The helix–coil transition revisited

Abstract

In this article, we perform a dynamic Monte Carlo simulation study of the helix-coil transition by using a bond-fluctuation lattice model. The results of the simulations are compared with those predicted by the Zimm-Bragg statistical thermodynamic theory with propagation and nucleation parameters determined from simulation data. The Zimm-Bragg theory provides a satisfactory description of the helix-coil transition of a homopolypeptide chain of 32 residues (N = 32). For such a medium-length chain, however, the analytical equation based on a widely-used large-N approximation to the Zimm-Bragg theory is not suitable to predict the average length of helical blocks at low temperatures when helicity is high. We propose an analytical large-eigenvalue (lambda) approximation. The new equation yields a significantly improved agreement on the average helix-block length with the original Zimm-Bragg theory for both medium and long chain lengths in the entire temperature range. Nevertheless, even the original Zimm-Bragg theory does not provide an accurate description of helix-coil transition for longer chains. We assume that the single-residue nucleation of helix formation as suggested in the original Zimm-Bragg model might be responsible for this deviation. A mechanism of nucleation by a short helical block is proposed by us and provides a significantly improved agreement with our simulation data.

A refined hydrogen bond potential for flexible protein models

“…One of the most common tests for a backbone hydrogen bond potential is the study of the helix-coil transition, [28][29][30][31][32] as it is known that some homopeptidic chains naturally fold into a helix in diluted systems. 33,34 For us, this numerical experiment pursues two aims: to check whether our potential favors native helical states in diluted systems and to determine if other alternative structures are present in our simulations, allowed by the geometrical requirements of the defined interaction but lacking any physical meaning for a polypeptide chain.…”

Theory of Phase Transitions in Polypeptides and Proteins

“…Full atomistic molecular dynamics [116-118, 145, 146] and MonteCarlo based techniques [119,120,[147][148][149] were used for studying alanine tripeptide [116], alanine pentapeptide [117], alanine 13-and 15-peptide [145,150], alanine 21-peptide [118,120], mixed alanine-rich peptide [147] and Ala x peptide (with x=21, 30, 40, 50, 100) (See Sec: 5.4.2). The molecular dynamics simulations were carried out within the framework of classical mechanics with an empirical Hamiltonian usually referred as a forcefield.…”

“…The heat capacity of a system can be calculated as the derivative of the system's internal energy or derived from the energy fluctuations. Both methods have been used [119,[145][146][147][148][149], but no comparison between them have been made so far. It is not clear which one is more accurate and thus preferable.…”

Microscopic nucleation and propagation rates of an alanine-based α-helix

“…In this regard, the folding dynamics and mechanism of the α-helix have been extensively studied, either in the context of globular protein folding or as an individual and independent folding unit. 1–37 Currently, the most widely accepted theoretical framework to describe the α-helix folding properties is the helix-coil transition theory introduced by Zimm and Bragg 38–41 as well as Lifson and Roig. 40–42 In essence, this theory is a coarse-grained, one-dimensional (1D) Ising model, which treats the peptide in question as a linear chain of basic units, corresponding to the constituent residues or peptide groups that can adopt either a helical (H) or coil (C) state.…”

“…While such Ising-based models provide a sound theoretical framework for understanding the mechanism of the helix-coil transition, 39–41, 44, 46–50 it has proven rather difficult to experimentally assess the mechanistic details they infer, especially the microscopic rate constants of the nucleation and propagation events. This is due to the fact, at least in part, that (1) both events occur on a rapid timescale (i.e., on the nanosecond timescale for alanine-based α-helices); 1, 9, 10, 14, 16, 19, 30, 50 (2) their rates are not well separated; 4, 12, 31, 35, 51, 52 (3) among the sequential kinetic events involved in α-helix folding, the first one (i.e., nucleation) is the slowest; and (4) there is not a simple experimental signal that can be used to distinguish nucleation from propagation.…”