IGEM:Imperial/2010/Michaelis Menten
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Contents 
Model based on Michaelis Menten Kinetics (Weeks 4 and 5)
Motivation
We came up with a simple concept of output amplification, which is enhanced by using enzymes. It is beneficial for us to model the behaviour of our design so that we will be able to answer the following questions.
 How beneficial is the use of amplification? (Compare speed of response of transcription (and translation) with 1 or 2step amplification)
 How many amplification steps are beneficial to have? Will further adding of amplification steps introduce too many time delays?
 Is it better to use TEV all or HIV1?
Modelling should allows us to make a decision on which design is the most efficient one.
First Model
HIV1
Equations

Parameters

TEV
Equations

Parameters

Improved Model which accounts for enzyme reactions (28/07/2010)
TEV
Equations

Implementation in Matlab
The Matlab code for the different stages of amplification and diagrams can be found here.
Kinetic constants
GFP  TEV  split TEV  split GFP  

Km and k_{cat}    K_{m} = 0.061; k_{cat} = 0.16; [1]  40% of value for TEV   
Halflife or degradation rate  Halflife in B.sub approximately 1.5 hours  ?  ?  Halflife shorter than GFP 
Production rate in B.sub  ?  ?  ?  ? 
Conclusion
We were not able to obtain all the necessary constants. Hence, we decided to make educated guesses about possible relative values between the constants as well as varying them and observing the change in output.
As the result, we concluded that the amplification happens at each amplification level proposed. The magnitude of amplification varies depending on the constants. There is not much difference between using TEV or HIV1.
References
 Kapust R. et al (2001) Tobacco etch virus protease: mechanism of autolysis and rational design of stable mutants with wildtype catalytic proficiency. Protein Engineering. [Online] 14(12), 9931000. Available from: http://peds.oxfordjournals.org/cgi/reprint/14/12/993 [Accessed 28th July 2010]