dynamicFBA.m

function [concentrationMatrix,excRxnNames,timeVec,biomassVec] = ...
    dynamicFBA(model,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns,exclUptakeRxns)
%dynamicFBA Perform dynamic FBA simulation using the static optimization
%approach
%
% [concentrationMatrix,excRxnNames,timeVec,biomassVec]
% dynamicFBA(model,substrateRxns,initConcentrations,initBiomass,timeStep,nSteps,plotRxns,exclUptakeRxns)
%
%INPUTS
% model                 COBRA model structure
% substrateRxns         List of exchange reaction names for substrates
%                       initially in the media that may change (e.g. not
%                       h2o or co2)
% initConcentrations    Initial concentrations of substrates (in the same
%                       structure as substrateRxns)
% initBiomass           Initial biomass (must be non zero)
% timeStep              Time step size
% nSteps                Maximum number of time steps
%
%OPTIONAL INPUTS
% plotRxns              Reactions to be plotted (Default =
%                       {'EX_glc(e)','EX_ac(e)','EX_for(e)'})
% exclUptakeRxns        List of uptake reactions whose substrate
%                       concentrations do not change (Default =
%                       {'EX_co2(e)','EX_o2(e)','EX_h2o(e)','EX_h(e)'})
% 
%OUTPUTS
% concentrationMatrix   Matrix of extracellular metabolite concentrations
% excRxnNames           Names of exchange reactions for the EC metabolites
% timeVec               Vector of time points
% biomassVec            Vector of biomass values
%
% If no initial concentration is given for a substrate that has an open
% uptake in the model (i.e. model.lb < 0) the concentration is assumed to
% be high enough to not be limiting. If the uptake rate for a nutrient is
% calculated to exceed the maximum uptake rate for that nutrient specified
% in the model and the max uptake rate specified is > 0, the maximum uptake 
% rate specified in the model is used instead of the calculated uptake
% rate.
%
% NOTE: The dynamic FBA method implemented in this function is essentially 
% the same as the method described in
% [Varma, A., and B. O. Palsson. Appl. Environ. Microbiol. 60:3724 (1994)].
% This function does not implement the dynamic FBA using dynamic optimization approach
% described in [Mahadevan, R. et al. Biophys J, 83:1331-1340 (2003)].
%
% Markus Herrgard 8/22/06

if (nargin < 7)
    plotRxns = {'EX_glc(e)','EX_ac(e)','EX_for(e)'};
end

% Uptake reactions whose substrate concentrations do not change
if (nargin < 8)
    exclUptakeRxns = {'EX_co2(e)','EX_o2(e)','EX_h2o(e)','EX_h(e)'};
end

% Find exchange rxns
excInd = findExcRxns(model,false);
excInd = excInd & ~ismember(model.rxns,exclUptakeRxns);
excRxnNames = model.rxns(excInd);
length(excRxnNames)
% Figure out if substrate reactions are correct
missingInd = find(~ismember(substrateRxns,excRxnNames));
if (~isempty(missingInd))
    for i = 1:length(missingInd)
        fprintf('%s\n',substrateRxns{missingInd(i)});
    end
    error('Invalid substrate uptake reaction!');
end

% Initialize concentrations
substrateMatchInd = ismember(excRxnNames,substrateRxns);
concentrations = zeros(length(excRxnNames),1);
concentrations(substrateMatchInd) = initConcentrations;

% Deal with reactions for which there are no initial concentrations
originalBound = -model.lb(excInd);
noInitConcentration = (concentrations == 0 & originalBound > 0);
concentrations(noInitConcentration) = 1000;

biomass = initBiomass;

% Initialize bounds
uptakeBound =  concentrations/(biomass*timeStep);

% Make sure bounds are not higher than what are specified in the model
aboveOriginal = (uptakeBound > originalBound) & (originalBound > 0);
uptakeBound(aboveOriginal) = originalBound(aboveOriginal);
model.lb(excInd) = -uptakeBound;

concentrationMatrix = sparse(concentrations);
biomassVec = biomass;
timeVec(1) = 0;

fprintf('Step number\tBiomass\n');
h = waitbar(0,'Dynamic FBA analysis in progress ...');
for stepNo = 1:nSteps
    % Run FBA
    sol = optimizeCbModel(model,'max','one');
    mu = sol.f;
    if (sol.stat ~= 1 || mu == 0)
        fprintf('No feasible solution - nutrients exhausted\n');
        break;
    end
    uptakeFlux = sol.x(excInd);
    biomass = biomass*exp(mu*timeStep);
    %biomass = biomass*(1+mu*timeStep);
    biomassVec(end+1) = biomass;
    
    % Update concentrations
    concentrations = concentrations - uptakeFlux/mu*biomass*(1-exp(mu*timeStep));
    %concentrations = concentrations + uptakeFlux*biomass*timeStep;
    concentrations(concentrations <= 0) = 0;
    concentrationMatrix(:,end+1) = sparse(concentrations);
    
    % Update bounds for uptake reactions
    uptakeBound =  concentrations/(biomass*timeStep);
    % This is to avoid any numerical issues
    uptakeBound(uptakeBound > 1000) = 1000;
    % Figure out if the computed bounds were above the original bounds
    aboveOriginal = (uptakeBound > originalBound) & (originalBound > 0);
    % Revert to original bounds if the rate was too high
    uptakeBound(aboveOriginal) = originalBound(aboveOriginal);
    uptakeBound(abs(uptakeBound) < 1e-9) = 0;

    model.lb(excInd) = -uptakeBound;  
    
    fprintf('%d\t%f\n',stepNo,biomass);
    waitbar(stepNo/nSteps,h);
    timeVec(stepNo+1) = stepNo*timeStep;
end
if ( regexp( version, 'R20') )
        close(h);
end

selNonZero = any(concentrationMatrix>0,2);
concentrationMatrix = concentrationMatrix(selNonZero,:);
excRxnNames = excRxnNames(selNonZero);
selPlot = ismember(excRxnNames,plotRxns);

% Plot concentrations as a function of time
clf
subplot(1,2,1);
plot(timeVec,biomassVec);
axis tight
title('Biomass');
subplot(1,2,2);
plot(timeVec,concentrationMatrix(selPlot,:));
axis tight
legend(strrep(excRxnNames(selPlot),'EX_',''));