Difference between revisions of "Team:NYMU-Taipei/Model"
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| + | <th scope="col"&></th> | ||
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| + | <th>R</th> | ||
| + | <th>co2 productive rate</th> | ||
| + | <th></th> | ||
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| + | <tr> | ||
| + | <th>A1</th> | ||
| + | <th>preexponential factor at i=400</th> | ||
| + | <th></th> | ||
| + | <th>8.625*10^-5</th> | ||
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| + | <th>A2</th> | ||
| + | <th>preexponential factor at i=200</th> | ||
| + | <th></th> | ||
| + | <th>1.83885*10^-2</th> | ||
| + | </tr> | ||
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| + | <th>B1</th> | ||
| + | <th>activation energy at i=400</th> | ||
| + | <th>mol/J </th> | ||
| + | <th>6.45</th> | ||
| + | </tr> | ||
| + | <tr> | ||
| + | <th>B2</th> | ||
| + | <th>activation energy at i=200</th> | ||
| + | <th>mol/J</th> | ||
| + | <th>69.2</th> | ||
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Revision as of 08:32, 7 October 2017
Modeling is an extremely important part to our project, because it helps us accurately check and predict the results of the experiments, which are worked in the wet lab. In our project, there are two essential types of microalgae that play very important roles, Synechosistic PCC7942andChlorella vulgaris. The following will show our success in modeling.
Synechosistis PCC7942
The modeling from figure 1 to figure 5 belongs to the experiments of Synechosistis PCC7942 pigments.
Photosynthesis rate of algae
We want to use pigments to enhance the photosynthesis rate. Different pigments adsorb different wavelength of sunlight, and bring about different irradiance, temperature, and photosynthesis rate. These two models show the influence of irradiance and temperature on photosynthesis rate.
R=Rmax.i^n/(ki*exp(i.m)+i^n)
R
co2 productive rate
mol/g*min
0.000046
i
irradiance
uE/m^2
n
irradiance exponential constant
1.19
ki
productive coefficient
uE/(m^2)*s
174
m
constant
(m^2)*s /uE
0.0022
fig.1-1 Influence of irradiance on photosynthesis rate
R=A1exp(-E1/rT)-A2exp(-E2/rT)
R
co2 productive rate
A1
preexponential factor at i=400
1147.7
A2
preexponential factor at i=200
3.818*10^8
E1
activation energy at i=400
mol/J
42700
E2
activation energy at i=200
mol/J
77100
T
temperature
K
fig.1-2 Influence of temperature on photosynthesis rate
click to close
Simulation of energy absorption of each pigment
The simplified graph is used to calculate how much energy is absorbed by each pigment approximately, and also help us know the photon adsorption amount after conversion.
y=0.01*x-3.5, 400<=x<=500
y=1.5, 501<=x<=600
y=3-0.0025*x, 601<=x<=800
x:
y:
fig.2 Simulation of energy absorption of each pigment
click to close
Microalgae productivity in different temperature
After we get the influential degree on temperature, we can use our modeling to predict the productivity of microalgae at different temperature without other affecting factors. It is the modeling to ensure that our experiments are under control.
U = Umax*Kss
Umax = A*exp(-E/RT)
U
specific growth rate
day^-1
Umax
maximum specific growth rate
day^-1
Kss
substrate parameter
1
A
constant
day^-1
1.0114*10^10
E
activation energy
cal/mol
6842
R
gas constant
cal/K*mol
8.314
fig.3 Microalgae productivity in different temperature
click to close
Microalgae productivity in different pH
When our Synechosistis PCC7942 grows at each phase, the equilibrium of pH value is different. This model can be used to collocate with our device, and also accomplishing the purpose of enhance productivity.
R=A1exp(-B1/ph)-A2exp(-B2/pH)
R
co2 productive rate
A1
preexponential factor at i=400
8.625*10^-5
A2
preexponential factor at i=200
1.83885*10^-2
B1
activation energy at i=400
mol/J
6.45
B2
activation energy at i=200
mol/J
69.2
R: Co2 productive rate
A1: preexponential factor at i=400 //8.625*10^-5
A2: preexponential factor at i=200 //1.83885*10^-2
B1: activation energy at i=400 mol/J //6.45
B2: activation energy at i=200 mol/J //69.2
fig.4 Microalgae productivity in different pH
click to close
The relation between photosynthetic rate and total yield
The model tells us that theoretically there is no faster photosynthetic rate, only if more energy is absorbed. After working with other modeling, we can establish the relation between photosynthetic rate and total yield for the purpose of best balance.
R=Rmax.e^n/(ke*exp(e.m)+e^n)
Rmax: maximum rate mol/g*min //0.000046
e: absorbed energy w/m^2
n: energy exponential constant//1.252
ke: productive coefficient uE/(m^2)*s //157.88
m: constant (m^2)*s /uE//0.0035
fig.5 The relation between photosynthetic rate and total yield
click to close
Chlorella vulgaris
The modeling from figure 6 to figure 12 belongs to the experiments of Chlorella vulgaris nitrogen starvation.
Growth curve of Chlorella vulgaris
The timing of adding engineered E.coli or purified protein to Chlorella vulgaris culture is critical to our project. By analyzing the initial and final biomass concentration data, the instantaneous rate, which is based on reference time and other lab environment data, would be gained. We have simulated the change in biomass concentration throughout the culture cycle. The intermittent information in the culture medium at each point is ultimately gained through combining other modeling results, which aims to determine the best timing and 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.6-1 Growth curve of Chlorella vulgaris
fig.6-2 Growth rate of Chlorella vulgaris
click to close
Oil accumulation & Nirogen source consumption
By simulating common system of oil accumulation and nitrogen source consumption, we can not only get the reference data before the improvement, but also make it as a basic equation after joining some parameters or organisms 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.7 Oil accumulation and nirogen source consumption at normal situation
click to close
Biomass in different nitrogen concentration
To find out the best quantity of nitrogen removal, we model several situations of decreasing the biomass in different environment with different concentration of nitrogen, and then we can find the best productivity by comparison.
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.8 Biomass in different nitrogen concentration
click to close
Nitrogen concentration in nitrogen starvation
We put normal and modified nitrogen source systems together to see their demonstration, like speed and occasion. By constructing this model, we can find out the declining rate of each state, and then adjust experiments.
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.9 Nitrogen source in nitrogen starvation
click to close
Oil accumulation in nitrogen starvation
We predict that total lipid will increase under nitrogen starvation. The modeling provides the theoretical information of the maximum of productivity. This graph shows that if we use symbiotic microbe to make nitrogen source isolated from the system temporarily and successfully, the productivity will be enhanced.
dp/dt=k1(dx/dt)^2+k2(dx/dt)(x)+e
p: lipid concentrtion
K1: growth correlation coefficient g^2/g^2 //122.40085
K2: non-growth correlation coefficient g^-1 //0.28736
e: a perturbation g/l*hr //-0.078
fig.10 Oil accumulation in nitrogen starvation
click to close
Population of Co-cultured Chlorella vulgaris and Modified E.coli
According to our reference of experiment data, we find that E.coli can build a relationship, which is like symbiosis, with Chlorella vulgaris. Therefore, we build a model and use three kinds of values from different situation to simulate their change when they are co-cultured. According to this, we get the proper experimental proportion of them at each need.
x2=(ax-x^2/(1+b*x*z))/Rx+x/Yx
z2=(cz-z^2/(1+g*z*x))/Rz+z/Yz
X: chlorella vugaris
Z: e.coil
Rx: symbiosis coefficient g/hr //1.0000023
Rz: symbiosis coefficient g/hr //1.178
Yx: correlation coefficient//12.576
Yz: correlation coefficient//2.276
a: population constant //0.80467
c: population constant//0.61198
b: relative parameter //0.00027
g: relative parameter //0.0013
fig.11-1 Population of co-cultured Chlorella and modified E.coli
fig.11-2 Population of co-cultured Chlorella and modified E.coli
fig.11-3 Population of co-cultured Chlorella and modified E.coli
click to close
Nitrogen-lipid plot
This chart demonstrates the connection between initial nitrogen concentration and final lipid proportion in algae cell, and it tell us the approximate trend.
l=k(ln(b(ns+a))^-1)-e
l: lipid proportion in cell
k: constant g/100g //1.13372
b: yield coefficient//1.57172
ns: initial nitrogen concentration
a: regression constant//0.51653
e: a perturbation g/100g//-55.2776
fig.12 Nitrogen-lipid plot
click to close
Modeling is an extremely important part to our project, because it helps us accurately check and predict the results of the experiments, which are worked in the wet lab. In our project, there are two essential types of microalgae that play very important roles, Synechosistic PCC7942andChlorella vulgaris. The following will show our success in modeling.
Synechosistis PCC7942
The modeling from figure 1 to figure 5 belongs to the experiments of Synechosistis PCC7942 pigments.
We want to use pigments to enhance the photosynthesis rate. Different pigments adsorb different wavelength of sunlight, and bring about different irradiance, temperature, and photosynthesis rate. These two models show the influence of irradiance and temperature on photosynthesis rate.
R=Rmax.i^n/(ki*exp(i.m)+i^n)
| R | co2 productive rate | mol/g*min | 0.000046 |
|---|---|---|---|
| i | irradiance | uE/m^2 | |
| n | irradiance exponential constant | 1.19 | |
| ki | productive coefficient | uE/(m^2)*s | 174 |
| m | constant | (m^2)*s /uE | 0.0022 |
fig.1-1 Influence of irradiance on photosynthesis rate
R=A1exp(-E1/rT)-A2exp(-E2/rT)
| R | co2 productive rate | ||
|---|---|---|---|
| A1 | preexponential factor at i=400 | 1147.7 | |
| A2 | preexponential factor at i=200 | 3.818*10^8 | |
| E1 | activation energy at i=400 | mol/J | 42700 |
| E2 | activation energy at i=200 | mol/J | 77100 |
| T | temperature | K |
fig.1-2 Influence of temperature on photosynthesis rate
The simplified graph is used to calculate how much energy is absorbed by each pigment approximately, and also help us know the photon adsorption amount after conversion.
y=0.01*x-3.5, 400<=x<=500
y=1.5, 501<=x<=600
y=3-0.0025*x, 601<=x<=800
x:
y:
fig.2 Simulation of energy absorption of each pigment
After we get the influential degree on temperature, we can use our modeling to predict the productivity of microalgae at different temperature without other affecting factors. It is the modeling to ensure that our experiments are under control.
U = Umax*Kss
Umax = A*exp(-E/RT)
| U | specific growth rate | day^-1 | |
|---|---|---|---|
| Umax | maximum specific growth rate | day^-1 | |
| Kss | substrate parameter | 1 | |
| A | constant | day^-1 | 1.0114*10^10 |
| E | activation energy | cal/mol | 6842 |
| R | gas constant | cal/K*mol | 8.314 |
fig.3 Microalgae productivity in different temperature
When our Synechosistis PCC7942 grows at each phase, the equilibrium of pH value is different. This model can be used to collocate with our device, and also accomplishing the purpose of enhance productivity.
R=A1exp(-B1/ph)-A2exp(-B2/pH)
| R | co2 productive rate | ||
|---|---|---|---|
| A1 | preexponential factor at i=400 | 8.625*10^-5 | |
| A2 | preexponential factor at i=200 | 1.83885*10^-2 | |
| B1 | activation energy at i=400 | mol/J | 6.45 |
| B2 | activation energy at i=200 | mol/J | 69.2 |