Team:UFAM-UEA Brazil/MathModeling

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MATH MODELLING

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:

[1]

Where MerR is a repressor and releases when Hg²⁺ 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:

[2]

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)

(1)

[3]

At the equillibrium state, ie. [4], we have that the proportion of genes in the activated gene is

(2)

[5]

Where [6]

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

(3)

[7]

Where α is the production of mRNA due to the stochastic nature of the binding of merR for repressing the RNA Polymerase and δ1 is the degradation factor of mRNA. The reaction for production of RFP from mRNA is

[8]

so we derive the diferential equation (4) where δ2 is the degradation constant of [RFP]. The variation of exterior mercury is [9] from here we derive the differential equation

As the interior mercury is used by the inactive form of the gene, the variation of Hg²⁺ gin is