Team:Northwestern/Project/Modeling
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(→Modeling) 

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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.  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 Development'''== 
  +  The following schematic summarizes the mathematical model we formulated to describe our system.  
  +  
  +  
[[Image:SuperModeling.jpg600pxcenter]]  [[Image:SuperModeling.jpg600pxcenter]]  
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* C: Enzyme Substrate Complex (CHS3(NAcetylGlucosamine)Chitin or (NAG)n Complex)  * C: Enzyme Substrate Complex (CHS3(NAcetylGlucosamine)Chitin or (NAG)n Complex)  
* P: Protein Product (Chitin or (NAG)n+1)  * P: Protein Product (Chitin or (NAG)n+1)  
+  
+  
+  ==='''Constants'''===  
+  
+  Rate Constants:  
+  
+  * kIin  Inducer diffusion into cell from surrounding environment  
+  * kIout  Inducer diffusion out of cell to surrounding environment  
+  * kIif  Inducer and Repressor binding to form InducerRepressor Complex  
+  * kIir  InducerRepressor Complex unbinding to form Inducer and Repressor  
+  * kDbf  Repressor binding to DNA to form DNARepressor Complex  
+  * kDbr  DNARepressor Complex unbinding to form free unbound DNA  
+  * ktcribe  transcription  
+  * ktlate  translation  
+  * ksin  endogenous substrate production  
+  * kCf  SubstrateEnzyme Complex Formation  
+  * kCr  SubstrateEnzyme Complex unbinding to form Substrate and Enzyme  
+  * kP  SubstrateEnzyme Complex forming Product and Enzyme  
+  * kEdeg  Enzyme Degredation  
+  * kRdeg  RNA Degredation  
+  * kPdeg  Protein Degredation  
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The differential of the variables were found as follows:  The differential of the variables were found as follows:  
  * dIin = kIin*Iex  kIex*Iin + kIir*Ii  kIif*Iin*i  +  * dIin/dt = kIin*Iex  kIex*Iin + kIir*Ii  kIif*Iin*i 
  * dIi = kIif*Iin*i  kIir*Ii  +  * dIi/dt = kIif*Iin*i  kIir*Ii 
  * di = kIir*Ii  kIif*Iin*i + kDbr*Db  kDbf*i*Dunb  +  * di/dt = kIir*Ii  kIif*Iin*i + kDbr*Db  kDbf*i*Dunb 
  * dDb = kDbf*i*Dunb  kDbr*Db  +  * dDb/dt = kDbf*i*Dunb  kDbr*Db 
  * dDunb = kDbr*Db  kDbf*i*Dunb  +  * dDunb/dt = kDbr*Db  kDbf*i*Dunb 
  * dRe = ktscribe*Dunb  kRdeg*Re  +  * dRe/dt = ktscribe*Dunb  kRdeg*Re 
  * dE = ktslate*Re  kEdeg*E + kCr*CC + kP*CC  kCf*E*Si  +  * dE/dt = ktslate*Re  kEdeg*E + kCr*CC + kP*CC  kCf*E*Si 
  * dSi = ksin*So  kCf*E*Si + kCr*CC  +  * dSi/dt = ksin*So  kCf*E*Si + kCr*CC 
  * dCC = kCf*E*Si  kCr*CC  kP*CC  +  * dCC/dt = kCf*E*Si  kCr*CC  kP*CC 
  * dP = kP*CC  kPdeg*P  +  * dP/dt = kP*CC  kPdeg*P 
  ==='''  +  ==='''Assumptions'''=== 
  +  In order to determine the initial or steady state concentrations of the involved species and to determine the rate constants, the following assumptions were made:  
  
  IPTG  +  ===='''IPTG Diffusion'''==== 
  The  +  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.  
  
  +  ===='''Constant Determination'''====  
  +  Initially, the following initial concentration values were assumed:  
  +  * Iex: Described in the previous section  
+  * Iin: Internal IPTG initially assumed to be 0  
+  * Ii: 0, because no IPTG means IPTGrepressor complex  
+  * i: Value acquired from [5] as between 10^5 and 10^4 and adjusted to 9.973*10^5  
+  * Db: Calculated, knowing the expression vector is a 200 copy number plasmid; of the DNA, approximated that 90.08% is bound  
+  * Dunb: Calculated, knowing the expression vector is a 200 copy number plasmid; of the DNA, approximated that 9.92% is bound  
+  * Re: Determined to be 1.82735*10^4 by achieving steady state with the model  
+  * E: Determined to be 6.08*10^4 by achieving steady state with the model  
+  * So: External Substrate calculated by using amount added in enriched media as 33.9  
+  * Si: Determined from [3] to be 10^1  
+  * C: Determined to be 3*10^5by achieving steady state with the model  
+  * P: Determined to be 1*10^4 by achieving steady state with the model  
  +  The rate constant values were assumed to be the following:  
  +  * kIin: .05 yielded reasonable diffusion times  
+  * kIex: .05 since simple diffusion, the internal rate constant must be similar if not identical to the external rate constant  
+  * kIif: .01 yielded reasonable repressor/Inducer interactions  
+  * kIir: .01 yielded reasonable repressor/Inducer interactions  
+  * kDbf: 100 yielded reasonable DNA/repressor interactions  
+  * kDbr: .0011 yielded reasonable DNA/repressor interactions  
+  * ktscribe: .01 yielded reasonable production levels  
+  * ktslate: .01 yielded reasonable production levels  
+  * kRdeg: .003 yielded reasonable degredation  
+  * kEdeg: .003 yielded reasonable degredation  
+  * kPdeg: .003 yielded reasonable degredation  
+  * ksin: 0.000000009 yielded reasonable internalization of substrate  
+  * kCf: .01 yielded reasonable production levels  
+  * kCr: .01 yielded reasonable production levels  
+  * kP: .01 yielded reasonable production levels  
+  
+  
+  =='''Results'''==  
The plots of the noninduced and the induced system are as follows:  The plots of the noninduced and the induced system are as follows:  
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*Differentiate protein production between expression vectors with different Copy Number Plasmids.  *Differentiate protein production between expression vectors with different Copy Number Plasmids.  
+  
+  [[Image:loopydoops.gif]]  
=='''References'''==  =='''References'''== 
Revision as of 01:42, 28 October 2010
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Introduction / ObjectiveWe constructed a mathematical model to explore and characterize the operation as well as the modulation of our experimental system. In particular, we wanted to investigate the effect of varying parameters that we could experimentally modulate on the system. Those parameters include:
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:
IPTG DiffusionFirst, 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.
Constant DeterminationInitially, the following initial concentration values were assumed:
The rate constant values were assumed to be the following:
ResultsThe plots of the noninduced and the induced system are as follows:
Future ConcernsOverall, the model, though logical, is not yet fit for application, partially due to the lack of empirical data to which the model could be fit and/or tested. Once fit, the rate constant values and initial concentration values will be much more accurate. The following concerns deal primarily with problems that could possibly not be corrected even with empirical data.
Future WorkAside from being generally accurate, the model should perform the following functions:
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
