Back to Previous Chapter: Analytical Methods
Next chapter: Databases

Computational Modeling of Metabolic Control

Metabolomics is a systems biology look at the interactions of metabolic pathways within an organism. Computational tools are useful and necessary to model these complex interactions and predict outcomes of perturbations of the system. A computational model of mitochondria and electrophysiological metabolism has been established, and applied to data collected from analyses conducted on cardiac mitochondria and phosphate metabolites in striated muscle, in vivo. The model is based on kinetic and thermodynamic details of reaction mechanisms of biochemical species. Building such an elaborate and kinetically encompassing model necessitated a vast collection of quantitative data from respiring mitochondria under specific closely monitored conditions. These details were then catalogued along with their results. Further validation of the model resulted from in vitro data measurements from cardiac muscle and in vivo measurements from skeletal muscle. The model was capable of predicting the roles of NAD and ADP in tricarboxylic acid cycle dehydrogenase regulation, and determined that NAD was a more significant regulator. The model was also capable predicting the effects of cytosolic pH fluctuation. Specifically, the model determined that decreases in the pH resulted in mitochondrial membrane potential reduction, which in turn decreased the rate of ATP synthesis.

Current research suggests that a vast quantity of independent data collected from experiments on in vivo and ex vivo systems would provide a comprehensive model of mitochondria metabolism. Established predictions based upon this model indicated the mitochondrial redox state as a primary regulator of tricarboxylic acid cycle flux. This model also reinforces results from similarly conducted research supporting the determination of inorganic phosphate strongly affecting the mitochondria redox state. Specifically, it was determined that inorganic phosphate influences the tricarboxylic acid cycle as a substrate and a cofactor. The current model also determined that mitochondrial ATP synthesis is directly dependent upon ADP and inorganic phosphate activation of oxidative phosphorylation, as well as NAD and inorganic phosphate activation of the tricarboxylic acid cycle.

A future prospect for this model is expected to involve analyzing calcium regulation of mitochondrial energetics. This will require including the established roles of Ca2+ in regulating pyruvate dehydrogenase, isocitrate dehydrogenase, and -ketoglutarate dehydrogenase within the model.

References: http://www.jbc.org/cgi/content/full/282/34/24525

E-Cell2 Simulation System

Available for download at http://www.e-cell.org

Main Focus:

The E-Cell2 simulation system is a publicly available simulation system for modeling, simulation and analysis of complex, heterogeneous and multi-scale systems like the cell. Within this package, a computational tool for mitochondrial systems biology has been included. The model was developed by integrating enzyme kinetics studies previously published in the literature. Instead of looking at pathways individually, the model integrates the respiratory chain, the TCA cycle, fatty acid B-oxidation, and metabolite transport systems to allow an observation of the dynamic behavior of the mitochondria as a whole. The model should allow investigators to evaluate the influence of metabolite treatments on the organelle as a whole. This model is flexible and allows the incorporation of other models created by independent researchers. E-Cell is implemented in C++ computer language.

Additional literature about the model: http://bioinformatics.oxfordjournals.org/cgi/reprint/20/11/1795

New Terms:

Lineweaver-Burk plots: Also known as a double reciprocal plot, this is a graphical representation of the Lineweaver-Burk equation of enzyme kinetics. This method was developed before nonlinear regression was available to fit curve data into straight lines. The plot is used to provide a graphical analysis of the Michaelis-Menten equation and describe values for Vmax and KM.

Michaelis-Menten equation: This equation describes the relationship between the rate of substrate conversion by an enzyme to the concentration of the substrate. The equation is given below, where Km is the Michaelis constant, V is the rate of conversion, Vmax is the maximum rate of conversion, and [S] is the substrate concentration.

Fourth-order Runge-Kutta method: This is a method of numerically (approximately) integrating ordinary differential equations. It uses a trial step at the midpoint of an interval to cancel our lower-order error terms. The method is reasonably simple and robust, making it a good candidate for numerical solutions of differential equations. The method was developed by the German mathematicians C. Rung and M.W.Kutta.

TCA Cycle: Abbreviation for the tricarboxylic acid cycle. This is also commonly referred to as the citric acid cycle or the Krebs cycle (for its discovered Hans Krebs).

Quantitative Modeling: As opposed to experimental modeling which shows the general interactions of systems, quantitative modeling describes the precise concentrations of metabolite flux in and out of systems. Quantitative modeling has been made possible through mathematical analysis of biochemical models and has become essential to understand the cell at a systems level.

Bifurcation: In general, bifurcation is the splitting of a main body into two parts. In a dynamic system bifurcation is a period of doubling, quadrupling etc.

Connection to Biochemistry Metabolism Course:

The mitochondrial model includes processes we have studied in depth, including fatty acid B-oxidation (chapter 17) and the respiratory chain (chapter 20). It also includes inner-membrane transport system. We have looked at several transport systems, for example the citrate shuttle for acetate out of the mitochondria (chapter21). Another cycle included in the model, the TCA cycle or Citric Acid Cycle (chapter 16) was a large focus of our studies.

Computer Simulation of Metabolism:

Available at: http://www.hort.purdue.edu/cfpesp/models/models.htm

Main Focus:

The site has a good introduction to the utility of computational models for quantitatively analyzing traditional isotopic tracer methods and isotopic kinetic data. Experimental methods using stable isotope and radioisotope tracers to monitor kinetics of intermediates in metabolic pathways can be interpreted using computer routines to give insight into the fluxes and compartmentation of the pools of these metabolites. The site provides a breakdown of an example of a basic iterative computer model used to simulate labeling behavior of non-steady state intermediates. The important distinction is that iterative model can be applied to non-steady-state situations or to a situation with multiple pools of intermediates with different turnover rates, basic kinetic equations cannot.

New Terms:

Steady-state: Pools of intermediates and rates of reactions remain constant with time.

Non-steady state: Pools of intermediates expand and deplete with time.

Pulse-chase labeling kinetics: In this commonly used protocol, a cell sample is exposed to a radio-labeled compound for a brief period of time, referred to as a ‘pulse’. The quantity of labeling can be shown to be a function of the length of exposure time. After exposure, the sample is washed with a buffer solution. This removes the isotope. Next, there is a ‘chase’ step where the sample is incubated with a non-labeled form of the compound. These experiments are useful for following intra-cellular location of proteins or the transformation of a metabolite into others over a period of time/ through a biological pathway.

Effluxes: Refers to the movement of metabolites out of a cell or compartment.

Hill Coefficient: This is a measure of cooperativity in a binding process. It was originally worked out for the binding of oxygen to hemoglobin. A hill coefficient of 1 indicates independent binding, a hill coefficient greater than 1 indicates a positive cooperative binding of one ligand facilitates binding of subsequent ligands at other sites on the multimeric receptor complex.

GS/GOGAT Cycle: Responsible for glutamate synthesis. Within this process ammonia is assimilated and recycled. The GS stands for glutamine synthase and GOGAT stands for an NADPH-dependent glutamine:2-oxoglutarate amidotransferase (or glutamate synthase).

Connection to Biochemistry Metabolism Course:

Within this site pools of metabolic intermediates and multiple compartments are considered. We have explored the impact of compartmentalization as a form of regulation. For example in the regulation of hexokinase IV (glucokinase) when fructose 6-phosphate concentration in the liver is high, a nuclear binding protein draws hexokinase IV into the nucleus. This prevents it from acting in glycolysis. We have also looked at the significance of pools of activated intermediates (such as Acetly-CoA and succcinly-CoA) and reduced intermediates (such as NADH and NADPH) and the role their transport and availability plays in metabolic reactions.

JWS Online Cellular Systems Modeling

Available at http://jjj.biochem.sun.ac.za/index.html

Query for all organisms metabolic pathway simulations: http://jjj.biochem.sun.ac.za/cgi-bin/processModelSelection.py?organism=All&category=metabolism

Main Focus:

JWS Online is a systems biology tool for simulation of kinetic models from a curated model database. It provides access to a collection of published kinetics models divided into the categories of metabolism, gene expression, translation, cell cycle, enzymology, single transduction, and unknown. The models can be queried by this category and/or by the organism being modeled. Organisms available range from Homo Sapien to Dictyostelium. The models have been compiled from various authors (another query option), and are available for download or can be run within the website. Manuscript details (author, source, description, etc.) are also provided. Java applets are required to run the models. Within the models users can change enzyme parameters, run time simulations or do steady state analysis.

New Terms:

Curated Database: A curated database refers to a database that has been created and is maintained with a significant amount of ‘manual’ labor. Its creators typically monitor and update the content of the sight as appropriate.

Enzymology: The branch of chemistry concerned with the properties and actions of enzymes.

The Silicon Cell Project: Research initiative that JWS Online is a part of. The long term goal of this project is “the computation of Life at the cellular level on the basis of the complete genomic, transcriptomic, proteomic, metabolomic and cell-physiomic information that will become available in the forthcoming years”. Those involved predicted the initiative would take a decade to complete, and it began in 2000. (No word available as to how close they feel they are to completion).

Armoracia rausticana: Misspelled within the site (actual spelling Armoracia rusticana), this is the scientific name for the plant horseradish.

Entamoeba histolytica: This is a type of anaerobic parasitic protozoan. It infects primarily humans and other primates, leading to amoebic dysentery or amoebic liver abscess.

Leishmania infantum: This parasite is an intracellular pathogen of the immune system. It targets macrophages and dendritic cells, causing the disease Leishmaniasis which affects millions of people worldwide. A more severe and life-threatening form of the illness is caused by a different species, L. donovani.

Lactococcus lactic: This is a mesophilic fermentative bacterium which produces lactic acid from sugar (hexose) fermentation. Strains of this bacterium are used in the production of fermented milk products.

Connection to Biochemistry Metabolism Course:

Within this database many different models of metabolic pathways are available. For example, glycolysis pathways from many different authors are offered for E. coli, H. sapiens, L. lactis, S. cerevisiae, sugar cane, and more. By clicking ‘run’ we can see the pathway, for example for glycolysis in S. cervisiae. For our studies it is interesting to then compare that to the glycolysis pathway in humans. The ability to perturb any cofactor, intermediate, or enzyme in the system and see its affect on the entire system reinforces the connections we have been studying all year. For example, increasing ATP will decrease formation of Fructose 1,6-bisphosphate.

GEM System: Automatic Prototyping of Cell-wide Metabolic Pathway Models From Genomes

By: Kazuharu Arakawa,1 Yohei Yamada,1 Kosaku Shinoda,1 Yoichi Nakayama,1 and Masaru Tomita BMC Bioinformatics. 2006; 7: 168. Published online 2006 March 23. doi: 10.1186/1471-2105-7-168. Copyright © 2006 Arakawa et al; licensee BioMed Central Ltd.

Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1435936%20-%20peer%20review%20article

Main Focus:

Being able to model cellular processes on a systems wide level is a labor intensive process. This article introduces a new tool, the Genome-based Modeling (GEM) System, which makes this task accessible. It is a tool that simulates cell-wide metabolic pathways using genomic sequence data and other biological information from public repositories. The genomic sequence data (annotated or unannotated) is used to create a rough metabolic network from publicly available databases and allows for more specific information to be added retrospectively. The system works by matching coding regions of the genome sequence with reaction stoichiometry for qualitative modeling. Next, a cell-wide simulation is created using these reactions quantitatively modeled through kinetic equations. The computer-based model produced allows researchers to simulate and study complex dynamic biological systems, analyzing system-level behavior and testing experimental hypotheses. Most previous models are developed manually and/or focus on small pathways when dealing with dynamic modeling. An Escherichia coli metabolism model developed by the GEM system achieved 100% coverage of the KEGG database model, 92.38% when compared with the EcoCyc database, and 95.06% when compared with the iJR904 genome-scale model.

New Terms:

Systems Biology: The study of the integrated and interacting network of genes, proteins, and biochemical reactions in an organism as a whole.

Bottom-up Approach: In this context, refers to beginning the process of molecular modeling with a great amount of expert knowledge and experimental data. This information is combined to create a coherent model.

Top-Down Approach: Beginning with a complete model and using it to produce specific information. This is the approach taken by GEM by using genomic data to create a basic metabolic network, adding more specific information later.

Bottleneck: This is a process or event which creates a large backup in a system. Manual modeling of cellular networks has been referred to as a bottleneck in systems biology because it is a slow process that causes a backup in the large amount of information which goes into it.

Systems Biology Markup Language (SMBL): A standard format for systems biology information which is computer-readable. This format is required for input data in to many different simulation software packages. The automated output of GEM can be concerted to SBML.

GLIMMER: This is a system for identifying genes in microbial DNA. It is used within GEM to annotate genome data when unannotated data is given

MetaCyc Database: A database of non-redundant, experimentally elucidated metabolic pathways, containing over 900 pathways from more than 900 different organisms. The pathways are involved in bot primary and secondary metabolisms, as well as associated compounds, enzymes, and genes. This database is used to check pathways generated using GEM. http://metacyc.org/

COG: A database tool for genome-scale analysis of protein functions and evolution. GEM uses this resource to help annotate genomic data.

EcoCyc: This is a scientific database for the bacterium Escherichia coli K-12 MG 1655. The project performs a literature-based curation of the entire genome, and of transcriptional regulation, transporters, and metabolic pathways. http://ecocyc.org/

iJR904 genome-scale model: A complete, chemical description of E. coli metabolism. It includes 904 genes and 931 unique biochemical reactions.

Connection to Biochemistry Metabolism Course:

We have discussed how homeostasis within living cells is maintained in a “steady state dynamic”. This refers to the idea that while the gross composition of the cell stays the same over time, the concentrations of materials in the cell are constantly changing in response to changes in the environment and the needs of the organism. The GEM systems tool is a way of modeling the dynamic interactions within the cell which correspond to these changes. This is powerful because, while understanding metabolic pathways is helpful, being able to simulate them and experimentally model their actions under set conditions is extremely useful in research.

In class and the text we have also been exposed to the KEGG pathway database. This database models an integrated system of pathways, including the relationships of these pathways to genomic data, chemical building blocks of substances, and networks of interactions and relationships. GEM uses KEGG as a standard reference. By stating that their tool achieves 100% coverage when compared with KEGG, they are stating that their tool was able to identify all of the relationships that the KEGG database dose. Since KEGG is a well accepted resource for this type of information, this comparison signifies that their tools produces significant results.

Computational Model of In Vivo Human Energy Metabolism During Semistarvation and Refeeding

By: Kevin D. Hall Am J Physiol Endocrinol Metab 291: E23-E37, 2006. First published January 31, 2006; doi:10.1152/ajpendo.00523.2005 0193-1849/06

Available at http://ajpendo.physiology.org/cgi/content/full/291/1/E23

Main Focus:

This paper describes a mathematical model that relates dietary marco-nutrient intake to computed whole body expenditure, de novo lipogenesis, gluconeogenesis, and turnover and oxidation of carbohydrate, fat, and protein. Using the classic Minnesota human starvation experiment and published in vivo human data the model simulates measured body weight and fat mass changes during semi-starvation and refeeding. In conjunction with this, unmeasured metabolic fluxes underlying these body composition changes were predicted. The study also looks at body composition in terms of fat and lean tissue in relation to the in vivo metabolic fluxes that regulate this composition.

New Terms:

Minnesota Human Starvation Experiment: Performed at the University of Minnesota from November 1944 to December 1945, this experiment is renowned for its comprehensive set of careful measurements taken over an extended duration of precisely controlled feeding. The goal of the experiment was to investigate the physiological and physiological effects of severe and prolonged dietary restriction and the effectiveness of dietary rehabilitation strategies.

Lipolysis: The breakdown of lipids stored in the cell, or the hydrolysis of triacylglycereides to free fatty acids from fats.

Proteolysis: The breakdown of proteins in the cell.

PI: Protein intake rate in kcal/day

ProtOx: Rate of protein oxidation in kcal/day

FI: Fat intake rate in kcal/day

FatOx: Rate of fat oxidation in kcal/day

BCM: Body Cell Mass (in grams)

CI: Carbohydrate intake rate in kcal/day

CarbOx: Rate of carbohydrate oxidation in kcal/day

RMR: Resting metabolic rate in kcal/day

ProtOx: Rate of protein oxidation in kcal/day

Basal metabolic rate (BMR): The amount of energy normally required by an individual at rest in a neutrally temperature environment.

Connection to Biochemistry Metabolism Course:

As we have studied, the model showed connections between the daily content of body protein, glycogen, and fat and the daily average rates of proteolysis, glycolysis/ gluconeogenesis, and lipolysis, respectively. Based on what we have learned, in the starved state with a lack of these inputs (protein, glycogen, fat) we would expect a increase in proteolysis, a decrease in gluconeogenesis and an increase in glylcolysis, and an increase in lipolysis. This is exactly what the model showed in the semi-starved state. In the fed state, or refeeding state of the model, we see the opposite of these conditions.

An Enzyme Mechanism Language for the Mathematical Modeling of Metabolic Pathways

By: Chin-Rang Yang 1,3, Bruce E. Shapiro 4, Eric D. Mjolsness 2,3 and G. Wesley Hatfield 1,3,* Bioinformatics 2005 21(6):774-780; doi:10.1093/bioinformatics/bti068 Available at http://bioinformatics.oxfordjournals.org/cgi/content/full/21/6/774

Main Focus:

The goal of this project was to create mathematical models of common mechanisms that occur in metabolic pathways and other biological processes. The authors have developed kMech, a language extension of Cellerator, that models a suite of enzyme mechanisms. These enzyme mechanisms can be used within mathematical modeling of enzyme-related pathways. The reaction mechanisms are based on mass action kinetics and each generates a set of elementary reactions that are then translated into ordinary differential equations and association-dissociation reactions that can be solved by Mathematica. The simulations modeled by kMech procude graphic outputs. The program can be executed by Mathematica software installed in a Microssoft Windows, MacOS or Linux operating system. The advantage of kMech over traditional enzyme modeling approaches is that its reaction mechanisms incorporate multiple substrates, products, and regulatory mechanisms. It is a user-friendly tool which allows biologists to model biochemical pathway without knowledge of the underlying mathematics.

New Terms:

Cellerator: A tool for generating reaction network models of cellular processes

Mathematica: A widely used commercial computer algebra system that integrates numeric and symbolic computational engines with a graphical output and a programming language.

Mass Action Kinetics: Mass action kinetics states that the rate of a reaction if equal to the product of a rate constant (k) times the concentration of the substrate (S), also referred to as the mass.

Systems Biology Markup Language (SBML): A standard format for systems biology information that is computer-readable. This format is required for input data in to many different simulation software packages.

Steady-state Velocity Equations: Equations for enzyme modeling that set the derivatives of the concentrations of each reactant in the model to zero over time. This simplifies a set of non-linear differential equations to linear algebraic equations.

Connection to Biochemistry Metabolism Course:

The design of kMech allows it to model many single and multiple substrate enzyme mechanisms such as those we have studied in class, including feedback inhibition by allosteric, competitive and non-competitive mechanisms. These regulation mechanisms have been a focus of our course. One example of a model we have studied that falls into the category of allosteric inhibition is fructose 1,6-bisphosphatases inhibition by fructose 2,6-bisphossphate and AMP.

Articles and Web Pages for Review and Inclusion

Peer-Reviewed Article #1:

Computational Modeling of Cancer Cachexia

Curr Opin Clin Nutr Metab Care. 2008 May; 11(3): 214–221.

Main Focus

New Terms

New Term 1: Definition. (source: http://)
New Term 2: Definition. (source: http://)
New Term 3: Definition. (source: http://)
New Term 4: Definition. (source: http://)
New Term 5: Definition. (source: http://)
New Term 6: Definition. (source: http://)
New Term 7: Definition. (source: http://)
New Term 8: Definition. (source: http://)
New Term 9: Definition. (source: http://)
New Term 10: Definition. (source: http://)

Summary

Relevance to a Traditional Metabolism Course

Metabolomics/Computational Modeling of Metabolic Control

Contents

Computational Modeling of Metabolic Control

E-Cell2 Simulation System

Computer Simulation of Metabolism:

JWS Online Cellular Systems Modeling

GEM System: Automatic Prototyping of Cell-wide Metabolic Pathway Models From Genomes

Computational Model of In Vivo Human Energy Metabolism During Semistarvation and Refeeding

An Enzyme Mechanism Language for the Mathematical Modeling of Metabolic Pathways

Articles and Web Pages for Review and Inclusion