Control of Spatially Heterogeneous and Time-Varying Cellular Reaction Networks: A New Summation Law

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dc.creatorPeletier, Mark A.
dc.creatorWesterhoff, Hans V.
dc.creatorKholodenko, Boris N.
dc.date2002-11-06
dc.date.accessioned2026-07-07T04:52:43Z
dc.date.available2026-07-07T04:52:43Z
dc.descriptionA hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control Analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient, cannot be applied to spatially separated protein networks. The present paper unravels the principles that govern the control over the fluxes and intermediate concentrations in spatially heterogeneous reaction networks. Our main results are two types of the control summation theorems. The first type is a non-trivial generalization of the classical theorems to systems with spatially and temporally varying concentrations. In this generalization, the process of diffusion, which enters as the result of spatial concentration gradients, plays a role similar to other processes such as chemical reactions and membrane transport. The second summation theorem is completely novel. It states that the control by the membrane transport, the diffusion control coefficient multiplied by two, and a newly introduced control coefficient associated with changes in the spatial size of a system (e.g., cell), all add up to one and zero for the control over flux and concentration. Using a simple example of a kinase/phosphatase system in a spherical cell, we speculate that unless active mechanisms of intracellular transport are involved, the threshold cell size is limited by the diffusion control, when it is beginning to exceed the spatial control coefficient significantly.
dc.description19 pages, AMS-LaTeX, 6 eps figures included with geompsfi.sty
dc.identifierhttps://arxiv.org/abs/math/0211111
dc.identifierhttp://arxiv.org/abs/math/0211111
dc.identifierJournal of Theoretical Biology, Vol. 225, pp. 477-487 (2003)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65570
dc.subjectAnalysis of PDEs
dc.subjectQuantitative Biology
dc.subject35B30 (Primary) 35J60, 35K55 (Secondary)
dc.titleControl of Spatially Heterogeneous and Time-Varying Cellular Reaction Networks: A New Summation Law
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