# Team:Purdue/Modeling

### From 2008.igem.org

## Modeling Objectives

- Develop a mechanistics ODE model of the population to predict gene expression dynamics
- Question? .... Will the color production be fast enough to be useful to the user? Or will it be too late?
- What is the relationship between UV exposure and reporter gene expression?
- Can we construct a useful calibration curve of color as a function of UV?

## Modeling References

- 1997. "Mathematical model of the SOS response regulation of an excision repair deficient mutant of
*Escherichia coli*after UV light irradation". [1]. Off-the-shelf mechanistic model of the SOS response. Utilized as the basic model for our system. - 2005. "Response times and mechanisms of SOS induction by attaching promoters to GFP: "Precise Temporal Modulation in the Response of the SOS DNA Repair Network in Individual Bacteria" [2]. Potential Validation Data Set. Model should predict similar dynamics.

## Modeling the SOS response in a *uvr-* mutant (No nucleotide excision repair)

**Assumptions**

- The UV light intensity is constant and instantaneous.
- The bacteria are not undergoing any type of DNA repair at the time of UV exposure.
- Thymine dimer formation is the major DNA damage occurring.

**bound**LexA drops considerably within the first four minutes. This also correlates with the concentration of activated RecA (RecA*) going up appreciably. After approximately 60 minutes, the concentration of RecA returns to a normal level. We therefore consider this the "stopping" point of SOS. The problems with this model include:

- The model is based on an instantaneous irradiation of UV at 5 J/m^2.
- The model does not account for
*continuous*UV exposure. - The model does not account for any other proteins/genes that may be involved in SOS (ie. SulA).

- Giving us a mathematical, manipulateable model to mend for our purposes.
- Showing the general trend of how SOS behaves.
- Gives us a time frame for how our color reporters need to work to be feasible.

*All Calculations and the figures above were performed in MathCad, utilizing built in Runge-Kutta 4th order function, by Craig Barcus, utilizing the mathematical model presented by SV. Aksenov in 1997.*

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