Steady-State Predictions from a Compact Cooperative Kinetic Model of Cardiac Sarcomere Dynamics

Abstract

A compact model of cardiac sarcomere dynamics is useful when developing integrated models of whole ventricular function. Kinetic models can be simplified by separating slower from faster processes. The representation of faster processes can then be reduced to their equivalent equilibrium relationships. Analysis of cooperativity within a cardiac sarcomere is also aided by dealing with equilibria, which can be analyzed using statistical thermodynamics. These principles guided the formulation of a compact kinetic model of cardiac sarcomere dynamics. In this scheme there were three slower processes: (1) reversible transitions between weak and strong crossbridges, (2) detachment of strong crossbridges, (3) dissociation of calcium from regulatory units (RUs) having a strong crossbridge. In the overall kinetic scheme, an individual RU could exist in 6 states: 3 states of crossbridge binding (none, weak, strong) interacting with 2 states of calcium binding (yes, no). Exchanges between the 4 states without strong crossbridges occurred by rapid equilibria. Thus, in the reduced model only 3 kinetic states remained: (1) strong crossbridges attached to RUs where calcium was bound, (2) strong crossbridges remaining attached even after calcium had dissociated, (3) the equilibrium mixture of the 4 remaining states. Since strong crossbridges appear to act independently, rate constants between these 3 states were considered independent of neighboring RUs. However, cooperativity between neighboring RUs exerted major impacts on the mixture of 4 states interacting rapidly as equilibria. Applying the linear Ising Model of statistical thermodynamics, the grand partition function characterizing interactions between neighboring RUs included activating effects from strong crossbridges as well as free calcium ions. This model predicted steady-state relationships between force and pCa (given as Hill plots) that reproduced the experimentally observed bend toward less cooperative slope near half activation.