yeast_chemostat_ss
This program simulates steady-state values of a glucose limited chemostat with
S. cerveisiae. The basic overflow model is described in Monod kinetics terms in the
SIMSPEC file yeast_model.fig. It is the same model as used in the fedbatch simulations of
yeast (yeast_fedbatch). To obtain the yield coefficients and specific rates of ethanol,
oxygen and CO2, stoichiometric analysis is applied. Units are first translated to C-mole
before the stoichiometric analysis is made and finally, for the presentation, converted
back to gram units. The metabolic path is separated into i) aerobic metabolism (at
glucose concentrations up to a critical value, Gcrit corresponding to a critical uptake rate
qGcrit) and ii) fermentative (overflow) metabolism of the fraction of glucose uptake
which exceeds the qGcrit value . Finally the biomass and growth rates of these fluxes are
added.
For further information on the stoichiometric analysis see Fermentation Process
Engineering, chapt 5, (www.enfors.eu)
The model cannot account for oxygen limitation and ethanol inhibition.
Variables:
D
/h
Dilution rate
X
g/L
Biomass concentration
G
g/L
Glucose concentration
DOT %
Dissolved oxygen tension
E
g/L
Ethanol concentration
RQ
mol/mol
Respiratory quotient
my
/h
Specific growth rate
Xf
g/L
Fraction of biomass produced fermentatively
qO
g/g/h Specific oxygen consumption rate
Constants:
Yxgae g/g
Yxgf g/g/h
Kg
g/L
qGmax g/gh
Gcrit g/L
H
% /(g/L)
DOTstar
%
Gi
g/L
CMWg g/Cmol
CMWx g/Cmol
CMWe g/Cmol
DRx /Cmol
DRg /Cmol)
DRe /Cmol
DRo /mol
qm
g/gh
KLa
/h
Aerobic yield of biomass per glucose
Fermentative yield of biomass per glucose
Saturation constant for glucose
Max specific glucose uptake rate (Monod model)
Critical G above which overflow metabolism occurs
Conversion between % air sat and g/L units for DO
Equilibrium DOT
Inlet glucose concentration
Cmole weight of glucose
Cmole weight of biomass
Cmole weight of ethanol
Degree of reduction of biomass
Degree of reduction of glucose
Degree of reduction of ethanol
Degree of reduction of oxygen
maintenance coefficient
Vol. oxygen transfer coefficient
Algorithm:
G=0:0.001:10; % Glucose conc. vector
G=G';
% Convert to C mole:
g=G/CMWg;% glucose conc
gi=Gi/CMWg;% inlet glucose conc.
qmcmol=qm/CMWg*CMWx;% maintenance coeff.
kg=Kg/CMWg;% saturation const, for glucose
qgmax=qGmax/CMWg*CMWx;% qSmax glucose
gcrit=Gcrit/CMWg; % critical S for overflow
qgcrit=qgmax*gcrit/(gcrit+kg); %critical qS for overflow
yxgae=Yxgae/CMWx*CMWg; % aerobic Yx/s for glucose
yxgf=Yxgf/CMWx*CMWg; % fermentative Yx/s for glucose
%Glucose uptake kinetics
qg=qgmax*g./(g+kg);
qgae=qg;
qgae(find(qgae>qgcrit))=qgcrit;
qgf=qg-qgae;
% Aerobic path
myae=yxgae*qgae; % aerobic contribution to growth on glucose
yog=(DRx*yxgae-DRg)/DRo;% yield oxygen/glucose
qo=yog*qgae;% rate of oygen for glucose oxidation
yco2gae=1-yxgae;% aerobic CO2 yield
qco2gae= yco2gae*qgae;% rate of aerobic CO2 production
% Fermentative path
myf=yxgf*qgf;
yeg=(DRg-yxgf*DRx)/DRe;% yield of ethanol
qep=yeg*qgf; % specific ethanol prod. rate
yco2gf=1-yxgf-yeg; % fermentative yield of CO2
qco2gf=yco2gf*qgf; % spec. co2 prod. rate
% Biomass from the two paths:
deltag=gi-g; % Consumed glucose
xae=yxgae.*deltag.*qgae./qg; % Fraction to aerobic biomass
xf=yxgf.*deltag.*qgf./qg; % Fraction to fermentative biomass
% The sum
my=myae+myf;
D=my;
qco2=qco2gae+qco2gf;
x=xae+xf;
RQ=qco2./qo;
e=qep.*x./D;
% convert to g or mmol units
Xae=xae*CMWx;
Xf=xf*CMWx;
X=x*CMWx;
E=e*CMWe;
qO=qo/CMWx*32;% g/g/h
DOT=DOTstar-X.*qO*H/KLa;