Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

Abstract

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an a-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., a-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation ofthe Zimm-Bragg a and s parameters for helix initiation and helix growth. The calculated r and s parameters for the polyalanine c-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.Polypeptide chains can assume a variety of regular structures, many of which are also found as structural elements of proteins. Several theories of the helix-coil transition have been developed to quantitate the relation between the random state of the unfolded peptide (statistical coil) and the helical conformation (1-3). According to these theories, each amino acid can adopt one of only two states, helix and coil, and the helix-coil transition consists of two processes, helix initiation and helix growth. The former is difficult, because several consecutive residues must simultaneously assume the helical conformation, which is associated with a large entropy loss without concomitant stabilization by intramolecular interactions such as hydrogen bonds. The treatment by Zimm and Bragg (1) introduces two equilibrium constants, one for helix initiation, a, and the other for helix growth, s. Reliable oa and s parameters have been evaluated for polypeptides (4, 5).Molecular dynamics simulations have been used to compute theoretical estimates of the free energy of helix formation; these calculations employed thermodynamic integration or umbrella sampling with forced conformation change (6-8). However, the substantial conformation changes associated with the helix-coil transition make such calculations computationally difficult for long peptides, and the description that has emerged from these earlier calculations remains incomplete.Recently, Tropsha et al. (9) have reported the peptide growth simulation (PGS) method, which affords calculation of conformational free energy differences without the need for conformational forcing. This approach is based on methods developed earlier for calculating free energy differences between different conformations of amino acid side chains (10). According to the PGS method, identical polypeptides i...

Free Energy Determinants of Secondary Structure Formation: III. β-Turns and their Role in Protein Folding

“…The free energy cost of forming a b-turn is found to be of the order of 2 to 4 kcal/mol, a value that is comparable to the cost (about 4 kcal/mol) for a-helix initiation (Yang & Honig, 1995a;Wang et al, 1995). Indeed, the structure of the type I turn is close to that of a turn in a 3 10 helix, which is believed to be an intermediate a-helix initiation .…”

A coarse-grained model and associated lattice Monte Carlo simulation of the coil–helix transition of a homopolypeptide

“…[60][61][62][63][64] In recent years, some groups also attempted to determine these two parameters through computer simulations, and have obtained some important insights. 22,[65][66][67][68][69] In this paper, the values of and s are directly calculated from the dynamic process of helix formation. The calculation method will be discussed in detail in a later paper.…”

Direct computation of long time processes in peptides and proteins: Reaction path study of the coil‐to‐helix transition in polyalanine

“…[3][4][5] Both experiment and computer simulation have been used to define the parameters of such theories. [6][7][8][9][10] Computer simulations have now been used to investigate the dynamics of atomistic models of a peptide in solution for extended times. 11,12 The simulations have been used to parameterize simple models for the kinetics of helix formation.…”