# IGEM:IMPERIAL/2009/M2/Modelling/Analysis

The E.ncapsulator: the disease killer

# Preliminary Model 1: Genetic circuit

## Hypothesis

• When glucose concentrations are above threshold, there would not be any activation of production of colanic acid or trehalose.
• When glucose concentrations decrease below threshold, there will be strong activation of M2 and there will be an increase in protein production in the system.
• For decreased concentration of glucose, there will be increased amounts of colanic acid and trehalose produced.

## Equations

\begin{alignat}{2} \frac{d[m_i]}{dt} = \frac{km_i^{n_i}}{{[g]}^{n_i}+ km_i^{n_i}} - dm_i*[m_i] \qquad (1)\\ \frac{d[p_i]}{dt} = [m_i]*kp_i - dp_i*[p_i] \qquad (2)\\ where\ i = 1, 2, 3, 4, 5 \end{alignat}

### Legend

 Term Variable/Parameter Meaning/description 1 - RcsB 2 - B3023 3 - Waal Ligase 4 - OtsA 5 - OtsB g Variable Concentration of glucose mi Variable Concentration of ith mRNA pi Variable Concentration of ith protein ni Parameter Hill coefficient of ith mRNA

### Explanation of equations

• In equation (1), we have used a repressing hill function of glucose. This is because glucose, represses CRP, which activates our system. A decrease in [glucose] below threshold will activate M2 strongly.
• The genes are produced in parallel, hence the repressing hill function will appear in the mRNA equations, for all our proteins.

## Simulations

### Simulation 1: Effects of increasing glucose concentrations on production of protein

#### Explanations

• When there is a decrease in glucose concentration beyond threshold, there is a great increase in amount and rate of protein production.
• A short time delay is seen as transcription and translation takes time.