Mathematical model of excitation-contraction in a uterine smooth muscle cell

Uterine contractility is generated by contractions of myometrial smooth muscle cells (SMCs) that compose most of the myometrial layer of the uterine wall. Calcium ion (Ca²⁺) entry into the cell can be initiated by depolarization of the cell membrane. The increase in the free Ca²⁺ concentration within the cell initiates a chain of reactions, which lead to formation of cross bridges between actin and myosin filaments, and thereby the cell contracts. During contraction the SMC shortens while it exerts forces on neighboring cells. A mathematical model of myometrial SMC contraction has been developed to study this process of excitation and contraction. The model can be used to describe the intracellular Ca²⁺ concentration and stress produced by the cell in response to depolarization of the cell membrane. The model accounts for the operation of three Ca²⁺ control mechanisms: voltage-operated Ca²⁺ channels, Ca²⁺ pumps, and Na ⁺/Ca²⁺ exchangers. The processes of myosin light chain (MLC) phosphorylation and stress production are accounted for using the cross-bridge model of Hai and Murphy (Am J Physiol Cell Physiol 254: C99-C106, 1988) and are coupled to the Ca²⁺ concentration through the rate constant of myosin phosphorylation. Measurements of Ca²⁺, MLC phosphorylation, and force in contracting cells were used to set the model parameters and test its ability to predict the cell response to stimulation. The model has been used to reproduce results of voltage-clamp experiments performed in myometrial cells of pregnant rats as well as the results of simultaneous measurements of MLC phosphorylation and force production in human nonpregnant myometrial cells.