A peptide binds nonspecifically to double-stranded DNA

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 peptide binds nonspecifically to double-stranded DNA. Its footprint buries 12 nm212\,\mathrm{nm^2} of nonpolar surface area at the protein-DNA interface and releases 55 condensed Na+^+ counterions on binding, as measured at 100 mM100\,\mathrm{mM} NaCl and 298 K298\,\mathrm{K}. ((a)) Estimate the hydrophobic contribution to the binding free energy, using an area coefficient of about 4.2kBT4.2k_BT per nm2\mathrm{nm^2}. ((b)) Estimate the factor by which the binding constant KaK_a changes if the salt concentration is raised tenfold to 1 M1\,\mathrm{M}, using the counterion-release relation ∂ln⁡Ka/∂ln⁡csalt=−m\partial\ln K_a/\partial\ln c_{\rm salt}=-m. ((c)) The same DNA is transferred to 20 mM20\,\mathrm{mM} salt. Estimate its electrostatic persistence length ξel=κ−2/4ℓB\xi_{\rm el}=\kappa^{-2}/4\ell_B, with ℓB=0.715 nm\ell_B=0.715\,\mathrm{nm} and κ−1=0.304 nm/I/M\kappa^{-1}=0.304\,\mathrm{nm}/\sqrt{I/\mathrm{M}}, and compare it with the mechanical ξp≈50 nm\xi_p\approx50\,\mathrm{nm}.

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