Mathematical modelling of the calcium–left ventricular pressure relationship in the intact diabetic rat heart

Abstract

The objective was to characterize cross-bridge kinetics from the cytoplasmic calcium ion concentration ([Ca2+](i)) and the left ventricular pressure (LVP) in the early-stage diabetic rat heart under baseline conditions and upon beta-adrenergic stimulation. Four weeks after the induction of diabetes in rats by the injection of streptozotocin, the hearts were perfused according to Langendorff, and [Ca2+](i) was obtained by epifluorescence measurements using Indo-1 AM. [Ca2+](i) and LVP were measured simultaneously at a temporal resolution of 200 Hz. The input/output relationship between the Ca2+ and the pressure transients was described by a mathematical model representing the chemical binding of Ca2+ to troponin C on the actin myofilament (TnCA), and the subsequent cooperative force-producing cross-bridge formation of the Ca2+-TnCA complex with myosin. The kinetic parameters of this model were evaluated using a numerical optimization algorithm to fit the model equations to the experimental data. beta-adrenergic stimulation of the hearts with increasing doses of isoproterenol allowed quantification of the model parameters over an extended dynamic range, because isoproterenol administration increased developed pressure, heart rate, as well as [Ca2+](i) amplitude in a dose-dependent manner. Model analysis of the experimental data indicates that beta-adrenergic stimulation of healthy hearts resulted in a decreased sensitivity of TnCA for Ca2+, increased rates of cross-bridge cycling and decreased cooperativity. By contrast, the responses in cross-bridge kinetic parameters to isoproterenol stimulation were blunted in the 4-week diabetic heart. We conclude from our modelling results that myocardial cross-bridge cycling is impaired at the early stage of diabetes.