Abstract
We present a model to study how membrane surface negative charges can affect the electro-osmotic regulation properties of a cell. This model is based on the cellular analog proposed by Jakobsson, which includes passive and active ion transports; we further introduce the effect of membrane surface charges, using a generalized formulation of the Gouy–Chapman theory. We derive a system of nonlinear differential-algebraic equations (DAEs) which describes the dynamics of the cellular analog. The system admits a unique asymptotically stable stationary state, in which the Na-pump rate, which is crucial for electro-osmotic regulation, is inversely related to the Ca2+level in the extracellular milieu; numerical integration shows that this apparent inhibition of the Na-pump by external Ca2+results from a decrease in the electrostatic field produced by surface charges at the external side of the membrane. Furthermore, the degree of stability of the stationary state dramatically depends on the amount of negative charges on the membrane; a maximal stability is obtained for densities around - e /500 Å2, where the Na-pump is maximally activated by an increase in the Na content of the cytoplasm.
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