Team:NYMU-Taipei/Model
Modeling
Growth curve of Chlorella vulgaris
The timing of adding engineering E.coli or purified protein to Chlorella vulgaris culture is critical for our project. Through the initial, final biomass concentration data, the instantaneous rate of a reference time and other lab environment datas, we simulate the change in biomass concentration throughout the culture cycle. The status information in the culture medium at each point is then obtained through the other calculus to obtain the best timing point and the corresponding state.
ln(Xt/X0)/t=A+Bexp(-C(t-M))=μ(specific growth rate)
X: biomass concentration(g/l)
t: time(hr)
A: the asymptotic of ln Xt/Xo as t decrese indefinitely
B: the asymptotic of ln Xt/Xo as t increase indefinitely
C: the relative growth rate at time M
fig.1 Growth curve of Chlorella vulgaris
fig.2 Growth rate of Chlorella vulgaris
Oil accumulation & Nirogen source consumption
Simulating common system of oil accumulation and nitrogen source consumption, not only get the reference of state before the improvement as well as the stage information, but also as a basic equation after some parameters or organisms join into the system.
dP/dt=*dX/dt+*X;
dN/dt=-V*X;
V=((qM-Q)/(qM-q))*((Vm*N)/(N+Vh));
Q=(X0*Q0+N0-N)/X;
P: lipid
N: nitrogen
X: biomass
α: the instantaneous yield coefficient of product formation due to cell growth
β: the specific formation rate of product
q: Minimum N quota
qM: Maximum N quota
Q: N quota
Vm: Maximum uptake rate of nitrogen
Vh: Half-saturation coefficient
fig.3 Oil accumulation and nirogen source consumption at normal situation
Biomass in different nitrogen concentration
To find the optimal amount of nitrogen removal, we model biomass decrease in different nitrogen concentration environments, and then we can find the best productivity.
n2=exp((A+C*exp(-exp(-B(t-M))))*(t2-t1))*n1;
x2=x1+(n2-n1)*((k(ln(b(ns+a))^-1))-e);
n1: biomass at frist state
n2: biomass at secind state
x: biomass concentration(g/l)
t: time(hr)
A: the asymptotic of ln Xt/Xo as t decrese indefinitely //-39.9532
B: the asymptotic of ln Xt/Xo as t increase indefinitely //-0.0222
C: the relative growth rate at time M hr //45.6931
k: constant //8.15229
b:yield coefficient//1207.569
ns:initial nitrogen concentration
a:regression constant//0.01
e:a perturbation//0.50678
fig.4 Biomass in different nitrogen concentration
Nitrogen concentration in nitrogen starvation
Put normal and modified nitrogen source system together,see their demonstration, like speed and occasion.by constructing this model,we can find out the declining rate of each state,then adjust experiment.
dn/dt=Yxn*dx/dt+m*x
n: nitrogen concentration
Yxn: nitrate coefficient g/g 0.21016
m: maintenance parameter hr^-1 0.0014393
x: biomass concentration
fig.5 Nitrogen source in nitrogen starvation
123
descibe
fig.5
123
descibe
fig.5
123
descibe
fig.5
123
descibe
fig.5
