# Need help plotting modified kinetic equation

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Regina Maria on 13 Jun 2021
Edited: Star Strider on 17 Jun 2021
Hi, nice to meet you. I am trying to plot graphs (Substrate vs time, Biomass vs time, and Product vs time) from these modified kinetic equations below:
• EDIT (the dX/dt equation should be like this:)
dX/dt = miumax * S/(Ks*S*(S^2/Kxi)) * I/(KXI+I) * (1-X/Xm) *(1-P/Pm)
-dS/dt = 1/Yxs*(dX/dt) + 1/Yps*(dP/dt) + miusx*X
dP/dt = (Ypx*(dX/dt) + miupx*X) * S/(Kps+S+(S^2/Kpi)) * P/(Kp+P) * I/(KPI+I)
where miumax, Ks, Kxi, KXI, Xm, Pm, Yxs, Yps, miusx, Ypx, miupx, Kps, Kpi, Kp, and KPI are kinetic parameters; S, X, P are substrate concentration, biomass concentration, and product concentration respectively.
I have tried code this, but it is very far from perfect. Any little suggestion or solutions or comments are very welcomed! Thank you so much!
• EDIT
I attached a new MATLAB file in the comment section named "trycurvefit.m", which is a lot more understandable than this code below
function equation1
t = [1:1:20]; %time: 20 days
C0 = [0.1143; 0.9659; 0.004406]; %intial concentration of biomass, susbtrate, and product respectively
[t C] = ode15s(@fungsi,t,C0);
plot(t,C)
end
function dCdt = fungsi(t,C)
Yxs = 2.6872; Yps = 60.3616; miusx = 1.8216; Ypx = 20.7502; miupx = 6.0679; Kps = 0.0017; Kpi = 63.9593; Kp = 19.1078; KPI = 72.5525; %kinetic parameter values
dCdt(1,:) = (Yxs*(-dCdt(2,:) - (1/Yps)*dCdt(3,:) - miusx*C(1))); %dX/dt, i got this changing the dS/dt equation
dCdt(2,:) = (-1/Yxs)*dCdt(1,:)-(1/Yps)*dCdt(3,:)-miusx*C(1);%dS/dt
dCdt(3,:) = (Ypx*dCdt(1,:) + miupx*C(1))*(C(2)/(Kps+C(2)+C(2)^2/Kpi))*(C(3)/(Kp+C(3)))*(45/(KPI+45)); %dP/dt
end
%i also attach the substrate (S), biomass (X), and product (P) data, so the
%plot sholud be close to these datas
% S = [0.9659 0.6314 0.3819 0.2725 0.2177 0.1934 0.1812 0.1630 0.1326 0.1204 0.1022 0.0778 0.0657 0.0535 0.0413 0.0353 0.0292 0.0170 0.0048 0.0047]
% X = [0.1143 0.1508 0.1873 0.2603 0.5462 0.8138 1.0754 1.2032 1.3126 1.3856 1.6350 1.8600 2.0243 2.1277 2.3224 2.4258 2.5048 2.5353 2.5900 2.6386]
% P = [0.4406 0.7244 0.8622 1.0002 1.1380 1.4217 1.8510 2.5716 3.5832 6.0514 7.5001 8.8027 11.7077 15.1958 18.5373 21.0054 30.3182 36.5723 41.8075 53.5960]
Regina Maria on 17 Jun 2021
@James Tursa Hello, thank you for stopping by and give some advices! Yes, after posting this problem, I realised that my dX/dt equation should not be dependent to dS/dt like that. Therefore, I have revised the dX/dt equation and attached the code file in the previous comment I've posted. Thank you for the info!