A repressor protein locates its operator by first landing nonspecifically on DNA and…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Charges in salt water and the assembly of amphiphiles

Problem

A repressor protein locates its operator by first landing nonspecifically on DNA and then sliding along the double helix by one-dimensional diffusion, with sliding diffusion coefficient

D_1=0.05\,\mathrm{\mu m^2\,s^{-1}}

. Take the rise per base pair of double-stranded DNA as

0.34\,\mathrm{nm}

. ((a)) Using the one-dimensional random-walk relation for the mean-square displacement, estimate the time needed to slide to a target

100\,\mathrm{bp}

away. ((b)) The protein's nonspecific dissociation constant is such that its binding constant

K_a

falls by a factor of

25

when the salt concentration is raised fivefold, from

40\,\mathrm{mM}

200\,\mathrm{mM}

. Find the number of counterions

m

released on nonspecific binding. ((c)) Bjerrum length in water at

298\,\mathrm{K}

0.715\,\mathrm{nm}

(with

\varepsilon_r=78.4

). Assuming

\varepsilon_r

is unchanged, find the Bjerrum length at body temperature,

310\,\mathrm{K}

, and comment on whether this change could explain the factor of

25

in part (b). ((d)) In one or two sentences, use the counterion-release idea to explain why the melting temperature of DNA rises with salt concentration.

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