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 pH_i 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 K_ON 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]