IGEM:Imperial/2010/Michaelis Menten

Model based on Michaelis Menten Kinetics (Weeks 4 and 5)

Motivation: We have come up with a simple concept of amplification of output done by enzymes. Before the final constructs are assembled within the bacterial ogranism, it is beneficial for us to model the behaviour of our design.

The questions that need to be answered:

1. How beneficial is the use of amplification? (compare speeds of response of transcription based output to amplified outputs)
2. How many amplification steps are beneficial to have? (if too many amplification steps are involved, the associated time delay with expressing even amplfiied output may prove not to be beneficial.)
3. Does mixing of amplfication levels have a negative influence on the output? Is it better to use TEV all the way or HIV1? Modelling should allows us to make a decision on which design is more efficient.

First Model

HIV1

At each stage of amplification a distinct protease is being used

Equations m' = k_ho - d_ho * m p_h' = k_h * m - d_h * p_h p_ts' = k_ts * p_h - d_ts * p_ts p_g' = k_g * p_ts - d_g * p_g

Parameters k_ho...transcription rate of HIV1 d_ho...degradation rate ogf mRNA coding for HIV1 k_h...translation rate of HIV1 d_h...degradation rate of HIV1 k_ts...production rate of TEV by HIV1 d_ts...degradation rate of TEV k_g...production rate of GFP by TEB d_g...degradation rate of GFP

TEV

TEV is used at both stages of amplification

Equations m' = k_to - d_to * m p_t' = k_t * m - d_t * p_t p_ts' = k_ts * p_t - d_ts * p_ts p_g' = k_g1 * p_t + k_g2 * p_ts - d_g * p_g

Parameters k_to...rate of transcription by TEV d_to...degradation rate of mRNA coding for TEV k_t...rate of translation of TEV d_t...degradation rate of TEV k_ts...rate of production (fusion) of split TEV d_ts...degradation rate of split TEV k_g1...rate of production of GFP by full TEV k_g2...rate of production of GFP by split TEV d_g...degradation rate of GFP

Improved Model

Model improved to account for the enzymes (protease action)

Implementation in Matlab

The Matlab code for the different stages of amplification and diagrams can be found here.

Kinetic constants

Quality	GFP	TEV	split TEV	split GFP
Km and Kcat	Doesn't apply	TEV constants (Km and kcat)	40% of whole TEV	Doesn't apply
half-life or degradation rate	Half-life of GFP in Bacillus = 1.5 hours - ref. Chris	?	?	Half-life shorter than GFP
production rate in B.sub	?	?	?	?

Conclusion

We couldn't 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. It's magnitude varies depending on the constants. There doesn’t seem to be much difference in substitution of TEV with HIV1.