Authors: Yael Yaniv Raphael Sivan Amir Landesberg
Publish Date: 2006/04/26
Volume: 34, Issue: 5, Pages: 778-
Abstract
A model of the sarcomeric control of contraction at various loading conditions has to maintain three cardinal features stability controllability where the output can be controlled by the input and observability where the output reflects the effects of all the state variables The suggested model of the sarcomere couples calcium kinetics with crossbridge XB cycling and comprises two feedback mechanisms i the cooperativity whereby the number of forcegenerating strong XBs determines calcium affinity regulates XB recruitment and ii the mechanical feedback whereby shortening velocity determines XBs cycling rate controls the XBs contractile efficiency The sarcomere is described by a set of four firstorder nonlinear differential equations utilizing the Matlabs Simulink software Small oscillatory input was imposed when the state variables trajectories reached a steady state The linearized statespace representations of the model were calculated for various initial sarcomere lengths The analysis of the statespace representation validates the controllability and observability of the model The model has four poles three at the left side of the complex plane and one integrating pole at the origin Therefore the system is marginally stable The Laplace transform confirms that the state representation is minimal and is therefore observable and controllable The extension of the model to a multisarcomere lattice was explored and the effects of inhomogeneity and nonuniform activation were describedThe troponinC regulatory protein has one lowaffinity site for calcium binding that regulates XB cycling Calcium binding to this lowaffinity site regulates the rate of the actomyosin ATPase and XB transition from the weak to the strong conformation3The generated force is determined by the number of strong XBs N XB at states T and U in the single overlap region L s between the thin and thick filaments The number of the strong XBs N XB Eq 1 is a product of the density of strong regulatory units states T and U and the muscle volume of interest that is defined by the muscle crosssection area a and the single overlap length L sIn general the velocity is determined by coupling the equation for force development by the sarcomere Eq A8 with the equation that represents the load that the sarcomere encounters14 17 Coupling the force development by the sarcomere and the loading conditions yield an equation for the shortening velocity and this equation is used for solving the state equation Eqs A3–A6 including the sarcomere length
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