Mean first-passage time calculations for the coil-to-helix transition: Theactive helix Ising model

The kinetics and thermodynamics of the coil-to-helix transition is studied using a one-dimensional "Zimm-Bragg" Ising model. The mean first-passage ti me for the coil-to-helix transition is estimated within the "mean sequence" approximation. A generalized mean first-passage time equation is derived w here the transition rates may depend on the state of the system. The analyt ic expression for the mean first-passage time is evaluated, and the results are discussed as a function of energetic parameters. nucleation and propag ation constants, peptide length, and the initial fraction of coil. The equi librium thermodynamic properties of the model are shown to agree well with the Zimm-Bragg model, validating the mean sequence approximation. The time scales for helix formation are computed for a range of energetic parameters that determine the nucleation and propagation constants for the model. It is shown that, for a range of thermodynamically realistic parameters, the k inetic first-passage times are on the order of those measured experimentall y. The mean first-passage time approach implicitly allows for the possibili ty of multiple helix nucleation sites and multiple helical domains and make s no assumptions regarding the unidirectionality of helix propagation. Comp arison is made with the predictions of the "sequential kinetics" model of B rooks and the "kinetic zipper" model of Thompson et al. Extension of the mo del to the more general case of structure formation in proteins is discusse d.