Publications (3)7.03 Total impact
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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 Matlab's 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 described.  [Show abstract] [Hide abstract]
ABSTRACT: Analysis of the hystereses in the forcelength relationship at constant Ca(2+) concentration and in the forcecalcium relationship at constant sarcomere length (SL) provides insight into the mechanisms that control crossbridge (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 for which the XBs are in 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 Simulink software (Matlab). Counterclockwise (CCW) hysteresis, wherein the force response lags behind the SL oscillations, at a constant calcium level, is obtained in the forcelength plane when neglecting the mechanical feedback and accounting only for the cooperativity mechanism. Conversely, the force response precedes the SL oscillations, yielding a clockwise (CW) hysteresis when only the mechanical feedback is allowed to exist. In agreement with experimental observations, either CW or CCW hysteresis is obtained when both feedbacks coexist: CCW hystereses are obtained at low frequencies (<3 Hz), and the direction is reversed to CW at higher frequencies (>3 Hz). 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 forcecalcium relation is conveniently explained by the same cooperativity mechanism. We propose that a single cooperativity mechanism that depends on the number of strong XBs can explain the hystereses in the forcelength as well as in the forcecalcium relationships. 
Conference Paper: Identification of the intracellular control of the cardiac forcelength relationship: Analysis of the hystereses in the forcelength plane
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ABSTRACT: Revealing the mechanisms underlying the regulation of the cardiac muscle forcelength relation is of immense importance for the understanding the normal and failing heart functions. Our model of the intracellular control of contraction includes two feedback loops: 1. The cooperativity (positive feedback) mechanisms, whereby the number of force generating crossbridges (XBs) affects the rate of new XB recruitment. 2. The mechanical feedback, whereby the sarcomere velocity determines the time over which the XBs are at the strong state. The study aims to verify the ability of the model to explain the experimentally observed hystereses in the forcelength relations (at constant activation) and to determine the role of each feedback loop. The force response to large (>4%) sarcomere length (SL) oscillation lags the length changes at low frequencies (<4Hz), leading to a counterclock wise hysteresis. At high frequencies (>4Hz) the force precedes the SL oscillation and clockwise hysteresis appears. The model of the sarcomere, that couples calcium kinetics with XB dynamics, was built on Simulink. The force responses to SL oscillations were simulated at constant calcium concentration (activation). When the mechanical feedback is opened and only the cooperativity feedback exists, the force lags the SL. Opening the cooperativity mechanism and leaving only the mechanical feedback yields the opposite phenomenon and the force precedes the SL. The cooperativity dominates at low frequencies, when both feedbacks exist, while the mechanical feedback dominates at higher frequencies, in accordance with the experimental observations. The study emphasizes the role of each feedback.
Publication Stats
15  Citations  
7.03  Total Impact Points  
Top Journals
Institutions

2006

Technion  Israel Institute of Technology
 Electrical Engineering Group
H̱efa, Haifa District, Israel
