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Team:Bielefeld-Germany/Modell
From 2011.igem.org
(Created page with "{{Bielefeld_2011_Header}} ==Modelling of intracellular bisphenol A degradation== To model the BPA degradation by ''E. coli'' carrying BioBricks for BPA degradation (<partinfo>K...") |
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limit S<sub>2</sub> >= 0 | limit S<sub>2</sub> >= 0 | ||
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| + | The specific BPA degradation rate per cell q<sub>D</sub> is modelled with a Michaelis-Menten like kinetics. In the beginning of the cultivations, when ''E. coli'' growths on the imaginary substrate S<sub>1</sub>, there is no BPA degradation observed so the model looks like as follows: | ||
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| + | {BPA degradation} | ||
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| + | init BPA = BPA<sub>0</sub> | ||
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| + | BPA<sub>0</sub> = 0.53 | ||
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| + | dBPA/dt = if S<sub>1</sub> >= 0.01 then 0 else -q<sub>D</sub> * X | ||
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| + | q<sub>D</sub> = q<sub>D,max</sub> * BPA / (K<sub>BPA</sub> + BPA) | ||
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| + | q<sub>D,max</sub> = 0.013 | ||
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| + | K<sub>BPA</sub> = 1.6e-8 | ||
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| + | limit BPA >= 0 | ||
The modelling was done with the software [http://www.berkeleymadonna.com/ Berkeley Madonna] using [http://en.wikipedia.org/wiki/Runge–Kutta_methods#Common_fourth-order_Runge.E2.80.93Kutta_method common fourth-order Runge-Kutta] method to solve the equations. | The modelling was done with the software [http://www.berkeleymadonna.com/ Berkeley Madonna] using [http://en.wikipedia.org/wiki/Runge–Kutta_methods#Common_fourth-order_Runge.E2.80.93Kutta_method common fourth-order Runge-Kutta] method to solve the equations. | ||
Revision as of 12:42, 5 September 2011
Modelling of intracellular bisphenol A degradation
To model the BPA degradation by E. coli carrying BioBricks for BPA degradation (<partinfo>K123000</partinfo> and <partinfo>K123001</partinfo>) the cell growth of has to be described first. The observed growth of E. coli on (our) LB medium was [http://en.wikipedia.org/wiki/Diauxie diauxic] with two growth phases. Cell growth is in general described as
dX/dt = µ * X
with the specific growth rate µ and the cell count X. The specific growth rate is dependent on the concentration of the growth limiting substrate (e.g. glucose) and can be described as
µ = µmax S / (KS + S)
with the substrate concentration S, the Monod constant KS and the maximal specific growth rate µmax. Because LB medium is a complex medium we cannot measure the substrate concentration so we have to assume an imaginary substrate concentration. Due to the diauxic growth two different substrates are necessary to model the cell growth. The amount of a substrate S can be modelled as follows
dS/dt = qS * X
with the specific substrate consumption rate per cell qS. The whole model for the diauxic growth of E. coli on LB medium with two not measurable (imaginary) substrates looks like:
{Growth}
init x = x0
x0 = 0.133
dX/dt = µ * X
µ = if S1 >= 0.01 then µmax * S1 / (KS,1 + S1) else µmax * S2 / (KS,2 + S2)
µmax = 1.24
KS,1 = 10
KS,2 = 138.7
limit µ >= 0
limit X >= 0
{Substrate 1}
init S1 = S1,0
S1,0 = 6
dS1/dt = -qS,1 * X
qS,1 = 1.4
limit S1 >= 0
{Substrat 2}
init S2 = S2,0
S2,0 = 10
dS2/dt = if S1 >= 0.01 then 0 else -qS,2 * X
qS,2 = 0.32
limit S2 >= 0
The specific BPA degradation rate per cell qD is modelled with a Michaelis-Menten like kinetics. In the beginning of the cultivations, when E. coli growths on the imaginary substrate S1, there is no BPA degradation observed so the model looks like as follows:
{BPA degradation}
init BPA = BPA0
BPA0 = 0.53
dBPA/dt = if S1 >= 0.01 then 0 else -qD * X
qD = qD,max * BPA / (KBPA + BPA)
qD,max = 0.013
KBPA = 1.6e-8
limit BPA >= 0
The modelling was done with the software [http://www.berkeleymadonna.com/ Berkeley Madonna] using [http://en.wikipedia.org/wiki/Runge–Kutta_methods#Common_fourth-order_Runge.E2.80.93Kutta_method common fourth-order Runge-Kutta] method to solve the equations.
