Panel A: Schematic drawing of the model geometry showing the single t-tubule and its surrounding half-sarcomeres. The top surface of the cube is the surface membrane for the model compartment. Panel B: A diagram illustrating Ca²⁺ entrance and extrusion along the t-tubule and surface membrane and Ca²⁺ buffering and diffusion inside the cell when the SR release and uptake are inhibited.

Panel A: The finite element software package contained four components with data flowing from top to bottom. Panel B: Composite view of the subdomain–to-processor assignment used to partition the mesh on 10 processors.

Predicted 3-D Ca²⁺ concentration distributions (computed from the line-scan images in Figs. 4G–I) at Ca²⁺ peak of 68 ms are shown in panels A–C. In panel D the spatial profiles at Ca²⁺ peak along the scanning line (200nm from the surface of the t-tubule) are compared: gray line - Ca²⁺ pathways heterogeneously distributed on the t-tubule and surface membrane (see panel A); violet line - Ca²⁺ pathways uniformly distributed on the t-tubule (see panel B); pink line - Ca²⁺ pathways uniformly distributed via the sarcolemma (see panel C). Local Ca²⁺ concentration profiles at two different line-scan positions (0 nm - solid lines, 875 nm - ‘+’ plots) are superimposed in panels E–G. Along the t-tubule the three featured spots were (0μm - blue lines, 3.48 μm - green lines, 6.76 μm - red lines) and in the cell interior (0μm - blue lines, 1.63 μm - green lines, 6.51 μm - red lines). In panels E–G the Ca²⁺ pathways were distributed heterogeneously or uniformly in the t-tubule membrane (as in panels A and B) or evenly along the cell surface (as in panel C).

T-tubular network complexity in adult mammalian ventricular myoyctes. Cardiac sarcolemma including t-tubules was stained with Alexa-488-conjugated wheat germ agglutinin (WGA) in 80 μm vivratome sections of adult mouse ventricular myocardium and visualized using a 2-photon microscopy (Radians 2000, BioRad, objective: 60x oil, NA=1.40, ex 800 nm, em 508–558, 59 nm/pixel). T-tubules invaginated from the surface membrane are shown to develop extensively branching in the middle of myocyte. Surface membrane (blue arrows), t-tubules (white arrowheads), nucleus (Nuc), bar 2 μm. The image was kindly supplied by Masahiko Hoshijima and Takeharu Hayashi (unpublished data).

Panel A: The distribution of L-type Ca²⁺ current was computed (dashed line) by multiplying the experimentally measured cluster density and fluorescent intensity plots (solid line), [8], [16]. Panel B: The L-type Ca²⁺ current density was fitted and plotted (dashed line) using shape preserving function of the data reported in rats with SR blocked (solid line), [28].

Model predictions in the presence of 100 μM Fluo-3. The voltage-clamp protocol and the whole-cell L-type Ca²⁺ current used in this set of simulations are shown in panels A–B. Predicted global Na⁺/Ca²⁺, Ca²⁺ pump and leak currents and global Ca²⁺ transient when Ca²⁺ was uniformly distributed inside the cell are shown in panels C–F. Calcium concentrations visualized as line-scan images in transverse cell direction are shown in panels G–I. Panels J–L show the local Ca²⁺ transients taken at three featured spots along the scanning line (0.17μm – blue lines, 3.09μm – green lines, 6.65μm – red lines). In panels G and J the L-type Ca²⁺ current density followed heterogeneous distribution in the t-tubule that was 6 times higher than in surface membrane and increased 1.7 times along the length of t-tubule as shown in Fig. 2A. In panels H and K the L-type Ca²⁺ current density was uniform along the t-tubule and 6 times higher than in surface membrane. In panels I and L the L-type Ca²⁺ current density was homogeneous throughout the cell surface. In this numerical experiment Na⁺/Ca²⁺ current density was 3 times higher in the t-tubule membrane, Ca²⁺ pump was located only on the surface membrane, and Ca²⁺ leak was distributed homogeneously via the sarcolemma. Panel M illustrates local Ca²⁺ time-courses with re-plot from experimental data [8]. The re-plots were taken along the scanned line at 0μm (blue), 3.96μm (green) and 7.57μm (red) from the near surface location. Panels J and M demonstrate that model predictions are in agreement with the experiment only when Ca²⁺ influx and efflux pathways were distributed heterogeneously. The scanned lines (model and experiment) were located at 200nm from the surface of the t-tubule (see red line in Fig. 5A).

Model predictions in the absence of Fluo-3 with heterogeneous distribution of Ca²⁺ pathways via the cell membrane. Panels A and B show the voltage-clamp protocol and whole-cell L-type Ca²⁺ current used in this set of simulations. The predicted global Na⁺/Ca²⁺, Ca²⁺ pump and leak currents are presented in panels C–E. The global Ca²⁺ transient and Ca²⁺ concentrations visualized as line-scan image in the transverse cell direction are shown in panels F and G. In panel H the local Ca²⁺ transients at three spots along the scanning line are superimposed (blue line - 0.17μm, green line - 3.09μm, red line - 6.65μm). Panel K shows 3-D view of Ca²⁺ concentration distribution at Ca²⁺ peak (~68 ms). Scanning line in panels G–H and K was located at 200nm from the surface of the t-tubule. The local Ca²⁺ concentration profiles at two different line-scan positions (0 nm - solid lines, 875 nm - ‘+’ plots) are superimposed in panel I. Panel J is an expanded view of panel I. On the t-tubule membrane and in the cell interior the featured spots were chosen to be the same as in Fig. 5E.