Team:IBB Pune/Modeling
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- | <p><span style="font-weight:bold; font-size:200%; color:# | + | <p><span style="font-weight:bold; font-size:200%; color:#006600;">Modelling</span></p></html> |
<p>The aim of the modelling aspect of our project is to develop simulations that would enable us to predict the behavior of the export tag with the Snowdrift Game as the backdrop. </p> | <p>The aim of the modelling aspect of our project is to develop simulations that would enable us to predict the behavior of the export tag with the Snowdrift Game as the backdrop. </p> | ||
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- | <p><span style="font-weight:bold; font-size:200%; color:# | + | <p><span style="font-weight:bold; font-size:200%; color:#006600;"> |
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Project 1- A Model Of The Snowdrift Game</span> | Project 1- A Model Of The Snowdrift Game</span> | ||
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This model is for a Single iteration of the experiment i.e. the culture is initiated in shaker flask and allowed to grow. In order to find ESS or stable equilibria, we will have to repeatedly subculture the cells under similar conditions, by replacing the medium or supplying fresh medium. In such a setup, the input for the next cycle of experiments will be the output of the previous cycle of experiments. | This model is for a Single iteration of the experiment i.e. the culture is initiated in shaker flask and allowed to grow. In order to find ESS or stable equilibria, we will have to repeatedly subculture the cells under similar conditions, by replacing the medium or supplying fresh medium. In such a setup, the input for the next cycle of experiments will be the output of the previous cycle of experiments. | ||
- | = | + | <span style="font-weight:bold; font-size:125%; color:#006600;"><p>Assumptions</p></span> |
''At time t=0;'' | ''At time t=0;'' | ||
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*Extracellular Enzyme conc ('''Ec''') = 0 units/ml | *Extracellular Enzyme conc ('''Ec''') = 0 units/ml | ||
- | + | <span style="font-weight:bold; font-size:150%; color:#006600;"><p>Artificial assumptions</p></span> | |
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*<p>Glucose is consumed by all cells. Galactose is also consumed at the same rate Gc mg/cell/min/ml. | *<p>Glucose is consumed by all cells. Galactose is also consumed at the same rate Gc mg/cell/min/ml. | ||
*The metabolic benefit due to glucose and galactose is same.So effectively each lactose molecule gives rise to 2 glucose molecules</p> | *The metabolic benefit due to glucose and galactose is same.So effectively each lactose molecule gives rise to 2 glucose molecules</p> | ||
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*<p>Rate of degradation of enzyme is zero</p> | *<p>Rate of degradation of enzyme is zero</p> | ||
- | + | <span style="font-weight:bold; font-size:125%; color:#006600;"><p>Model</p></span> | |
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In this Model, | In this Model, | ||
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- | The Lactose that remains at time 't' is given by: | + | The Lactose that remains at time ''''t'''' is given by: |
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L = L - L * Ec * k2 .... (5) | L = L - L * Ec * k2 .... (5) | ||
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- | The net Glucose present in the medium at time 't' is given by: | + | The net Glucose present in the medium at time ''''t'''' is given by: |
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G = G +(( 2* L* Ec* k2)-( N * Gc) .... (6) | G = G +(( 2* L* Ec* k2)-( N * Gc) .... (6) | ||
- | + | <span style="font-weight:bold; font-size:125%; color:#006600;"><p>Results</p></span> | |
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[[Image:Pic1.GIF |center|400px|thumbnail|Plot of lactose and glucose levels at k2=1, Gc = 0.0001 mg/cell/min, R=0.99, c=0.001 ]] | [[Image:Pic1.GIF |center|400px|thumbnail|Plot of lactose and glucose levels at k2=1, Gc = 0.0001 mg/cell/min, R=0.99, c=0.001 ]] | ||
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Latest revision as of 00:03, 22 October 2009