Help with setting up Continuous flux bound modification

MIDCP
1

Hi, I am trying to understand how to turn the following equations into matlab code that works within the CVX.
within this formulation j= set of reactions and i = set of metabolites

load ‘Ecoli_core_model.mat’

c=model.c;
S=model.S;
lb=model.lb;
ub=model.ub;

nrxns=length(model.rxns);
% FBA
cvx_begin
variables v(nrxns)
minimize (c’v)
subject to
Sv == 0
lb <= v <= ub
cvx_end

The following above is the Flux balance analysis part which would be corresponding to equation 10.
But here is about where my understanding of this stops.

CosMos formula.png1095×624 35.1 KB

And eventually we will have to try to formulate this whole thing. Which is beyond me.
This is from the journal paper “Constraint-based strain design using continuous
modifications (CosMos) of flux bounds finds new
strategies for metabolic engineering” by Cameron Cotten and Jennifer L. Reed (2013)
I’ve tried to do this but i don’t seem to be able, since I just started to learn using Matlab this February and my background is in Biochemistry, but my prof. wants me to study this but this is something I am unable to figure out on my own.

Can someone show me how to formulate this? Been reading a lot of material but I lack the understanding of some key concepts.

Best regards.
Arnar Sigurdsson

2

Here is the bilevel formulation of the problem.
Think I might have to solve this one before

bilevel.png1100×465 22.8 KB

3

Your problem, equations 20-33 looks like a mixed integer Linear Programming problem, which should be straightforward to enter in CVX. You need to declare the appropriate variables as binary, as shown in http://web.cvxr.com/cvx/doc/basics.html#variables , and you must have a version of CVX and solver which can solver mixed integer (linear programming) problems, as discussed in http://web.cvxr.com/cvx/doc/solver.html#solvers .

If you need help in the modeling aspect or understanding the paper, that is beyond the scope of this forum.

4

Thank you.
I will look into links you sent.