Francis A. Ortega

Cell-specific cardiac electrophysiology models.

The traditional cardiac model-building paradigm involves constructing a composite model using data collected from many cells. Equations are derived for each relevant cellular component (e.g., ion channel, exchanger) independently. After the equations for all components are combined to form the composite model, a subset of parameters is tuned, often arbitrarily and by hand, until the model output matches a target objective, such as an action potential. Unfortunately, such models often fail to accurately simulate behavior that is dynamically dissimilar (e.g., arrhythmia) to the simple target objective to which the model was fit. In this study, we develop a new approach in which data are collected via a series of complex electrophysiology protocols from single cardiac myocytes and then used to tune model parameters via a parallel fitting method known as a genetic algorithm (GA). The dynamical complexity of the electrophysiological data, which can only be fit by an automated method such as a GA, leads to more accurately parameterized models that can simulate rich cardiac dynamics. The feasibility of the method is first validated computationally, after which it is used to develop models of isolated guinea pig ventricular myocytes that simulate the electrophysiological dynamics significantly better than does a standard guinea pig model. In addition to improving model fidelity generally, this approach can be used to generate a cell-specific model. By so doing, the approach may be useful in applications ranging from studying the implications of cell-to-cell variability to the prediction of intersubject differences in response to pharmacological treatment.

Rapid Genetic Algorithm Optimization of a Mouse Computational Model: Benefits for Anthropomorphization of Neonatal Mouse Cardiomyocytes

While the mouse presents an invaluable experimental model organism in biology, its usefulness in cardiac arrhythmia research is limited in some aspects due to major electrophysiological differences between murine and human action potentials (APs). As previously described, these species-specific traits can be partly overcome by application of a cell-type transforming clamp (CTC) to anthropomorphize the murine cardiac AP. CTC is a hybrid experimental-computational dynamic clamp technique, in which a computationally calculated time-dependent current is inserted into a cell in real-time, to compensate for the differences between sarcolemmal currents of that cell (e.g., murine) and the desired species (e.g., human). For effective CTC performance, mismatch between the measured cell and a mathematical model used to mimic the measured AP must be minimal. We have developed a genetic algorithm (GA) approach that rapidly tunes a mathematical model to reproduce the AP of the murine cardiac myocyte under study. Compared to a prior implementation that used a template-based model selection approach, we show that GA optimization to a cell-specific model results in a much better recapitulation of the desired AP morphology with CTC. This improvement was more pronounced when anthropomorphizing neonatal mouse cardiomyocytes to human-like APs than to guinea pig APs. CTC may be useful for a wide range of applications, from screening effects of pharmaceutical compounds on ion channel activity, to exploring variations in the mouse or human genome. Rapid GA optimization of a cell-specific mathematical model improves CTC performance and may therefore expand the applicability and usage of the CTC technique.

Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility

Arrhythmias result from disruptions to cardiac electrical activity, although the factors that control cellular action potentials are incompletely understood. We combined mathematical modelling with experiments in heart cells from guinea pigs to determine how cellular electrical activity is regulated. A mismatch between modelling predictions and the experimental results allowed us to construct an improved, more predictive mathematical model. The balance between two particular potassium currents dictates how heart cells respond to perturbations and their susceptibility to arrhythmias.

Voltage and calcium dynamics both underlie cellular alternans in cardiac myocytes.

Cardiac alternans, a putative trigger event for cardiac reentry, is a beat-to-beat alternation in membrane potential and calcium transient. Alternans was originally attributed to instabilities in transmembrane ion channel dynamics (i.e., the voltage mechanism). As of this writing, the predominant view is that instabilities in subcellular calcium handling are the main underlying mechanism. That being said, because the voltage and calcium systems are bidirectionally coupled, theoretical studies have suggested that both mechanisms can contribute. To date, to our knowledge, no experimental evidence of such a dual role within the same cell has been reported. Here, a combined electrophysiological and calcium imaging approach was developed and used to illuminate the contributions of voltage and calcium dynamics to alternans. An experimentally feasible protocol, quantification of subcellular calcium alternans and restitution slope during cycle-length ramping alternans control, was designed and validated. This approach allows simultaneous illumination of the contributions of voltage and calcium-driven instability to total cellular instability as a function of cycle-length. Application of this protocol in in vitro guinea-pig left-ventricular myocytes demonstrated that both voltage- and calcium-driven instabilities underlie alternans, and that the relative contributions of the two systems change as a function of pacing rate.

Dynamic clamp in cardiac and neuronal systems using RTXI.

The injection of computer-simulated conductances through the dynamic clamp technique has allowed researchers to probe the intercellular and intracellular dynamics of cardiac and neuronal systems with great precision. By coupling computational models to biological systems, dynamic clamp has become a proven tool in electrophysiology with many applications, such as generating hybrid networks in neurons or simulating channelopathies in cardiomyocytes. While its applications are broad, the approach is straightforward: synthesizing traditional patch clamp, computational modeling, and closed-loop feedback control to simulate a cellular conductance. Here, we present two example applications: artificial blocking of the inward rectifier potassium current in a cardiomyocyte and coupling of a biological neuron to a virtual neuron through a virtual synapse. The design and implementation of the necessary software to administer these dynamic clamp experiments can be difficult. In this chapter, we provide an overview of designing and implementing a dynamic clamp experiment using the Real-Time eXperiment Interface (RTXI), an open-source software system tailored for real-time biological experiments. We present two ways to achieve this using RTXIs modular format, through the creation of a custom user-made module and through existing modules found in RTXIs online library.

Cardiac myocyte model parameter sensitivity analysis and model transformation using a genetic algorithm

Cardiac arrhythmia is the disruption of the normal electrical rhythm of the heart and is a leading cause of mortality around the world. To study arrhythmogenesis, mathematical models of cardiac myocytes and tissues have been effectively employed to investigate cardiac electrodynamics. However, among individual myocytes, there is phenotypic variability that is dependent on factors such as source location in the heart, genetic variation, and even different experimental protocols. Thus, established cardiac myocyte models constrained by experimental data are often untuned to new phenomena under investigation. In this study, we show direct links to parameter changes and differing electrical phenotypes. First, we present results exploring model sensitivity to physiological parameters underpinning electrical activity. Second, we outline a genetic algorithm based approach for tuning model parameters to fit cardiac myocyte behavior. Third, we use a genetic algorithm to transform one model type to another, relating simulation to experimental data. This model transformation demonstrates the potential of genetic algorithms to extend the utility of cardiac myocyte models by comparing different functional regions in the heart.

Global Optimization of Ventricular Myocyte Model to Multi-Variable Objective Improves Predictions of Drug-Induced Torsades de Pointes

In silico cardiac myocyte models present powerful tools for drug safety testing and for predicting phenotypical consequences of ion channel mutations, but their accuracy is sometimes limited. For example, several models describing human ventricular electrophysiology perform poorly when simulating effects of long QT mutations. Model optimization represents one way of obtaining models with stronger predictive power. Using a recent human ventricular myocyte model, we demonstrate that model optimization to clinical long QT data, in conjunction with physiologically-based bounds on intracellular calcium and sodium concentrations, better constrains model parameters. To determine if the model optimized to congenital long QT data better predicts risk of drug-induced long QT arrhythmogenesis, in particular Torsades de Pointes risk, we tested the optimized model against a database of known arrhythmogenic and non-arrhythmogenic ion channel blockers. When doing so, the optimized model provided an improved risk assessment. In particular, we demonstrate an elimination of false-positive outcomes generated by the baseline model, in which simulations of non-torsadogenic drugs, in particular verapamil, predict action potential prolongation. Our results underscore the importance of currents beyond those directly impacted by a drug block in determining torsadogenic risk. Our study also highlights the need for rich data in cardiac myocyte model optimization and substantiates such optimization as a method to generate models with higher accuracy of predictions of drug-induced cardiotoxicity.

Overexpression of Map3k7 activates sinoatrial node-like differentiation in mouse ES-derived cardiomyocytes

In vivo, cardiomyocytes comprise a heterogeneous population of contractile cells defined by unique electrophysiologies, molecular markers and morphologies. The mechanisms directing myocardial cells to specific sub-lineages remain poorly understood. Here we report that overexpression of TGFβ-Activated Kinase (TAK1/Map3k7) in mouse embryonic stem (ES) cells faithfully directs myocardial differentiation of embryoid body (EB)-derived cardiac cells toward the sinoatrial node (SAN) lineage. Most cardiac cells in Map3k7-overexpressing EBs adopt markers, cellular morphologies, and electrophysiological behaviors characteristic of the SAN. These data, in addition to the fact that Map3k7 is upregulated in the sinus venous—the source of cells for the SAN—suggest that Map3k7 may be an endogenous regulator of the SAN fate.

Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology Testing

Dynamic clamp, a hybrid-computational-experimental technique that has been used to elucidate ionic mechanisms underlying cardiac electrophysiology, is emerging as a promising tool in the discovery of potential anti-arrhythmic targets and in pharmacological safety testing. Through the injection of computationally simulated conductances into isolated cardiomyocytes in a real-time continuous loop, dynamic clamp has greatly expanded the capabilities of patch clamp outside traditional static voltage and current protocols. Recent applications include fine manipulation of injected artificial conductances to identify promising drug targets in the prevention of arrhythmia and the direct testing of model-based hypotheses. Furthermore, dynamic clamp has been used to enhance existing experimental models by addressing their intrinsic limitations, which increased predictive power in identifying pro-arrhythmic pharmacological compounds. Here, we review the recent advances of the dynamic clamp technique in cardiac electrophysiology with a focus on its future role in the development of safety testing and discovery of anti-arrhythmic drugs.