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
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document6.047/6.878 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 fluxbalance 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 fluxbalance 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 fluxbalance cone and thus no
longer be feasible in the absence of the j
th
reaction. We can determine the new constrained fluxbalance cone and
calculate the new optimum set of fluxes to maximize our objective function, predicting the effect of the knockout on
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 ManolisKellis
 FBA, mycolic acid, expression levels

Click to edit the document details