Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum.

The t-tubules of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca(2+)). To investigate how the t-tubule microanatomy and the distribution of membrane Ca(2+) flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca(2+) signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca(2+) signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca(2+) flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca(2+) buffers, including the Ca(2+) indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca(2+) transients was found when the Ca(2+) flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca(2+) signals are predicted. Even at modest elevation of Ca(2+), reached during Ca(2+) influx, large and steep Ca(2+) gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca(2+) flux density along the cell membrane support initiation and propagation of Ca(2+) waves in rat myocytes.

Diffusional channeling in the sulfate-activating complex: combined continuum modeling and coarse-grained brownian dynamics studies.

Enzymes required for sulfur metabolism have been suggested to gain efficiency by restricted diffusion (i.e., channeling) of an intermediate APS(2-) between active sites. This article describes modeling of the whole channeling process by numerical solution of the Smoluchowski diffusion equation, as well as by coarse-grained Brownian dynamics. The results suggest that electrostatics plays an essential role in the APS(2-) channeling. Furthermore, with coarse-grained Brownian dynamics, the substrate channeling process has been studied with reactions in multiple active sites. Our simulations provide a bridge for numerical modeling with Brownian dynamics to simulate the complicated reaction and diffusion and raise important questions relating to the electrostatically mediated substrate channeling in vitro, in situ, and in vivo.