Of the ions involved in the intricate workings of the heart, calcium is considered perhaps the most important. It is crucial to the very process that enables the chambers of the heart to contract and relax, a process called excitation-contraction coupling. It is important to understand in quantitative detail exactly how calcium is moved around the various organelles of the myocyte in order to bring about excitation-contraction coupling if we are to understand the basic physiology of heart function. Furthermore, spatial microdomains within the cell are important in localizing the molecular players that orchestrate cardiac function.

Cardiac excitation–contraction coupling

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Spontaneous local increases in the concentration of intracellular calcium, called "calcium sparks," were detected in quiescent rat heart cells with a laser scanning confocal microscope and the fluorescent calcium indicator fluo-3 Estimates of calcium flux associated with the sparks suggest that calcium sparks result from spontaneous openings of single sarcoplasmic reticulum (SR) calcium-release channels, a finding supported by ryanodine-dependent changes of spark kinetics At resting intracellular calcium concentrations, these SR calcium-release channels had a low rate of opening (approximately 00001 per second) An increase in the calcium content of the SR, however, was associated with a fourfold increase in opening rate and resulted in some sparks triggering propagating waves of increased intracellular calcium concentration The calcium spark is the consequence of elementary events underlying excitation-contraction coupling and provides an explanation for both spontaneous and triggered changes in the intracellular calcium concentration in the mammalian heart

https://science.sciencemag.org/content/sci/262/5134/740.full.pdf

Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle

The Na+/Ca2+ exchanger, an ion transport protein, is expressed in the plasma membrane (PM) of virtually all animal cells. It extrudes Ca2+ in parallel with the PM ATP-driven Ca2+ pump. As a reversible transporter, it also mediates Ca2+ entry in parallel with various ion channels. The energy for net Ca2+ transport by the Na+/Ca2+ exchanger and its direction depend on the Na+, Ca2+, and K+ gradients across the PM, the membrane potential, and the transport stoichiometry. In most cells, three Na+ are exchanged for one Ca2+. In vertebrate photoreceptors, some neurons, and certain other cells, K+ is transported in the same direction as Ca2+, with a coupling ratio of four Na+ to one Ca2+ plus one K+. The exchanger kinetics are affected by nontransported Ca2+, Na+, protons, ATP, and diverse other modulators. Five genes that code for the exchangers have been identified in mammals: three in the Na+/Ca2+ exchanger family (NCX1, NCX2, and NCX3) and two in the Na+/Ca2+ plus K+ family (NCKX1 and NCKX2). Genes homologous to NCX1 have been identified in frog, squid, lobster, and Drosophila. In mammals, alternatively spliced variants of NCX1 have been identified; dominant expression of these variants is cell type specific, which suggests that the variations are involved in targeting and/or functional differences. In cardiac myocytes, and probably other cell types, the exchanger serves a housekeeping role by maintaining a low intracellular Ca2+ concentration; its possible role in cardiac excitation-contraction coupling is controversial. Cellular increases in Na+ concentration lead to increases in Ca2+ concentration mediated by the Na+/Ca2+ exchanger; this is important in the therapeutic action of cardiotonic steroids like digitalis. Similarly, alterations of Na+ and Ca2+ apparently modulate basolateral K+ conductance in some epithelia, signaling in some special sense organs (e.g., photoreceptors and olfactory receptors) and Ca2+-dependent secretion in neurons and in many secretory cells. The juxtaposition of PM and sarco(endo)plasmic reticulum membranes may permit the PM Na+/Ca2+ exchanger to regulate sarco(endo)plasmic reticulum Ca2+ stores and influence cellular Ca2+ signaling.

https://www.physiology.org/doi/pdf/10.1152/physrev.1999.79.3.763

Sodium/Calcium Exchange: Its Physiological Implications

Ca(2+) regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament, which regulate strong cross-bridge binding to actin. Structural and biochemical studies suggest that the position of tropomyosin (Tm) and troponin (Tn) on the thin filament determines the interaction of myosin with the binding sites on actin. These binding sites can be characterized as blocked (unable to bind to cross bridges), closed (able to weakly bind cross bridges), or open (able to bind cross bridges so that they subsequently isomerize to become strongly bound and release ATP hydrolysis products). Flexibility of the Tm may allow variability in actin (A) affinity for myosin along the thin filament other than through a single 7 actin:1 tropomyosin:1 troponin (A(7)TmTn) regulatory unit. Tm position on the actin filament is regulated by the occupancy of NH-terminal Ca(2+) binding sites on TnC, conformational changes resulting from Ca(2+) binding, and changes in the interactions among Tn, Tm, and actin and as well as by strong S1 binding to actin. Ca(2+) binding to TnC enhances TnC-TnI interaction, weakens TnI attachment to its binding sites on 1-2 actins of the regulatory unit, increases Tm movement over the actin surface, and exposes myosin-binding sites on actin previously blocked by Tm. Adjacent Tm are coupled in their overlap regions where Tm movement is also controlled by interactions with TnT. TnT also interacts with TnC-TnI in a Ca(2+)-dependent manner. All these interactions may vary with the different protein isoforms. The movement of Tm over the actin surface increases the "open" probability of myosin binding sites on actins so that some are in the open configuration available for myosin binding and cross-bridge isomerization to strong binding, force-producing states. In skeletal muscle, strong binding of cycling cross bridges promotes additional Tm movement. This movement effectively stabilizes Tm in the open position and allows cooperative activation of additional actins in that and possibly neighboring A(7)TmTn regulatory units. The structural and biochemical findings support the physiological observations of steady-state and transient mechanical behavior. Physiological studies suggest the following. 1) Ca(2+) binding to Tn/Tm exposes sites on actin to which myosin can bind. 2) Ca(2+) regulates the strong binding of M.ADP.P(i) to actin, which precedes the production of force (and/or shortening) and release of hydrolysis products. 3) The initial rate of force development depends mostly on the extent of Ca(2+) activation of the thin filament and myosin kinetic properties but depends little on the initial force level. 4) A small number of strongly attached cross bridges within an A(7)TmTn regulatory unit can activate the actins in one unit and perhaps those in neighboring units. This results in additional myosin binding and isomerization to strongly bound states and force production. 5) The rates of the product release steps per se (as indicated by the unloaded shortening velocity) early in shortening are largely independent of the extent of thin filament activation ([Ca(2+)]) beyond a given baseline level. However, with a greater extent of shortening, the rates depend on the activation level. 6) The cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force but does not affect the rate of force development. 7) Strongly attached, cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner. 8) Strongly attached and cycling cross bridges can enhance Ca(2+) binding to cardiac TnC, but influence skeletal TnC to a lesser extent. 9) Different Tn subunit isoforms can modulate the cross-bridge detachment rate as shown by studies with mutant regulatory proteins in myotubes and in in vitro motility assays. (ABSTRACT TRUNCATED)

https://www.physiology.org/doi/pdf/10.1152/physrev.2000.80.2.853

Regulation of Contraction in Striated Muscle

Excitation-contraction coupling was studied in mammalian cardiac cells in which the opening probability of L-type calcium (Ca2+) channels was reduced. Confocal microscopy during voltage-clamp depolarization revealed distinct local transients in the concentration of intracellular calcium ions ([Ca2+]i). When voltage was varied, the latency to occurrence and the relative probability of occurrence of local [Ca2+]i transients varied as predicted if Ca2+ release from the sarcoplasmic reticulum (SR) was linked tightly to Ca2+ flux through L-type Ca2+ channels but not to that through the Na-Ca exchanger or to average [Ca2+]i. Voltage had no effect on the amplitude of local [Ca2+]i transients. Thus, the most efficacious "Ca2+ signal" for activating Ca2+ release from the SR may be a transient microdomain of high [Ca2+]i beneath an individual, open L-type Ca2+ channel.

https://science.sciencemag.org/content/sci/268/5213/1042.full.pdf

Local calcium transients triggered by single L-type calcium channel currents in cardiac cells

1. The mechanisms that control release of Ca2+ from the sarcoplasmic reticulum (SR) of guinea-pig ventricular cells were studied by observing intracellular calcium concentration ([Ca2+]i transients) and membrane currents in voltage-clamped guinea-pig ventricular myocytes perfused internally with Fura-2. 2. Sarcolemmal Ca2+ current was identified through the use of tetrodotoxin (TTX) and Ca2+ channel antagonists (verapamil) and agonists (Bay K 8644). 3. Changes in [Ca2+]i attributable to release of Ca2+ from the SR were identified through the use of ryanodine, which abolishes the ability of the SR to release Ca2+. Ryanodine-sensitive increases in [Ca2+]i could be elicited either by depolarization or by repolarization (from depolarizing pulses to relatively positive membrane potentials). 4. At appropriate voltages, it is the initial fast change in [Ca2+]i elicited by either depolarization or repolarization that is abolished by ryanodine, and is defined here as ryanodine sensitive. 5. The amplitude of the ryanodine-sensitive [Ca2+]i transient elicited by depolarization had a bell-shaped dependence on membrane potential with a maximum of about 500 nM at 10 mV, and with the upper minimum between 60 and 70 mV. Verapamil-sensitive current activated over approximately the same potential range as the [Ca2+]i transient, with a peak amplitude at 10 mV, and a reversal potential of 65 mV. 6. When a holding potential of -68 mV and TTX (30 microM) were used, the most negative pulse potential at which activation of an inward current occurred was -49 mV while changes in [Ca2+]i occurred at -43 mV. 7. Ryanodine-sensitive increases in [Ca2+]i elicited by repolarization (tail transients) were maximal for repolarization to 0 mV. Smaller changes in [Ca2+]i than maximal were elicited by repolarization to both more positive and more negative potentials than 0 mV. The peak amplitude of the verapamil-sensitive tail currents elicited by repolarization increased continuously as the membrane was repolarized to potentials more negative than 60 mV. 8. Increasing depolarizing pulse duration beyond 10-20 ms did not increase the amplitude of the [Ca2+]i transient, but prolonged it. 9. The experimental results are compared to the predictions of two theories on the mechanism of excitation-contraction coupling: Ca2+-induced release of Ca2+ (CICR), as it has been formulated from data in skinned cardiac cells, and a charge-coupled release mechanism (CCRM), as it has been formulated to explain excitation-contraction coupling in skeletal muscle. 10. Some of the results are clearly not consistent with certain features of a charge-coupled release mechanism.(ABSTRACT TRUNCATED AT 400 WORDS)

Mechanism of release of calcium from sarcoplasmic reticulum of guinea-pig cardiac cells.

Digital imaging of calcium indicator signals (fura-2 fluorescence) from single cardiac cells has revealed different subcellular patterns of cytoplasmic calcium ion concentration ([Ca2+]i) that are associated with different types of cellular appearance and behavior. In any population of enzymatically isolated rat heart cells, there are mechanically quiescent cells in which [Ca2+]i is spatially uniform, constant over time, and relatively low; spontaneously contracting cells, which have an increased [Ca2+]i, but in which the spatial uniformity of [Ca2+]i is interrupted periodically by spontaneous propagating waves of high [Ca2+]i; and cells that are hypercontracted (rounded up) and that have higher levels of [Ca2+]i than the other two types. The observed cellular and subcellular heterogeneity of [Ca2+]i in isolated cells indicates that experiments performed on suspensions of cells should be interpreted with caution. The spontaneous [Ca2+]i fluctuations previously observed without spatial resolution in multicellular preparations may actually be inhomogeneous at the subcellular level.

Cellular and subcellular heterogeneity of [Ca2+]i in single heart cells revealed by fura-2

Drug-induced triggered arrhythmias in heart muscle involve oscillations of membrane potential known as delayed or early afterdepolarizations (DADs or EADs). We examined the mechanism of DADs and EADs in ferret ventricular muscle. Membrane potential, tension and aequorin luminescence were measured during exposure to elevated [Ca2+]0, strophanthidin and/or isoproterenol (to induce DADs), or cesium chloride (to induce EADs). Ryanodine (10(-9)-10(-6) M), an inhibitor of Ca2+ release from the sarcoplasmic reticulum, rapidly suppressed DADs and triggered arrhythmias. When cytoplasmic Ca2+-buffering capacity was enhanced by loading cells with the Ca2+ chelators BAPTA or quin2, DADs were similarly inhibited, as were contractile force and aequorin luminescence. In contrast to DADs, EADs induced by Cs were not suppressed by ryanodine or by loading with intracellular Ca2+ chelators. The possibility that transsarcolemmal Ca2+ entry might produce EADs was evaluated with highly specific dihydropyridine Ca channel agonists and antagonists. Bay K8644 (100-300 nM) potentiated EADs, whereas nitrendipine (3-20 microM) abolished EADs. We conclude that DADs and DAD-related triggered arrhythmias are activated by an increase in intracellular free Ca2+ concentration, whereas EADs do not require elevated [Ca2+]i but rather arise as a direct consequence of Ca2+ entry through sarcolemmal slow Ca channels.

/pdf/mechanisms-of-arrhythmogenic-delayed-and-early-5dn7qa1gdk.pdf

Mechanisms of arrhythmogenic delayed and early afterdepolarizations in ferret ventricular muscle.

The influence of short-term changes in stimulation pattern, both on the strength of contraction and on the amplitude of intracellular free-Ca2+ transients, was investigated in ferret papillary muscles. Intracellular free-Ca2+ concentration ([Ca2+]) was assessed from the luminescence emitted from muscles microinjected with the Ca2+-sensitive photoprotein aequorin. The relationships between the strength of contraction and changes in stimulation pattern lasting 1-2 beats could be described by monoexponential functions, all with very similar time constants (approximately 750 ms at 30 degrees C). Over the entire range that could be obtained, the strength of contraction, quantified by either peak tension or peak rate of tension development, was found to be linearly correlated with peak estimated [Ca2+]. Potential errors in the estimation of [Ca2+] from aequorin luminescence were analysed. To assess the influence of spatial non-homogeneities of [Ca2+] on the estimate of [Ca2+], a model of Ca2+ diffusion in heart muscle was developed. The possible effect of using an inaccurate calibration curve was also examined. The results of these analyses indicate that [Ca2+] estimated from aequorin luminescence should be proportional to, if not equal to, true spatial average [Ca2+] (errors less than 7%). Given the conclusion of the analysis described above, it is inferred from points 2 and 3 that the relationships between peak spatial average [Ca2+] and short-term changes in stimulation pattern are also represented by monoexponential functions, with time constants closely similar to those for the mechanical measurements. Exposure to ryanodine, a substance believed to inhibit the release of Ca2+ from sarcoplasmic reticulum, produced striking alterations in the pattern of variations in [Ca2+] mentioned above. These alterations are consistent with the hypothesis that the functions described above depend essentially upon properties of the sarcoplasmic reticulum.

Withrow Gil Wier

Papers

Local calcium transients triggered by single L-type calcium channel currents in cardiac cells

Mechanism of release of calcium from sarcoplasmic reticulum of guinea-pig cardiac cells.

Cellular and subcellular heterogeneity of [Ca2+]i in single heart cells revealed by fura-2

Mechanisms of arrhythmogenic delayed and early afterdepolarizations in ferret ventricular muscle.

Intracellular calcium transients underlying the short‐term force‐interval relationship in ferret ventricular myocardium.