Team:Northwestern/Project/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 diffusing inducer.

Using simple enzyme kinetics equations, we elected to mathematically simulate the following model:

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.

This model was fitted with empirical data using cp-lacpi-gfp to estimate the rate constant, and therefore the effects of varying cp, lacpi, and rbs on enzyme and final product production.

MATLAB file provided upon request.

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

Pool Levels of UDP N-Acetylglucosamine and UDP NAcetylglucosamine-Enolpyruvate in Escherichia coli and Correlation with Peptidoglycan Synthesis DOMINIQUE MENGIN-LECREULX, BERNARD FLOURET, AND JEAN VAN HEIJENOORT* E.R. 245 du C.N.R.S., Institut de Biochimie, Universit' Paris-Sud, Orsay, 91405, France Received 9 February 1983/Accepted 15 March 1983 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC217602/pdf/jbacter00247-0262.pdf

Diffusion in Biofilms Philip S. Stewart Center for Biofilm Engineering and Department of Chemical Engineering, Montana State University–Bozeman, Bozeman, Montana, 59717-3980 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC148055/pdf/0965.pdf

Regulation of the Synthesis of the Lactose Repressor 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/jbacter00335-0105.pdf