Reaction coordinates of biomolecular isomerization

Abstract

Transition path sampling has been applied to the molecular dynamics of the alanine dipeptide in vacuum and in aqueous solution. The analysis shows that more degrees of freedom than the traditional dihedral angles, and , are necessary to describe the reaction coordinates for isomerization of this molecule. In vacuum, an additional dihedral angle is identified as significant. In solution, solvent variables are shown to play a significant role, and this role appears to be more specific than can be captured by friction models. Implications for larger molecules are discussed.T his paper concerns the dynamical variables relevant to kinetics of biomolecular isomerization. The backbone dihedral angles and do serve well as order parameters characterizing the stable isomeric states of polypeptides (1). This fact does not, however, imply that and are satisfactory for describing the dynamics of transitions between these states. Indeed, for large enough molecules, clustering of hydrophobic units can lead to drying (2, 3). The nucleation of this phenomenon manifestly involves motion of solvent. On the smaller length scales characterizing side-chain motions, effects from solvent are apparent as well (4). On these scales, it often is assumed that the dynamical role of secondary variables can be captured implicitly, through the mean forces on angles like and and through friction and random local forces (5). We test this idea in this paper through the analysis of trajectories of the alanine dipeptide in vacuum and aqueous solution. We establish that other variables in addition to and are important. Most significantly, we find that solvent degrees of freedom are relevant components to the reaction coordinates for isomerization. Although the dipeptide is a relatively simple molecule, our findings would seem to carry over to the small-length scale motions of more complex biopolymers. Specifically, our results suggest the inadequacy of implicit solvent models for treating the dynamical effects of solvation. Although implicit solvent models can be used to calculate averaged solvent effects, such models are not able to describe a possibly important rearrangement of individual solvent molecules occurring during a transition correctly. Fig. 1 illustrates the ball and stick model and the important dihedral angles of the alanine dipeptide. This molecule often is studied in theoretical work (6-13) because it is among the simplest systems to exhibit some of the important features common to biomolecules. It has the basic elements of a polypeptide backbone with more than one long-lived conformational state. It forms hydrogen bonds with water in aqueous solution. This bonding or solvation in general is responsible for the stability of one of the conformers. The molecule in vacuum has two stable conformers: the C 7eq state with Ϸ Ϫ86°and Ϸ 68°a nd the C ax state with Ϸ 50°and Ϸ Ϫ50°. In solution, these positions shift slightly, for instance, the C 7eq state is located around Ϸ Ϫ80°and Ϸ 160°. In addition, two other states, ␣ R and ␣ L , become s...

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