response to a conformational change that exposes a nuclear localization sequence (NLS), which is normally buried in the protein interior in the inactive conformation and thus makes the NFAT inaccessible to transport by importin. The NLS becomes exposed in response to the progressive dephosphorylation of specific serine residues in its regulatory domain. This dephosphorylation occurs in response to an increase of intracellular calcium ions that activate calcineurin, which then dephosphorylates the masking residues. Once a sufficient number of sites have been dephosphorylated, conformational changes expose...

Hierarchic Stochastic Modelling Applied to Intracellular Ca2+ Signals

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