A mathematical model to study the regulation of active stress production in GI smooth muscle

Abstract

In the gastrointestinal (GI) system, motility is governed by the contraction and relaxation of smooth muscle (SM) in response to many regulatory factors. SM in a hollow organ like stomach exhibits two types of contraction: tonic, to maintain the shape of the organ, and phasic, in response to neurotransmitters, hormones or other signaling molecules. Motility disorders such as dysphagia, gastroesophageal reflux disease, irritable bowel syndrome and hypotensive or hypertensive disorders all involve abnormal SM function. Hence, it is important to gain a deeper understanding of contraction and its regulation in GI SM cells. Skeletal muscle cells have force-velocity curves in which shortening velocities are determined only by load and the myosin isoform. In contrast, when smooth muscle activation is altered, e.g. by changing a hormone or agonist concentration, a different set of velocity-stress curves can be obtained. This difference is due to the regulation of both the number of active cross bridges (determining force) and their average cycling rates (determining the velocity). The regulatory system depends on the phosphorylation of cross-bridges, which in turn depends on cytosolic Ca2+ levels. Thus, a model has been proposed to study the effects of (a) Ca2+ concentration on the kinetics of myosin phosphorylation, (b) cross-bridge cycling rates, and (c) the latch state on tonic and phasic contractions. The objective of the model is to describe the regulation of myosin phosphorylation and active stress production in terms of the intracellular Ca2+ concentration. A mathematical formulation of cross bridge cycling has been adapted from the literature and the parameters have been fitted to experimental data from GI SM. Here it was assumed that the Ca2+-calmodulin mediated phosphorylation of myosin is the primary determinant of the kinetics of cross bridge cycling. This model is the first step towards developing a dynamic model of GI SM contraction.