Team:Aberdeen Scotland/hillinput

Repression of a Promoter

During repression of a promoter a repressor protein, X, binds to a DNA site of the promoter, D. The product of this binding process is [XD]. [XD] can also fall apart into [X] and [D] again:

 

(I)

where k_on describes the collisions of X and D that occur per time per protein at a given concentration and k_off determines the strength of the chemical binding X and D. In form of a differential equation, the rate of change of [XD] is described by

 

(II)

At steady state the concentration [XD] does not change.

 

(II.1)

 

(II.2)

 

(II.3)

 

(II.4)

Equation (II.4) is called the chemical equilibrium constant equation, where Kd is the dissociation or equilibrium constant. Kd has units of concentration. Therefore, transcription of a gene only happens whenever the repressor is not bound. That is when D is free. The total concentration of the DNA sites [DT] can be written with the help of the conservation law:

 

or

(III)

Substituting (III) in (II.4) we find

 

(IV)

 

(IV.1)

 

(IV.2)

 

(IV.3)

 

(IV.4)

 

(IV.5)

 

(IV.6)

As a result, the probability describing that the site D is free is dependent on [X]. The promoter activity, p, is defined by

 

or

(V)

where β is the maximal transcription rate of the promoter. If then [X] = K_d and the promoter activity is reduced by 50%. This [X] needed to repress the promoter activity by a half is called the repression coefficient.