A transcription factor is a molecule that binds to a specific DNA sequence in or

Question

A transcription factor is a molecule that binds to a specific DNA sequence in order to control the expression of the nearby genetic material. In this problem we will look at the process by which the factor finds the correct sequence to bind to. Assume that factor can bind loosely to a DNA sequence that does not match the target sequence. After every 10 ns the molecule will move 1 base pair with a 50/50 chance that the move is to the left or to the right.

(a) After 100 ns, what is the probability that the transcription factor is 6 base pairs to the left of where it started? (hint: treat each step like the coin flip example from lecture)

(b) Where is the most likely place for the factor to be after 100 ns? What is the probability that it ends up at the most likely place?

(c) Does your answer from part (b) mean that the factor will never find its target sequence? Why or why not?

Explanation / Answer

Sigma factor introduces a major change in the affinity of RNA polymerase for DNA. The holoenzyme has a drastically reduced ability to recognize loose binding sites¡Xthat is, to bind to any general sequence of DNA. The association constant for the reaction is reduced by a factor of ~104, and the half-life of the complex is <1 second. So sigma factor destabilizes the general binding ability very considerably.

· Excess core enzyme exists largely as closed loose complexes, because the enzyme enters into them rapidly and leaves them slowly. There is very little, if any, free core enzyme.

· There is enough sigma factor for about one third of the polymerases to exist as holoenzymes, and they are distributed between loose complexes at nonspecific sites and binary complexes (mostly closed) at promoters.

· About half of the RNA polymerases consist of core enzymes engaged in transcription.

RNA polymerase moves by random diffusion. Holoenzyme very rapidly associates with, and dissociates from, loose binding sites. So it could continue to make and break a series of closed complexes until (by chance) it encounters a promoter. Then its recognition of the specific sequence would allow tight binding to occur by formation of an open complex.

For RNA polymerase to move from one binding site on DNA to another, it must dissociate from the first site, find the second site, and then associate with it. Movement from one site to another is limited by the speed of diffusion through the medium. Diffusion sets an upper limit for the rate constant for associating with a 60 bp target of <108 M¡V1 sec¡V1. But the actual forward rate constant for some promoters in vitro appears to be ~108 M¡V1 sec¡V1, at or above the diffusion limit. If this value applies in vivo, the time required for random cycles of successive association and dissociation at loose binding sites is too great to account for the way RNA polymerase finds its promoter.

RNA polymerase must therefore use some other means to seek its binding sites. The process could be speeded up if the initial target for RNA polymerase is the whole genome, not just a specific promoter sequence. By increasing the target size, the rate constant for diffusion to DNA is correspondingly increased, and is no longer limiting.

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