Team:Northwestern/Project/Modeling
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(→Future Considerations) 

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=='''Results'''==  =='''Results'''==  
+  
+  ==='''1. IPTG Diffusion'''===  
+  
+  First, in order to determine the diffusion of IPTG when applied (sprayed) at the top layer throughout the biofilm, Fick's Diffusion equation was used to create a finitetimedifferential mathematical model, which is graphically displayed below.  
[[Image:loopydoops.gif]]  [[Image:loopydoops.gif]]  
+  
+  Once sprayed, the model predicts that the IPTG diffuses down the biofilm and stabilizes throughout the biofilm layer.  
+  
+  
+  ==='''2. Effect of Inducer on Product Generation'''===  
+  
+  As inducer levels are easily experimentally adjustable, we wanted to know the effect of the adjustment.  
+  
+  [[Image:NUigemmodeling1.jpg]]  
+  
+  As shown above, the model predicts that a greater level of IPTG leads to  
+  
+  
+  ==='''3. Effect of Repressor on Product Generation'''===  
+  
+  Repressor levels are also experimentally adjustable by changing the repressor producing segment of the part, and so we wanted to know the effect of the adjustment.  
+  
+  [[Image:NUigemmodeling2.jpg]]  
+  
+  As shown above, the model predicts that  
+  
+  
+  ==='''4. Effect of Promoter on Product Generation'''===  
+  
+  The promoter preceding the gene can be changed to different promoters, and we wanted to know the effect of this adjustment.  
+  
+  [[Image:NUigemmodeling3.jpg]]  
+  
+  As shown above, the model predicts that  
+  
+  
+  ==='''5. Effect of Ribosome Binding Site on Product Generation'''===  
+  
+  The Ribosome Binding Site preceding the gene can be changed to different Ribosome Binding Sites, and we wanted to know the effect of this adjustment.  
+  
+  [[Image:NUigemmodeling4.jpg]]  
+  
+  As shown above, the model predicts that  
+  
+  
+  ==='''6. Effect of DNA Copy Number on Product Generation'''===  
+  
+  The DNA part could be ligated into a different plasmids with varying copy numbers; we wanted to know the effect of this adjustment.  
+  
+  [[Image:NUigemmodeling5.jpg]]  
+  
+  As shown above, the model predicts that  
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*Currently the model only predicts only a 10% increase in product when induced by what is suspected to be a significant concentration of inducer.  *Currently the model only predicts only a 10% increase in product when induced by what is suspected to be a significant concentration of inducer.  
*The model assumes constant substrate production rate; this assumption may or may not be accurate.  *The model assumes constant substrate production rate; this assumption may or may not be accurate.  
+  
=='''References'''==  =='''References'''== 
Revision as of 02:28, 28 October 2010
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Introduction / ObjectiveThe general objective of our experimental system is to perform the following functions:
The objective of our model is to explore and characterize the system, and the effect of parameter modulation on the system. In terms of our iGEM project, this model was employed to explore the effect of IPTG concentration and diffusion, lacI concentration (determined by the combination part of constitutive promoter, ribosome binding site, lacI gene, double terminator, lac promoter/operon), and the ribosome binding site (of the final productproducing enzyme) on the concentrations of all species involved  described in the following sections  and especially on Chitin Synthase and Chitin concentration and the corresponding rates. Model DevelopmentThe following schematic summarizes the mathematical model we formulated to describe our system.
Variables
ConstantsRate Constants:
EquationsThe differential of the variables were found as follows:
AssumptionsIn order to determine the initial or steady state concentrations of the involved species and to determine the rate constants, the following assumptions were made:
First, Fick's Law of Diffusion was modeled through MATLAB. The diffusion constant used was 220um^2/s.[4] It was assumed that IPTG was not consumed nor degraded We also assumed that IPTG uptake was minor was compared to the concentration in the biofilm, and so that the external IPTG was determined solely by Fick's Law, not by internalization.
Initially, the following initial concentration values were assumed:
The rate constant values were assumed to be the following:
Results1. IPTG DiffusionFirst, in order to determine the diffusion of IPTG when applied (sprayed) at the top layer throughout the biofilm, Fick's Diffusion equation was used to create a finitetimedifferential mathematical model, which is graphically displayed below. Once sprayed, the model predicts that the IPTG diffuses down the biofilm and stabilizes throughout the biofilm layer.
2. Effect of Inducer on Product GenerationAs inducer levels are easily experimentally adjustable, we wanted to know the effect of the adjustment. As shown above, the model predicts that a greater level of IPTG leads to
3. Effect of Repressor on Product GenerationRepressor levels are also experimentally adjustable by changing the repressor producing segment of the part, and so we wanted to know the effect of the adjustment. As shown above, the model predicts that
4. Effect of Promoter on Product GenerationThe promoter preceding the gene can be changed to different promoters, and we wanted to know the effect of this adjustment. As shown above, the model predicts that
5. Effect of Ribosome Binding Site on Product GenerationThe Ribosome Binding Site preceding the gene can be changed to different Ribosome Binding Sites, and we wanted to know the effect of this adjustment. As shown above, the model predicts that
6. Effect of DNA Copy Number on Product GenerationThe DNA part could be ligated into a different plasmids with varying copy numbers; we wanted to know the effect of this adjustment. As shown above, the model predicts that
Future ConsiderationsAlthough the this model, as shown, captures the topology of our engineered network, its predictive prowess can be improved by obtaining constants and parameters from empirical observations. In acquiring data, using the actual Chitin vector would be most helpful, but if not viable, then an alternative method is to characterize the system using GFP instead of CHS3 and fluorescence as an indicator of product generation. The resulting data could be used to fit the parameters of the model. Possible future work:
References1. A novel structured kinetic modeling approach for the analysis of plasmid instability in recombinant bacterial cultures William E. Bentley, Dhinakar S. Kompala Article first published online: 18 FEB 2004 DOI: 10.1002/bit.260330108 http://onlinelibrary.wiley.com/doi/10.1002/bit.260330108/pdf
Jongdae Lee, W. Fred Ramirez Article first published online: 19 FEB 2004 DOI: 10.1002/bit.260390608 http://onlinelibrary.wiley.com/doi/10.1002/bit.260390608/pdf
DOMINIQUE MENGINLECREULX, BERNARD FLOURET, AND JEAN VAN HEIJENOORT* E.R. 245 du C.N.R.S., Institut de Biochimie, Universit' ParisSud, Orsay, 91405, France Received 9 February 1983/Accepted 15 March 1983 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC217602/pdf/jbacter002470262.pdf
Philip S. Stewart Center for Bioﬁlm Engineering and Department of Chemical Engineering, Montana State University–Bozeman, Bozeman, Montana, 597173980 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC148055/pdf/0965.pdf
PATRICIA L. EDELMANN' AND GORDON EDLIN Department of Genetics, University of California, Davis, California 95616 Received for publication 21 March 1974 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC245824/pdf/jbacter003350105.pdf
MATLAB mfile
%IPTG PREDETERMINATION
