Team:SMS Shenzhen/Model

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SMS: Mathematical Modeling

1.Translation System

Consider a deterministic model for the central theorem.

We assume the reactions are homogenous, not compartmented, and are all 1st order reactions. Therefore, we may obtain the following model equations. In the model equation, we denote DNA as A, mRNA as B, and protein as C.

The parameters of the model equations:

These equations can be written in matric form:

Where X and N are vectors comprised of concentrations of A, B and C, dX/dt is the rate of change of X, θ is a vector of model parameters.

1.iPTG Induction Model

The main purpose of this model is the prediction of intracellular iPTG concentration related to protein production.

Culture medium volume can be calculated using the difference between V and V_cel.

iPTG evolution can be written as

These two equations describe the variation with time of extracellular and intracellular IPTG concentration (subindex “e” denotes extracellular and sub-index “i” denotes intracellular) as function of the net transport rate (r) and dilution (first and second term on the right side). These two equations can both be derived using mass balances as shown below:

In which