Mapping the Backbone Dihedral Free-Energy Surfaces in Small Peptides in Solution Using Adiabatic Free-Energy Dynamics

Abstract

Ramachandran surfaces for the alanine di- and tripeptides in gas phase and solution are mapped out using the recently introduced adiabatic free-energy dynamics (AFED) approach introduced by Rosso et al. (J. Chem. Phys. 2002, 116, 4389) as applied to the CHARMM22 force field. It is shown that complete surfaces can be mapped out with an order of magnitude of greater efficiency with the AFED approach than they can using the popular umbrella sampling method. In the alanine dipeptide, it is found, in agreement with numerous other studies using the CHARMM22 force field, that the lowest free-energy structure is the extended beta conformation, (phi, psi) = (-81, 81), while in solution, the extended beta, (phi, psi) = (-81, 153) and right-handed alpha-helical, (phi, psi) = (-81, 63) conformations are nearly isoenergetic. In solution, a secondary minimum at (phi, psi) = (63, -81), corresponding to a C(7)ax conformation, occurs approximately 2.3 kcal/mol above the global free-energy minimum. The alanine tripeptide, a system that has received considerably less attention in the literature, is found to exhibit a similar structure to the alanine dipeptide with the extended beta conformation being the free-energy minimum in the gas phase and the beta and right-handed alpha-helical conformations being isoenergetic in solution. These studies indicate that the AFED method can be a powerful tool for studying multidimensional free-energy surfaces in complex systems.

Exploring Multidimensional Free Energy Landscapes Using Time-Dependent Biases on Collective Variables

“…In particular, (φ, ψ)-integration over the basins corresponding to the C 7eq and C 7ax conformations, characterized by a long-lived intramolecular hydrogen bond, yields a free energy difference of 2.5 kcal/ mol, in favor of the equatorial motif. 78,96 The metadynamics calculation yields a free energy landscape identical to that determined by means of ABF (data not shown). Fast-relaxing, low-friction systems such as NANMA do not place high demands on the algorithms used to sample them, as demonstrated by early successes obtained with limited sampling and unsophisticated algorithms.…”

“…82 Furthermore, in several instances, NANMA has served as a discriminating test case for assessing the performance of novel numerical schemes. 8,83,96 In the present work, determination of the two-dimensional free energy landscape of NANMA only represents the necessary preamble to an independent series of computations based on variables of higher collectivity than the mere φ and ψ torsional angles of the backbone. However predictable, the results of these preliminary free energy calculations depicted in Figure 1 agree quantitatively with previous investigations; see, for instance, ref 96.…”

“…8,83,96 In the present work, determination of the two-dimensional free energy landscape of NANMA only represents the necessary preamble to an independent series of computations based on variables of higher collectivity than the mere φ and ψ torsional angles of the backbone. However predictable, the results of these preliminary free energy calculations depicted in Figure 1 agree quantitatively with previous investigations; see, for instance, ref 96. In particular, (φ, ψ)-integration over the basins corresponding to the C 7eq and C 7ax conformations, characterized by a long-lived intramolecular hydrogen bond, yields a free energy difference of 2.5 kcal/ mol, in favor of the equatorial motif.…”

Introducing sampling entropy in repository based adaptive umbrella sampling

“…This has become a classical example to test enhanced sampling approaches. 20,24,27,[36][37][38][39][40] In our simulations, the alanine dipeptide is described by the CHARMM27 force field. 41 For the aqueous phase, the simulation of one alanine dipeptide molecule and 245 TIP3P water 42 molecules was performed in a cubic box of 19.7429 Å with periodic boundary conditions.…”

Modified single sweep method for reconstructing free-energy landscapes

“…Single sweep combines two steps. The first employs the temperature accelerated molecular dynamics (TAMD) introduced by the same authors [8] (see also [9][10][11][12] for related work) to generate a trajectory in the collective variables that efficiently explores relevant regions of the free energy landscape even in the presence of barriers. In the second step, points along this trajectory are chosen as centers for an interpolation grid and the free energy is represented as a linear combination of radial basis functions [13,14], e.g.…”