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MIT6_047f08_lec22_note22 - MIT OpenCourseWare...

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MIT OpenCourseWare http://ocw.mit.edu 6.047 / 6.878 Computational Biology: Genomes, Networks, Evolution Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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6.047/6.878 Lecture 22: Metabolic Modeling 2 November 20, 2008 1 Review In the last lecture, we discussed how to use linear algebra to model metabolic networks with flux-balance analysis (FBA), which depends only on the stoichiometry of the reactions, not the kinetics. The metabolic network is represented as an n × m matrix M whose columns are the m reactions occurring in the network and whose rows are the n products and reactants of these reactions. The entry M(i, j) represents the relative amount of metabolite i consumed or produced by reaction j. A positive value indicates production; a negative value indicates consumption. The nullspace of this matrix consists of all the m × 1 reaction flux vectors that are possible given that the metabolic system is in steady state; i.e. all the sets of fluxes that do not change the metabolite concentrations. The nullspace ensures that the system is in steady state, but it there are also additional constraints in biological systems: fluxes cannot be infinite, and each reaction can only travel in the forward direction (in cases where the backward reaction is also biologically possible, it is included as a separate column in the matrix). After bounding the fluxes and constraining the directions of the reactions, the resulting space of possible flux vectors is called the constrained flux- balance cone. The edges of the cone are known as its extreme pathways. By choosing an objective function—some linear combination of the fluxes—to maximize, we can calculate the optimal values for the fluxes using linear programming and the simplex algorithm. For example, the objective function may be a weighted sum of all the metabolite fluxes that represents the overall growth rate of the cell (growth objective). Alternatively, we can maximize use of one particular product by find the m × 1 flux vector that is in the flux-balance cone and has the largest negative value of that product. At the end of the last lecture, we also discussed knockout phenotype predictions, a classic application of metabolic modeling. Experimental biologists often gather information about the function of a protein by generating transgenic organisms in which the gene encoding that protein has been disrupted, or knocked out. We can simulate in silico the effect of knocking out a particular enzyme on metabolism by assuming that the reaction catalyzed by that enzyme does not occur at all in the knockout: zeroing out the j th column of M effectively removes the j th reaction from the network. What used to be an optimal solution may now lie outside of the constrained flux-balance cone and thus no longer be feasible in the absence of the j th reaction. We can determine the new constrained flux-balance cone and calculate the new optimum set of fluxes to maximize our objective function, predicting the effect of the knockout on
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