Daniel A. Beard

Energy balance for analysis of complex metabolic networks

Predicting behavior of large-scale biochemical networks represents one of the greatest challenges of bioinformatics and computational biology. Computational tools for predicting fluxes in biochemical networks are applied in the fields of integrated and systems biology, bioinformatics, and genomics, and to aid in drug discovery and identification of potential drug targets. Approaches, such as flux balance analysis (FBA), that account for the known stoichiometry of the reaction network while avoiding implementation of detailed reaction kinetics are promising tools for the analysis of large complex networks. Here we introduce energy balance analysis (EBA)--the theory and methodology for enforcing the laws of thermodynamics in such simulations--making the results more physically realistic and revealing greater insight into the regulatory and control mechanisms operating in complex large-scale systems. We show that EBA eliminates thermodynamically infeasible results associated with FBA.

A Biophysical Model of the Mitochondrial Respiratory System and Oxidative Phosphorylation

A computational model for the mitochondrial respiratory chain that appropriately balances mass, charge, and free energy transduction is introduced and analyzed based on a previously published set of data measured on isolated cardiac mitochondria. The basic components included in the model are the reactions at complexes I, III, and IV of the electron transport system, ATP synthesis at F1F0 ATPase, substrate transporters including adenine nucleotide translocase and the phosphate–hydrogen co-transporter, and cation fluxes across the inner membrane including fluxes through the K+/H+ antiporter and passive H+ and K+ permeation. Estimation of 16 adjustable parameter values is based on fitting model simulations to nine independent data curves. The identified model is further validated by comparison to additional datasets measured from mitochondria isolated from rat heart and liver and observed at low oxygen concentration. To obtain reasonable fits to the available data, it is necessary to incorporate inorganic-phosphate-dependent activation of the dehydrogenase activity and the electron transport system. Specifically, it is shown that a model incorporating phosphate-dependent activation of complex III is able to reasonably reproduce the observed data. The resulting validated and verified model provides a foundation for building larger and more complex systems models and investigating complex physiological and pathophysiological interactions in cardiac energetics.

Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation, metabolite transport, and electrophysiology

A computational model of mitochondrial metabolism and electrophysiology is introduced and applied to analysis of data from isolated cardiac mitochondria and data on phosphate metabolites in striated muscle in vivo. This model is constructed based on detailed kinetics and thermodynamically balanced reaction mechanisms and a strict accounting of rapidly equilibrating biochemical species. Since building such a model requires introducing a large number of adjustable kinetic parameters, a correspondingly large amount of independent data from isolated mitochondria respiring on different substrates and subject to a variety of protocols is used to parameterize the model and ensure that it is challenged by a wide range of data corresponding to diverse conditions. The developed model is further validated by both in vitro data on isolated cardiac mitochondria and in vivo experimental measurements on human skeletal muscle. The validated model is used to predict the roles of NAD and ADP in regulating the tricarboxylic acid cycle dehydrogenase fluxes, demonstrating that NAD is the more important regulator. Further model predictions reveal that a decrease of cytosolic pH value results in decreases in mitochondrial membrane potential and a corresponding drop in the ability of the mitochondria to synthesize ATP at the hydrolysis potential required for cellular function.

Extreme Pathways and Kirchhoff's Second Law

The application of the loop law to eliminate thermodynamically infeasible solutions gives us an additional set of useful physicochemical constraints to determine allowable behavior of biochemical reaction networks. By utilizing the type III extreme pathways, the loop law can be implemented in flux balance without needing to perform a bilinear optimization. The importance of adding these constraints into genome-scale models now needs to be evaluated. In addition, the energy balance theory presented by Beard et al. (2002)xEnergy balance for analysis of complex metabolic networks. Beard, D.A., Liang, S., and Qian, H. Biophys. J. 2002; 83: 79–86Abstract | Full Text | Full Text PDF | PubMedSee all ReferencesBeard et al. (2002) provides a foundation for constraints-based analysis of reaction-free energies in large-scale biochemical systems and thus expands the scope of information available from constraints-based modeling of biochemical networks.

Modeling advection and diffusion of oxygen in complex vascular networks.

AbstractA realistic geometric model for the three-dimensional capillary network geometry is used as a framework for studying the transport and consumption of oxygen in cardiac tissue. The nontree-like capillary network conforms to the available morphometric statistics and is supplied by a single arterial source and drains into a pair of venular sinks. We explore steady-state oxygen transport and consumption in the tissue using a mathematical model which accounts for advection in the vascular network, nonlinear binding of dissolved oxygen to hemoglobin and myoglobin, passive diffusion of freely dissolved and protein-bound oxygen, and Michaelis–Menten consumption in the parenchymal tissue. The advection velocity field is found by solving the hemodynamic problem for flow throughout the network. The resulting system is described by a set of coupled nonlinear elliptic equations, which are solved using a finite-difference numerical approximation. We find that coupled advection and diffusion in the three-dimensional system enhance the dispersion of oxygen in the tissue compared to the predictions of simplified axially distributed models, and that no “lethal corner,” or oxygen-deprived region occurs for physiologically reasonable values for flow and consumption. Concentrations of 0.5–1.0 mM myoglobin facilitate the transport of oxygen and thereby protect the tissue from hypoxia at levels near its p50 that is, when local oxygen consumption rates are close to those of delivery by flow and myoglobin-facilitated diffusion, a fairly narrow range.

Big Data Analytics in Healthcare.

The rapidly expanding field of big data analytics has started to play a pivotal role in the evolution of healthcare practices and research. It has provided tools to accumulate, manage, analyze, and assimilate large volumes of disparate, structured, and unstructured data produced by current healthcare systems. Big data analytics has been recently applied towards aiding the process of care delivery and disease exploration. However, the adoption rate and research development in this space is still hindered by some fundamental problems inherent within the big data paradigm. In this paper, we discuss some of these major challenges with a focus on three upcoming and promising areas of medical research: image, signal, and genomics based analytics. Recent research which targets utilization of large volumes of medical data while combining multimodal data from disparate sources is discussed. Potential areas of research within this field which have the ability to provide meaningful impact on healthcare delivery are also examined.

The Fractal Nature of Myocardial Blood Flow Emerges from a Whole-Organ Model of Arterial Network

Mammalian hearts exhibit a heterogeneous spatial distribution of blood flows, but flows in near-neighbor regions correlate strongly. Also, tracer 15O-water washout after injection into the inflow shows a straight log-log relationship between outflow concentration and time. To uncover the role of the arterial network in governing these phenomena, morphometric data were used to construct a mathematical model of the coronary arterial network of the pig heart. The model arterial network, built in a simplified three-dimensional representation of tissue geometry, satisfies the statistical morphometric data on segment lengths, diameters and connectivities reported for real arterial networks. The model uses an avoidance algorithm to position successive vascular segments in the network. Assuming flows through the network to be steady, the calculated regional flow distributions showed (1) the degree of heterogeneity observed in normal hearts; (2) spatial self-similarity in local flows; (3) fractal spatial correlations, all with the same fractal dimension found in animal studies; (4) pressure distributions along the model arterial network comparable to those observed in nature, with maximal resistances in small vessels. In addition, the washout of intravascular tracer showed tails with power law slopes that fitted h(t) = at–α–1 with the exponents α = 2 for the reconstructed networks compared with those from experimental outflow concentration-time curves with α = 2.1 ± 0.3. Thus, we concluded that the fractal nature of spatial flow distribution in the heart, and of temporal intravascular washout, are explicable in terms of the morphometry of the coronary network.

Minimum Information About a Simulation Experiment (MIASE).

Reproducibility of experiments is a basic requirement for science. Minimum Information (MI) guidelines have proved a helpful means of enabling reuse of existing work in modern biology. The Minimum Information Required in the Annotation of Models (MIRIAM) guidelines promote the exchange and reuse of biochemical computational models. However, information about a model alone is not sufficient to enable its efficient reuse in a computational setting. Advanced numerical algorithms and complex modeling workflows used in modern computational biology make reproduction of simulations difficult. It is therefore essential to define the core information necessary to perform simulations of those models. The Minimum Information About a Simulation Experiment (MIASE, Glossary in Box 1) describes the minimal set of information that must be provided to make the description of a simulation experiment available to others. It includes the list of models to use and their modifications, all the simulation procedures to apply and in which order, the processing of the raw numerical results, and the description of the final output. MIASE allows for the reproduction of any simulation experiment. The provision of this information, along with a set of required models, guarantees that the simulation experiment represents the intention of the original authors. Following MIASE guidelines will thus improve the quality of scientific reporting, and will also allow collaborative, more distributed efforts in computational modeling and simulation of biological processes.

Phosphate metabolite concentrations and ATP hydrolysis potential in normal and ischaemic hearts

To understand how cardiac ATP and CrP remain stable with changes in work rate – a phenomenon that has eluded mechanistic explanation for decades – data from 31phosphate‐magnetic resonance spectroscopy (31P‐MRS) are analysed to estimate cytoplasmic and mitochondrial phosphate metabolite concentrations in the normal state, during high cardiac workstates, during acute ischaemia and reactive hyperaemic recovery. Analysis is based on simulating distributed heterogeneous oxygen transport in the myocardium integrated with a detailed model of cardiac energy metabolism. The model predicts that baseline myocardial free inorganic phosphate (Pi) concentration in the canine myocyte cytoplasm – a variable not accessible to direct non‐invasive measurement – is approximately 0.29 mm and increases to 2.3 mm near maximal cardiac oxygen consumption. During acute ischaemia (from ligation of the left anterior descending artery) Pi increases to approximately 3.1 mm and ATP consumption in the ischaemic tissue is reduced quickly to less than half its baseline value before the creatine phosphate (CrP) pool is 18% depleted. It is determined from these experiments that the maximal rate of oxygen consumption of the heart is an emergent property and is limited not simply by the maximal rate of ATP synthesis, but by the maximal rate at which ATP can be synthesized at a potential at which it can be utilized. The critical free energy of ATP hydrolysis for cardiac contraction that is consistent with these findings is approximately −63.5 kJ mol−1. Based on theoretical findings, we hypothesize that inorganic phosphate is both the primary feedback signal for stimulating oxidative phosphorylation in vivo and also the most significant product of ATP hydrolysis in limiting the capacity of the heart to hydrolyse ATP in vivo. Due to the lack of precise quantification of Piin vivo, these hypotheses and associated model predictions remain to be carefully tested experimentally.

Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Processes

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and reverse fluxes and free energy for any chemical process operating in a steady state. This relationship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state in dilute solution, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.