sb3-hw11-2016 - JHU 580.429 SB3 HW11 Combinatorial...

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JHU 580.429 SB3 HW11: Combinatorial transcription factor binding 1. A gene exists in an unbound state, G , and also binds to two activating transcription factors, X and Y . ODE models for binding are G + nX GX n G + nY GY n with forward and reverse rate constants k f and k r and fixed total gene concentration G T = G + GX n + GY n . Assume that steady state has been reached and that the concentrations of X and Y are sufficiently large to be unaffected by binding. (a) What is the concentration ratio GX n / G ? (b) What is the concentration ratio GY n / G ? (c) What is the fraction f of active DNA, f = ( GX n + GY n ) / G T ? (d) Your answer to the previous question should have the form ( x n + y n ) / ( 1 + x n + y n ) , where x and y are related to concentrations X and Y and other model parameters. In the xy -plane for the range x 0 ... 5, y 0 ... 5, plot the lines corresponding to f = 1 / 2 (solid), f = 0 . 25 (dotted), and f = 0 . 75 (dotted) for n = 2 (thin lines) and n = 4 (thick lines). (e) Defining logical inputs as a = Θ ( x > 1 ) and b = Θ ( y > 1 ) , with Θ ( u ) = 1 if u is true and 0 if false, what logical function of a and b does the active region resemble?
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