Wiki/Team:Imperial College London/Drylab/Autoinduction/Analysis/Kompala

Assumptions

• Michaelis Menten Assumptions (see drug kinetics model) have been applied in the kinetics of consumption of enzyme and substrate
• Effects of competition and induction can be represented by probabilistic variables (u and v) and are directly dependent on the rate of consumption of any given substrate S_i within the mixture
• More details about assumptions made for each individual variable are described in the paper.

Predictions

• In a mixture of substrates, glucose is always used up first by the culture, and then any other secondary source present in the medium.
• The time length of the primary and secondary exponential phases of growth in the biomass depend on the initial concentration of carbon sources.
• This will help to predict the switching point between two sources.
• In our project:
  • The primary Carbon source: Provides repression of the CRP promoter and delays the start of the encapsulation phase (Module 2)
  • The secondary Carbon Source: Will power the system once the primary source has been used up. Finding the best secondary carbon source can help us draw a relationship with the output yield of colanic acid.

The actual model...
When a mixture of substrates is placed in a Biomass (B), the interaction of the Biomass with any given substrate (S_(i)) is given by:

E_i is the enzyme catalyzing the metabolism of S_(i )and Y_(i ) is a yield coefficient for the particular substrate. They then define a generic formula for the system of differential equations given by:

Further explanation: