Sarcolemmal calcium binding sites in heart: II. Mathematical model for diffusion of calcium released from the sarcoplasmic reticulum into the diadic region

We present a model for predicting the temporal and spatial dependence of [Ca] in the cardiac subsarcolemmal diadic region (cleft), following Ca release from the 'feet' of the sarcoplasmic reticulum. This region is modeled as a disc 10 nm thick, 430 nm in radius, with or without Ca binding sites and open at its periphery to the cytosol. [Ca] is computed for three diffusion coefficients (100, 20 and 4% of aqueous diffusion), following release of a 20-msec square pulse sufficient to produce 50% maximal contractile force, or repetitive release (400/min) of such pulses. Numerical solutions are obtained for the general diffusion/binding problem and analytic solutions for the case of no binding sites. For the middle value of diffusion coefficient, and in the absence of binding sites, [Ca] rises to ~1.5 mM in 20-msec and then falls to ~0.1 μM in 100 μM for roughly half of each cycle. Two major implications of the predicted [Ca] are: (i) The effect of Ca binding sites on [Ca] will cause Ca efflux from the cleft via the Na-Ca exchanger (K(m)(Ca) ~ 20 μM) to continue at a significant level for >200 msec. (ii) The time constant for inactivation of release from the 'feet' must be much greater than for activation if Ca-induced Ca release is to continue for >1-2 msec.