There is a growing body of experimental evidence suggesting that the Ca2+ signaling in ventricular myocytes is characterized by high gradient near the cell membrane and a more uniform Ca2+ distribution in the cell interior –. An important reason for this phenomenon might be that in these cells the t-tubular system forms a network of extracellular space, extending deep into the cell interior. This allows the electrical signal, that propagates rapidly along the cell membrane, to reach the vicinity of the sarcoplasmic reticulum (SR) where intracellular Ca2+ required for myofilament activation is stored , –. Early studies of cardiac muscle showed that the t-tubules are found at intervals of ~2 μm along the longitudinal cell axis in close proximity to the Z-disks of the sarcomeres . Subsequent studies have demonstrated that the t-tubular system has also longitudinal extensions –, .
The SR is an entirely intracellular, membrane-bounded compartment that abuts but is not continuous with the sarcolemma. The junctions where SR approaches the sarcolemma contain specialized proteins , , . The sarcolemmal L-type Ca2+ channels (LCC) are located primarily at the SR junctions where the Ca2+ release channels in the SR, the ryanodine receptors (RyRs), exist , , , –. The RyRs are arranged in organized arrays of hundreds of receptors up to 200 nm in diameter.
The concept that the LCCs and RyRs form a local functional unit (release unit, RU) is supported by the observations of Ca2+ sparks. Ca2+ sparks reflect the nearly synchronous activation of a cluster of about 6–20 RyRs at a single junction. Ca2+ sparks are the fundamental units of the SR Ca2+ release both at rest and during cell excitation , –. Thus, the microanatomy of t-tubules and SR permits spatially homogeneous and synchronized SR Ca2+ release throughout the cell. During physiologically normal excitation-contraction coupling (EC-coupling) a several thousand Ca2+ sparks in each cell are synchronized in time by the action potential to achieve a spatially homogeneous Ca2+ transient , –, , . It has also been observed that the spatially uniform Ca2+ transient might be achieved if the SR Ca2+ release and uptake are abolished . However the mechanisms underlying cell activation synchrony and Ca2+ homogeneous distribution still remains unclear.
Recent immunohistochemical studies but one  have demonstrated also that marked variations in the distribution of Ca2+-handling proteins (L-type Ca2+ channel, Na+/Ca2+ exchanger, sarcolemmal Ca2+ ATPase) along the cell membrane probably exist , , , . The analysis suggests that most of the L-type Ca2+ channels are concentrated in the t-tubules (from 3 to 9 times more in the t-tubule membrane than on the surface sarcolemma) and that the concentration of LCC along the t-tubule increases toward the center of the cell , .
Studies on the distribution of the main Ca2+ efflux pathway, the Na+/Ca2+ exchanger (NCX), are more controversial. All studies but one  have reported NCX to localize both to the surface and t-tubule membrane, and most studies suggest that the NCX is 1.7 to 3.5 times more concentrated in the t-tubule membrane, , –. However, Kieval et al. data  indicate the NCX is more evenly distributed. The distribution of the sarcolemmal Ca2+ ATPase is also unclear . Only one study reports that in hamster and canine ventricular cells this Ca2+ efflux pathway is located predominantly in the surface membrane . In summary, the observed differences in the spatial distribution and molecular architecture of Ca2+ microdomains suggest that significant differences in the EC-coupling between the cell surface and cell interior may exist. However how the localization of Ca2+-handling proteins along the sarcolemma regulates the intracellular Ca2+ signaling still remains uncertain.
Taken together above studies demonstrate that remarkable amount of fundamental quantitative data on the ventricular cell structure and function has been accumulated. Recently it has been also emphasized that biophysically realistic computational models, incorporating transverse-axial t-tubular system and considering geometric irregularities and inhomogeneities in the distribution of ion-transporting proteins, are missing and needed , . For this reason, our main goal here was to develop a detailed 3-D model at the sub-cellular level that would allow us to examine how the distribution of Ca2+ fluxes via t-tubule and surface membrane may affect Ca2+-entry, diffusion and buffering. Thus, SR Ca2+ uptake and release was not included here. The current model of the rat ventricular myocyte includes: (1) a simplified 3-D geometry of a single t-tubule and its surrounding half-sarcomeres; (2) the spatially distributed L-type Ca2+ channel, Na+/Ca2+ exchanger, sarcolemmal Ca2+ pump and background Ca2+ leak along the sarcolemma; and (3) the stationary and mobile endogenous Ca2+ buffers (troponin C, ATP, calmodulin) and the exogenous mobile Ca2+ buffer, Fluo-3.
The results suggest that, in the presence of 100 μM Fluo-3, the model is able to predict a uniform Ca2+ distribution inside the cell if Ca2+ microdomains are distributed heterogeneously along the cell membrane. In the absence of Ca2+ indicator the model predicts non-uniform Ca2+ distribution in the cytoplasm and high Ca2+ gradient near the cell edges when the Ca2+ flux pathways were distributed heterogeneously. We concluded that the distribution of Ca2+ handling proteins along the cell membrane might be another important mechanism regulating ventricular EC-coupling. These model predictions are in qualitative agreement with published experimental data in rat ventricular myocytes . Preliminary results of this work have been presented to the Biophysical Society in abstract form .
It is important to mention here that this 3-D sub-cellular model of single t-tubule and surrounding structures also yields insights across two other scales of biological organization: a microscopic scale of individual Ca2+ RU and a whole-cell scale. It allows us not only to extend the analysis further to integrate models of individual Ca2+ RU, SR Ca2+ pump or leak but also to examine how experimentally suggested spatial distributions of these Ca2+ transporters , , , – may affect the behavior of a single RU or the mechanisms underling a synchronized SR Ca2+ release. Future modeling efforts will be focused on replacing the idealistic t-tubule and surrounding structures geometries with more realistic or to include several surrounding t-tubules and other sub-cellular organelles that might help to understand better normal and pathophysiological mechanisms.