Team:KU Leuven/Project/Glucosemodel/MeS/Modelling-FBA

INLEIDING DIE NOG GESCHREVEN MOET WORDEN

COBRA stands for Constraint-Based Reconstruction and Analysis (COBRA) approach. This approach provides a biochemically and genetically consistent framework for the generation of hypotheses and the testing of functions of microbial cells. Probably the most used analysis in COBRA is the Flux Balance Analysis (FBA) which will be discussed in more detail below.

COBRA has been successfully applied to study the possible phenotypes that arise from a genome (Covert, Schilling et al. 2001). COBRA consists of two fundamental steps. First, a GENRE (=GEnome-scale Network REconstruction) is formed, and second, the appropriate constraints are applied to form the corresponding GEMS (GEnome-scale Model in Silico). Cellular functions can be limited by different types of constraints in a biological system: e.g. physico-chemical constraints, topo-biological, environmental and regulatory constraints.

1. Physico-chemical constraints refer to reaction rates, enzyme turnover rates, diffusion rates etc. Moreover mass, energy and momentum must be conserved and biochemical reactions must result in a negative free-energy change to proceed in the forward direction.
2. Topo-biological constraints refer to the crowding of molecules in the cell. An example is the organisation of DNA in Escherichia coli by spatio-temporal patterns (Huang, Zhang et al. 2003). Therefore there are two competing needs that constrain the physical arrangement of DNA in the cell.
3. Environmental constraints are nutrient availability, pH, temperature, osmolarity and the availability of electron acceptors. They are time and condition dependent. Environmental constraints are of fundamental importance for the quantitative analysis of microorganisms. Defined media and environmental conditions are needed to integrate data into quantitative models that are both accurately descriptive and predictive.
4. Regulatory constraints differ from the others because they are self-imposed and are subject to evolutionary change. For this reason, these constraints may be referred to as regulatory restraints, in contrast to 'hard' physico-chemical constraints and time-dependent environmental constraints. On the basis of environmental conditions, regulatory constraints allow the cell to eliminate suboptimal phenotypic states and to confine itself to behaviours of increased fitness. Regulatory constraints are implemented by the cell in various ways, including the amount of gene products made (transcriptional and translational regulation) and their activity (enzyme regulation).

Two fundamental types of constraints exist: balances and bounds (Price, Reed et al. 2004). Balances are constraints that are associated with conserved quantities such as energy, mass etc. while bounds are constraints that limit numerical ranges of individual variables and parameters such as concentrations, fluxes or kinetic constants. At steady state, there is no accumulation or depletion of metabolites in a metabolic network, so the production rate of each metabolite in the network must equal its rate of consumption. This balance of fluxes can be represented mathematically as S . v = 0, where v is a vector of fluxes through the metabolic network and S is the stoichiometric matrix containing the stoichiometry of all reactions in the network.

Both bound and balance constraints limit the functional states of reconstructed networks that are allowed. In mathematical terms, the range of allowable network states is described by a solution space which, in biology, represents the phenotypic potential of an organism. All allowable network states are contained in this solution space. (Covert and Palsson 2003; Price, Papin et al. 2003)

In recent years, many new in silico methods have been developed using the COBRA framework. Many methods can be used such as finding best or optimal states in the allowable range; investigating flux dependencies; studying all allowable states; altering possible phenotypes as a consequence of genetic variations; and defining and imposing further constraints (Covert, Schilling et al. 2001).

Determination of optimal or best states

This can be achieved through mathematical descriptions of desired network functions which takes the form of an objective function (Z). Z can express 3 different functions: the exploration of the phenotypical potential of the GENRE (Papin, Price et al. 2002, Schilling, Covert et al. 2002); the determination of likely physiological states by choosing the objective function as such (ATP production); the design of strains towards a specific engineering goal (improved production of a desired secreted product). The objective function Z can be either a linear or nonlinear function.
The following should be noted: in silico modelling in biology differs from that in the physico-chemical sciences where a single and unique solution is sought. This means that there can be multiple network states or flux distributions with the same outcome (optimal value of the objective function). Therefore, the need for enumerating alternate optima arises. We performed flux variability analysis to understand the complete set of alternate optima.

Flux variability analysis (FVA)

Flux variability analysis determines the full range of numerical values for each flux in the network, while still satisfying the given constraints and optimizing a particular objective (Mahadevan and Schilling 2003).

Single parameter perturbation: robustness calculations