Kinetics and reaction coordinate for the isomerization of alanine dipeptide by a forward flux sampling protocol

Abstract

Forward flux sampling (FFS) simulations were used to study the kinetics of alanine dipeptide both in vacuum and in explicit solvent. The recently proposed FFS least-squares estimation approach and an algorithm that optimizes the position of the interfaces were implemented to determine a reaction coordinate that adequately describes the transition dynamics. A new method is also introduced to try to ensure that the ensemble of "starting points" (for the trial trajectories) is properly sampled. The rate constant estimates for the C7(eq)-->C5 transition of alanine dipeptide in vacuum were used to demonstrate the consistency between Monte Carlo and molecular dynamics (MD) simulations. FFS-MD simulations were then performed for the study of the beta(2)/alpha(R)-->C5/C7(eq) transition in explicit solvent. The kinetic results for both systems in vacuum and explicit solvent are in general agreement with previous experimental and computational studies for this peptide. In vacuum, an additional dihedral angle besides the one typically used as order parameter is identified as a significant variable in the reaction coordinate model. In solution, several dihedral angles and variables that describe the solvent action on the molecule's dynamics are found to play a significant role in the description of the system's dynamics.

Randomized tree construction algorithm to explore energy landscapes

“…Figure 7 and Figure 8 show transition paths for the direct and reverse transition between pairs of minima {α L , C ax 7 } and {α R , P II }, respectively. These transitions, that are known to be fast transitions [52], do not require to cross the lines φ = 0 • or φ = 120 • . They mainly involve the variation of bond torsion ψ, and the paths lead from one minima to the other via a single saddle-point in all the cases.…”

A new perspective on transition states: χ1 separatrix

“…With this choice of force-field, there are three main ensembles of configurations that are populated with high probabilities and are separated by free energy barriers, these are the c 7 , c 5 , and C ax isomers (The c 7 and c 5 isomers are also known as C 7eq and C 7eq ). 9,16,22 The barrier separating the c 7 and c 5 isomers is sufficiently high that the c 7 to c 5 isomerization can be considered isolated from the C ax minimum on the short time scales we simulate. The effective isolation from the C ax minima allows us to observe the χ 1 separatrix separating the c 7 and c 5 isomers.…”

“…In studies of alanine dipeptide, a priori coordinates used to identify the reactant and product states are typically the peptide dihedral angles, φ and ψ, and reactants and products are rectangular boxes in φ and ψ around well known isomers. 16,21,22 The chosen coordinates in these cases are well known as good coordinates for the system.…”

“…, z n ), and a rectangular box (in z) is defined surrounding the local probability maxima where the reactant and product states are presumed to be. 8,10,22 For example, in the seminal paper introducing the iso-committor approach in protein folding, p-fold, 8 Du et al chose as coordinates for a protein folding reaction the fraction of native contacts, Q, and total number of contacts, K, with values near the observed free energy minima obtained with these coordinates as the definition of the reactant and product. In studies of alanine dipeptide, a priori coordinates used to identify the reactant and product states are typically the peptide dihedral angles, φ and ψ, and reactants and products are rectangular boxes in φ and ψ around well known isomers.…”

“…This system is a typical testbed for new methods in molecular dynamics problems. 9,16,22 Alanine dipeptide consists in a single alanine amino acid with acetylated and methylated peptide bonds, with 22 atoms in total. Because of its small size, it is computationally feasible to sample its conformational space extensively.…”