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Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.

Changes in cytosolic free Mg2+and adenosine nucleotide phosphates affect cardiac excitability and contractility. To investigate how modulation by Mg2+, ATP, and ADP of KATPand L-type Ca2+channels influences excitation-contraction coupling, we incorporated equations for intracellular ATP and MgADP regulation of the KATPcurrent and MgATP regulation of the L-type Ca2+current in an ionic-metabolic model of the canine ventricular myocyte. The new model: 1), quantitatively reproduces a dose-response relationship for the effects of changes in ATP on KATPcurrent, 2), simulates effects of ADP in modulating ATP sensitivity of KATPchannel, 3), predicts activation of Ca2+current during rapid increase in MgATP, and 4), demonstrates that decreased ATP/ADP ratio with normal total Mg2+or increased free Mg2+with normal ATP and ADP activate KATPcurrent, shorten action potential, and alter ionic currents and intracellular Ca2+signals. The model predictions are in agreement with experimental data measured under normal and a variety of pathological conditions.

Objective:Magnesium regulates a large number of cellular processes. Small changes in intracellular free Mg2+([Mg2+]i) may have important effects on cardiac excitability and contractility. We investigated the effects of [Mg2+]ion cardiac excitation-contraction coupling.Methods:We used our ionic-metabolic model that incorporates equations for Ca2+and Mg2+buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na+-K+pump, sarcolemmal and sarcoplasmic Ca2+pumps).Results:Model results indicate that variations in cytosolic Mg2+level might sensitively affect diastolic and systolic Ca2+, sarcoplasmic Ca2+content, Ca2+influx through L-type channels, efficiency of the Na+/Ca2+exchanger and action potential shape. The analysis suggests that the most important reason for the observed effects is a modified normal function of sarcoplasmic Ca2+-ATPase pump by altered diastolic MgATP levels.Conclusion:The model is able to reproduce qualitatively a sequence of events that correspond well with experimental observations during cardiac excitation-contraction coupling in mammalian ventricular myocytes.

Ca2+signaling in cells is largely governed by Ca2+diffusion and Ca2+binding to mobile and stationary Ca2+buffers, including organelles. To examine Ca2+signaling in cardiac atrial myocytes, a mathematical model of Ca2+diffusion was developed which represents several subcellular compartments, including a subsarcolemmal space with restricted diffusion, a myofilament space, and the cytosol. The model was used to quantitatively simulate experimental Ca2+signals in terms of amplitude, time course, and spatial features. For experimental reference data, L-type Ca2+currents were recorded from atrial cells with the whole-cell voltage-clamp technique. Ca2+signals were simultaneously imaged with the fluorescent Ca2+indicator Fluo-3 and a laser-scanning confocal microscope. The simulations indicate that in atrial myocytes lacking T-tubules, Ca2+movement from the cell membrane to the center of the cells relies strongly on the presence of mobile Ca2+buffers, particularly when the sarcoplasmic reticulum is inhibited pharmacologically. Furthermore, during the influx of Ca2+large and steep concentration gradients are predicted between the cytosol and the submicroscopically narrow subsarcolemmal space. In addition, the computations revealed that, despite its low Ca2+affinity, ATP acts as a significant buffer and carrier for Ca2+, even at the modest elevations of [Ca2+]ireached during influx of Ca2+.

We extended the model of the ventricular myocyte by Winslow et al. (Circ. Res. 1999, 84:571–586) by incorporating equations for Ca2+ and Mg2+ buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na+-K+ pump, sarcolemmal and sarcoplasmic Ca2+ pumps). The results indicate that, under normal conditions, Ca2+ binding by low-affinity ATP and diffusion of CaATP may affect the amplitude and time course of intracellular Ca2+ signals. The model also suggests that a fall in ATP/ADP ratio significantly reduces sarcoplasmic Ca2+ content, increases diastolic Ca2+, lowers systolic Ca2+, increases Ca2+ influx through L-type channels, and decreases the efficiency of the Na+/Ca2+ exchanger in extruding Ca2+ during periodic voltage-clamp stimulation. The analysis suggests that the most important reason for these changes during metabolic inhibition is the down-regulation of the sarcoplasmic Ca2+-ATPase pump by reduced diastolic MgATP levels. High Ca2+ concentrations developed near the membrane might have a greater influence on Mg2+, ATP, and ADP concentrations than that of the lower Ca2+ concentrations in the bulk myoplasm. The model predictions are in general agreement with experimental observations measured under normal and pathological conditions.