Kenneth Tran

A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca2+ (SERCA) Pump

We present a biophysically based kinetic model of the cardiac SERCA pump that consolidates a range of experimental data into a consistent and thermodynamically constrained framework. The SERCA model consists of a number of sub-states with partial reactions that are sensitive to Ca(2+) and pH, and to the metabolites MgATP, MgADP, and Pi. Optimization of model parameters to fit experimental data favors a fully cooperative Ca(2+)-binding mechanism and predicts a Ca(2+)/H(+) counter-transport stoichiometry of 2. Moreover, the order of binding of the partial reactions, particularly the binding of MgATP, proves to be a strong determinant of the ability of the model to fit the data. A thermodynamic investigation of the model indicates that the binding of MgATP has a large inhibitory effect on the maximal reverse rate of the pump. The model is suitable for integrating into whole-cell models of cardiac electrophysiology and Ca(2+) dynamics to simulate the effects on the cell of compromised metabolism arising in ischemia and hypoxia.

A Metabolite-Sensitive, Thermodynamically Constrained Model of Cardiac Cross-Bridge Cycling: Implications for Force Development during Ischemia

We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum force production. Our model, based on a model of cross-bridge kinetics that was developed by others, reproduces many of the observed effects of MgATP, MgADP, Pi, and H(+) on force development while retaining the force/length/Ca(2+) properties of the original model. We introduce three new parameters to account for the competitive binding of H(+) to the Ca(2+) binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters, along with the Pi and H(+) regulatory steps within the cross-bridge cycle, were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H(+)]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia.

Streptozotocin-induced diabetes prolongs twitch duration without affecting the energetics of isolated ventricular trabeculae

BackgroundDiabetes induces numerous electrical, ionic and biochemical defects in the heart. A general feature of diabetic myocardium is its low rate of activity, commonly characterised by prolonged twitch duration. This diabetes-induced mechanical change, however, seems to have no effect on contractile performance (i.e., force production) at the tissue level. Hence, we hypothesise that diabetes has no effect on either myocardial work output or heat production and, consequently, the dependence of myocardial efficiency on afterload of diabetic tissue is the same as that of healthy tissue.MethodsWe used isolated left ventricular trabeculae (streptozotocin-induced diabetes versus control) as our experimental tissue preparations. We measured a number of indices of mechanical (stress production, twitch duration, extent of shortening, shortening velocity, shortening power, stiffness, and work output) and energetic (heat production, change of enthalpy, and efficiency) performance. We calculated efficiency as the ratio of work output to change of enthalpy (the sum of work and heat).ResultsConsistent with literature results, we showed that peak twitch stress of diabetic tissue was normal despite suffering prolonged duration. We report, for the first time, the effect of diabetes on mechanoenergetic performance. We found that the indices of performance listed above were unaffected by diabetes. Hence, since neither work output nor change of enthalpy was affected, the efficiency-afterload relation of diabetic tissue was unaffected, as hypothesised.ConclusionsDiabetes prolongs twitch duration without having an effect on work output or heat production, and hence efficiency, of isolated ventricular trabeculae. Collectively, our results, arising from isolated trabeculae, reconcile the discrepancy between the mechanical performance of the whole heart and its tissues.

Reduced mechanical efficiency in left-ventricular trabeculae of the spontaneously hypertensive rat.

Long‐term systemic arterial hypertension, and its associated compensatory response of left‐ventricular hypertrophy, is fatal. This disease leads to cardiac failure and culminates in death. The spontaneously hypertensive rat (SHR) is an excellent animal model for studying this pathology, suffering from ventricular failure beginning at about 18 months of age. In this study, we isolated left‐ventricular trabeculae from SHR‐F hearts and contrasted their mechanoenergetic performance with those from nonfailing SHR (SHR‐NF) and normotensive Wistar rats. Our results show that, whereas the performance of the SHR‐F differed little from that of the SHR‐NF, both SHR groups performed less stress‐length work than that of Wistar trabeculae. Their lower work output arose from reduced ability to produce sufficient force and shortening. Neither their heat production nor their enthalpy output (the sum of work and heat), particularly the energy cost of Ca2+ cycling, differed from that of the Wistar controls. Consequently, mechanical efficiency (the ratio of work to change of enthalpy) of both SHR groups was lower than that of the Wistar trabeculae. Our data suggest that in hypertension‐induced left‐ventricular hypertrophy, the mechanical performance of the tissue is compromised such that myocardial efficiency is reduced.

Comparison of the Gibbs and Suga formulations of cardiac energetics: the demise of "isoefficiency".

Two very different sorts of experiments have characterized the field of cardiac energetics over the past three decades. In one of these, Gibbs and colleagues measured the heat production of isolated papillary muscles undergoing isometric contractions and afterloaded isotonic contractions. The former generated roughly linear heat vs. force relationships. The latter generated enthalpy-load relationships, the peak values of which occurred at or near peak isometric force, i.e., at a relative load of unity. Contractile efficiency showed a pronounced dependence on afterload. By contrast, Suga and coworkers measured the oxygen consumption (Vo(2)) while recording the pressure-volume-time work loops of blood-perfused isolated dog hearts. From the associated (linear) end-systolic pressure-volume relations they derived a quantity labeled pressure-volume area (PVA), consisting of the sum of pressure-volume work and unspent elastic energy and showed that this was linearly correlated with Vo(2) over a wide range of conditions. This linear dependence imposed isoefficiency: constant contractile efficiency independent of afterload. Neither these data nor those of Gibbs and colleagues are in dispute. Nevertheless, despite numerous attempts over the years, no demonstration of either compatibility or incompatibility of these disparate characterizations of cardiac energetics has been forthcoming. We demonstrate that compatibility between the two formulations is thwarted by the concept of isoefficiency, the thermodynamic basis of which we show to be untenable.

Why has reversal of the actin-myosin cross-bridge cycle not been observed experimentally?

We trace the history of attempts to determine whether the experimentally observed diminution of metabolic energy expenditure when muscles lengthen during active contraction is consistent with reversibility of biochemical reactions and, in particular, with the regeneration of ATP. We note that this scientific endeavor has something of a parallel flavor to it, with both early and more recent experiments exploiting both isolated muscle preparations and exercising human subjects. In tracing this history from the late 19th century to the present, it becomes clear that energy can be (at least transiently) stored in a muscle undergoing an eccentric contraction but that this is unlikely to be due to the regeneration of ATP. A recently developed, thermodynamically constrained model of the cross-bridge cycle provides additional insight into this conclusion.

Myocardial twitch duration and the dependence of oxygen consumption on pressure-volume area: experiments and modelling

•  The energy expenditure of the heart is linearly related to its work performance, as measured by its development of pressure–volume area. •  We have explored the basis of this phenomenon both experimentally (by measuring the heat production of isolated ventricular tissue undergoing cyclic contraction and relaxation) and theoretically (using mathematical modelling). •  We provide the first evidence that the heat production of isolated trabeculae undergoing fixed‐end contractions varies linearly with force–length area, and confirm that twitch duration increases progressively with muscle length. •  Mathematical modelling reveals that length‐dependent prolongation of the twitch reflects length‐ (or, equivalently, force‐) dependent binding of Ca2+ to troponin‐C, together with Ca2+‐dependent crossbridge cooperativity. •  Mathematical modelling further reveals that the apparent linear dependence of heat production on force–length area is remarkably robust against departures from the linearity of length‐dependent twitch duration.

Does the intercept of the heat–stress relation provide an accurate estimate of cardiac activation heat?

The heat of activation of cardiac muscle reflects the metabolic cost of restoring ionic homeostasis following a contraction. The accuracy of its measurement depends critically on the abolition of crossbridge cycling. We abolished crossbridge activity in isolated rat ventricular trabeculae by use of blebbistatin, an agent that selectively inhibits myosin II ATPase. We found cardiac activation heat to be muscle length independent and to account for 15–20% of total heat production at body temperature. We conclude that it can be accurately estimated at minimal muscle length.

Regulation of cardiac cellular bioenergetics: mechanisms and consequences

The regulation of cardiac cellular bioenergetics is critical for maintaining normal cell function, yet the nature of this regulation is not fully understood. Different mechanisms have been proposed to explain how mitochondrial ATP production is regulated to match changing cellular energy demand while metabolite concentrations are maintained. We have developed an integrated mathematical model of cardiac cellular bioenergetics, electrophysiology, and mechanics to test whether stimulation of the dehydrogenase flux by Ca2+ or Pi, or stimulation of complex III by Pi can increase the rate of mitochondrial ATP production above that determined by substrate availability (ADP and Pi). Using the model, we show that, under physiological conditions the rate of mitochondrial ATP production can match varying demand through substrate availability alone; that ATP production rate is not limited by the supply of reducing equivalents in the form of NADH, as a result of Ca2+ or Pi activation of the dehydrogenases; and that ATP production rate is sensitive to feedback activation of complex III by Pi. We then investigate the mechanistic implications on cytosolic ion homeostasis and force production by simulating the concentrations of cytosolic Ca2+, Na+ and K+, and activity of the key ATPases, SERCA pump, Na+/K+ pump and actin‐myosin ATPase, in response to increasing cellular energy demand. We find that feedback regulation of mitochondrial complex III by Pi improves the coupling between energy demand and mitochondrial ATP production and stabilizes cytosolic ADP and Pi concentrations. This subsequently leads to stabilized cytosolic ionic concentrations and consequentially reduced energetic cost from cellular ATPases.

Semantics-Based Composition of Integrated Cardiomyocyte Models Motivated by Real-World Use Cases

Semantics-based model composition is an approach for generating complex biosimulation models from existing components that relies on capturing the biological meaning of model elements in a machine-readable fashion. This approach allows the user to work at the biological rather than computational level of abstraction and helps minimize the amount of manual effort required for model composition. To support this compositional approach, we have developed the SemGen software, and here report on SemGen’s semantics-based merging capabilities using real-world modeling use cases. We successfully reproduced a large, manually-encoded, multi-model merge: the “Pandit-Hinch-Niederer” (PHN) cardiomyocyte excitation-contraction model, previously developed using CellML. We describe our approach for annotating the three component models used in the PHN composition and for merging them at the biological level of abstraction within SemGen. We demonstrate that we were able to reproduce the original PHN model results in a semi-automated, semantics-based fashion and also rapidly generate a second, novel cardiomyocyte model composed using an alternative, independently-developed tension generation component. We discuss the time-saving features of our compositional approach in the context of these merging exercises, the limitations we encountered, and potential solutions for enhancing the approach.