Flux Balance Analysis

Flux Balance AnalysisThe Central Dogma

Figure 1. The central dogmaDNA:DNA (deoxyribonucleic acid) is the blueprint that makes up the genetic instructions for all living organisms. DNA is made up of four bases called adenine (A), thymine (T), guanine (G) and cytosine (C) connected to one another in strands by a sugar and phosphate backbone. If you could zoom in and look at DNA, it looks like a twisted ladder that is called a double helix. In the ladder, the rungs are made up of bases connected to one another (A always binding to T and G always binding to C) and the sides of the ladder are the sugar and phosphate backbone. DNA is organized in a cell in chromosomes. In humans, there are 23 pairs of chromosomes. The whole set of chromosomes in an organism is called its genome.

Genes and Proteins:Genes are sections of DNA on the chromosome that code for proteins. Proteins are responsible for the majority of the activities of a cell. An example of a familiar protein is insulin. This protein is produced by beta cells in the pancreas to process glucose. Synthetic insulin is often used to regulate glucose levels in people with Type I diabetes. Humans have about 20,500 protein coding genes in their genome.

Making Proteins:To make a protein, the DNA is first transcribed into messenger RNA (mRNA), which contains A, C, G and uracil (U) instead of T. This is a single stranded molecule vs. the double-stranded DNA. Cells have a huge protein and RNA machine called the ribosome that can then "read" the mRNA and translate it into protein. It is called translation because the nucleotides that make up the DNA and RNA aretranslatedinto the alphabet of proteins, which are made up of amino acids.

2Metabolic Pathways and fluxesMetabolism - life-sustaining chemical transformations within the cells of living organisms

Metabolites intermediate products of metabolism Metabolic Pathways Way to represent metabolism

Metabolic Flux - Rate of turnover of molecules through a metabolic pathway

Figure 2 Metabolic pathwayThe size and complexity of metabolic networks often limit our ability to test and analyze metabolism using more traditional simulation methods such as reaction kinetics, where the mechanisms or reactions and their regulation are modeled individually and in detail.3Genome Scale Metabolic NetworksGenes -> Enzymes (Central Dogma)Enzymes -> Metabolic Networks (Catalysts)

Genes -> Metabolic Networks

Integration of genomic and metabolomic data

Cell Modeling

Figure 3. The reconstruction processFBA identifies the optimal flux pattern of a network that would allow the system to achieve a particular objective, typically the maximization of biomass production.4What is FBA?Mathematical approach to analyse flow of metabolites in metabolic networks

Figure 4. A simplified core carbon metabolic networkWe need this analysis to build the cell model

All known metabolic reactionsGenes that encode each enzymes5Steps in FBA System Definition(A,B,C metabolitesvi internal fluxbi exchange flux)Mass BalanceConstraints (Thermodynamic, experimental)Optimization

Figure 5. Steps in FBASystem definition Identifying pathways from literature, genes and their corresponding enzymes

S stoichiometric matrix (row represents one compound, column represents one reaction) (sparse matrix, less compounds, more reactions)

many solutions Sv = 0 (mass balance) (assuming steady state)

thermodynamical constraints, max flux through a system

optimized with respect to certain objective function example growth in biomass 6ApplicationsAnalysis of Genome Scale Metabolic NetworksDrug Target IdentificationMetabolic EngineeringRefinement of metabolic networksGene deletions, improving the understanding of microbial metabolism, metabolic engineering, identification of potential drug targets (in case of pathogenic organisms)Gene deletion studies help in identifying enzymes which when deleted adversely affect the flux, possible drug targetsReconstruction of an organism which has been proved useful, identifying parameters like growth yield , network robustness and gene essentiality, bio-tech applicationsMetabolic gaps, inconsistencies with experimental data help to refine network7ChallengesSolution as good as constraintsFocuses only on enzyme part of genomeReconstruction of GSMNs a challengeRelevance of objective functionsRegulatory Networks not consideredA lot of time to be invested in a quality reconstruction of networks, including selection of constraintsIncomplete nature of annotationComplete GSMNs not avalaibleNot all cells optimise growth, biological relevance of objective functions to be considered, no general obj func.FBA doesnt integrate regulatory information. Environment conditions etc.

It doesnt consider hormones.

8rFBAModification of FBAIncludes boolean regulatory information

Figure 6. Feedback network

trans = IF(G) AND NOT (B)rxn = IF (A) AND (E) 9Steps in rFBAFigure 7 Solution space in rFBA Introduce adjustable constraints using boolean operations (regulatory events dependant on time)Quasi steady state assumption Reduction in solution space

Quasi steady state assumption transcriptional regulation order few minutes or slower, metabolic transients very fastThis method works by iteratively predicting a regulatory andmetabolic steady state for short successive time intervals. Foreach time interval, a regulatory state that is consistent with themetabolic steady state of the previous interval (and with theavailability of nutrients in the changing growth media) iscomputed. Then, FBA is used to find a steady-state fluxdistribution that is consistent with the regulatory state of thecurrent time interval. The new metabolic state possibly leadsto a new regulatory state, and the process is further iterated.The main limitation of this approach is that it arbitrarilychooses one single metabolic steady state at each time interval,from a space of possible solutions provided by rFBA. Thisarbitrary choice of specific regulatory and metabolic trajectoriesleaves out a whole space of possible dynamic fluxprofiles uncharacterized.10Advantages over FBAQuantitative dynamic simulation of substrate uptake, cell growth and by-product secretion

Qualitative simulation of gene transcription events and the presence of proteins in the cell

Investigation of the systemic effects of imposing temporary regulatory constraints on the solution spaceRefer to regulation of gene expression in flux balance models of metabolism

1. The quantitative predictions made by the combinedregulatory/metabolic model are completelyunpredictable using FBA alone under manyconditions. Example 1 illustrates this point. Thediauxic growth curve shown in Fig. 5 is a completelydi!erent result than would be obtained byFBA alone, which would incorrectly predict themaximal possible uptake of both Carbon1 andCarbon2

3. Different time intervals, different effects11Methods like rFBAiFBA Integrated ordinary differential equations model with rFBA

SR-FBA identifies a metabolicregulatory steady stateIn the case of RFBA, themetabolic networkis not only restricted by mass, thermodynamic, and energy constraints,but also by the gene regulatory network that controls it.Steady-state RFBA (SRFBA) (12) and integrated FBA (iFBA) (13)are similar methods based on Boolean logic. SR-FBA uses the samegenome-scale integrated metabolic regulatory network as RFBAbut characterizes its steady-state behavior, whereas iFBA uses differentialequations to model a subset of the regulatory network.Methods based on stochastic models or differential equations (14,15) are usually restricted to modeling small systems and have notbeen extended thus far to the genome scale.

In this chapter, we give an overview of PROM (probabilistic regulation of metabolism) (7), a method that utilizes probabilities to denote gene states and interactions between genes and transcription factors in order to enable straightforward integration of transcriptional and metabolic networks for modeling purposes

PROM has shown improved results compared to previous approaches to integrate metabolism and transcriptional regulation such as regulatory FBA (RFBA)

Another benefit of PROM is that it estimates regulatory strengths automatically from high-throughput data, as opposed to the laborious manual process RFBA models are based on. Because PROM networks can be learned from high-throughput data, these models can be comprehensive, in contrast to the manually curated approaches that require extensive literature surveys. In addition, RFBA relies on Boolean logic, which has the drawback of only allowing two states for the regulated reactions: either fully active or completely inactive. PROM introduces probabilistic, soft constraints that can be automatically quantified from microarray data, thereby overcoming the limitations of RFBA 12DisadvantagesManual curation a tedious process

Modelling restricted to smaller and extensively studied models

On/Off approach gives only qualitative analysisabsence of an automated algorithm for determining the Boolean rules for relating the regulator with its target. Although the manual process can be accurate in modeling metabolic regulation, manual reconstruction greatly limits the number of interactions that can be modeled, and thus very few genome-scale metabolic-regulatory models existed

simplifies the relationship between the transcriptome and the metabolome to a binary process, wherein genes and reaction fluxes can only have two states in the population: on or off

because of the manual nature of this process, the interaction rules are also qualitative in nature, with genes being turned completely on or off, and cannot take intermediate values.

Given the large number of interactions, it is extremely difficult to write Boolean rules and identify significant interactions at the genome scale.

This process also requires extensive literature search, which is why the first two metabolic-regulatory models were made for the extremely well studied model organisms Escherichia coli and Saccharomyces cerevisiae.

13PROM (probabilisticregulation of metabolism)Automatically quantifies the interactions from high-throughput data, no need of manually curation

Uses conditional probabilities for modeling transcriptional regulation rather than boolean

Greatly increases the capacity to generate genome-scale integrated models14PROM inputsReconstructed genome scale metabolic networks

Regulatory network structure consisting of transcription factors (TFs) and their targets

Gene expression data under various environmental and genetic perturbationsGene expressionis the process by which information from ageneis used in the synthesis of a functionalgene product

Additional interactions involving enzyme regulation by metabolites and proteins (if available)

1. The genome-scale reconstruction of the metabolic network of the organism(13). The creation of metabolic reconstructions is often a laborious, painstaking process. Researchers either manually collect the necessary stoichiometric information from the literature, or the network is downloaded from organism-specific databases when available, with subsequent annotation and improvement of the data to make the model functional and in agreement with experimental data. Over the last 10 years, the metabolic network reconstructions of several organisms have been published and are publicly accessible. The simulation of the metabolic network within the PROM method is performed using FBA subject to additional constraints and a penalty function

2. A regulatory network structure,which consists of a list of transcription factors,the targets of these transcription factors,and their interactions(14). These transcriptional regulatory networks have generally been constructed based on high-throughput proteinDNA interaction data and/or statistical inference of functional relationships from genomic and transcriptomic data (1519).

3. A collection of gene expression data measured under different conditions,which will allow the observation of various phenotypes for the organism under study. Ideally, the microarray data that are chosen represent a diverse number of conditions under which gene expression has been measured 15Analysis ToolsFlux Balance Analysis (FBA)

Flux Variability Analysis (FVA)

Kolmogorov Smirnov TestFlux Variability AnalysisDetermine the variability of fluxes in the networkOriginal objective value fixedEach reaction maximized and minimized to get feasible range of fluxes

In this LP-based approach the emphasis is on determining the maximum and minimum values of all the fluxes that will satisfy the constraints and allow for the same optimal objective value. It must be noted that this approach does not identify all possible alternate optimal solutions, but rather the range of flux variability that is possible within any given solution.

value of the original objective is fixed and each reaction in the network is maximized and subsequently minimized to determine the feasible range of flux values foreach reaction.

17Kolmogorov Smirnov TestNonparametric test for the equality of continuous, one-dimensional probability distributions Compare two separate samples or a sample with a reference probability distributionMakes no assumption about distributionUsed to select those pairs of TFs and targets for which the targets expression changes significantly wrt the TF state

Steps in PROMKolmogorov-Smirnov statistic used to get TF and target interactionsProbabilities used to represent gene states and interactions between a gene and TF Eg - the probability of gene A being active when the regulating transcription factor B is not active is represented by P(A=1|B=0)

For the purpose of constructing the integrated metabolic regulatory network, it is important that the PROM method takes advantage of the abundance of high-throughput data that is currently available for most organisms. From these data, the transcriptional regulatory network of the organism can be quantified statistically, similar to the probabilistic Boolean networks of Shmulevich et al. (20). From the gene expression data that are available for the organism in question, only those that involve the expression of metabolic genes are retained (see Note 3). The data are then normalized and screened for false positives using the Kolmogorov Smirnov statistic (Subheading 2.3), and only significant interactions, defined by P