We have developed a mathematical model of the mouse ventricular myocyte action potential (AP) from voltage-clamp data of the underlying currents and Ca2+ transients. Wherever possible, we used Markov models to represent the molecular structure and function of ion channels. The model includes detailed intracellular Ca2+ dynamics, with simulations of localized events such as sarcoplasmic Ca2+ release into a small intracellular volume bounded by the sarcolemma and sarcoplasmic reticulum. Transporter-mediated Ca2+ fluxes from the bulk cytosol are closely matched to the experimentally reported values and predict stimulation rate-dependent changes in Ca2+ transients. Our model reproduces the properties of cardiac myocytes from two different regions of the heart: the apex and the septum. The septum has a relatively prolonged AP, which reflects a relatively small contribution from the rapid transient outward K+ current in the septum. The attribution of putative molecular bases for several of the component currents enables our mouse model to be used to simulate the behavior of genetically modified transgenic mice.

Kv4.3 inactivation is a complex multiexponential process, which can occur from both closed and open states. The fast component of inactivation is modulated by the N-terminus, but the mechanisms mediating the other components of inactivation are controversial. We studied inactivation of Kv4.3 expressed in Xenopus laevis oocytes, using the two-electrode voltage-clamp technique. Inactivation during 2000 ms pulses at potentials positive to the activation threshold was described by three exponents (46 +/- 3, 152 +/- 13, and 930 +/- 50 ms at +50 mV, n = 7) whereas closed-state inactivation (at potentials below threshold) was described by two exponents (1079 +/- 119 and 3719 +/- 307 ms at -40 mV, n = 9). The fast component of open-state inactivation was dominant at potentials positive to -20 mV. Negative to -30 mV, the intermediate and slow components dominated inactivation. Inactivation properties were dependent on pulse duration. Recovery from inactivation was strongly dependent on voltage and pulse duration. We developed an 11-state Markov model of Kv4.3 gating that incorporated a direct transition from the open-inactivated state to the closed-inactivated state. Simulations with this model reproduced open- and closed-state inactivation, isochronal inactivation relationships, and reopening currents. Our data suggest that inactivation can proceed primarily from the open state and that multiple inactivation components can be identified.

Kv1.4 encodes a slowly recovering transient outward current ( I to), which inactivates by a fast N-type (intracellular ball and chain) mechanism but has slow recovery due to C-type inactivation. C-type inactivation of the NH2-terminal deletion mutant (fKv1.4ΔN) was inhibited by 98 mM extracellular K+concentration ([K+]o), whereas N-type was unaffected. In 98 mM [K+]o, removal of intracellular K+ concentration ([K+]i) speeded C-type inactivation but had no effect on N-type inactivation, suggesting that C-type inactivation is sensitive to K+ binding to intracellular sites. C-type inactivation is thought to involve closure of the extracellular pore mouth. However, a valine to alanine mutation on the intracellular side of S6 (V561A) of fKv1.4ΔN alters recovery and results in anomalous speeding of C-type inactivation with increasing [K+]o. Extracellular pH (pHo) modulated both N- and C-type inactivation through an S5-H5 linker histidine (H508) with acidosis speeding both N- and C-type inactivation. Mutation of an extracellular lysine to a tyrosine (K532Y) slowed C-type inactivation and inhibited the pH dependence of both N- and C-type inactivation. These results suggest that mutations, [K+], and pH modulate inactivation through membrane-spanning mechanisms involving S6.

Rapidly inactivating, voltage-dependent K+ currents play important roles in both neurones and cardiac myocytes. Kv4 channels form the basis of these currents in many neurones and cardiac myocytes and their mechanism of inactivation appears to differ significantly from that reported for Shaker and Kv1.4 channels. In most channel gating models, inactivation is coupled to the kinetics of activation. Hence, there is a need for a rigorous model based on comprehensive experimental data on Kv4.

Channels are water‐filled membrane‐spanning proteins, which undergo conformational changes as they gate, i.e. open or close. These conformational changes affect both the shape of the channel and the volume of the water‐filled pore. We measured the changes in pore volume associated with activation, deactivation, C‐type inactivation and recovery in an N‐terminal‐deleted mutant of the Kv1.4 K+ channel (Kv1.4ΔN) expressed in Xenopus oocytes. We used giant‐patch and cut‐open oocyte voltage clamp techniques and applied solutes which are too large to enter the pore mouth to exert osmotic pressure and thus favour smaller pore volume conformations. Applied intracellular osmotic pressure (300 mm sucrose) sped inactivation (time constants (τinactivation): control, 0.66 ± 0.09 s; hyperosmotic solution, 0.29 ± 0.04 s; n= 5, P < 0.01), sped deactivation (τdeactivation: control, 18.8 ± 0.94 ms; hyperosmotic solution, 8.01 ± 1.92 ms; n= 5, P < 0.01), and slowed activation (τactivation: control, 1.04 ± 0.05 ms; hyperosmotic solution, 1.96 ± 0.31 ms; n= 5, P < 0.01). These effects were reversible and solute independent. We estimated the pore volume change on inactivation to be about 4500 Å3. Osmotic pressure had no effect when applied extracellularly. These data suggest that the intracellular side of the pore closes during C‐type inactivation and the volume change is similar to that associated with activation or deactivation. This is also similar to the pore volume estimated from the crystal structure of KcsA and MthK K+ channels. Intracellular osmotic pressure also strongly inhibited re‐opening currents associated with recovery from inactivation, which is consistent with a physical similarity between the C‐type inactivated and resting closed state.

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The β1-adrenergic signaling system plays an important role in the functioning of cardiac cells. Experimental data shows that the activation of this system produces inotropy, lusitropy, and chronotropy in the heart, such as increased magnitude and relaxation rates of [Ca2+]i transients and contraction force, and increased heart rhythm. However, excessive stimulation of β1-adrenergic receptors leads to heart dysfunction and heart failure. In this paper, a comprehensive, experimentally based mathematical model of the β1-adrenergic signaling system for mouse ventricular myocytes is developed, which includes major subcellular functional compartments (caveolae, extracaveolae, and cytosol). The model describes biochemical reactions that occur during stimulation of β1-adrenoceptors, changes in ionic currents, and modifications of Ca2+ handling system. Simulations describe the dynamics of major signaling molecules, such as cyclic AMP and protein kinase A, in different subcellular compartments; the effects of inhibition of phosphodiesterases on cAMP production; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca2+ handling proteins; modifications of action potential shape and duration; magnitudes and relaxation rates of [Ca2+]i transients; changes in intracellular and transmembrane Ca2+ fluxes; and [Na+]i fluxes and dynamics. The model elucidates complex interactions of ionic currents upon activation of β1-adrenoceptors at different stimulation frequencies, which ultimately lead to a relatively modest increase in action potential duration and significant increase in [Ca2+]i transients. In particular, the model includes two subpopulations of the L-type Ca2+ channels, in caveolae and extracaveolae compartments, and their effects on the action potential and [Ca2+]i transients are investigated. The presented model can be used by researchers for the interpretation of experimental data and for the developments of mathematical models for other species or for pathological conditions.

myocytes; computer simulation; inactivation; calcium-induced calcium release; excitation-contraction coupling CALCIUM IS OF VITAL IMPORTANCE in cells as both a transmembrane electrical signaling ion and a second messenger (3-5, 7, 36, 50, 59). The diverse range of Ca 2ϩ -mediated effects is particularly evident in cardiac myocytes, where the initial transmembrane flux of ions through L-type Ca 2ϩ channels contributes to the action potential (6,25,40,46 (5,10,18,36,59,73). [Ca 2ϩ ] i cycling is a fundamental part of normal cellular function, so any malfunction or perturbation of the systems that handle Ca 2ϩ can result in heart failure or fibrillation (21,33,44,45,49,58,60,67,69,75).Recently, CICR has been observed at the subcellular level in the form of Ca 2ϩ "sparks," which are extremely large, extremely localized increases in [Ca 2ϩ ] (18,19,29,34,35). Spontaneously occurring sparks have been observed. They can trigger a subcellular Ca 2ϩ wave that can propagate throughout the cell (17,30,35). Ca 2ϩ sparks were initially thought to reflect the opening and closing of a single SR ryanodine receptor (RyR) (18). However, they have been subsequently shown to be the result of the opening of a single L-type Ca 2ϩ channel (38), which is sufficient to initiate CICR from a cluster of RyRs (36). The number and timing of sparks depend in a nonmonotonic manner on the amplitude of the membrane depolarization.One of the most important features of intracellular [Ca 2ϩ ] cycling is the graded release of Ca 2ϩ from the SR (9,11,14). Recently, Rice et al. (57) published a model of graded CICR based on a Monte-Carlo simulation with a bell-shaped profile for the both integrated and peak RyR Ca 2ϩ release fluxes. Our model generates graded release through biophysically distinct mechanisms. The Rice et al. model (57) postulates that graded release occurs through stochastic changes in the release channel. Subsequent variants (64) added additional deterministic elements of structure, but the main mechanism of graded release remained stochastic. In contrast, our model assumes a physiological variability in diadic junction morphology to generate graded release. The models are, therefore, inherently different at a qualitative level, and there will be testable differences in predicted behavior between these models.In this paper, we present a new model of cardiac Ca 2ϩ handling that incorporates a novel Markov model for L-type Ca 2ϩ channels and graded SR Ca 2ϩ release in response to voltage-clamp simulations. We hypothesize that the structural inhomogeneity of the local calcium release subsystems is responsible for graded release. To model this situation, we introduced eight calcium release subsystems with different characteristics. The model myocyte has a series of physically distinct subsystems that represent the area where the junctional SR comes in close proximity to the T-tubular membrane. Each subsystem is a relatively small subspace volume bounded by the sarcolemma, which contains between one and eight L-type Ca 2ϩ ch...