Computational approaches for understanding energy metabolism

Abstract

There has been a surge of interest in understanding the regulation of metabolic networks involved in disease in recent years. Quantitative models are increasingly being used to interrogate the metabolic pathways that are contained within this complex disease biology. At the core of this effort is the mathematical modeling of central carbon metabolism involving glycolysis and the citric acid cycle (referred to as energy metabolism). Here, we discuss several approaches used to quantitatively model metabolic pathways relating to energy metabolism and discuss their formalisms, successes, and limitations.

Figure 1. (A) A simple geometric illustration of an FBA problem

Constant constraints on the Vi limit the feasible solution to an n-dimensional cube (shown in gray). Further linear constraints from the S matrix create a cone of feasible solutions (blue). Linear programming algorithms find an optimal solution on a vertex (illustrated with orange circle). (B and C) Depiction of a simple metabolic network with compartmentalization and its associated stoichiometric matrix. The three compartments, denoted with subscripts b, e, and c represent the boundary, extracellular environment, and cytosol. The boundary is what separates the model from its environment, and mass balance is not assumed at the boundary; this allows for the implementation of source and sink reactions.

Figure 2. Schematic representation of Fluxomics tools

Important to fluxomics are both the mathematical and computational tools for non-labeled and labeled techniques, as well as the analytical methods used to obtain data and parameters. Metabolite concentrations and kinetic parameters are obtained primarily from both Gas Chromatography and Liquid Chromatography Mass-Spectrometry (GC-MS and LC-MS), Nuclear Magnetic Resonance (NMR), UV-V is spectroscopy, electrochemistry, Förster (Fluorescence) resonance energy transfer (FRET), Positron Emission Tomography (PET), Liquid Scintillation Counting (LSC), and classical enzymology. Sequence data is employed in the construction of organism models, whereas proteomics and expression data find use in the creation of tissue or cell-type specific models. High-quality expression data such as RNA-Seq and Ribosomal Footprinting are beginning to find uses in flux prediction. Several prominent genome-scale techniques include Flux Balance Analysis (FBA), Minimization of Metabolic Adjustment (MoMA), Energy Balance Analysis (EBA), ExPas (Extreme Pathways), and Elementary Mode Analysis (EMA). Isotope-based approaches include stable isotope techniques (mostly convenient 13C MFA and other nuclei, namely 17O, 31P, 2H and 15N used to study central metabolism), hyperpolarized 13C (Dynamic Nuclear Polarization (DNP)) and radio-isotopes which are studied with PET and LSC. Well-established MFA tools include isotopomer and positional modeling which could be studied dynamically or at steady-state (SS). With hyperpolarized technique it is possible to extract energy-related fluxes like Pyruvate dehydrogenase flux Fpdh, Lactate production rate Flac and Tricarboxylic Acid Flux Ftca (e.g. with [1- or 2-13C]Pyr as tracers). With other nuclei, the metabolic rate of Oxygen consumption MRO2 and ATP production MRATP and Amino Acids fluxes (AA) could be accessed directly. Advanced isotopomer techniques include cumomer approach with Elementary Metabolite Units (EMU) and Bonded Cumomers frameworks designed to reduce the number of independent variables while retaining all measurable isotopomer information. Non-labeled techniques along with genome-scale analysis include biochemical kinetics modeling tools to study metabolic and signaling networks and their regulation architecture with established tools like Metabolic Control Analysis (MCA) and Global Sensitivity Analysis (GSA). Additional sensitivity analysis should be conducted e.g. with Monte-Carlo techniques like Markov Chain Monte-Carlo (MCMC, Bayesian) analysis to check the reliability of extracted metabolic parameters, including fluxes.