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

SummaryWe 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 < 3 msec. Adding binding sites reduces peak [Ca] to ∼0.6 mm but prolongs its decline, requiring ∼200 msec to reach 20 μm. For repetitive release [Ca] is > 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 NaCa exchanger (Km(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 Cainduced Ca release is to continue for > 1–2 msec.