Partitioning of a polymer into a nanoscopic protein pore obeys a simple scaling law

The dependence of the rate on polymer mass was examined for the reaction of four sulfhydryl-directed poly(ethylene glycol) reagents with cysteine residues located in the lumen of the staphylococcal α-hemolysin pore. The logarithms of the apparent rate constants for a particular site in the lumen were proportional to N, the number of repeat units in a polymer chain. The proportionality constant was -(a/D)^5/3, where a is the persistence length of the polymer (≈3.5Å) and D is the diameter of the pore. Despite some incongruencies with the assumptions of the derivation, the result suggests that the polymers partition into the lumen of the pore according to the simple scaling law of Daoud and de Gennes, c_pore/c_solution = exp(-N(a/D)^5/3). Therefore, the measured reaction rates yield an estimate of the diameter of the pore and might be applied to determine the approximate dimensions of cavities within other similar proteins.