MODEL OF RFP PRODUCTION

1. Modelling

We want to characterize the promoter’s velocity of expression due to presence of mercury, so we will attach an RFP gene to it to produce.

First we will model the production of RFP due to Hg²⁺ at stationary time phase with this configuration. Then we add the initial phase consideration

1.1 Stationary time phase.

The GMO we have is:

Where MerR is a repressor and releases when H2+ is presented in the interior of the cell, we will note this amount as Hgin and the exterior as Hgout. And Promoter nP is the promoter which velocity we want to characterize. The activation of the gene in the pressence of Hgin is represented like:

where G is the inactive form of gene repressed by merR, and X is its active form. Through the law of mass action we derive the diferential equation

(1)

At the equillibrium state, ie. , we have that the proportion of genes in the activated gene is

(2)

Where

So this is the average production rate of a typical gene, so the average mRNA production will be

(3)