IGEM:IMPERIAL/2007/Projects/Modelling/Notes

Modelling: Notes

• Introduction
• Tutorial
• Notes
• References

This section shall be expanded systematically. Furthermore, the tutorial on Modelling Techniques will be held on Tuesday, 31 July 2007.

Dynamics and Response Time of Gene Regulation

Consider the following transcription interaction:

[math]\displaystyle{ X \rightarrow Y }[/math]

where [math]\displaystyle{ X }[/math] is a transcription factor and [math]\displaystyle{ Y }[/math] is a protein product of gene y whose activity is regulated.

The task involves determining the dynamics of the reaction, involving the concentration of protein [math]\displaystyle{ Y }[/math] and its response time. Protein production is balanced by the opposing processes: protein degradation and dilution. Degradation refers to the breakdown of proteins; dilution, a reduction in the concentration of the protein due to an increase of cellular volume, a consequence of cellular growth.
Let [math]\displaystyle{ \alpha }[/math] be the combined rate of degradation and dilution, i.e.

[math]\displaystyle{ \alpha }[/math] = [math]\displaystyle{ \alpha_{deg} }[/math] + [math]\displaystyle{ \alpha_{dil} }[/math]

The change in protein (Y) concentration is the difference between protein production (first order reaction) and degradation/dilution, namely: