Jonathan R. Silva

Computational biology in the study of cardiac ion channels and cell electrophysiology

The cardiac cell is a complex biological system where various processes interact to generate electrical excitation (the action potential, AP) and contraction. During AP generation, membrane ion channels interact nonlinearly with dynamically changing ionic concentrations and varying transmembrane voltage, and are subject to regulatory processes. In recent years, a large body of knowledge has accumulated on the molecular structure of cardiac ion channels, their function, and their modification by genetic mutations that are associated with cardiac arrhythmias and sudden death. However, ion channels are typically studied in isolation (in expression systems or isolated membrane patches), away from the physiological environment of the cell where they interact to generate the AP. A major challenge remains the integration of ion-channel properties into the functioning, complex and highly interactive cell system, with the objective to relate molecular-level processes and their modification by disease to whole-cell function and clinical phenotype. In this article we describe how computational biology can be used to achieve such integration. We explain how mathematical (Markov) models of ion-channel kinetics are incorporated into integrated models of cardiac cells to compute the AP. We provide examples of mathematical (computer) simulations of physiological and pathological phenomena, including AP adaptation to changes in heart rate, genetic mutations in SCN5A and HERG genes that are associated with fatal cardiac arrhythmias, and effects of the CaMKII regulatory pathway and beta-adrenergic cascade on the cell electrophysiological function.

Subunit Interaction Determines IKs Participation in Cardiac Repolarization and Repolarization Reserve

Background—The role of IKs, the slow delayed rectifier K+ current, in cardiac ventricular repolarization has been a subject of debate. Methods and Results—We develop a detailed Markov model of IKs and its α-subunit KCNQ1 and examine their kinetic properties during the cardiac ventricular action potential at different rates. We observe that interaction between KCNQ1 and KCNE1 (the β-subunit) confers kinetic properties on IKs that make it suitable for participation in action potential repolarization and its adaptation to rate changes; in particular, the channel develops an available reserve of closed states near the open state that can open rapidly on demand. Conclusions—Because of its ability to form an available reserve, IKs can function as a repolarization reserve when IKr, the rapid delayed rectifier, is reduced by disease or drug and can prevent excessive action potential prolongation and development of arrhythmogenic early afterdepolarizations.

Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium

Computational models of cardiac myocytes are important tools for understanding ionic mechanisms of arrhythmia. This work presents a new model of the canine epicardial myocyte that reproduces a wide range of experimentally observed rate-dependent behaviors in cardiac cell and tissue, including action potential (AP) duration (APD) adaptation, restitution, and accommodation. Model behavior depends on updated formulations for the 4-aminopyridine-sensitive transient outward current (I(to1)), the slow component of the delayed rectifier K(+) current (I(Ks)), the L-type Ca(2+) channel current (I(Ca,L)), and the Na(+)-K(+) pump current (I(NaK)) fit to data from canine ventricular myocytes. We found that I(to1) plays a limited role in potentiating peak I(Ca,L) and sarcoplasmic reticulum Ca(2+) release for propagated APs but modulates the time course of APD restitution. I(Ks) plays an important role in APD shortening at short diastolic intervals, despite a limited role in AP repolarization at longer cycle lengths. In addition, we found that I(Ca,L) plays a critical role in APD accommodation and rate dependence of APD restitution. Ca(2+) entry via I(Ca,L) at fast rate drives increased Na(+)-Ca(2+) exchanger Ca(2+) extrusion and Na(+) entry, which in turn increases Na(+) extrusion via outward I(NaK). APD accommodation results from this increased outward I(NaK). Our simulation results provide valuable insight into the mechanistic basis of rate-dependent phenomena important for determining the hearts response to rapid and irregular pacing rates (e.g., arrhythmia). Accurate simulation of rate-dependent phenomena and increased understanding of their mechanistic basis will lead to more realistic multicellular simulations of arrhythmia and identification of molecular therapeutic targets.

Kv7.1 ion channels require a lipid to couple voltage sensing to pore opening

Voltage-gated ion channels generate dynamic ionic currents that are vital to the physiological functions of many tissues. These proteins contain separate voltage-sensing domains, which detect changes in transmembrane voltage, and pore domains, which conduct ions. Coupling of voltage sensing and pore opening is critical to the channel function and has been modeled as a protein–protein interaction between the two domains. Here, we show that coupling in Kv7.1 channels requires the lipid phosphatidylinositol 4,5-bisphosphate (PIP2). We found that voltage-sensing domain activation failed to open the pore in the absence of PIP2. This result is due to loss of coupling because PIP2 was also required for pore opening to affect voltage-sensing domain activation. We identified a critical site for PIP2-dependent coupling at the interface between the voltage-sensing domain and the pore domain. This site is actually a conserved lipid-binding site among different K+ channels, suggesting that lipids play an important role in coupling in many ion channels.

Voltage-sensor movements describe slow inactivation of voltage-gated sodium channels I: Wild-type skeletal muscle NaV1.4

The number of voltage-gated sodium (NaV) channels available to generate action potentials in muscles and nerves is adjusted over seconds to minutes by prior electrical activity, a process called slow inactivation (SI). The basis for SI is uncertain. NaV channels have four domains (DI–DIV), each with a voltage sensor that moves in response to depolarizing stimulation over milliseconds to activate the channels. Here, SI of the skeletal muscle channel NaV1.4 is induced by repetitive stimulation and is studied by recording of sodium currents, gating currents, and changes in the fluorescence of probes on each voltage sensor to assess their movements. The magnitude, voltage dependence, and time course of the onset and recovery of SI are observed to correlate with voltage-sensor movements 10,000-fold slower than those associated with activation. The behavior of each voltage sensor is unique. Development of SI over 1–160 s correlates best with slow immobilization of the sensors in DI and DII; DIII tracks the onset of SI with less fidelity. Showing linkage to the sodium conduction pathway, pore block by tetrodotoxin affects both SI and immobilization of all the sensors, with DI and DII significantly suppressed. Recovery from SI correlates best with slow restoration of mobility of the sensor in DIII. The findings suggest that voltage-sensor movements determine SI and thereby mediate NaV channel availability.

Multi-scale electrophysiology modeling: from atom to organ

In excitable cells, the molecular motions of ion channels are linked to the whole cell physiology via the transmembrane potential (Vm). To examine such events at the cellular level, we recently proposed a model that links the molecular dynamics (MD) and electrostatics of the slow delayed rectifier K

Modeling Subunit Cooperativity in Opening of Tetrameric Ion Channels

Most potassium channels are tetramers of four homologous polypeptides (subunits). During channel gating, each subunit undergoes several conformational changes independent of the state of other subunits before reaching a permissive state, from which the channel can open. However, transition from the permissive states to the open state involves a concerted movement of all subunits. This cooperative transition must be included in Markov models of channel gating. Previously, it was implemented by considering all possible combinations of four subunit states in a much larger expanded model of channel states (e.g., 27,405 channel states versus 64 subunit states), which complicates modeling and is computationally intense, especially when accurate modeling requires a large number of subunit states. To overcome these complexities and retain the tetrameric molecular structure, a modeling approach was developed to incorporate the cooperative transition directly from the subunit models. In this approach, the open state is separated from the subunit models and represented by the net flux between the open state and the permissive states. Dynamic variations of the probability of state residencies computed using this direct approach and the expanded model were identical. Implementation of the direct approach is simple and its computational time is orders-of-magnitude shorter than the equivalent expanded model.

Slow inactivation of Na(+) channels.

Prolonged depolarizing pulses that last seconds to minutes cause slow inactivation of Na(+) channels, which regulates neuron and myocyte excitability by reducing availability of inward current. In neurons, slow inactivation has been linked to memory of previous excitation and in skeletal muscle it ensures myocytes are able to contract when K(+) is elevated. The molecular mechanisms underlying slow inactivation are unclear even though it has been studied for 50+ years. This chapter reviews what is known to date regarding the definition, measurement, and mechanisms of voltage-gated Na(+) channel slow inactivation.

Voltage-sensor movements describe slow inactivation of voltage-gated sodium channels II: A periodic paralysis mutation in NaV1.4 (L689I)

In skeletal muscle, slow inactivation (SI) of NaV1.4 voltage-gated sodium channels prevents spontaneous depolarization and fatigue. Inherited mutations in NaV1.4 that impair SI disrupt activity-induced regulation of channel availability and predispose patients to hyperkalemic periodic paralysis. In our companion paper in this issue (Silva and Goldstein. 2013. J. Gen. Physiol. http://dx.doi.org/10.1085/jgp.201210909), the four voltage sensors in NaV1.4 responsible for activation of channels over microseconds are shown to slowly immobilize over 1–160 s as SI develops and to regain mobility on recovery from SI. Individual sensor movements assessed via attached fluorescent probes are nonidentical in their voltage dependence, time course, and magnitude: DI and DII track SI onset, and DIII appears to reflect SI recovery. A causal link was inferred by tetrodotoxin (TTX) suppression of both SI onset and immobilization of DI and DII sensors. Here, the association of slow sensor immobilization and SI is verified by study of NaV1.4 channels with a hyperkalemic periodic paralysis mutation; L689I produces complex changes in SI, and these are found to manifest directly in altered sensor movements. L689I removes a component of SI with an intermediate time constant (∼10 s); the mutation also impedes immobilization of the DI and DII sensors over the same time domain in support of direct mechanistic linkage. A model that recapitulates SI attributes responsibility for intermediate SI to DI and DII (10 s) and a slow component to DIII (100 s), which accounts for residual SI, not impeded by L689I or TTX.

Ion channel associated diseases: overview of molecular mechanisms.

Mechanisms Mark A. Zaydman,†,‡,§ Jonathan R. Silva,†,‡,§ and Jianmin Cui*,†,‡,§ †Department of Biomedical Engineering, Washington University, Saint Louis, Missouri 63130, United States ‡Center for the Investigation of Membrane Excitability Disorders, Washington University, Saint Louis, Missouri 63130, United States Cardiac Bioelectricity and Arrhythmia Center, Washington University, Saint Louis, Missouri 63130, United States