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

We made two different models for our methyl salicylate part. This model describes our Flux Balance Analysis (FBA), the other model can be found here.
We ran the FBA using the COBRA Toolbox for MATLAB..

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

This involves the determination of the consequences of enzyme defects on functional states of GENREs. The value of the flux is re-constrained through the affected reaction. This new value is used to recompute the optimal state for the enzyme defect. If the enzymatic function is reduced due to the defect, but the exact numbers are unknown, the flux can be sequentially changed through the reaction of interest and the objective function can be optimized at each step. Plotting the resulting optimal value versus the flux value through the reaction of interest creates a linear curve. Here the slope represents the reduced scientific cost, which can be used to determine the sensitivity of the Flux Balance Analysis (FBA) solution.
The reduced cost is the derivative of the objective function with respect to an internal reaction with zero flux (this gives an indication on how much each particular reaction affects the objective). In COBRA this is given as vector n (FBAsolution.n). A similar measure is the shadow price (the name reflects the “cost aspect” in the equation). This is the derivative of the objective function with respect to the exchange flux of a metabolite i.e. how much will the addition of a metabolite increase or decrease the objective. In COBRA this is given as vector m (FBA solution.m).

We used an E. coli model from 2007 (iAF1260 by Feist, AM. et al.) in all the following COBRA toolbox analyses.

As a first step we tried to predict the growth under default conditions for this model. This gave us the following results (after setting the biomass as objective function): for E. coli under default conditions a growth rate of 0.737 hr^-1 is predicted. The sensitivity of this solution is indicated by either the shadow price or the reduced cost. Shadow prices are the derivative of the objective function with respect to the exchange flux of a metabolite. They indicate how much the addition of that metabolite will increase or decrease the objective. Reduced costs are the derivatives of the objective function with respect to an internal reaction with 0 flux, indicating how much each particular reaction affects the objective.

In a next step we wanted to add the reactions which are necessary for our model, but lacking in the iAF1260 model.
We added 'pchA', 'chor[c] -> ichor[c]' for the isochorismate synthesis reaction, 'pchB', 'ichor[c] -> sali[c] + pyr[c]' for the salicylate synthesis reaction and 'BSMT1', 'sali[c] -> methylsalicylate' for the methyl salicylate synthesis reaction.
When we performed the growth calculation analysis for this modified model and with the biomass set as objective function, we also observed a growth rate of 0.737 hr-1 and thus can conclude that no adverse effect on the E. coli growth rate was predicted by adding these reactions.

Since our bacteria will be grown on LB medium, we changed the default medium settings towards those for LB medium. This means that we set all the exchange reactions to zero except for the exchange reactions for metabolites present in the LB medium. The lower reaction bounds of the following reactions were all set to -1000 since this allows maximal uptake of the respective metabolites:
EX_glc(e), EX_phe_L(e), EX_cys_L(e), EX_ile_L(e), EX_ins(e), EX_hxan(e), EX_h2o(e), EX_o2(e), EX_co2(e), EX_nh4(e), EX_so4(e), EX_ca2(e), EX_h(e), EX_k(e), EX_mg2(e), EX_na1(e), EX_fe3(e), EX_nac(e), EX_thym(e), EX_ade(e), EX_thr_L(e), EX_val_L(e), EX_pro_L(e), EX_his_L(e), EX_leu_L(e), EX_ura(e), EX_tyr_L(e), EX_trp_L(e), EX_met_L(e), EX_ser_L(e), EX_arg_L(e), EX_asp_L(e), EX_lys_L(e), EX_lys_L(e), EX_ala_L(e), EX_zn2(e), EX_cd2(e), EX_glyc(e), EX_gln_L(e)

When we performed the growth calculation with the biomass as objective function the flux to chorismate was 0.274 mol/hr in non-LB medium conditions and the growth of E. coli 0.737 hr^-1. When we do the same but for the LB medium conditions we observe the flux to chorismate as 0.059 mol/hr and a growth rate of 66.88 hr.This suggests that LB-medium is beneficial for E.coli growth, but lowers the flux towards chorismate. This can be explained by the fact that the availability of certain nutrients in the medium reduces the need for a flux towards chorismate (a precursor of methyl salicylate). It is possible that the extra drain created by our system cannot easily be compensated by the cell. This stresses the importance of our aroG BioBrick (Part:BBa_K1060000) approach, where we aim for a higher flux towards chorismate. This BioBrick contains mutations that can prevent the repression by Phenylalanine, that would occur otherwise and is in favour of chorismate production at the same time. ^-1.

We were also interested to see how the maximal production of MeS is related to the maximal growth of E.Coli under minimal conditions. Therefore we set the objective function to MeS and set the lower bound for the biomass at different percentages of the maximal growth rate predicted with the biomass as objective function.

Performing the same calculations but for LB medium conditions gave us the following graph:

As seen in the graphs, there is a linear correlation between maximal flux towards MeS and maximal E.Coli growth. This linear correlation is qualitatively similar both under minimal growth conditions as in LB medium conditions and shows that we are dealing with a trade off. This means that it is important to choose wisely where at the curve the best trade off between maximal cell growth and maximal flux towards MeS can be achieved, if a lower E.Coli yield is preferred in advantage of a higher flux to MeS a value at the left side of the graph should be considered, whereas a value to the right would give a higher E.Coli production rate and a lower flux towards MeS. This is consistent when taking into account the results from the wetlab since we observed lower growth curves for higher concentrations of added salicylate. If we assume that the production of SAM (S-adenosylmethionine) a common cosubstrate of the methyltransferase reaction from salicylate to methylsalicylate, is important for cell metabolism, providing higher levels of salicylate would increase the availability of SAM. However a toxic effect might take place at high levels of salicylate because higher levels of SAM are associated with higher homocysteine levels (product that stays behind when methylgroup has been transferred to substrate). Homocysteine has already been shown to be toxic for E.Coli strains and might explain the ceiling we observe for adding salicylate in hopes of higher MeS fluxes.

Covert, M. W. and B. O. Palsson (2003). "Constraints-based models: regulation of gene expression reduces the steady-state solution space." J Theor Biol 221(3): 309-325.
Covert, M. W., C. H. Schilling, I. Famili, J. S. Edwards, Goryanin, II, E. Selkov and B. O. Palsson (2001). "Metabolic modeling of microbial strains in silico." Trends Biochem Sci 26(3): 179-186.
Feist, AM et al. (2007) “A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.” Mol. Syst. Biol. 3 121.
Huang, J., Q. Zhang and T. Schlick (2003). "Effect of DNA superhelicity and bound proteins on mechanistic aspects of the Hin-mediated and Fis-enhanced inversion." Biophys J 85(2): 804-817.
Mahadevan, R. and C. H. Schilling (2003). "The effects of alternate optimal solutions in constraint-based genome-scale metabolic models." Metab Eng 5(4): 264-276.
Orth, J. D., I. Thiele, and B.O. Palsson (2010). "What is Flux Balance Analysis?" Nature Biotechnology (28): 245-248.
Papin, J. A., N. D. Price, J. S. Edwards and B. B. Palsson (2002). "The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy." J Theor Biol 215(1): 67-82.
Price, N. D., J. A. Papin, C. H. Schilling and B. O. Palsson (2003). "Genome-scale microbial in silico models: the constraints-based approach." Trends Biotechnol 21(4): 162-169.
Price, N. D., J. L. Reed and B. O. Palsson (2004). "Genome-scale models of microbial cells: evaluating the consequences of constraints." Nat Rev Microbiol 2(11): 886-897.
Schilling, C. H., M. W. Covert, I. Famili, G. M. Church, J. S. Edwards and B. O. Palsson (2002). "Genome-scale metabolic model of Helicobacter pylori 26695." J Bacteriol 184(16): 4582-4593.