Strong inference for systems biology

Glycolysis model shows that allostery maintains high ATP and limits accumulation of intermediates

Glycolysis is a conserved metabolic pathway that produces ATP and biosynthetic precursors. It is not well understood how the control of mammalian glycolytic enzymes through allosteric feedback and mass action accomplishes various tasks of ATP homeostasis, such as controlling the rate of ATP production, maintaining high and stable ATP levels, ensuring that ATP hydrolysis generates a net excess of energy, and maintaining glycolytic intermediate concentrations within physiological levels. To investigate these questions, we developed a biophysical model of glycolysis based on enzyme rate equations derived from in vitro kinetic data. This is the first biophysical model of human glycolysis that successfully recapitulates the above tasks of ATP homeostasis and predicts absolute concentrations of glycolytic intermediates and isotope tracing kinetics that align with experimental measurements in human cells. We use the model to show that mass action alone is sufficient to control the ATP production rate and maintain the high energy of ATP hydrolysis. Meanwhile, allosteric regulation of hexokinase and phosphofructokinase by ATP, ADP, inorganic phosphate, and glucose-6-phosphate is required to maintain high ATP levels and to prevent uncontrolled accumulation of phosphorylated intermediates of glycolysis. Allosteric feedback achieves the latter by maintaining hexokinase and phosphofructokinase enzyme activity at one-half of ATP demand and, thus, inhibiting the reaction of Harden and Young, which otherwise converts glucose to supraphysiological levels of phosphorylated glycolytic intermediates at the expense of ATP. Our methodology provides a roadmap for a quantitative understanding of how metabolic homeostasis emerges from the activities of individual enzymes.

A simulation study on the role of mitochondria-sarcoplasmic reticulum Ca2+ interaction in cardiomyocyte energetics during exercise

Previous studies demonstrated that the mitochondrial Ca2+ uniporter MCU and the Na+-Ca2+ exchanger NCLX exist in proximity to the sarcoplasmic reticulum (SR) ryanodine receptor RyR and the Ca2+ pump SERCA, respectively, creating a mitochondria-SR Ca2+ interaction. However, the physiological relevance of the mitochondria-SR Ca2+ interaction has remained unsolved. Furthermore, although mitochondrial Ca2+ has been proposed to be an important factor regulating mitochondrial energy metabolism, by activating NADH-producing dehydrogenases, the contribution of the Ca2+-dependent regulatory mechanisms to cellular functions under physiological conditions has been controversial. In this study, we constructed a new integrated model of human ventricular myocyte with excitation-contraction-energetics coupling and investigated systematically the contribution of mitochondria-SR Ca2+ interaction, especially focusing on cardiac energetics during dynamic workload transitions in exercise. Simulation analyses revealed that the spatial coupling of mitochondria and SR, particularly via mitochondrial Ca2+ uniport activity-RyR, was the primary determinant of mitochondrial Ca2+ concentration, and that the Ca2+-dependent regulatory mechanism facilitated mitochondrial NADH recovery during exercise and contributed to the stability of NADH in the workload transition by about 40%, while oxygen consumption rate and cytoplasmic ATP level were not influenced. We concluded that the mitochondria-SR Ca2+ interaction, created via the uneven distribution of Ca2+ handling proteins, optimizes the contribution of the mitochondrial Ca2+-dependent regulatory mechanism to stabilizing NADH during exercise. KEY POINTS: The mitochondrial Ca2+ uniporter protein MCU and the Na+-Ca2+ exchanger protein NCLX are reported to exist in proximity to the sarcoplasmic reticulum (SR) ryanodine receptor RyR and the Ca2+ pump SERCA, respectively, creating a mitochondria-SR Ca2+ interaction in cardiomyocytes. Mitochondrial Ca2+ (Ca2+ mit) has been proposed to be an important factor regulating mitochondrial energy metabolism, by activating NADH-producing dehydrogenases. Here we constructed an integrated model of a human ventricular myocyte with excitation-contraction-energetics coupling and investigated the role of the mitochondria-SR Ca2+ interaction in cardiac energetics during exercise. Simulation analyses revealed that the spatial coupling particularly via mitochondrial Ca2+ uniport activity-RyR is the primary determinant of Ca2+ mit concentration, and that the activation of NADH-producing dehydrogenases by Ca2+ mit contributes to NADH stability during exercise. The mitochondria-SR Ca2+ interaction optimizes the contribution of Ca2+ mit to the activation of NADH-producing dehydrogenases.

Guidelines for mechanistic modeling and analysis in cardiovascular research

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Integrated Functions of Cardiac Energetics, Mechanics, and Purine Nucleotide Metabolism

Purine nucleotides play central roles in energy metabolism in the heart. Most fundamentally, the free energy of hydrolysis of the adenine nucleotide adenosine triphosphate (ATP) provides the thermodynamic driving force for numerous cellular processes including the actin-myosin crossbridge cycle. Perturbations to ATP supply and/or demand in the myocardium lead to changes in the homeostatic balance between purine nucleotide synthesis, degradation, and salvage, potentially affecting myocardial energetics and, consequently, myocardial mechanics. Indeed, both acute myocardial ischemia and decompensatory remodeling of the myocardium in heart failure are associated with depletion of myocardial adenine nucleotides and with impaired myocardial mechanical function. Yet there remain gaps in the understanding of mechanistic links between adenine nucleotide degradation and contractile dysfunction in heart disease. The scope of this article is to: (i) review current knowledge of the pathways of purine nucleotide depletion and salvage in acute ischemia and in chronic heart disease; (ii) review hypothesized mechanisms linking myocardial mechanics and energetics with myocardial adenine nucleotide regulation; and (iii) highlight potential targets for treating myocardial metabolic and mechanical dysfunction associated with these pathways. It is hypothesized that an imbalance in the degradation, salvage, and synthesis of adenine nucleotides leads to a net loss of adenine nucleotides in both acute ischemia and under chronic high-demand conditions associated with the development of heart failure. This reduction in adenine nucleotide levels results in reduced myocardial ATP and increased myocardial inorganic phosphate. Both of these changes have the potential to directly impact tension development and mechanical work at the cellular level. © 2024 American Physiological Society. Compr Physiol 14:5345-5369, 2024.

How can we fully realize the potential of mathematical and biological models to reintegrate biology?

Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function.

The Axes of Life: A roadmap for understanding dynamic multiscale systems

The biological challenges facing humanity are complex, multi-factorial, and are intimately tied to the future of our health, welfare, and stewardship of the Earth. Tackling problems in diverse areas, such as agriculture, ecology, and health care require linking vast data sets that encompass numerous components and spatio-temporal scales. Here, we provide a new framework and a road map for using experiments and computation to understand dynamic biological systems that span multiple scales. We discuss theories that can help understand complex biological systems and highlight the limitations of existing methodologies and recommend data generation practices. The advent of new technologies such as big data analytics and artificial intelligence can help bridge different scales and data types. We recommend ways to make such models transparent, compatible with existing theories of biological function, and to make biological data sets readable by advanced machine learning algorithms. Overall, the barriers for tackling pressing biological challenges are not only technological, but also sociological. Hence, we also provide recommendations for promoting interdisciplinary interactions between scientists.

Quantifying the effect of dobutamine stress on myocardial Pi and pH in healthy volunteers: A 31 P MRS study at 7T

Purpose

Phosphorus spectroscopy (³¹P‐MRS) is a proven method to probe cardiac energetics. Studies typically report the phosphocreatine (PCr) to adenosine triphosphate (ATP) ratio. We focus on another ³¹P signal: inorganic phosphate (Pi), whose chemical shift allows computation of myocardial pH, with Pi/PCr providing additional insight into cardiac energetics. Pi is often obscured by signals from blood 2,3‐diphosphoglycerate (2,3‐DPG). We introduce a method to quantify Pi in 14 min without hindrance from 2,3‐DPG.

Methods

Using a ³¹P stimulated echo acquisition mode (STEAM) sequence at 7 Tesla that inherently suppresses signal from 2,3‐DPG, the Pi peak was cleanly resolved. Resting state UTE‐chemical shift imaging (PCr/ATP) and STEAM ³¹P‐MRS (Pi/PCr, pH) were undertaken in 23 healthy controls; pH and Pi/PCr were subsequently recorded during dobutamine infusion.

Results

We achieved a clean Pi signal both at rest and stress with good 2,3‐DPG suppression. Repeatability coefficient (8 subjects) for Pi/PCr was 0.036 and 0.12 for pH. We report myocardial Pi/PCr and pH at rest and during catecholamine stress in healthy controls. Pi/PCr was maintained during stress (0.098 ± 0.031 [rest] vs. 0.098 ± 0.031 [stress] P = .95); similarly, pH did not change (7.09 ± 0.07 [rest] vs. 7.08 ± 0.11 [stress] P = .81). Feasibility for patient studies was subsequently successfully demonstrated in a patient with cardiomyopathy.

Conclusion

We introduced a method that can resolve Pi using 7 Tesla STEAM ³¹P‐MRS. We demonstrate the stability of Pi/PCr and myocardial pH in volunteers at rest and during catecholamine stress. This protocol is feasible in patients and potentially of use for studying pathological myocardial energetics.

Perspective: Dimensions of the scientific method

The scientific method has been guiding biological research for a long time. It not only prescribes the order and types of activities that give a scientific study validity and a stamp of approval but also has substantially shaped how we collectively think about the endeavor of investigating nature. The advent of high-throughput data generation, data mining, and advanced computational modeling has thrown the formerly undisputed, monolithic status of the scientific method into turmoil. On the one hand, the new approaches are clearly successful and expect the same acceptance as the traditional methods, but on the other hand, they replace much of the hypothesis-driven reasoning with inductive argumentation, which philosophers of science consider problematic. Intrigued by the enormous wealth of data and the power of machine learning, some scientists have even argued that significant correlations within datasets could make the entire quest for causation obsolete. Many of these issues have been passionately debated during the past two decades, often with scant agreement. It is proffered here that hypothesis-driven, data-mining-inspired, and "allochthonous" knowledge acquisition, based on mathematical and computational models, are vectors spanning a 3D space of an expanded scientific method. The combination of methods within this space will most certainly shape our thinking about nature, with implications for experimental design, peer review and funding, sharing of result, education, medical diagnostics, and even questions of litigation.

Cardiac Metabolic Limitations Contribute to Diminished Performance of the Heart in Aging

Changes in the myocardial energetics associated with aging-reductions in creatine phosphate/ATP ratio, total creatine, and ATP-mirror changes observed in failing hearts compared to healthy controls. Similarly, both aging and heart failure are associated with significant reductions in cardiac performance and maximal left ventricular cardiac power output compared with young healthy individuals. Based on these observations, we hypothesize that reductions in the concentrations of cytoplasmic adenine nucleotide, creatine, and phosphate pools that occur with aging impair the myocardial capacity to synthesize ATP at physiological free energy levels and that the resulting changes to myocardial energetic status impair the mechanical pumping ability of the heart. The purpose of this study is to test these hypotheses using an age-structured population model for myocardial metabolism in the adult female population and to determine the potential impact of reductions in key myocardial metabolite pools in causing metabolic/energetic and cardiac mechanical dysfunction associated with aging. To test these hypotheses, we developed a population model for myocardial energetics to predict myocardial ATP, ADP, creatine phosphate, creatine, and inorganic phosphate concentrations as functions of cardiac work and age in the adult female population. Model predictions support our hypotheses and are consistent with previous experimental observations. The major findings provide a novel, to our knowledge, theoretical and computational framework for further probing complex relationships between the energetics and performance of the heart with aging.

Differential equation methods for simulation of GFP kinetics in non-steady state experiments

Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non-steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis.

Human Cardiac 31P-MR Spectroscopy at 3 Tesla Cannot Detect Failing Myocardial Energy Homeostasis during Exercise

Phosphorus-31 magnetic resonance spectroscopy (³¹P-MRS) is a unique non-invasive imaging modality for probing in vivo high-energy phosphate metabolism in the human heart. We investigated whether current ³¹P-MRS methodology would allow for clinical applications to detect exercise-induced changes in (patho-)physiological myocardial energy metabolism. Hereto, measurement variability and repeatability of three commonly used localized ³¹P-MRS methods [3D image-selected in vivo spectroscopy (ISIS) and 1D ISIS with 1D chemical shift imaging (CSI) oriented either perpendicular or parallel to the surface coil] to quantify the myocardial phosphocreatine (PCr) to adenosine triphosphate (ATP) ratio in healthy humans (n = 8) at rest were determined on a clinical 3 Tesla MR system. Numerical simulations of myocardial energy homeostasis in response to increased cardiac work rates were performed using a biophysical model of myocardial oxidative metabolism. Hypertrophic cardiomyopathy was modeled by either inefficient sarcomere ATP utilization or decreased mitochondrial ATP synthesis. The effect of creatine depletion on myocardial energy homeostasis was explored for both conditions. The mean in vivo myocardial PCr/ATP ratio measured with 3D ISIS was 1.57 ± 0.17 with a large repeatability coefficient of 40.4%. For 1D CSI in a 1D ISIS-selected slice perpendicular to the surface coil, the PCr/ATP ratio was 2.78 ± 0.50 (repeatability 42.5%). With 1D CSI in a 1D ISIS-selected slice parallel to the surface coil, the PCr/ATP ratio was 1.70 ± 0.56 (repeatability 43.7%). The model predicted a PCr/ATP ratio reduction of only 10% at the maximal cardiac work rate in normal myocardium. Hypertrophic cardiomyopathy led to lower PCr/ATP ratios for high cardiac work rates, which was exacerbated by creatine depletion. Simulations illustrated that when conducting cardiac ³¹P-MRS exercise stress testing with large measurement error margins, results obtained under pathophysiologic conditions may still lie well within the 95% confidence interval of normal myocardial PCr/ATP dynamics. Current measurement precision of localized ³¹P-MRS for quantification of the myocardial PCr/ATP ratio precludes the detection of the changes predicted by computational modeling. This hampers clinical employment of ³¹P-MRS for diagnostic testing and risk stratification, and warrants developments in cardiac ³¹P-MRS exercise stress testing methodology.

Feedback Regulation and Time Hierarchy of Oxidative Phosphorylation in Cardiac Mitochondria

To determine how oxidative ATP synthesis is regulated in the heart, the responses of cardiac mitochondria oxidizing pyruvate to alterations in [ATP], [ADP], and inorganic phosphate ([Pi]) were characterized over a range of steady-state levels of extramitochondrial [ATP], [ADP], and [Pi]. Evolution of the steady states of the measured variables with the flux of respiration shows that: (1) a higher phosphorylation potential is achieved by mitochondria at higher [Pi] for a given flux of respiration; (2) the time hierarchy of oxidative phosphorylation is given by phosphorylation subsystem, electron transport chain, and substrate dehydrogenation subsystems listed in increasing order of their response times; (3) the matrix ATP hydrolysis mass action ratio [ADP] × [Pi]/[ATP] provides feedback to the substrate dehydrogenation flux over the entire range of respiratory flux examined in this study; and finally, (4) contrary to previous models of regulation of oxidative phosphorylation, [Pi] does not modulate the activity of complex III.

Catalytic Coupling of Oxidative Phosphorylation, ATP Demand, and Reactive Oxygen Species Generation

Competing models of mitochondrial energy metabolism in the heart are highly disputed. In addition, the mechanisms of reactive oxygen species (ROS) production and scavenging are not well understood. To deepen our understanding of these processes, a computer model was developed to integrate the biophysical processes of oxidative phosphorylation and ROS generation. The model was calibrated with experimental data obtained from isolated rat heart mitochondria subjected to physiological conditions and workloads. Model simulations show that changes in the quinone pool redox state are responsible for the apparent inorganic phosphate activation of complex III. Model simulations predict that complex III is responsible for more ROS production during physiological working conditions relative to complex I. However, this relationship is reversed under pathological conditions. Finally, model analysis reveals how a highly reduced quinone pool caused by elevated levels of succinate is likely responsible for the burst of ROS seen during reperfusion after ischemia.

Conceptions of Good Science in Our Data-Rich World

Scientists have been debating for centuries the nature of proper scientific methods. Currently, criticisms being thrown at data-intensive science are reinvigorating these debates. However, many of these criticisms represent long-standing conflicts over the role of hypothesis testing in science and not just a dispute about the amount of data used. Here, we show that an iterative account of scientific methods developed by historians and philosophers of science can help make sense of data-intensive scientific practices and suggest more effective ways to evaluate this research. We use case studies of Darwin's research on evolution by natural selection and modern-day research on macrosystems ecology to illustrate this account of scientific methods and the innovative approaches to scientific evaluation that it encourages. We point out recent changes in the spheres of science funding, publishing, and education that reflect this richer account of scientific practice, and we propose additional reforms.

Improving the physiological realism of experimental models

The Virtual Physiological Human (VPH) project aims to develop integrative, explanatory and predictive computational models (C-Models) as numerical investigational tools to study disease, identify and design effective therapies and provide an in silico platform for drug screening. Ultimately, these models rely on the analysis and integration of experimental data. As such, the success of VPH depends on the availability of physiologically realistic experimental models (E-Models) of human organ function that can be parametrized to test the numerical models. Here, the current state of suitable E-models, ranging from in vitro non-human cell organelles to in vivo human organ systems, is discussed. Specifically, challenges and recent progress in improving the physiological realism of E-models that may benefit the VPH project are highlighted and discussed using examples from the field of research on cardiovascular disease, musculoskeletal disorders, diabetes and Parkinson's disease.

A model qualification method for mechanistic physiological QSP models to support model-informed drug development

Mechanistic physiological modeling is a scientific method that combines available data with scientific knowledge and engineering approaches to facilitate better understanding of biological systems, improve decision‐making, reduce risk, and increase efficiency in drug discovery and development. It is a type of quantitative systems pharmacology (QSP) approach that places drug‐specific properties in the context of disease biology. This tutorial provides a broadly applicable model qualification method (MQM) to ensure that mechanistic physiological models are fit for their intended purposes.

Studying Cellular Signal Transduction with OMIC Technologies

In the gulf between genotype and phenotype exists proteins and, in particular, protein signal transduction systems. These systems use a relatively limited parts list to respond to a much longer list of extracellular, environmental, and/or mechanical cues with rapidity and specificity. Most signaling networks function in a highly non-linear and often contextual manner. Furthermore, these processes occur dynamically across space and time. Because of these complexities, systems and "OMIC" approaches are essential for the study of signal transduction. One challenge in using OMIC-scale approaches to study signaling is that the "signal" can take different forms in different situations. Signals are encoded in diverse ways such as protein-protein interactions, enzyme activities, localizations, or post-translational modifications to proteins. Furthermore, in some cases, signals may be encoded only in the dynamics, duration, or rates of change of these features. Accordingly, systems-level analyses of signaling may need to integrate multiple experimental and/or computational approaches. As the field has progressed, the non-triviality of integrating experimental and computational analyses has become apparent. Successful use of OMIC methods to study signaling will require the "right" experiments and the "right" modeling approaches, and it is critical to consider both in the design phase of the project. In this review, we discuss common OMIC and modeling approaches for studying signaling, emphasizing the philosophical and practical considerations for effectively merging these two types of approaches to maximize the probability of obtaining reliable and novel insights into signaling biology.

Computational analysis of the regulation of Ca(2+) dynamics in rat ventricular myocytes

Force-frequency relationships of isolated cardiac myocytes show complex behaviors that are thought to be specific to both the species and the conditions associated with the experimental preparation. Ca(2+) signaling plays an important role in shaping the force-frequency relationship, and understanding the properties of the force-frequency relationship in vivo requires an understanding of Ca(2+) dynamics under physiologically relevant conditions. Ca(2+) signaling is itself a complicated process that is best understood on a quantitative level via biophysically based computational simulation. Although a large number of models are available in the literature, the models are often a conglomeration of components parameterized to data of incompatible species and/or experimental conditions. In addition, few models account for modulation of Ca(2+) dynamics via β-adrenergic and calmodulin-dependent protein kinase II (CaMKII) signaling pathways even though they are hypothesized to play an important regulatory role in vivo. Both protein-kinase-A and CaMKII are known to phosphorylate a variety of targets known to be involved in Ca(2+) signaling, but the effects of these pathways on the frequency- and inotrope-dependence of Ca(2+) dynamics are not currently well understood. In order to better understand Ca(2+) dynamics under physiological conditions relevant to rat, a previous computational model is adapted and re-parameterized to a self-consistent dataset obtained under physiological temperature and pacing frequency and updated to include β-adrenergic and CaMKII regulatory pathways. The necessity of specific effector mechanisms of these pathways in capturing inotrope- and frequency-dependence of the data is tested by attempting to fit the data while including and/or excluding those effector components. We find that: (1) β-adrenergic-mediated phosphorylation of the L-type calcium channel (LCC) (and not of phospholamban (PLB)) is sufficient to explain the inotrope-dependence; and (2) that CaMKII-mediated regulation of neither the LCC nor of PLB is required to explain the frequency-dependence of the data.

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.

Mechanistic modeling confronts the complexity of molecular cell biology

Mechanistic modeling has the potential to transform how cell biologists contend with the inescapable complexity of modern biology. I am a physiologist–electrical engineer–systems biologist who has been working at the level of cell biology for the past 24 years. This perspective aims 1) to convey why we build models, 2) to enumerate the major approaches to modeling and their philosophical differences, 3) to address some recurrent concerns raised by experimentalists, and then 4) to imagine a future in which teams of experimentalists and modelers build—and subject to exhaustive experimental tests—models covering the entire spectrum from molecular cell biology to human pathophysiology. There is, in my view, no technical obstacle to this future, but it will require some plasticity in the biological research mind-set.

In silico model-based inference: a contemporary approach for hypothesis testing in network biology

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics.

Bidirectional cargo transport: moving beyond tug of war

Vesicles, organelles and other intracellular cargo are transported by kinesin and dynein motors, which move in opposite directions along microtubules. This bidirectional cargo movement is frequently described as a 'tug of war' between oppositely directed molecular motors attached to the same cargo. However, although many experimental and modelling studies support the tug-of-war paradigm, numerous knockout and inhibition studies in various systems have found that inhibiting one motor leads to diminished motility in both directions, which is a 'paradox of co-dependence' that challenges the paradigm. In an effort to resolve this paradox, three classes of bidirectional transport models--microtubule tethering, mechanical activation and steric disinhibition--are proposed, and a general mathematical modelling framework for bidirectional cargo transport is put forward to guide future experiments.

Unchanged mitochondrial organization and compartmentation of high-energy phosphates in creatine-deficient GAMT-/- mouse hearts

Disruption of the creatine kinase (CK) system in hearts of CK-deficient mice leads to changes in the ultrastructure and regulation of mitochondrial respiration. We expected to see similar changes in creatine-deficient mice, which lack the enzyme guanidinoacetate methyltransferase (GAMT) to produce creatine. The aim of this study was to characterize the changes in cardiomyocyte mitochondrial organization, regulation of respiration, and intracellular compartmentation associated with GAMT deficiency. Three-dimensional mitochondrial organization was assessed by confocal microscopy. On populations of permeabilized cardiomyocytes, we recorded ADP and ATP kinetics of respiration, competition between mitochondria and pyruvate kinase for ADP produced by ATPases, ADP kinetics of endogenous pyruvate kinase, and ATP kinetics of ATPases. These data were analyzed by mathematical models to estimate intracellular compartmentation. Quantitative analysis of morphological and kinetic data as well as derived model fits showed no difference between GAMT-deficient and wild-type mice. We conclude that inactivation of the CK system by GAMT deficiency does not alter mitochondrial organization and intracellular compartmentation in relaxed cardiomyocytes. Thus, our results suggest that the healthy heart is able to preserve cardiac function at a basal level in the absence of CK-facilitated energy transfer without compromising intracellular organization and the regulation of mitochondrial energy homeostasis. This raises questions on the importance of the CK system as a spatial energy buffer in unstressed cardiomyocytes.

Sensitivity analysis of flux determination in heart by H₂ ¹⁸O -provided labeling using a dynamic Isotopologue model of energy transfer pathways

To characterize intracellular energy transfer in the heart, two organ-level methods have frequently been employed: inversion and saturation transfer, and dynamic labeling. Creatine kinase (CK) fluxes obtained by following oxygen labeling have been considerably smaller than the fluxes determined by saturation transfer. It has been proposed that dynamic labeling determines net flux through CK shuttle, whereas saturation transfer measures total unidirectional flux. However, to our knowledge, no sensitivity analysis of flux determination by oxygen labeling has been performed, limiting our ability to compare flux distributions predicted by different methods. Here we analyze oxygen labeling in a physiological heart phosphotransfer network with active CK and adenylate kinase (AdK) shuttles and establish which fluxes determine the labeling state. A mathematical model consisting of a system of ordinary differential equations was composed describing enrichment in each phosphoryl group and inorganic phosphate. By varying flux distributions in the model and calculating the labeling, we analyzed labeling sensitivity to different fluxes in the heart. We observed that the labeling state is predominantly sensitive to total unidirectional CK and AdK fluxes and not to net fluxes. We conclude that measuring dynamic incorporation of into the high-energy phosphotransfer network in heart does not permit unambiguous determination of energetic fluxes with a higher magnitude than the ATP synthase rate when the bidirectionality of fluxes is taken into account. Our analysis suggests that the flux distributions obtained using dynamic labeling, after removing the net flux assumption, are comparable with those from inversion and saturation transfer.

In heart, the movement of energy metabolites between force-producing myosin, other ATPases, and mitochondria is vital for its function and closely related to heart pathologies. In addition to diffusion, transport of ATP, ADP, Pi, and phosphocreatine occurs along parallel pathways such as the adenylate kinase and creatine kinase shuttles. Two organ-level methods have been developed to study the relative flux through these pathways. However, their results differ. It was recently demonstrated that studies often suffer from the exclusion of compartmentation from their metabolic models. One study overcame this limitation by using compartmental models and statistical methods on multiple experiments. Here, we analyzed the sensitivity of the other method - dynamic labeling of phosphoryl groups and inorganic phosphate. For that, we composed a mathematical model tracking enrichment of the metabolites and evaluated sensitivity of labeling to different flux distribution scenarios. Our study shows that the dynamic method provides a measure of total flux, and not net flux as presumed previously, making the fluxes predicted from both methods consistent. Importantly, conclusions derived on the basis of labeling analysis, particularly those regarding the net flux through the shuttles in control and pathological cases, need to be reevaluated.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

Insulin activation of plasma nonesterified fatty acid uptake in metabolic syndrome

OBJECTIVE

Insulin control of fatty acid metabolism has long been deemed dominated by suppression of adipose lipolysis. The goal of the present study was to test the hypothesis that this single role of insulin is insufficient to explain observed fatty acid dynamics.

METHODS AND RESULTS

Fatty acid kinetics were measured during a meal tolerance test and insulin sensitivity assessed by intravenous glucose tolerance test in overweight human subjects (n=15; body mass index, 35.8 ± 7.1 kg/m(2)). Non-steady state tracer kinetic models were formulated and tested using ProcessDB software. Suppression of adipose fatty acid release, by itself, could not account for postprandial nonesterified fatty acid concentration changes, but adipose suppression combined with insulin activation of fatty acid uptake was consistent with the measured data. The observed insulin K(m) for nonesterified fatty acid uptake was inversely correlated with both insulin sensitivity of glucose uptake (intravenous glucose tolerance test insulin sensitivity; r=-0.626; P=0.01) and whole body fat oxidation after the meal (r=-0.538; P=0.05).

CONCLUSIONS

These results support insulin regulation of fatty acid turnover by both release and uptake mechanisms. Activation of fatty acid uptake is consistent with the human data, has mechanistic precedent in cell culture, and highlights a new potential target for therapies aimed at improving the control of fatty acid metabolism in insulin-resistant disease states.

Computational modeling of mitochondrial energy transduction

Mitochondria are the power plant of the heart, burning fat and sugars to supply the muscle with the adenosine triphosphate (ATP) free energy that drives contraction and relaxation during each heart beat. This function was first captured in a mathematical model in 1967. Today, interest in such a model has been rekindled by ongoing in silico integrative physiology efforts such as the Cardiac Physiome project. Here, the status of the field of computational modeling of mitochondrial ATP synthetic function is reviewed.

Detailed kinetics and regulation of mammalian 2-oxoglutarate dehydrogenase

Background

Mitochondrial 2-oxoglutarate (α-ketoglutarate) dehydrogenase complex (OGDHC), a key regulatory point of tricarboxylic acid (TCA) cycle, plays vital roles in multiple pathways of energy metabolism and biosynthesis. The catalytic mechanism and allosteric regulation of this large enzyme complex are not fully understood. Here computer simulation is used to test possible catalytic mechanisms and mechanisms of allosteric regulation of the enzyme by nucleotides (ATP, ADP), pH, and metal ion cofactors (Ca²⁺ and Mg²⁺).

Results

A model was developed based on an ordered ter-ter enzyme kinetic mechanism combined with con-formational changes that involve rotation of one lipoic acid between three catalytic sites inside the enzyme complex. The model was parameterized using a large number of kinetic data sets on the activity of OGDHC, and validated by comparison of model predictions to independent data.

Conclusions

The developed model suggests a hybrid rapid-equilibrium ping-pong random mechanism for the kinetics of OGDHC, consistent with previously reported mechanisms, and accurately describes the experimentally observed regulatory effects of cofactors on the OGDHC activity. This analysis provides a single consistent theoretical explanation for a number of apparently contradictory results on the roles of phosphorylation potential, NAD (H) oxidation-reduction state ratio, as well as the regulatory effects of metal ions on ODGHC function.

Facilitated diffusion of myoglobin and creatine kinase and reaction-diffusion constraints of aerobic metabolism under steady-state conditions in skeletal muscle

The roles of creatine kinase (CK) and myoglobin (Mb) on steady-state facilitated diffusion and temporal buffering of ATP and oxygen, respectively, are assessed within the context of a reaction-diffusion model of muscle energetics. Comparison of the reaction-diffusion model with experimental data from a wide range of muscle fibers shows that the experimentally observed skeletal muscle fibers are generally not limited by diffusion, and the model further indicates that while some muscle fibers operate near the edge of diffusion limitation, no detectable effects of Mb and CK on the effectiveness factor, a measure of diffusion constraints, are observed under steady-state conditions. However, CK had a significant effect on average ATP concentration over a wide range of rates and length scales within the reaction limited regime. The facilitated diffusion functions of Mb and CK become observable in the model for larger size cells with low mitochondrial volume fraction and for low boundary O(2) concentration and high ATP demand, where the fibers may be limited by diffusion. From the transient analysis it may be concluded that CK primarily functions to temporally buffer ATP as opposed to facilitating diffusion while Mb has a small temporal buffering effect on oxygen but does not play any significant role in steady-state facilitated diffusion in skeletal muscle fibers under most physiologically relevant regions.

Mechanisms of glucose sensing in the pancreatic β-cell: A computational systems-based analysis

Pancreatic β-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm with a subsequent influx of calcium and the eventual secretion of insulin. The mechanisms of glucose sensing in the pancreatic β-cell involve the coupling of cytoplasmic and mitochondrial processes. Our analysis, based on mathematical models of data from multiple sources has implications for β-cell function and the treatment of type 2 diabetes (Fridlyand and Philipson, 2010). This β-cell glucose response model correctly predicts changes in the ATP/ADP ratio, cytoplasmic and mitochondrial calcium levels, and other metabolic parameters in response to alterations in substrate delivery at steady-state and during cytoplasmic calcium oscillations. Here we consider how peculiarities of β-cell pathways that result in dysfunction can be a consequence of specific mechanisms of glucose sensitivity, using our computational systems-based analysis. We found that the mitochondrial membrane potential must be relatively low in β-cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in cellular respiratory activity. Our analysis additionally demonstrates how activity of lactate dehydrogenase, uncoupling proteins, and the redox shuttles all working in concert can regulate β-cell function. We further show that a decreased mitochondrial membrane potential may lead to a low rate of production of reactive oxygen species in β-cells under physiological conditions. This computational systems analysis aids in providing a more complete understanding of the complex process of β-cell glucose sensing.

Analyzing the functional properties of the creatine kinase system with multiscale 'sloppy' modeling

In this study the function of the two isoforms of creatine kinase (CK; EC 2.7.3.2) in myocardium is investigated. The 'phosphocreatine shuttle' hypothesis states that mitochondrial and cytosolic CK plays a pivotal role in the transport of high-energy phosphate (HEP) groups from mitochondria to myofibrils in contracting muscle. Temporal buffering of changes in ATP and ADP is another potential role of CK. With a mathematical model, we analyzed energy transport and damping of high peaks of ATP hydrolysis during the cardiac cycle. The analysis was based on multiscale data measured at the level of isolated enzymes, isolated mitochondria and on dynamic response times of oxidative phosphorylation measured at the whole heart level. Using 'sloppy modeling' ensemble simulations, we derived confidence intervals for predictions of the contributions by phosphocreatine (PCr) and ATP to the transfer of HEP from mitochondria to sites of ATP hydrolysis. Our calculations indicate that only 15±8% (mean±SD) of transcytosolic energy transport is carried by PCr, contradicting the PCr shuttle hypothesis. We also predicted temporal buffering capabilities of the CK isoforms protecting against high peaks of ATP hydrolysis (3750 µM*s(-1)) in myofibrils. CK inhibition by 98% in silico leads to an increase in amplitude of mitochondrial ATP synthesis pulsation from 215±23 to 566±31 µM*s(-1), while amplitudes of oscillations in cytosolic ADP concentration double from 77±11 to 146±1 µM. Our findings indicate that CK acts as a large bandwidth high-capacity temporal energy buffer maintaining cellular ATP homeostasis and reducing oscillations in mitochondrial metabolism. However, the contribution of CK to the transport of high-energy phosphate groups appears limited. Mitochondrial CK activity lowers cytosolic inorganic phosphate levels while cytosolic CK has the opposite effect.

Intracellular Energetic Units regulate metabolism in cardiac cells

This review describes developments in historical perspective as well as recent results of investigations of cellular mechanisms of regulation of energy fluxes and mitochondrial respiration by cardiac work - the metabolic aspect of the Frank-Starling law of the heart. A Systems Biology solution to this problem needs the integration of physiological and biochemical mechanisms that take into account intracellular interactions of mitochondria with other cellular systems, in particular with cytoskeleton components. Recent data show that different tubulin isotypes are involved in the regular arrangement exhibited by mitochondria and ATP-consuming systems into Intracellular Energetic Units (ICEUs). Beta II tubulin association with the mitochondrial outer membrane, when co-expressed with mitochondrial creatine kinase (MtCK) specifically limits the permeability of voltage-dependent anion channel for adenine nucleotides. In the MtCK reaction this interaction changes the regulatory kinetics of respiration through a decrease in the affinity for adenine nucleotides and an increase in the affinity for creatine. Metabolic Control Analysis of the coupled MtCK-ATP Synthasome in permeabilized cardiomyocytes showed a significant increase in flux control by steps involved in ADP recycling. Mathematical modeling of compartmentalized energy transfer represented by ICEUs shows that cyclic changes in local ADP, Pi, phosphocreatine and creatine concentrations during contraction cycle represent effective metabolic feedback signals when amplified in the coupled non-equilibrium MtCK-ATP Synthasome reactions in mitochondria. This mechanism explains the regulation of respiration on beat to beat basis during workload changes under conditions of metabolic stability. This article is part of a Special Issue entitled "Local Signaling in Myocytes."

Stimulatory effects of calcium on respiration and NAD(P)H synthesis in intact rat heart mitochondria utilizing physiological substrates cannot explain respiratory control in vivo

Mitochondrial TCA cycle dehydrogenase enzymes have been shown to be stimulated by Ca(2+) under various substrate and ADP incubation conditions in an attempt to determine and understand the role of Ca(2+) in maintaining energy homeostasis in working hearts. In this study, we tested the hypothesis that, at physiological temperature and 1 mM extramitochondrial free magnesium, Ca(2+) can stimulate the overall mitochondrial NAD(P)H generation flux in rat heart mitochondria utilizing pyruvate and malate as substrates at both subsaturating and saturating concentrations. In both cases, we found that, in the physiological regime of mitochondrial oxygen consumption observed in the intact animal and in the physiological range of cytosolic Ca(2+) concentration averaged per beat, Ca(2+) had no observable stimulatory effect. A modest apparent stimulatory effect (22-27%) was observable at supraphysiological maximal ADP-stimulated respiration at 2.5 mM initial phosphate. The stimulatory effects observed over the physiological Ca(2+) range are not sufficient to make a significant contribution to the control of oxidative phosphorylation in the heart in vivo.

Giant sucking sound: can physiology fill the intellectual void left by the reductionists?

Molecular reductionism has so far failed to deliver the broad-based therapeutic insights that were initially hoped for. This form of reductionism is now being replaced by so-called "systems biology." This is a nebulously defined approach and/or discipline, with some versions of it relying excessively on hypothesis-neutral approaches and only minimally informed by key physiological concepts such as homeostasis and regulation. In this context, physiology is uniquely positioned to continue to provide impressive levels of both biological and therapeutic insight by using hypothesis-driven "classical" approaches and concepts to help frame what might be described as the "pieces of the puzzle" that emerge from molecular reductionism. The strength of physiology as a "bridge" between reductionism and epidemiology, along with its unparalleled ability to generate therapeutic insights and opportunities justifies increased attention and emphasis on our discipline into the future. Arguments relevant to this set of assertions are advanced and this paper, which was based on the 2011 Adolph Lecture, represents an effort to fill the intellectual void left by reductionism and improve scientific progress.

Mitochondrial approaches to protect against cardiac ischemia and reperfusion injury

The mitochondrion is a vital component in cellular energy metabolism and intracellular signaling processes. Mitochondria are involved in a myriad of complex signaling cascades regulating cell death vs. survival. Importantly, mitochondrial dysfunction and the resulting oxidative and nitrosative stress are central in the pathogenesis of numerous human maladies including cardiovascular diseases, neurodegenerative diseases, diabetes, and retinal diseases, many of which are related. This review will examine the emerging understanding of the role of mitochondria in the etiology and progression of cardiovascular diseases and will explore potential therapeutic benefits of targeting the organelle in attenuating the disease process. Indeed, recent advances in mitochondrial biology have led to selective targeting of drugs designed to modulate or manipulate mitochondrial function, to the use of light therapy directed to the mitochondrial function, and to modification of the mitochondrial genome for potential therapeutic benefit. The approach to rationally treat mitochondrial dysfunction could lead to more effective interventions in cardiovascular diseases that to date have remained elusive. The central premise of this review is that if mitochondrial abnormalities contribute to the etiology of cardiovascular diseases (e.g., ischemic heart disease), alleviating the mitochondrial dysfunction will contribute to mitigating the severity or progression of the disease. To this end, this review will provide an overview of our current understanding of mitochondria function in cardiovascular diseases as well as the potential role for targeting mitochondria with potential drugs or other interventions that lead to protection against cell injury.

Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle

Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction-diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction-diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle.

Simulation of cellular biochemical system kinetics

The goal of realistically and reliably simulating the biochemical processes underlying cellular function is achievable through a systematic approach that makes use of the broadest possible amount of in vitro and in vivo data, and is consistent with all applicable physical chemical theories. Progress will be facilitated by establishing: (1) a concrete self-consistent theoretical foundation for systems simulation; (2) extensive and accurate databases of thermodynamic properties of biochemical reactions; (3) parameterized and validated models of enzyme and transporter catalytic mechanisms that are consistent with physical chemical theoretical foundation; and (4) software tools for integrating all these concepts, data, and models into a cohesive representation of cellular biochemical systems. Ongoing initiatives are laying the groundwork for the broad-based community cooperation that will be necessary to pursue these elements of a strategic infrastructure for systems simulation on a large scale.

Identifying physiological origins of baroreflex dysfunction in salt-sensitive hypertension in the Dahl SS rat

Salt-sensitive hypertension is known to be associated with dysfunction of the baroreflex control system in the Dahl salt-sensitive (SS) rat. However, neither the physiological mechanisms nor the genomic regions underlying the baroreflex dysfunction seen in this rat model are definitively known. Here, we have adopted a mathematical modeling approach to investigate the physiological and genetic origins of baroreflex dysfunction in the Dahl SS rat. We have developed a computational model of the overall baroreflex heart rate control system based on known physiological mechanisms to analyze telemetry-based blood pressure and heart rate data from two genetic strains of rat, the SS and consomic SS.13(BN), on low- and high-salt diets. With this approach, physiological parameters are estimated, unmeasured physiological variables related to the baroreflex control system are predicted, and differences in these quantities between the two strains of rat on low- and high-salt diets are detected. Specific findings include: a significant selective impairment in sympathetic gain with high-salt diet in SS rats and a protection from this impairment in SS.13(BN) rats, elevated sympathetic and parasympathetic offsets with high-salt diet in both strains, and an elevated sympathetic tone with high-salt diet in SS but not SS.13(BN) rats. In conclusion, we have associated several important physiological parameters of the baroreflex control system with chromosome 13 and have begun to identify possible physiological mechanisms underlying baroreflex impairment and hypertension in the Dahl SS rat that may be further explored in future experimental and modeling-based investigation.

Cardiac cell modelling: observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field.

Application of the principles of systems biology and Wiener's cybernetics for analysis of regulation of energy fluxes in muscle cells in vivo

The mechanisms of regulation of respiration and energy fluxes in the cells are analyzed based on the concepts of systems biology, non-equilibrium steady state kinetics and applications of Wiener’s cybernetic principles of feedback regulation. Under physiological conditions cardiac function is governed by the Frank-Starling law and the main metabolic characteristic of cardiac muscle cells is metabolic homeostasis, when both workload and respiration rate can be changed manifold at constant intracellular level of phosphocreatine and ATP in the cells. This is not observed in skeletal muscles. Controversies in theoretical explanations of these observations are analyzed. Experimental studies of permeabilized fibers from human skeletal muscle vastus lateralis and adult rat cardiomyocytes showed that the respiration rate is always an apparent hyperbolic but not a sigmoid function of ADP concentration. It is our conclusion that realistic explanations of regulation of energy fluxes in muscle cells require systemic approaches including application of the feedback theory of Wiener’s cybernetics in combination with detailed experimental research. Such an analysis reveals the importance of limited permeability of mitochondrial outer membrane for ADP due to interactions of mitochondria with cytoskeleton resulting in quasi-linear dependence of respiration rate on amplitude of cyclic changes in cytoplasmic ADP concentrations. The system of compartmentalized creatine kinase (CK) isoenzymes functionally coupled to ANT and ATPases, and mitochondrial-cytoskeletal interactions separate energy fluxes (mass and energy transfer) from signalling (information transfer) within dissipative metabolic structures – intracellular energetic units (ICEU). Due to the non-equilibrium state of CK reactions, intracellular ATP utilization and mitochondrial ATP regeneration are interconnected by the PCr flux from mitochondria. The feedback regulation of respiration occurring via cyclic fluctuations of cytosolic ADP, Pi and Cr/PCr ensures metabolic stability necessary for normal function of cardiac cells.

Structure-function relationships in feedback regulation of energy fluxes in vivo in health and disease: mitochondrial interactosome

The aim of this review is to analyze the results of experimental research of mechanisms of regulation of mitochondrial respiration in cardiac and skeletal muscle cells in vivo obtained by using the permeabilized cell technique. Such an analysis in the framework of Molecular Systems Bioenergetics shows that the mechanisms of regulation of energy fluxes depend on the structural organization of the cells and interaction of mitochondria with cytoskeletal elements. Two types of cells of cardiac phenotype with very different structures were analyzed: adult cardiomyocytes and continuously dividing cancerous HL-1 cells. In cardiomyocytes mitochondria are arranged very regularly, and show rapid configuration changes of inner membrane but no fusion or fission, diffusion of ADP and ATP is restricted mostly at the level of mitochondrial outer membrane due to an interaction of heterodimeric tubulin with voltage dependent anion channel, VDAC. VDAC with associated tubulin forms a supercomplex, Mitochondrial Interactosome, with mitochondrial creatine kinase, MtCK, which is structurally and functionally coupled to ATP synthasome. Due to selectively limited permeability of VDAC for adenine nucleotides, mitochondrial respiration rate depends almost linearly upon the changes of cytoplasmic ADP concentration in their physiological range. Functional coupling of MtCK with ATP synthasome amplifies this signal by recycling adenine nucleotides in mitochondria coupled to effective phosphocreatine synthesis. In cancerous HL-1 cells this complex is significantly modified: tubulin is replaced by hexokinase and MtCK is lacking, resulting in direct utilization of mitochondrial ATP for glycolytic lactate production and in this way contributing in the mechanism of the Warburg effect. Systemic analysis of changes in the integrated system of energy metabolism is also helpful for better understanding of pathogenesis of many other diseases.