# Team:Michigan/Modeling

HOME THE TEAM THE PROJECT MODELING REGISTRY PARTS NOTEBOOK SAFETY

# The Toluene Terminator Model

## Overview :

The following mathematical model examines the dynamics of the suicide mechanism that employed tunable repression. As outlined in the project description, the Pu promoter is placed in front of a repressor system that would inhibit the production of holin and lysozyme, while a constitutive promoter is placed in front of the gene for antiholin. In the presence of toluene, the Pu promoter would be activated, leading to repression of holin/lysozyme production and therefore cell survival. In the absence of toluene, the Pu promoter would not be activated, and as a result holin and lysozyme would be produced, leading to cell death.

## Cell Growth/Death

Cell Lysis happens when holin creates pores in membrane and lysozyme enters Assume rate of cell death â[holin](# cells), rate of cell growth in exponential phase

## Transcription of Repressor :

đ([đ]) is a function of toluene concentration

Use Hill Equation to describe binding affinity of toluene to Pu promoter.

## Transcription of Lysozyme and Holin:

Assume transcription rate is proportional to # of free operator sites (which should be the same for both lysozyme and holin, since they are downstream of the same promoter)

Assume transcription rates for H and L are the same

## Repression of Lysozyme and Holin Transcription

Repressor binds with free operator site, preventing transcription of lysozyme and holin. Use a model invoking law of mass action.

Assuming that fops and Rfops do not undergo spontaneous degradation.

## Production of Repressor

Using the translation rate for R and taking into consideration the binding of R with fops,

## Production of Proteins

Production of antiholin, under constitutive promoter, is at a constant rate ÎłA, which depends on the promoter that is used

Dimerization: Since holin and antiholin form a complex

Using the translation rates and incorporating dimerization using the law of mass action,

## Assumptions

Can set ÎłA equal to rate of production of holin in the case that all operating sites are free

• This is in order to balance antiholin and holin levels without repression
• This can be tuned so that timing of cell death works out
• Set antiholin production rate to that of holin in the absence of repression
• Put this through the transcription and translation equations to obtain production rate

Assume degradation rates of all mRNAs are the same

• Can directly search for these rates in literature
• Can use half life to calculate rate