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

If there are some key condition changed, we use following equation to correct the model. (we culture the microalgae in incubator ,it surrounding temperature is stable.)

μ=KI/(Ki+I+I^2/Kii);

=μmS/(Ks+S+S^2/Kss);

μm=μm*/(Kn+N+N^2/Knn);

K: constant.
Ki: saturation constant of light intensity
Kii: inhibition constant of light intensity
Ks: inhibition constant of substrate
Kss: saturation constant of substrate
μm: maximum specific growth rate
Kn: inhibition constant of nitrogen
Knn: saturation constant of nitrogen
μm*: constant

fig.1 Growth curve of Chlorella vulgaris

fig.2 Growth rate of Chlorella vulgaris