Team:Northwestern/Project/Modeling
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=='''Modeling'''== | =='''Modeling'''== | ||
+ | |||
+ | Status: Under Development | ||
+ | |||
+ | The purpose of Modeling was to characterize expression vectors in terms of expression level and time-delay, all activated by a diffused inducer. | ||
+ | |||
Using simple enzyme kinetics equations, we elected to mathematically simulate the following model: | Using simple enzyme kinetics equations, we elected to mathematically simulate the following model: | ||
[[Image:SuperModeling.jpg|500px|center]] | [[Image:SuperModeling.jpg|500px|center]] | ||
- | |||
- | Matlab was used to generate a theoretical model where IPTG would diffuse down the biofilm as according to Fick's Law of Diffusion. | + | Variables: |
+ | Iex: External Inducer, determined by diffusion through Fick's law (IPTG in our experiment) | ||
+ | Iin: Internal Inducer (IPTG) | ||
+ | Ii: Inducer bound to Repressor (IPTG bound to lacI) | ||
+ | i: Repressor (lacI) | ||
+ | Db: Repressor-bound DNA (lacI-bound DNA(CHS3) region in plasmid) | ||
+ | Dunb: transcribe-able or Repressor-unbound DNA (lacI-unbound DNA(CHS3)) | ||
+ | Re: mRNA for Enzyme (CHS3 mRNA) | ||
+ | E: Enzyme (CHS3) | ||
+ | S: Substrate (N-Acetyl Glucosamine) | ||
+ | C: Enzyme Substrate Complex (CHS3-(N-Acetyl-Glucosamine)-Chitin or (NAG)n Complex) | ||
+ | P: Protein Product (Chitin or (NAG)n+1) | ||
+ | |||
+ | Matlab was used to generate a theoretical model where IPTG would diffuse down the biofilm as according to Fick's Law of Diffusion and initiate the process. | ||
The extracellular substrate concentration was assumed to be much greater than the uptake/use, and so would diffuse in at a constant rate. | The extracellular substrate concentration was assumed to be much greater than the uptake/use, and so would diffuse in at a constant rate. | ||
This model was fitted with empirical data using cp-lacpi-gfp to estimate the effect of varying cp, lacpi, and rbs on enzyme and final product production. | This model was fitted with empirical data using cp-lacpi-gfp to estimate the effect of varying cp, lacpi, and rbs on enzyme and final product production. | ||
+ | |||
+ | References: | ||
+ | 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 | ||
+ | |||
+ | Mathematical modeling of induced foreign protein production by recombinant bacteria | ||
+ | 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 | ||
|} | |} |
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