We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca(2+) handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH(2), which in turn are used by the electron transport chain to establish a proton motive force (Delta mu(H)), driving the F(1)F(0)-ATPase. In addition, mitochondrial matrix Ca(2+), determined by Ca(2+) uniporter and Na(+)/Ca(2+) exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (Delta Psi(m)), and matrix concentrations of Ca(2+), NADH, ADP, and TCA cycle intermediates. The model is used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of adenine nucleotide exchange, and Ca(2+). The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca(2+) dynamics, and respiratory control. Significant increases in oxygen consumption (V(O(2))), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca(2+), are obtained when the Ca(2+)-sensitive dehydrogenases are the main rate-controlling steps of respiratory flux. These responses diminished when control is shifted downstream (e.g., the respiratory chain or adenine nucleotide translocator). The time-dependent behavior of the model, under conditions simulating an increase in workload, closely reproduces experimentally observed mitochondrial NADH dynamics in heart trabeculae subjected to changes in pacing frequency. The steady-state and time-dependent behavior of the model support the hypothesis that mitochondrial matrix Ca(2+) plays an important role in matching energy supply with demand in cardiac myocytes.

Diffusion tensor magnetic resonance imaging (MRI) is a possible new means of elucidating the anatomic structure of the myocardium. It enjoys several advantages over traditional histological approaches, including the ability to rapidly measure fiber organization in isolated, perfused, arrested hearts, thereby avoiding fixation and sectioning of artifacts. However, quantitative validation of this MRI method has been lacking. Here, fiber orientations estimated in the same locations in the same heart using both diffusion tensor MRI and histology are compared in a total of two perfused rabbit hearts. Fiber orientations were statistically similar for both methods and differed on average by 12° at any single location. This is similar to the 10° uncertainty in fiber orientation achieved with histology. In addition, imaging studies performed in a total of seven hearts support a level of organization beyond the myofiber, the recently described laminar organization of the ventricular myocardium.

Abstract-Ca2ϩ transients measured in failing human ventricular myocytes exhibit reduced amplitude, slowed relaxation, and blunted frequency dependence. In the companion article (O'Rourke B, Kass DA, Tomaselli GF, Kääb S, Tunin R, Marbán E. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart, I: experimental studies. Circ Res. 1999;84:562-570 Key Words: excitation-contraction coupling Ⅲ heart failure Ⅲ midmyocardial ventricular action potential Ⅲ Ca 2ϩ transient R ecent studies using the canine tachycardia pacinginduced model of heart failure 1-8 demonstrate that changes in cellular electrophysiological and excitationcontraction (E-C) coupling processes are qualitatively similar to those observed in cells isolated from failing human heart. In human heart failure, I K1 current density measured at hyperpolarized membrane potentials is reduced by Ϸ50%, 9,10 and density of the transient outward current I to1 is reduced by Ϸ75% in subepicardial 11 and Ϸ40% in midmyocardial ventricular cells 9 and is unchanged in subendocardial ventricular cells. 11 The magnitude of I K1 is reduced by Ϸ40%, and that of I to1 by Ϸ70% in failing canine midmyocardial cells. 5 Expression of proteins involved in E-C coupling is also altered in human heart failure. Sarcoplasmic reticulum (SR) Ca 2ϩ ATPase mRNA level, 12-16 protein level, 12,17,18 and uptake rate 19 are reduced by Ϸ50% in end-stage heart failure. Na ϩ /Ca 2ϩ exchanger (NCX) mRNA levels are increased by Ϸ55% to 79%, 12,20 and NCX protein levels increase 36% to 160%. 12,20 -22

actan@jhu.edu.

We construct a detailed mathematical model for Ca2+ regulation in the ventricular myocyte that includes novel descriptions of subcellular mechanisms based on recent experimental findings: 1) the Keizer-Levine model for the ryanodine receptor (RyR), which displays adaptation at elevated Ca2+; 2) a model for the L-type Ca2+ channel that inactivates by mode switching; and 3) a restricted subspace into which the RyRs and L-type Ca2+ channels empty and interact via Ca2+. We add membrane currents from the Luo-Rudy Phase II ventricular cell model to our description of Ca2+ handling to formulate a new model for ventricular action potentials and Ca2+ regulation. The model can simulate Ca2+ transients during an action potential similar to those seen experimentally. The subspace [Ca2+] rises more rapidly and reaches a higher level (10-30 microM) than the bulk myoplasmic Ca2+ (peak [Ca2+]i approximately 1 microM). Termination of sarcoplasmic reticulum (SR) Ca2+ release is predominately due to emptying of the SR, but is influenced by RyR adaptation. Because force generation is roughly proportional to peak myoplasmic Ca2+, we use [Ca2+]i in the model to explore the effects of pacing rate on force generation. The model reproduces transitions seen in force generation due to changes in pacing that cannot be simulated by previous models. Simulation of such complex phenomena requires an interplay of both RyR adaptation and the degree of SR Ca2+ loading. This model, therefore, shows improved behavior over existing models that lack detailed descriptions of subcellular Ca2+ regulatory mechanisms.

We present a new approach to molecular classification based on mRNA comparisons. Our method, referred to as the top-scoring pair(s) (TSP) classifier, is motivated by current technical and practical limitations in using gene expression microarray data for class prediction, for example to detect disease, identify tumors or predict treatment response. Accurate statistical inference from such data is difficult due to the small number of observations, typically tens, relative to the large number of genes, typically thousands. Moreover, conventional methods from machine learning lead to decisions which are usually very difficult to interpret in simple or biologically meaningful terms. In contrast, the TSP classifier provides decision rules which i) involve very few genes and only relative expression values (e.g., comparing the mRNA counts within a single pair of genes); ii) are both accurate and transparent; and iii) provide specific hypotheses for follow-up studies. In particular, the TSP classifier achieves prediction rates with standard cancer data that are as high as those of previous studies which use considerably more genes and complex procedures. Finally, the TSP classifier is parameter-free, thus avoiding the type of over-fitting and inflated estimates of performance that result when all aspects of learning a predictor are not properly cross-validated.

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.

We describe a unique mitochondrial oscillator that depends on oxidative phosphorylation, reactive oxygen species (ROS), and mitochondrial inner membrane ion channels. Cell-wide synchronized oscillations in mitochondrial membrane potential (Delta Psi(m)), NADH, and ROS production have been recently described in isolated cardiomyocytes, and we have hypothesized that the balance between superoxide anion efflux through inner membrane anion channels and the intracellular ROS scavenging capacity play a key role in the oscillatory mechanism. Here, we formally test the hypothesis using a computational model of mitochondrial energetics and Ca(2+) handling including mitochondrial ROS production, cytoplasmic ROS scavenging, and ROS activation of inner membrane anion flux. The mathematical model reproduces the period and phase of the observed oscillations in Delta Psi(m), NADH, and ROS. Moreover, we experimentally verify model predictions that the period of the oscillator can be modulated by altering the concentration of ROS scavengers or the rate of oxidative phosphorylation, and that the redox state of the glutathione pool oscillates. In addition to its role in cellular dysfunction during metabolic stress, the period of the oscillator can be shown to span a wide range, from milliseconds to hours, suggesting that it may also be a mechanism for physiological timekeeping and/or redox signaling.