M.Sc Thesis

M.Sc StudentYaniv Yael
SubjectIdentification of the Sarcomere Contraction Control
DepartmentDepartment of Electrical and Computer Engineering
Supervisors PROFESSOR EMERITUS Raphael Sivan (Deceased)
ASSOCIATE PROF. Amir Landesberg


Analysis of the hystereses in the force-length relation at constant calcium concentration and in the force-calcium relation at constant sarcomere length (SL) provides insight into the mechanisms that control cross-bridge (XB) recruitment. The hystereses are related here to two mechanisms that regulate the number of strong XBs: The cooperativity, whereby the number of strong XBs determines calcium affinity, and the mechanical feedback, whereby the shortening velocity determines the duration in which the XBs are at the strong state. The study simulates the phenomena and defines the role of these feedbacks. The model that couples calcium kinetics with XB cycling was built on Matlab's Simulink. Counterclockwise (CCW) hysteresis is obtained in the force-length plane, when only the cooperativity mechanism exists. Conversely clockwise (CW) hysteresis is obtained when only the mechanical feedback exists. In agreement with the experimental observations CCW hystereses are obtained at low frequencies (<3Hz) and the direction is reversed to CW at higher frequencies (>3Hz). The cooperativity dominates at low frequencies and allows the muscle to adapt XB recruitment to slow changes in the loading conditions. The changeover frequency from CCW to CW hysteresis defines the velocity limit above which the muscle absorbs rather than generates energy.  The hysteresis in the force-calcium relation is conveniently explained by the same cooperativity mechanism. The model developed has the three cardinal features: stability, observability and controllability. To validate these features of the model, linearization was performed. The system has four poles, three at the left side of the complex plane and one integrating pole at the origin. Therefore the system has BIBO stability. The system is minimal and is therefore observable and controllable; the system output is controlled by the input and the output reflects all the properties of the system. This model, that is based on the description of the intracellular control of the sarcomere contraction, can be integrated to describe cardiac and multiple skeletal muscle.