Improved Prediction of Drug-Induced Torsades de Pointes Through Simulations of Dynamics and Machine Learning Algorithms.

The ventricular arrhythmia Torsades de Pointes (TdP) is a common form of drug-induced cardiotoxicity, but prediction of this arrhythmia remains an unresolved issue in drug development. Current assays to evaluate arrhythmia risk are limited by poor specificity and a lack of mechanistic insight. We addressed this important unresolved issue through a novel computational approach that combined simulations of drug effects on dynamics with statistical analysis and machine-learning. Drugs that blocked multiple ion channels were simulated in ventricular myocyte models, and metrics computed from the action potential and intracellular (Ca(2+) ) waveform were used to construct classifiers that distinguished between arrhythmogenic and nonarrhythmogenic drugs. We found that: (1) these classifiers provide superior risk prediction; (2) drug-induced changes to both the action potential and intracellular (Ca(2+) ) influence risk; and (3) cardiac ion channels not typically assessed may significantly affect risk. Our algorithm demonstrates the value of systematic simulations in predicting pharmacological toxicity.

Differential sensitivity of Ca²+ wave and Ca²+ spark events to ruthenium red in isolated permeabilised rabbit cardiomyocytes.

Spontaneous Ca²(+) waves in cardiac muscle cells are thought to arise from the sequential firing of local Ca²(+) sparks via a fire-diffuse-fire mechanism. This study compares the ability of the ryanodine receptor (RyR) blocker ruthenium red (RuR) to inhibit these two types of Ca²(+) release in permeabilised rabbit ventricular cardiomyocytes. Perfusing with 600 nm Ca²(+) (50 µm EGTA) caused regular spontaneous Ca²(+) waves that were imaged with the fluorescence from Fluo-5F using a laser-scanning confocal microscope. Addition of 4 µm RuR caused complete inhibition of Ca²(+) waves in 50% of cardiomyocytes by 2 min and in 100% by 4 min. Separate experiments used 350 µm EGTA (600 nm Ca²(+)) to limit Ca²(+) diffusion but allow the underlying Ca(2+) sparks to be imaged. The time course of RuR-induced inhibition did not match that of waves. After 2 min of RuR, none of the characteristics of the Ca²(+) sparks were altered, and after 4 min Ca²(+) spark frequency was reduced ∼40%; no sparks could be detected after 10 min. Measurements of Ca(2+) within the SR lumen using Fluo-5N showed an increase in intra-SR Ca²(+) during the initial 2-4 min of perfusion with RuR in both wave and spark conditions. Computational modelling suggests that the sensitivity of Ca²(+) waves to RuR block depends on the number of RyRs per cluster. Therefore inhibition of Ca²(+) waves without affecting Ca²(+) sparks may be explained by block of small, non-spark producing clusters of RyRs that are important to the process of Ca²(+) wave propagation.

Training in systems pharmacology: predoctoral program in pharmacology and systems biology at Mount Sinai School of Medicine.

Our recently developed predoctoral training program in pharmacology and systems biology prepares students to become experts in systems-level models of disease that identify therapeutic targets and predict adverse effects or new uses of existing therapeutics. Multiple computational modeling modes are introduced throughout a curriculum that integrates basic cell and molecular sciences with the physiology and pathophysiology of disease states. Problem-based learning exercises enable students from different experimental and computational backgrounds to design experiments and interpret data quantitatively.

Molecular identification of a TTX-sensitive Ca(2+) current.

The TTX-sensitive Ca(2+) current [I(Ca(TTX))] observed in cardiac myocytes under Na(+)-free conditions was investigated using patch-clamp and Ca(2+)-imaging methods. Cs(+) and Ca(2+) were found to contribute to I(Ca(TTX)), but TEA(+) and N-methyl-D-glucamine (NMDG(+)) did not. HEK-293 cells transfected with cardiac Na(+) channels exhibited a current that resembled I(Ca(TTX)) in cardiac myocytes with regard to voltage dependence, inactivation kinetics, and ion selectivity, suggesting that the cardiac Na(+) channel itself gives rise to I(Ca(TTX)). Furthermore, repeated activation of I(Ca(TTX)) led to a 60% increase in intracellular Ca(2+) concentration, confirming Ca(2+) entry through this current. Ba(2+) permeation of I(Ca(TTX)), reported by others, did not occur in rat myocytes or in HEK-293 cells expressing cardiac Na(+) channels under our experimental conditions. The report of block of I(Ca(TTX)) in guinea pig heart by mibefradil (10 microM) was supported in transfected HEK-293 cells, but Na(+) current was also blocked (half-block at 0.45 microM). We conclude that I(Ca(TTX)) reflects current through cardiac Na(+) channels in Na(+)-free (or "null") conditions. We suggest that the current be renamed I(Na(null)) to more accurately reflect the molecular identity of the channel and the conditions needed for its activation. The relationship between I(Na(null)) and Ca(2+) flux through slip-mode conductance of cardiac Na(+) channels is discussed in the context of ion channel biophysics and "permeation plasticity."

Nonuniform responses of transmembrane potential during electric field stimulation of single cardiac cells.

The response of cellular transmembrane potentials (V(m)) to applied electric fields is a critical factor during electrical pacing, cardioversion, and defibrillation, yet the coupling relationship of the cellular response to field intensity and polarity is not well documented. Isolated guinea pig ventricular myocytes were stained with a voltage-sensitive fluorescent dye, di-8-ANEPPS (10 microM). A green helium-neon laser was used to excite the fluorescent dye with a 15-micrometers-diameter focused spot, and subcellular V(m) were recorded optically during field stimulation directed along the long axis of the cell. The membrane response was measured at the cell end with the use of a 30-ms S1-S2 coupling interval and a 10-ms S2 pulse with strength of up to approximately 500-mV half-cell length potential (field strength x one-half the cell length). The general trends show that 1) the response of V(m) at the cell end occurs in two stages, the first being very rapid (<1 ms) and the second much slower in time scale, 2) the rapid response consists of hyperpolarization when the cell end faces the anode and depolarization when the cell end faces the cathode, 3) the rapid response varies nonlinearly with field strengths and polarity, being relatively larger for the hyperpolarizing responses, and 4) the slower, time-dependent response has a time course that varies in slope with field strength. Furthermore, the linearity of the dye response was confirmed over a voltage range of -280 to +140 mV by simultaneous measurements of optically and electrically recorded V(m). These experimental findings could not be reproduced by the updated, Luo-Rudy dynamic model but could be explained with the addition of two currents that activate outside the physiological range of voltages: a hypothetical outward current that activates strongly at positive potentials and a second current that represents electroporation of the cell membrane.

Separation between virtual sources modifies the response of cardiac tissue to field stimulation.

INTRODUCTION: While it is now understood that the tissue geometry and the electric field distribution are important in generating virtual electrodes, the effects of interaction between a collection of electrodes have not been examined. To develop a basis for understanding such interactions, we have studied a single pair of oppositely polarized virtual sources. Although such oppositely polarized pairs of virtual electrodes can be generated by a variety of field distributions and tissue geometries, we examine one simple system that incorporates the salient features of source interaction. METHODS AND RESULTS: Our model system is a homogeneous tissue strip stimulated by a uniform extracellular field. To clarify virtual source interaction, we show that field stimulated tissue can be equivalently polarized by a set of intracellular current sources with magnitude and distribution defined by the generalized activating function. In our model system, an intracellular current source is produced at one edge of the tissue and an intracellular current sink at the other. Therefore, the tissue length acts to modulate the overlap, or interaction, between the polarizations arising from each source. To quantify the effects of source interaction, the chronaxie and rheobase values of the strength-duration relation were determined for source separations varying between 1.0 cm and 100 microm (active membrane dynamics were modeled with the Luo-Rudy phase I formulation). At all separations >3.0 mm, the chronaxie was constant at 3.09 msec and the rheobase was 0.38 V/cm. Under 0.2 mm, the chronaxie decreased to 0.55 msec while the rheobase increased linearly with the inverse of source separation. The dependence of these parameters on separation primarily reflects passive electrotonic interactions between the two virtual electrodes. However, the exact values are strongly dependent upon active tissue properties-largely the inward rectifier potassium channel and activation of the sodium current. CONCLUSION: Tissue excitation in response to field stimulation is strongly modulated by the proximity of, and therefore the interaction between, oppositely polarized virtual electrode sources.

Postshock potential gradients and dispersion of repolarization in cells stimulated with monophasic and biphasic waveforms.

INTRODUCTION: Even though the clinical advantage of biphasic defibrillation waveforms is well documented, the mechanisms that underlie this greater efficacy remain incompletely understood. It is established, though, that the response of relatively refractory cells to the shock is important in determining defibrillation success or failure. We used two computer models of an isolated ventricular cell to test the hypothesis that biphasic stimuli cause a more uniform response than the equivalent monophasic shocks, decreasing the likelihood that fibrillation will be reinduced. METHODS AND RESULTS: Models of reciprocally polarized and uniformly polarized cells were used. Rapid pacing and elevated [K]o were simulated, and either 10-msec rectangular monophasic or 5-msec/5-msec symmetric biphasic stimuli were delivered in the relative refractory period. The effects of stimulus intensity and coupling interval on response duration and postshock transmembrane potential (Vm) were quantified for each waveform. With reciprocal polarization, biphasic stimuli caused a more uniform response than monophasic stimuli, resulting in fewer large gradients of Vm (only for shock strengths < or = 1.25x threshold vs < or = 2.125x threshold) and a smaller dispersion of repolarization (1611 msec2 vs 1835 msec2). The reverse was observed with uniform polarization: monophasic pulses caused a more uniform response than did biphasic stimuli. CONCLUSION: These results show that the response of relatively refractory cardiac cells to biphasic stimuli is less dependent on the coupling interval and stimulus strength than the response to monophasic stimuli under conditions of reciprocal polarization. Because this may lead to fewer and smaller spatial gradients in Vm, these data support the hypothesis that biphasic defibrillation waveforms will be less likely to reinduce fibrillation. Further, published experimental results correlate to a greater degree with conditions of reciprocal polarization than of uniform polarization, providing indirect evidence that interactions between depolarized and hyperpolarized regions play a role in determining the effects of defibrillation shocks on cardiac tissue.

Stretch-induced changes in arrhythmogenesis and excitability in experimentally based heart cell models.

Mechanoelectric coupling in the heart is well documented and has been suggested as a cause of arrhythmia. One hypothesized mechanism for the stretch sensitivity of cardiac muscle is the presence of stretch-activated channels (SACs). This study uses modeling to explore the influence of SACs on cardiac resting potential, excitation threshold, and action potential in the context of arrhythmia. We added a putative SAC, modeled as a linear, time-independent conductance with reversal potential of -20 or -50 mV, to guinea pig and frog ventricular membrane models. Increased stretch conductance led to resting potential depolarization, a decreased excitation threshold, altered action potential duration, and, under certain conditions, early afterdepolarizations. We conclude that stretch increases cellular excitability, making the heart prone to ectopic activity. Regional effects of stretch on action potential duration can vary and are influenced by factors such as the SAC reversal potential, ionic conditions, and baseline currents, all of which may lead to an increased dispersion of refractoriness throughout the heart and therefore an increased risk of arrhythmia.

A generalized activating function for predicting virtual electrodes in cardiac tissue.

To fully understand the mechanisms of defibrillation, it is critical to know how a given electrical stimulus causes membrane polarizations in cardiac tissue. We have extended the concept of the activating function, originally used to describe neuronal stimulation, to derive a new expression that identifies the sources that drive changes in transmembrane potential. Source terms, or virtual electrodes, consist of either second derivatives of extracellular potential weighted by intracellular conductivity or extracellular potential gradients weighted by derivatives of intracellular conductivity. The full response of passive tissue can be considered, in simple cases, to be a convolution of this "generalized activating function" with the impulse response of the tissue. Computer simulations of a two-dimensional sheet of passive myocardium under steady-state conditions demonstrate that this source term is useful for estimating the effects of applied electrical stimuli. The generalized activating function predicts oppositely polarized regions of tissue when unequally anisotropic tissue is point stimulated and a monopolar response when a point stimulus is applied to isotropic tissue. In the bulk of the myocardium, this new expression is helpful for understanding mechanisms by which virtual electrodes can be produced, such as the hypothetical "sawtooth" pattern of polarization, as well as polarization owing to regions of depressed conductivity, missing cells or clefts, changes in fiber diameter, or fiber curvature. In comparing solutions obtained with an assumed extracellular potential distribution to those with fully coupled intra- and extracellular domains, we find that the former provides a reliable estimate of the total solution. Thus the generalized activating function that we have derived provides a useful way of understanding virtual electrode effects in cardiac tissue.

Modeling the interaction between propagating cardiac waves and monophasic and biphasic field stimuli: the importance of the induced spatial excitatory response.

INTRODUCTION: Biphasic (BP) defibrillation waveforms have been shown to be significantly more efficacious than equivalent monophasic (MP) waveforms. However, when defibrillation fails, it tends to do so first in distal regions of the heart where induced field gradient magnitudes are lowest. We tested the hypothesis that the improved efficacy of BP waveforms results from their enhanced ability to prevent the initiation of new postshock activation fronts behind preexisting wavetails, rather than from any significantly improved ability to terminate preexisting wavefronts. METHODS AND RESULTS: An idealized computer model of a one-dimensional cardiac strand was used to investigate the spatial and temporal interactions between an underlying propagation front (or tail) and uniform MP or BP field stimuli of various intensities. Axial discontinuities from intercellular junctions induced sawtooth patterns of polarization during such field stimuli, enabling the shocks to interact directly with all cells. MP and BP diastolic thresholds were essentially equal. All suprathreshold MP and BP field stimuli successfully terminated preexisting wavefronts by directly depolarizing tissue ahead of those fronts, thus blocking their continued progression. However, the postshock response at the wavetail was significantly dependent on the shape and strength of the administered field. Low-strength MP stimuli induced an all-or-none excitation response across the wavetail, producing a sharp spatial transmembrane voltage gradient from which a new sustained anterogradely propagating wavefront was initiated. In contrast, low-strength BP field stimuli induced a spatially graded excitatory response whose voltage gradient was insufficient to initiate such a wavefront. Higher-strength MP and BP stimuli both produced graded excitatory responses with no subsequent propagation. CONCLUSIONS: Shock-induced spatial "all-or-none" excitatory responses facilitate, and graded excitatory responses prevent, the postshock initiation of new propagating wavefronts. Moreover, BP field stimuli can induce such graded excitatory responses at significantly lower stimulus strengths than otherwise equivalent MP stimuli. Therefore, these results support an alternative "graded excitatory response" mechanism for the improved efficacy of BP over MP field stimuli in low gradient regions.

Mechanisms of cardiac cell excitation with premature monophasic and biphasic field stimuli: a model study.

The mechanisms by which extracellular electric field stimuli induce the (re)excitation of cardiac cells in various stages of refractoriness are still not well understood. We modeled the interactions between an isolated cardiac cell and imposed extracellular electric fields to determine the mechanisms by which relatively low-strength uniform monophasic and biphasic field stimuli induce premature reexcitations. An idealized ventricular cell was simulated with 11 subcellular membrane patches, each of which obeyed Luo-Rudy (phase 1) kinetics. Implementing a standard S1-S2 pulse protocol, strength-interval maps of the cellular excitatory responses were generated for rectangular monophasic and symmetric biphasic field stimuli of 2, 5, 10, and 20 ms total duration. In contrast to previously documented current injection studies, our results demonstrate that a cardiac cell exhibits a significantly nonmonotonic excitatory response to premature monophasic and, to a much lesser degree, biphasic field stimuli. Furthermore, for monophasic stimuli at low field strengths, the cell is exquisitely sensitive to the timing of the shock, demonstrating a classic all-or-none depolarizing response. However, at higher field strengths this all-or-none sensitivity reverts to a more gradual transition of excitatory responses with respect to stimulus prematurity. In contrast, biphasic stimuli produce such graded responses at all suprathreshold stimulus strengths. Similar behaviors are demonstrated at all S2 stimulus durations tested. The generation of depolarizing (sodium) currents is triggered by one or more of the sharp field gradient changes produced at the stimulus edges-i.e., make, break, and transphasic (for biphasic stimuli)-with the magnitude of these edge-induced current contributions dependent on both the prematurity and the strength of the applied field. In all cases, however, depolarizing current arises from the partial removal of sodium inactivation from at least part of the cell, because of either the natural process of repolarization or a localized acceleration of this process by the impressed field.

Cardiac responses to premature monophasic and biphasic field stimuli. Results from cell and tissue modeling studies.

Experimental and clinical observations confirm that certain biphasic (BP) defibrillation shocks are significantly more efficacious than equivalent monophasic (MP) shocks, yet the mechanisms underlying these improvements are still not well understood. The authors used two separate, but related, computer models to investigate in detail the excitation responses of active cardiac cells and tissue to idealized premature extracellular MP and BP field stimuli. The results revealed a large disparity in MP and BP excitation responses to low-strength, but not high-strength, fields. In particular, at these low-strength levels, the polarity reversal within BP shocks effectively extends excitability to earlier cellular refractory states than can be achieved with simple MP shocks. Moreover, whereas low-strength MP shocks induce a distinct all-or-none excitatory response to varying shock prematurities, the excitatory response to equivalent BP shocks remains highly graded. In tissue simulations where such field stimuli intersected propagating wave fronts, the all-or-none excitatory response elicited by low-strength MP shocks created a postshock discontinuity in the spatial transmembrane voltage profile, which initiated a new propagation wave front. In contrast, the graded excitatory response elicited by BP waveforms effectively prevented the formation of postshock wave fronts. High-strength MP and BP stimuli prevented renewed propagation equally well. In conclusion, these results suggest a new mechanisms for BP defibrillation superiority over MP waveforms: that the graded excitatory response to BP stimuli at low-field strengths effectively prevents the formation of large spatial transmembrane voltage gradients, which can lead to renewal of propagated wave fronts.