BENG 212: Systems Biology and Bioengineering II
Assignment #1
Due January 24, 2013 – 11:59 PM
Accepted submission format:
Your submission must be a ".zip" file e-mailed to [email protected]. Inside should be:
(1) a single ".pdf" document with responses to all the questions below and (2) a ".mat" matlab
file with the stoichiometric/elemental matrices (one or more for each part of the homework -labeled) so I can check your work thoroughly. For problems 1 and 3 have a metabolite and
reaction matrix so that the identity of columns/rows is known e.g. problem1.mets,
problem1.rxns, and problem1.S. For problem 2 have a metabolite and element matrix so
that the identity of columns/rows is known e.g. problem2.mets, problem2.elements,
problem2.E. Please do not deviate from this convention. 20 points will be deducted from the
total 100 for every day this assignment is received late.
Part 1 – Construction of the stoichiometric matrix
1. Constuct S matrices for the TCA cycle and pentose phosphate pathway
Shown below is an example of a simple S matrix representing the ten well known
reactions of glycolysis.
Using any biochemistry textbook as a guide, construct an S matrix for the TCA cycle and
an S matrix for the pentose phosphate pathway. Include exchange reactions (input and output).
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It is up to you to determine exactly which reactions and metabolites to include, and how to best
arrange the matrices.
2. Combine S matrices and construct the E matrix for QC/QA
Now combine the reactions and metabolites from your TCA cycle and pentose phosphate
pathway S matrices with the glycolysis S matrix (given in problem 1) to form one large S matrix.
It may be necessary to add some reactions that weren’t in any of the 3 matrices from problem 1
(such as pyruvate to acetyl-coA, or anaplerotic reactions). Next, construct an E (elemental)
matrix for the compounds in this network. Multiply E*S (probably should use Matlab for this).
Is your S matrix elementally balanced? If not, what changes must be made?
3. Expand the glycolysis S matrix to include enzymes
Expand the reactions in the glycolysis network to include glycolytic enzymes in the
reactions. For example, convert the phosphoglycerate mutase reaction (3PG <==> 2PG) to the
new reactions:
3PG + PGM <==> 3PG-PGM
3PG-PGM <==> 2PG-PGM
2PG-PGM <==> 2PG + PGM
where PGM is the enzyme and 3PG-PGM and 2PG-PGM are enzymes with substrates bound.
Construct a new S matrix for this network.
4. Coupling constraints
Above, you've added enzymes as "components" of your network. These components are
exchanged with the system since they are not produced internally. Using this simple
formulation, will enzymes be required at steady state? That is, will the system be forced to
exchange PGM? Why or why not?
To get around this pesky problem we've devised a simple solution, but we have to introduce
some parameters (this is atypical for genome-scale models of metabolism but we are pushing the
limits now).
3PG + PGM <==> 3PG-PGM
(reaction 1)
3PG-PGM <==> 2PG-PGM
(reaction 2)
2PG-PGM <==> 2PG + PGM
(reaction 3)
PGM --> (PGM goes to nothing, or is passed to a daughter cell)
(reaction 4)
We add the following constraint to the network:
Flux through reaction 4 in the forward direction ≥ k*Flux through reaction 1 in the forward
direction.
Please give a biological/physical interpretation of what this "k" is. Using this new formulation,
will enzymes be required at steady state? Why or why not?
In answering this question, assume that proteins never degrade; they are simply passed to
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daughter cells during cell division. Also, you can assume that the network is operating under
conditions that are enzyme-limited and that the enzyme can run the reaction from 3PG to 2PG at
a turnover rate of 200/s (and that reaction 1 is rate limiting). No reactions are able to run in
reverse under the particular experimental conditions we are trying to model here.
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