Question

You carry out some kinetics experiments and discover that the rate constant for protein binding to random DNA sequence is 2.7-fold faster than for binding the binding site. What is the ratio of their dissociation rates? Briefly discuss the likely molecular reasons for why one dissociation rate is slower than the other.

Answer 1

Let the two reactions be-

equation (1) P stands for protein, D stands for DNA sequence and P-D stands for protein- DNA complex

let the rate constant of this reaction be k_a and dissociation constant be K₁

equation (2) B stands for binding site and P-B stands for protein-binding site complex

let the rate constant of this reaction be k_b and dissociation constant be K₂

its given that k_a = 2.7 k_b Equation (3)

K₁ = [P-D]/[P] [D]

K₂ = [P-B]/[P] [B]

equation (A)

rate of equation (1)

rate = k_a [P] [D] equation (4)

rate of equation (2)

rate = k_b [P] [B] equation (5)

divide equation (4) by equation (5)

rate1/rate2 = k_a [P] [D]   / k_b [P] [B] ​

rate1/rate2 = 2.7 k_b [D] / k_b [B]

rate1/rate2 = 2.7 [D]/ [B]

[B]/[D] = 2.7 rate2/rate1

put this value of [B]/[D] in equation (A)

k₁/k₂ = 2.7 [P-D] rate2/ [P-B] rate1

so, the ratio of dissociation rates will be k₁/k_{2 =} 2.7 [P-D] rate2/ [P-B] rate1​

the dissociation rate in case of DNA is faster than in the case of binding site because the binding betweeon protein and DNA sequence wil be much stronger than the binding site.