TIGER: Toolbox for integrating genomescale metabolic models, expression data, and transcriptional regulatory networks
 Paul A Jensen^{1},
 Kyla A Lutz^{1} and
 Jason A Papin^{1}Email author
DOI: 10.1186/175205095147
© Jensen et al; licensee BioMed Central Ltd. 2011
Received: 12 April 2011
Accepted: 23 September 2011
Published: 23 September 2011
Abstract
Background
Several methods have been developed for analyzing genomescale models of metabolism and transcriptional regulation. Many of these methods, such as Flux Balance Analysis, use constrained optimization to predict relationships between metabolic flux and the genes that encode and regulate enzyme activity. Recently, mixed integer programming has been used to encode these geneproteinreaction (GPR) relationships into a single optimization problem, but these techniques are often of limited generality and lack a tool for automating the conversion of rules to a coupled regulatory/metabolic model.
Results
We present TIGER, a Toolbox for Integrating Genomescale Metabolism, Expression, and Regulation. TIGER converts a series of generalized, Boolean or multilevel rules into a set of mixed integer inequalities. The package also includes implementations of existing algorithms to integrate highthroughput expression data with genomescale models of metabolism and transcriptional regulation. We demonstrate how TIGER automates the coupling of a genomescale metabolic model with GPR logic and models of transcriptional regulation, thereby serving as a platform for algorithm development and largescale metabolic analysis. Additionally, we demonstrate how TIGER's algorithms can be used to identify inconsistencies and improve existing models of transcriptional regulation with examples from the reconstructed transcriptional regulatory network of Saccharomyces cerevisiae.
Conclusion
The TIGER package provides a consistent platform for algorithm development and extending existing genomescale metabolic models with regulatory networks and highthroughput data.
Background
ConstraintBased Reconstruction and Analysis (COBRA) methods have allowed the study of metabolism on a genomewide scale [1]. These models have been used to understand the interplay between environmental and genetic perturbations and the metabolic capabilities of an organism. Applications of COBRA methods have led to increased understanding in the fields of bioprocess optimization [2], pathogenicity [3], symbiosis [4], biofuel production [5], and human disease [6].
The GeneProteinReaction relationship
COBRA models often contain two sets of biological information, a matrix of stoichiometric data for metabolic reactions, and a mapping between geneencoding enzymes and the reactions they catalyze (the geneproteinreaction, or GPR, relationship). Predicting the metabolic capabilities of a COBRA model is possible with Flux Balance Analysis (FBA), a twostage mathematical technique based on the observation that metabolic networks often display optimal dynamics [7]. In the first stage of FBA, genes in the modeled organism are classified as either "on" or "off" to create an in silico genetic state. Turning genes "off" can be used to simulate significant reductions in expression levels or complete knockouts. The GPR for each reaction, represented as a binary rule, determines if a sufficient collection of proteins (isozymes, enzymatic subunits, etc.) is present for the reaction to carry flux. All reactions with satisfied GPR rules are collected into a stoichiometric matrix. The second stage of FBA uses linear programming to calculate a thermodynamicallyfeasible, massbalanced flux distribution that maximizes the flux through an objective reaction. The objective reactions used in FBA vary among organisms, ranging from ATP maintenance to biomass production [8]. By assuming that the fluxes through a metabolic network have evolved to maximize an objective, FBA eliminates the need for detailed kinetic information for each of the thousands of reactions in a complete metabolic reconstruction.
The GPR rules do not always describe a onetoone mapping between genes and reactions (where one gene encodes a complete enzyme that independently catalyzes one reaction). For example, a COBRA reconstruction for the yeast Saccharomyces cerevisiae[9] contains 1266 metabolic reactions; 231 (18.3%) of these reactions have complex GPR associations. The most complex GPR in this model involves the products of 18 open reading frames. The entire set of GPR rules contains 340 instances of isozymelike behavior (two proteins both able to fully catalyze a reaction) and 279 different complexes of protein subunits.
Because of the complexity of the GPR mappings, early extensions to FBA were reaction, rather than gene, centric. For example, the OptKnock [2] algorithm removed reactions from a FBA model to design a strain of E. coli with optimal production of a metabolic byproduct. Ideally, OptKnock would operate by removing genes, not reactions, since it is not straightforward to independently remove reactions from a biological system without genetic manipulations. An optimization using genes as decision variables would require a method for encoding the GPR logic into a set of linear inequalities. This encoding was developed as SRFBA [10] using a mixed integer optimization approach for GPR logic and other Boolean regulatory rules. An SRFBAbased approach was later used to develop OptORF, a method to design microbial strains through gene knockouts and overexpression [11]. Other genecentric, FBArelated algorithms have been developed, each using a variation of the SRFBA method [12–14]. However, a general software platform for coupling GPR rules of arbitrary complexity with a COBRA model using mixed integer programming was not available. Such a tool would speed the development of new algorithms by removing the need for researchers to reimplement this complex process.
Transcriptional regulatory networks
The accuracy of COBRA models has been improved through the addition of transcriptional regulatory networks (TRNs) [15, 16]. The TRN is a set of rules that relate the expression states of metabolic genes to various genetic and environmental cues. Because of the paucity of kinetic details available to describe these relationships, genomescale models often represent gene expression and environmental cues in a binary, "on" or "off" format. This approach allows TRNs to be described with Boolean logic.
The first genomescale TRNs were applied to models of Escherichia coli[15] and Saccharomyces cerevisiae[16] metabolism. The rules were written in standard Boolean format, where each Boolean variable is given by an explicit function of the other variables. This method creates two significant problems. First, the TRN uses the absence or presence of metabolites in the extracellular environment to calculate which genes (and, subsequently, reactions) will be active. However, certain metabolic pathways secrete byproducts into the extracellular space, thereby changing the environment. Studies with the E. coli and S. cerevisiae TRNs used an iterative approach [17]  applying the TRN to the metabolic network in a starting environment, determining which metabolites would be secreted, and then repeating the process in the new environment until the environment no longer changes between iterations. A more straightforward approach would be to solve the TRN and metabolic networks simultaneously by formulating both problems in a single optimization.
Feasible states for explicit and implicit rules
State  Feasibility  

mig1  mth1  rgt1  glnL  Explicit  Implicit 
0  0  0  0  •  
0  0  0  1  •  
0  0  1  0  •  
0  0  1  1  
0  1  0  0  
0  1  0  1  •  
0  1  1  0  •  • 
0  1  1  1  
1  0  0  0  •  • 
1  0  0  1  •  • 
1  0  1  0  •  
1  0  1  1  
1  1  0  0  
1  1  0  1  
1  1  1  0  
1  1  1  1 
Objectives
Software suites have been developed to enable COBRA analyses. Packages such as CellNetAnalyzer [18], the BioMet Toolbox [19], and the COBRA Toolbox [20] implement several useful algorithms for studying COBRA models and TRNs. However, to date, no single software platform has been developed to 1.) convert COBRA models and TRNs into integrated optimization problems, 2.) analyze these integrated models with existing algorithms to incorporate highthroughput expression data, and 3.) allow users to easily develop new algorithms for the integrated models. To overcome these limitations, we present a Toolbox for Integrating Genomescale metabolism, Expression, and Regulation (TIGER). TIGER automatically converts a list of implicit or explicit GPR and TRN rules into a set of linear inequalities; these equations are integrated with an existing COBRA model. The software allows rules to be written in a generalized Boolean format, enabling TRN logic to more accurately reflect the underlying biology. We demonstrate how this increased expressivity can overcome inconsistencies in existing TRN models. We will also show how TIGER simplifies the development of genecentric extensions to FBA by improving three algorithms for integrating highthroughput expression data with a COBRA model.
Implementation
Creating rules
These GPR relationships can be described as a Boolean expression using the standard operators and and or. For example, a reaction that is catalyzed by either of two isozymes, the second of which is composed of two subunits, would have a GPR of the form "isozyme_{1}or (isozyme_{2a}and isozyme_{2b})". Two expressions are joined with an implication operator (⇒ or ⇔ corresponding to "if" and "if and only if"), to form a rule. For GPR associations, rules are formed as "GPR ⇔ reaction", where reaction is an indicator variable that constrains the flux through a reaction to be zero when the GPR expression is false.
TIGER expressions allow additional features to describe logical relationships that are more complex than those typically found in GPRs. The not operator allows logical negation, which is often used to construct rules for transcriptional repression. Expressions can also contain conditionals that compare the numerical values of individual variables. If a gene g was known to be expressed when glucose uptake is greater than 10 flux units, this relationship could be represented by the rule "glc_ex > 10 ⇒ g", where "glc_ex" is the glucose exchange reaction in the metabolic model. Any two expressions of arbitrary complexity can be combined as a rule and parsed by TIGER. The grammar used by TIGER for rules was designed to resemble logical operations in common programming languages and to be compatible with the GPRs of widelyused COBRA models. A complete description of the TIGER syntax appears in Additional File 1.
Any variable in a TIGER model can be declared with multiple levels. Such declarations are made when rules are added to a model using the add_rule function in two ways: 1.) setting the default upper bound to all variables to any integer greater than one, or 2.) providing a list of variable names and a set of upper and lower bounds.
Rule simplification
Simple Boolean rules can be represented by systems of linear inequalities of integer variables [21]. A general Boolean rule can be converted by the following procedure to a set of simple rules before conversion to an MILP.
Thus, if x and y are binary, $\stackrel{\u0304}{x}=\u0233=1$, so I is binary as well.
TIGER applies the above substitutions recursively, creating indicator variables as necessary until all rules are simple. Each simple rule is converted to a set of linear inequalities that are added as constraints to the model structure. If a variable name already appears in the model, TIGER assumes that these variables represent the same quantity and thus allows new rules to be added to an existing model without recompiling previous rules. At the same time, TIGER creates variables to substitute for negated variables. For efficiency, TIGER ensures that only one negated variable is created for each original variable, regardless of the number of times the negated expression appears in the set of simple rules. Details of the conversion between simple rules and inequalities, along with methods for handling conditionals, are provided in Additional File 1.
Reaction coupling
where v_{ i } is the flux through the i th reaction, with lower and upper bounds ${v}_{i}^{min}$ and ${v}_{i}^{max}$.
Model structure
The type of (in)equality for each constraint in A is determined by the character vector ctype. The type of variable for each entry in x is specified by the field vartype, where 'c', 'b', and 'i' denote continuous, binary, and general integer variables. Reaction fluxes are continuous variables, while all other variables are either binary or integer depending on the corresponding upper bound. The fields rownames and varnames contain descriptive names of the constraints and variables, stored as cell arrays of strings. Functions in TIGER allow variables to be interchangeably referenced by their name, column index, or through Matlab's logical indexing features.
The format for TIGER models is designed for compatibility with the model structure for the COBRA Toolbox [20]. TIGER can use a COBRA Toolbox model as a starting point for converting a genomescale reconstruction; therefore, any model in a file format supported by the COBRA Toolbox (SBML, Simpheny, etc.) can be converted to a TIGER model.
Accessing the MILP solver
TIGER uses a custom Matlab class CMPI (Common Mathematical Programming Interface) to create and solve mathematical programming problems. CMPI defines a consistent structure for MILP (and mixedinteger quadratic programming, MIQP) problems, providing independence from the underlying MILP solver software. TIGER currently supports the CPLEX, Gurobi (via Gurobi MEX), and GLPK (via GLPK Mex) software packages, all of which are freely available for academic use. Porting TIGER to use a new solver requires modifying only the CMPI method solve_mip to specify the new interface. CMPI also provides a standardized method for configuring common solver parameters (maximum solution time, optimality and feasibility tolerances, etc.).
Previous work has indicated that the computation time of some FBArelated algorithms, such as Flux Variability Analysis [22], can be reduced by saving information about the problem structure between calls to the MILP solver [23]. CMPI provides a method, solve_multiple_milps, to preserve the solver state between successive calls to the CPLEX optimizer and reduce runtime in this manner. (Gurobi and GLPK currently do not support this feature in their Matlab interfaces.) If the CPLEX optimizer is not installed, CMPI will automatically make successive calls to the installed optimizer. While this removes the potential speed increase from using solver restarts, it allows TIGER code to remain solver independent and portable.
Using TIGER
TIGER source code and installation instructions are available online at http://bme.virginia.edu/csbl/downloads/ or http://csbl.bitbucket.org/tiger The version of TIGER used for the examples in this study is included as Additional File 2. All functions in the toolbox are documented using Matlab's "help" facilities. Complete documentation and a stepbystep tutorial are also available on the TIGER website. The software includes a testing suite to verify the installation. These tests contain examples that build a TIGER structure from a simple COBRA model, add a set of TRN rules, call a MILP solver, and display the solution.
Results and Discussion
Refining integrated models for Saccharomyces cerevisiae
TIGER was used to couple the 1266 reactions in iND750 [9], a genomescale model of Saccharomyces cerevisiae metabolism, with 750 metabolic genes. The resulting TIGER model contained 4498 constraints in 3214 variables. A model of S. cerevisiae transcriptional regulation, iMH805 [16], was added. The additional 805 rules contributed 1057 constraints and 562 variables to the TIGER model. The conversion took 53.66 s for iND750 and 20.31 s to add the TRN using an Intel 3.2 GHz i7quad core processor running Linux.
As mentioned above, previous methods for integrating TRNs involve an iterative process, alternating between calculating gene states from a given environment and determining an environment based on metabolic byproducts [17]. However, the multiple layers of trascriptional regulation may require several iterations of this method to reach a stable gene state. The number of iterations to reach a stable state varies by environment and cannot easily be determined a priori[24]. In fact, some feedback mechanisms in TRNs may lead to a stable cycle of gene activation/inactivation rather than a single gene state. TIGER solves the TRN and FBA problems simultaneously, so the resulting gene state is always stable (or an optimal state inside a stable cycle).
Applying largescale TRNs to COBRA models may result in infeasible models, i.e., models unable to produce any biomass. This is often due to a small number of rules that turn off reactions that are essential for biomass production. Previous work has developed techniques for finding which rules create the model infeasibility [13]. TIGER includes the function find_infeasible_rules to identify rules that prevent feasible solutions to the resulting MILP. Given a model and a set of rules that prevent a feasible solution, find_infeasible_rules creates a MILP that preserves the logic of the rules but allows each rule to be artificially satisfied. The objective of this MILP is to minimize the number of rules that must be artificially satisfied while finding a feasible solution for the model. (Details of this process are available in Additional File 1.)
Gene states for erg11 regulation
Iteration  

Start  1  2  3  4  Rule  
O_{2}[e]  1  1  1  1  1  
glucose [e]  1  1  1  1  1  
hap1  0  1  1  1  1  O_{2}[e] or not ROX1 
rox1  0  0  1  1  1  O_{2}[e] and HAP1 
erg11  1  1  1  0  0  O_{2}[e] and HAP1 and (not ROX1) 
erg11  1  1  1  1  1  O_{2}[e] and HAP1 and (high_o2 or not ROX1) 
The set of refined rules (20,21,23) reproduces the correct growth phenotype in aerobic glucose conditions. This example demonstrates a threestep procedure for refining existing TRN models using TIGER: 1.) apply the existing TRN to a COBRA model, 2.) use the find_infeasible_rules function to identify rules that cause the model to differ from a known phenotype, and 3.) reexamine the evidence for these rules and make appropriate modifications. As shown in the previous example, new biological information can often be incorporated into existing rules using TIGER's support for complex logical expressions.
Improved methods for expression data
Coupling the GPR with a metabolic model is a starting point for several algorithms designed to refine metabolic models by integrating highthroughput gene or protein expression data. The TIGER package contains implementations of three of these methods.
GIMME
GIMME was designed to generate contextspecific metabolic networks by designating each reaction as "on" or "off" [26]. Given expression data and a minimum expression threshold, GIMME calculates a normalized gene "score" for each reaction by averaging the expression values of all genes that appear in the GPR for the reaction. Reactions with a score below a cutoff are turned off; only reactions scoring above the cutoff are allowed to carry flux. Because this thresholding does not guarantee a functioning model, an optimization problem is formed to minimize the number of "off" reactions that must carry flux when the model produces a minimum objective flux.
The GIMME algorithm is an excellent candidate for conversion to a genecentric approach. Rather than average the gene expression values for each reaction, a simpler approach is to turn genes "on" or "off" if their expression is above or below a threshold. Using an integrated GPR/metabolic model, an optimization problem could reactivate "off" genes to allow the network to produce an objective flux. TIGER provides a gimme function that implements this genecentric approach. Similar to the original algorithm, TIGER's GIMME uses the distance below the expression threshold as a weight when selecting genes for reactivation. In addition to removing discrepancies caused by the averaging of gene expression values over each reaction, TIGER's integrated approach allows GIMME to identify each gene as either "on" or "off" in the resulting network (GIMME originally reported only the state of each reaction).
Expression data for GIMME example
Gene  Expression  Simple thresholding  GIMME 

g _{4}  13  1  1 
g _{5a}  6  0  1 
g _{5b}  12  1  1 
g _{6}  2  0  0 
g _{7a}  18  1  1 
g _{7b}  6  0  1 
g _{8a}  2  0  0 
g _{8b}  4  0  0 
iMAT
for each reaction flux v_{ i } and some small flux ε. The optimization attempted to preserve the reaction classifications while enforcing that the resulting set of reaction fluxes be feasible (mass balanced). The massbalance approach attempts to yield functional models in multicellular organisms that lack a clearly defined metabolic objective.
TIGER includes a genecentric version of the iMAT algorithm. Because TIGER allows multilevel variables, each gene in the GPR is allowed to occupy a state of low (0), medium (1), or high (2) activity. The multilevel operators in the GPR then combine the gene expression values to create a reaction indicator with the same three levels. Rules are added to enforce the constraints in equation (24). Additionally, if a metabolic objective is available for the organism, the flux through the corresponding objective reaction can be constrained above a minimum value.
Activity levels for iMAT example
Gene  Activity level 

g _{4}  medium 
g _{5a}  low 
g _{5b}  low 
g _{6}  high 
g _{7a}  high 
g _{7b}  high 
g _{8a}  medium 
g _{8b}  high 
MADE
Metabolic Adjustment by Differential Expression (MADE) removes the need for a predefined "on"/"off" threshold when integrating expression data [12]. Instead, MADE uses the differential expression between two or more conditions to determine which genes or proteins are likely to be "on" or "off". If a gene increases significantly between conditions 1 and 2, MADE attempts to turn the gene "off" in condition 1 and "on" in condition 2. The expression data are mapped while ensuring model functionality in all conditions, and the statistical significance of the expression changes are used to prioritize discrepancies.
The TIGER implementation of MADE offers two improvements. First, genes are allowed to be multilevel instead of binary. The user is allowed to define a mapping between the multiple levels of gene expression and the flux constraints for the corresponding reactions. Second, TIGER MADE allows comparisons among states that do not appear as a linear sequence. The original MADE algorithm used a series of n conditions C_{1}, C_{2}, ..., C_{ n } , and n  1 sets of expression data describing the changes C_{1} → C_{2}, C_{2} → C_{3}, ..., C_{n1}→ C_{ n } . TIGER MADE allows any number of connections between the n states.
Expression data for MADE example
Fold change  MADE states  

Gene  1 → 2  P  2 → 3  P  3 → 1  P  1  2  3 
g _{4}  2.1  0.68  3.0  0.08  0.7  0.15  1  1  1 
g _{5a}  0.5  0.45  8.0  0.44  0.8  0.22  1  0  1 
g _{5b}  1.1  0.07  0.1  0.49  2.2  0.03  1  1  0 
g _{6}  3.6  0.05  1.6  0.22  0.4  0.48  0  1  1 
g _{7a}  1.4  0.38  4.2  0.40  1.8  0.43  1  1  1 
g _{7b}  2.3  0.04  0.4  0.19  0.3  0.12  1  1  1 
g _{8a}  1.3  0.40  7.3  0.21  0.2  0.45  0  0  1 
g _{8b}  0.9  0.89  4.1  0.83  0.1  0.28  0  0  1 
Source code for all of the examples in Figure 4 are available in the file test/gimme_imat_made_examples.m of the TIGER distribution.
Conclusions
We have presented TIGER, a software platform for converting generalized Boolean and multilevel rules to mixedinteger linear programs, and coupling these rules to genomescale models of metabolism. The flexibility of TIGER's generalized rule format allows for a more accurate description of biological processes such as catalysis by isozymes and multimeric proteins, metabolic flux control, and transcriptional regulation. These features were used to identify and correct inconsistencies within an existing TRN model of Saccharomyces cerevisiae. We have also demonstrated how TIGER can be used as a starting point for implementing and improving existing algorithms for genomescale analysis.
In addition to adding implementations of other genecentric algorithms to TIGER, we are exploring methods to improve the solution efficiency of the generated MILP. Possible strategies include exploiting indicator constraints, speciallyorderedsets (SOS), and other solver optimizations through CMPI.
Availability and requirements
Project name: TIGER
Project home page:http://bme.virginia.edu/csbl/downloads or http://csbl.bitbucket.org/tiger
Operating system: Platform independent
Programming language: Matlab
Other requirements: Matlab v7.0 or higher, a MixedInteger Linear Programming solver (e.g. CPLEX, Gurobi, or GLPK)
License: MIT
Nonacademic use restrictions: None
List of abbreviations used
 TIGER:

Toolbox for Integrating Genomescale metabolism, Expression, and Regulation
 COBRA:

COnstraintBased Reconstruction and Analysis
 FBA:

Flux Balance Analysis
 GPR:

GeneProteinReaction
 TRN:

Transcriptional Regulatory Network
 MILP:

MixedInteger Linear Program
 SRFBA:

SteadyState Regulatory FBA
 iND750:

Genomescale model of Saccharomyces cerevisiae metabolism
 iMH805:

Genomescale transcriptional regulatory network for Saccharomyces cerevisiae.
 CMPI:

Common Mathematical Programming Interface
 GIMME:

Gene Inactivity Moderated by Metabolism and Expression
 iMAT:

Integrative Metabolic Analysis Tool
 MADE:

Metabolic Adjustment by Differential Expression.
Declarations
Acknowledgements and Funding
We thank the reviewers for their thoughtful suggestions. Charles Haggart tested many of the functions and offered helpful feedback. This work is supported by the NSF (GRF to PAJ, REU to KAL, and CAREER award 0643548 to JP) and the NIH (R01 GM088244 to JP).
Authors’ Affiliations
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