Mathematical description of geometric and kinematic aspects of smooth muscle plasticity and some related morphometrics

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Abstract
Despite considerable investigation, the mechanisms underlying the functional properties of smooth muscle are poorly understood. This can be attributed, at least in part, to a lack of knowledge about the structure and organization of the contractile apparatus inside the muscle cell. Recent observations of the plasticity of smooth muscle and of morphometry of the cell have provided enough information for us to propose a quantitative, although highly simplified, model for the geometric arrangement of contractile units and their collective kinematic functions in smooth muscle, particularly airway smooth muscle. We propose that, to a considerable extent, contractile machinery restructures upon activation of the muscle and adapts to cell geometry at the time of activation. We assume that, under steady-state conditions, the geometric arrangement of contractile units and the filaments within these units determines the kinematic characteristics of the muscle. The model successfully predicts the results of experiments on airway smooth muscle plasticity relating to maximal force generation, maximal velocity of shortening, and the variation of compliance with adapted length. The model is also concordant with morphometric observations that show an increase in myosin filament density when muscle is adapted to a longer length. The model provides a framework for design of experiments to quantitatively test various aspects of smooth muscle plasticity in terms of geometric arrangement of contractile units and the muscle's mechanical properties.