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Journal of Neuroscience, Vol 14, 4705-4715, Copyright © 1994 by Society for Neuroscience

ARTICLE

Linearized models of calcium dynamics: formal equivalence to the cable equation

A Zador and C Koch
Neuroscience Program, Yale University School of Medicine, New Haven, Connecticut 06520.

The dynamics of calcium and other diffusible second messengers play an important role in intracellular signaling. We show here the conditions under which nonlinear equations governing the diffusion, extrusion, and buffering of calcium can be linearized. Because the resulting partial differential equation is formally identical to the one-dimensional cable equation, quantities analogous to the input resistance, space constant, and time constant--familiar from the study of passive electrical propagation--can be defined. Using simulated calcium dynamics in an infinite cable and in a dendritic spine as examples, we bound the errors due to the linearization, and show that parameter uncertainty is so large that most nonlinearities can usually be ignored: robust phenomena in the nonlinear model are also present in the linear model.

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