For transcription to start the RNA polymerase bound to the promoter needs to und
ID: 167229 • Letter: F
Question
For transcription to start the RNA polymerase bound to the promoter needs to undergo a conformational change to the so-called open complex. The rate of open complex formation is often much smaller than the rates for the polymerase binding and falling off the promoter. Here we investigate within a simple model how this state of affairs might justify the equilibrium assumption underlying thermodynamic models of gene regulation, namely that the equilibrium probability that the promoter is occupied by the RNA polymerase determines the level of gene expression. (a) Write down the chemical kinetics equations for this situation. Consider three states: RNA polymerase bound nonspecifically on the DNA (N), RNA polymerase bound to the promoter in the closed complex (C), and RNA polymerase bound to the promoter in the open complex (O). To simplify matters take both the rate for NC and the rate for CN to be k. Assume that the transition C O is irreversible, with rate R (we live in MM-kinetics world) (b) For R = 0, show that in the steady state there are equal numbers of RNA polymerases in the N and C states. What is the steady state in the case R does not equal 0? (c) For the case R does not equal 0, show that for times 1/k t 1/ the numbers of RNA polymerases in the N and C states are equal, as would be expected in equilibrium.
Explanation / Answer
b)[RNAP] + [P]---[RNA-P]c----kon-----[RNAP-P]o----kf----[RNAP]e + [P], the number of RNA polymerases is the same in closed as open conformation as the equation and stoichiometric concentration of RNA polymerase is assumed with power 1 as [RNAP-P]1 and the stoichiometric power is not taken as n.
forward--Kon, reverse--Koff , RNAP-Pc--closed conformation of RNA-polymerase-promoter complex, RNA-Po--RNA polymerase-promoter complex, RNAe--RNA elongation complex.
rate of transcription initiation after the binding of RNA polymerase on promoter complex--[RNAP]/Kd +[RNAP] x kf.
kd= dissociation constant =koff/kon.
N=RNA polymerase bound non specifically on the promoter depicted as the intermediate stage.--[RNAP-P]o1(N)
O=RNA polymerase bound on the promoter with open conformation.
C=RNA polymerase bound on the promoter with closed conformation.
-10bp region on the DNA is prone to melting and attains an open conformation after the binding of RNA polymerase on the entire 15bp region of DNA.
c))[RNAP] + [P]---[RNA-P]c----kon-----[RNAP-P]o--kf1-[RNAP-P]O1(N)---kf2--[RNAP]e + [P].
if the rate of reaction of the formation of open complex from closed complex is irreversible, still the numbr of RNA polymerases is the same as depicted from the equation.
equation for calculating the rate kinetics----
kon[RNAP][P]=koff+kf[RNAP-P]c.
ke[RNAP-P]o=kf[RNAP-P]c,
[Pt]=[P]+[RNAP-P]o +[RNAP-P]c.
rate of occupancy of promoter by RNA polymerase=kf/1+(kf+koff)/kon[RNAP].
and the number of RNA polymerase molecules are the same.
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