sb3-hw8-2016 - JHU 580.429 SB3 HW8 Transcription factor...

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JHU 580.429 SB3 HW8: Transcription factor binding The following questions consider binding of a transcription factor protein, denoted X , to a gene promoter with N binding sites. The number of transcription factors bound is denoted n , and in the general case n ∈ { 0 , 1 , 2 , 3 ,..., N } . The number of copies of the gene with n sites bound is denoted G n . The total number of copies of the gene is the constant G T = N n = 0 G n , and the fraction of copies in state n is G n / G T . The transcription rate for a copy of the gene with n transcription factors bound is denoted ν n , and the total transcriptional rate is β = N n = 0 ν n G n . We will assume that ν 0 = 0 and that increased binding gives increased transcription, which implies that the maximum possible transcription rate occurs when G N is the only occupied state. Thus, the maximum transcription rate is β max = ν N G T . The concentration of transcription factor is suffi- ciently large that changes in the value of unbound X need not be considered. All questions assume that binding has reached equilibrium.
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