A user-friendly computational model to study Ca2+ waves in rat ventricular myocytes.

Intracellular acidosis is an important modulator of cardiac excitation and contraction, and a potent trigger of electrical arrhythmia, partly through its ability to stimulate acid extruders, which indirectly raises sarcoplasmic reticulum (SR) Ca2+. When this effect is large (a condition known as Ca2+-overload), cardiac myocytes engage in a mode of Ca2+ signaling in which Ca2+ release from the SR to myoplasm occurs in self-propagating succession along the length of the cell. This event is called a Ca2+ wave and is fundamentally a diffusion-reaction phenomenon that is best described with a mathematical model. Wave properties, e.g. frequency, velocity, amplitude and relaxation time are useful parameters to infer how acidic pH affects Ca2+-related components inside the cell, such as the sarco/endoplasmic reticulum Ca2+ ATPase (SERCA), myoplasmic Ca2+ buffers and the ryanodine receptor (RyR). We present a new, continuum mathematical model, based on previous work (1), that simulates spontaneous Ca2+ waves generated during intracellular acidosis and Ca2+-overload. The model, developed with a user-friendly interface in Matlab, is capable of reproducing Ca2+ sparks and wave failure, collision and annihilation. In particular, Ca2+ sparks are modeled by a random function that regulates the opening and closing probability of RyRs, which in turn controls the likelihood of wave generation. Numerical simulations predict that, during Ca2+-overloading conditions, spontaneous Ca2+ wave generation significantly helps the cell to control and maintain at a constant level the myoplasmic and luminal Ca2+ concentration, as suggested in (2). Increasing Ca2+ wave frequency and speed enhances this mechanism, thus giving a simple explanation of what observed experimentally in rat isolated ventricular myocytes, where reducing pHi increased to 360% (by 60 s) wave frequency, together with increasing wave velocity up to 140%. Inhibiting the sarcolemmal Na2+/H2+ exchanger (NHE) suppressed wave frequency but not the increased velocity. In the model, this behaviour can be reproduced by decreasing KON of the lumped Ca2+ buffers, which is experimentally expected being independent of NHE activity. Wave frequency reduction during NHE inhibition can be explained by a fall in SR Ca2+ content mediated by H+-reduced SERCA activity no longer supported by NHE-driven Ca2+ import on NCX. The model shows that reducing SERCA maximum flux instead of its affinity best accounts for the observed experimental change in wave amplitude and relaxation time. Our model successfully reproduces Ca2+ waves using experimentally-derived variables and highlights the importance of SR Ca2+ load on wave propagation. At present, we are developing a model to describe a cardiac multicellular system connected by gap junctions, providing Ca2+ and H+ intercellular diffusion. [ABSTRACT FROM AUTHOR]