Kinetics of the Helix-Coil Transition of Polypeptides

Theory of the kinetics of the helix-coil transition in two-chain, coiled coils. 2. The finite chain

“…7q(lcosh 9) = -/?Ca (11)(12) Observe that eq [11][12] gives the correct form when ß = O(siu;0)1!2 = 1), q = 0 and reproduces the N = " limit exactly. Hence, we conclude that our approximate equilibrium solution for q,(") is valid except for residues very close to the ends.…”

“…gives dqy/dt = -a|79y cosh 0 -{y/2)(qj.l + qj+1) + 79(1 -cosh )} (11)(12)(13) which cosh defined in eq 11-11. However, since the qy(°°) are related by eq II-10b, we have…”

“…The second set of terms, [7/(IVl)][(qt(0) -9iH)/(q(0) -q(~))], corrects for the winding (or rewinding) of the ends and is always positive. Thus, eq [11][12][13][14][15][16][17] implies that the initial slope probes the kinetics of the flipping of the same cooperative domains as in the infinite chain plus a contribution from the chain ends.…”

“…On the other hand, eq II-3a and II-3b provide us with the exact mean initial slope, wherein X" = (' Xy(0) -xyH)/[(IVl)(q(0) -? (»))] (11)(12)(13)(14)(15)(16)(17)(18) ;=i where ;•( ) is defined in eq II-3b. The procedure for the calculation of the equilibrium values of the various correlation functions is found in the Appendix.…”

“…Up until this point, we have not specified how cosh 0 is determined. If our approximate description of the dynamics is valid, we should be able to determine cosh 0 from the exact initial slope defined in eq 11-18 by cosh 0 = 1 + ^-(IV-I)"1 <?i(0) ~<?i(°°) q(0) -q(°°) (II- 19) Substituting cosh 0 determined from eq [11][12][13][14][15][16][17][18][19] into eq II-6b should give the correct mean helix content, thus, providing a check on the validity of the approximations I-III. In eq 11-19 as well as in eq II-15a and 11-16, we employ equilibrium values for the q; calculated from the exact equilibrium theory, viz., eq A-6.…”