Team:DTU-Denmark/Kinetic Model

From 2013.igem.org

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It is necessary to know or estimate the enzyme concentration if kcat values are used. The Taipeh Team did this with another kinetic model, but we are missing information about many of this models parameters so the result would be very inexact. Therefore we chose to use four different enzyme concentrations in our model: 100, 500, 1000 and 100 000 enzymes per cell corresponding to low, medium, high and very high concentrations of enzyme. These numbers are based on [4].
It is necessary to know or estimate the enzyme concentration if kcat values are used. The Taipeh Team did this with another kinetic model, but we are missing information about many of this models parameters so the result would be very inexact. Therefore we chose to use four different enzyme concentrations in our model: 100, 500, 1000 and 100 000 enzymes per cell corresponding to low, medium, high and very high concentrations of enzyme. These numbers are based on [4].
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 +
-!
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We also need to know how much ammonia the water we want to treat will contain. The ammonia concentration in different types of waste water is given in [5] as 1 mg/l in aquatic cultures, 10 mg/l for municipal waste water and more than 100 mg/l for industrial waste water. So the concentrations we want to look at in our model are: 1 mg/l, 10 mg/l, 100 mg/l and 500 mg/l ammonia.
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 +
The modeling was done in MATLAB using the Systems Biology Toolbox [6] and the models equations are given below. Results are shown in Figures 1-2.
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 +
-!
== The reactor ==
== The reactor ==
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'''2.1 Continuous stirred tank reactor CSTR'''
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With our genetically engineered E. colis we want to treat ammonia polluted waste water. The fastest way to do this would be in a continuous process like a continuous stirred tank reactor (CSTR). Ideally this process would generate an amount of nitrous oxide that is so large that the energy needed for running the system can be delivered by catalytically decomposing the nitrous oxide. We are planing to test a simple CSTR system but hold the engineered E. coli back in the reactor, so that the outgoing water is free of bacteria. Also we will need to use two CSTRs in sequence because the second mutant requires anaerobic conditions. A picture of two CSTR reactors in series can be found in Figure 3. Another interesting solution would be to grow a bacterial biofilm on solid carriers as shown in Figure 4, a technology known as moving bed biofilm reactor.
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 +
A CSTR can be bilanced using the following equation [7]:
 +
 +
-!
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 +
Figure 1: Kinetic modeling of Mutant 1. Nitrite concentration over time based on kinetic parameters found in literature and for different enzyme and substrate (here NO<sub>2</sub>) concentrations.
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 +
-!
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 +
Figure 2: Kinetic modeling of Mutant 2. Nitrous oxide concentration over time based on kinetic parameters found in literature and for different enzyme and substrate (here NO<sub>2</sub>) concentrations.
 +
 +
-!
 +
 +
Figure 3: Two CSTRs in series taken from http://www.umich.edu/ elements/a-syLearn/bits/cstr/.
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 +
-!
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Figure 4: In moving bed biofilm reactors the biofilm is grown on carriers as shown above. The picture is taken from http://www.hydrotech-group.com/en/products/industrial-wwtp/mbbr/.
 +
 +
-!
 +
For a CSTR perfect mixing is assumed, which means that the concentrations of all compounds are the same everywhere in the reactor and also at the exit point. If the system is run in steady state the so called design equation can be used to calculate the necessary volume of the reactor:
 +
 +
-!
 +
 +
We can split the molar flow rate of species j into concentration of species j times flow. The reaction rate is dependent on the substrate concentration and can be described with Michaelis-Menten kinetics in our case: -! . So we can calculate the volume of the first reactor for series of different flow rates and substrate concentrations.
 +
To include the right enzyme concentration we need to estimate how many cells per litre we will have in the reactor and how many enzymes each cell will contain. It was estimated that the cells take up 40% of the volume in the reactor and that they contain 750 copies of each protein of the pathway (see above) resulting in a enzyme concentration of 2.4917x10<sup>-4</sup> mmol/l.
== References ==
== References ==
{{:Team:DTU-Denmark/Templates/EndPage}}
{{:Team:DTU-Denmark/Templates/EndPage}}

Revision as of 14:22, 28 September 2013

Kinetic model of the Pathway

We are applying kinetic modeling to investigate how long it takes a cell to produce a certain amount of nitrous oxide. The reactions of the pathway we are trying to integrate in E. coli are:

Mutant 1: NH3 → NH2OH → NO2

Mutant 2: NO2 → NO → N2O

The iGEM team from Taipei in 2012 was using Nir and Nos in their project as well and did some kinetic modeling based on literature research. To describe product formation by the enzymes they used the Michaelis-Menten approach:

-!

Some of the necessary parameters can be found in literature, they are listed in Table 1.

It is necessary to know or estimate the enzyme concentration if kcat values are used. The Taipeh Team did this with another kinetic model, but we are missing information about many of this models parameters so the result would be very inexact. Therefore we chose to use four different enzyme concentrations in our model: 100, 500, 1000 and 100 000 enzymes per cell corresponding to low, medium, high and very high concentrations of enzyme. These numbers are based on [4].

-! We also need to know how much ammonia the water we want to treat will contain. The ammonia concentration in different types of waste water is given in [5] as 1 mg/l in aquatic cultures, 10 mg/l for municipal waste water and more than 100 mg/l for industrial waste water. So the concentrations we want to look at in our model are: 1 mg/l, 10 mg/l, 100 mg/l and 500 mg/l ammonia.

The modeling was done in MATLAB using the Systems Biology Toolbox [6] and the models equations are given below. Results are shown in Figures 1-2.

-!

The reactor

2.1 Continuous stirred tank reactor CSTR

With our genetically engineered E. colis we want to treat ammonia polluted waste water. The fastest way to do this would be in a continuous process like a continuous stirred tank reactor (CSTR). Ideally this process would generate an amount of nitrous oxide that is so large that the energy needed for running the system can be delivered by catalytically decomposing the nitrous oxide. We are planing to test a simple CSTR system but hold the engineered E. coli back in the reactor, so that the outgoing water is free of bacteria. Also we will need to use two CSTRs in sequence because the second mutant requires anaerobic conditions. A picture of two CSTR reactors in series can be found in Figure 3. Another interesting solution would be to grow a bacterial biofilm on solid carriers as shown in Figure 4, a technology known as moving bed biofilm reactor.

A CSTR can be bilanced using the following equation [7]:

-!

Figure 1: Kinetic modeling of Mutant 1. Nitrite concentration over time based on kinetic parameters found in literature and for different enzyme and substrate (here NO2) concentrations.

-!

Figure 2: Kinetic modeling of Mutant 2. Nitrous oxide concentration over time based on kinetic parameters found in literature and for different enzyme and substrate (here NO2) concentrations.

-!

Figure 3: Two CSTRs in series taken from http://www.umich.edu/ elements/a-syLearn/bits/cstr/.

-!

Figure 4: In moving bed biofilm reactors the biofilm is grown on carriers as shown above. The picture is taken from http://www.hydrotech-group.com/en/products/industrial-wwtp/mbbr/.

-! For a CSTR perfect mixing is assumed, which means that the concentrations of all compounds are the same everywhere in the reactor and also at the exit point. If the system is run in steady state the so called design equation can be used to calculate the necessary volume of the reactor:

-!

We can split the molar flow rate of species j into concentration of species j times flow. The reaction rate is dependent on the substrate concentration and can be described with Michaelis-Menten kinetics in our case: -! . So we can calculate the volume of the first reactor for series of different flow rates and substrate concentrations. To include the right enzyme concentration we need to estimate how many cells per litre we will have in the reactor and how many enzymes each cell will contain. It was estimated that the cells take up 40% of the volume in the reactor and that they contain 750 copies of each protein of the pathway (see above) resulting in a enzyme concentration of 2.4917x10-4 mmol/l.

References