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Meeting with Matthieu Bultelle

For our first model (simple GFP production):

General remarks:

  • Half-life is approximately 20 minutes
  • Time-constant = 1/d [1/s] (d is the degradation constant)
  • GFP degradation is generally long
  • mRNA degradation is generally fast
  • Chemical bindings is generally very fast [<ms]
  • Threshold of detection for GFP. [p] has to be bigger than the threshold value. We want a fast rise to the threshold value. This system has an analytical solution, for which we can solve: p = (s/d)*(1-e^(-dt)).
  • How do we find threshold values? Literature or experiments
  • General constraints for our system are: fast rise to the threshold and crossing threshold as early as possible

For our second model:

(Gene activated by stimulus, s varies with [activator], enzyme cleaves GFP)

We cannot use Michaelis-Menten because of the assumption that it uses:

  • Vmax is proportional to the overall concentration of the enzyme.

But we are producing enzyme, so Vmax will change! Therefore, the conservation E0 = E + ES does not hold for our system.

  • Substrate >> Enzyme.

Since we are producing both substrate and enzyme, we have roughly the same amount of substrate and enzyme.

  • Enzyme affinity to substrate has to be high.

We cannot use the Michaelis-Menten model, so we have to solve from 1st principle (which just means writing down all of the biochemical equations and solving for these). When simulating, change orders of magnitude to see what our system does. Remember: Cascading introduces delays, however, the advantage of cascading is a fast rise to the threshold value.


  • There are three states that TEV can be in: free, degraded or bound+working

We need to find the degradation rate of TEV. If the half-life is quite big (~10 hours) then we could use a modified version of Michaelis-Menten.

  • What happens if TEV degrades very fast?

Steady-state; There won't be many ensymes. Therefore, Vmax will be very small and our system won't be very efficient.


  • Substrate: whole TEV
  • Product: split TEV
  • Enzyme: HIV
  • Model the recombination of split TEV!
  • Don't forget amplification of noise!