Exploring the Helix-Coil Transition via All-Atom Equilibrium Ensemble Simulations

Abstract

The ensemble folding of two 21-residue alpha-helical peptides has been studied using all-atom simulations under several variants of the AMBER potential in explicit solvent using a global distributed computing network. Our extensive sampling, orders of magnitude greater than the experimental folding time, results in complete convergence to ensemble equilibrium. This allows for a quantitative assessment of these potentials, including a new variant of the AMBER-99 force field, denoted AMBER-99 phi, which shows improved agreement with experimental kinetic and thermodynamic measurements. From bulk analysis of the simulated AMBER-99 phi equilibrium, we find that the folding landscape is pseudo-two-state, with complexity arising from the broad, shallow character of the "native" and "unfolded" regions of the phase space. Each of these macrostates allows for configurational diffusion among a diverse ensemble of conformational microstates with greatly varying helical content and molecular size. Indeed, the observed structural dynamics are better represented as a conformational diffusion than as a simple exponential process, and equilibrium transition rates spanning several orders of magnitude are reported. After multiple nucleation steps, on average, helix formation proceeds via a kinetic "alignment" phase in which two or more short, low-entropy helical segments form a more ideal, single-helix structure.

Comparison of multiple Amber force fields and development of improved protein backbone parameters

“…All molecular dynamics simulations for Gly 3 and Ala 3 tetrapeptides were carried out with the sander module in AMBER8 7 using several different force fields as discussed in the main text: ff94 5 , ff99 11 , Garcia's modification of ff94 13 with C-N-C α -C and N-C α -C-N terms zeroed (denoted ff94gs in the text), Pande's modified ff99 19 with C-N-C α -C term replaced by the one from ff94 (denoted ff99ϕ), ff03 24 (as present in AMBER8 distribution) and ff99SB developed as described above. The time step was 2 fs, and all bonds involving hydrogen were constrained by SHAKE with a tolerance of 10 −4 Å. Glycine and alanine tetrapeptide systems were solvated by approximately 520 TIP3P 33 water molecules in a periodic box.…”

“…Because the backbone dihedral parameters are shared by all amino acids, regardless of the type of sidechain, their cumulative effect is most likely responsible for the bias towards the specific secondary structure. This recently motivated us 12,18 and others 13,19 to revisit backbone dihedral parametrization for ff94/ff99. Garcia and Sanbonmatsu 13 simply zeroed the torsion potential for φ and ψ (although as we explain below, only some of the φ/ψ terms were removed) and noted improved agreement with experimental helix-coil parameters.…”

“…Garcia and Sanbonmatsu 13 simply zeroed the torsion potential for φ and ψ (although as we explain below, only some of the φ/ψ terms were removed) and noted improved agreement with experimental helix-coil parameters. More recently, Sorin and Pande 19,20 modified ff99 by replacing its φ dihedral parameters with the ones from ff94. This improved the agreement with experimental kinetic and thermodynamic measurements for folding of two 21-residue α-helical peptides.…”

“…This definition of dihedrals was originally implemented in ff94, with φ and ψ fit independently to glycine data and φ′ and ψ′ used to adjust the behavior for alanine. Later modifications of ff94, such as ff96, ff99, Garcia's 13 , Pande's 19 and ours 12,18 only changed the first set of φ/ψ terms, using them to adjust backbone preferences for alanine. Thus the new ϕ and ψ parameters were fit in the presence of the ff94 alanine-based φ′ and ψ′, and will only give their intended behavior when they accompany these φ′ and ψ′ dihedrals.…”

Protein folding: Then and now

“…Rate predictions have been likewise performed using molecular dynamics simulations using explicit water models such as the TIP3P [131] and SPC [132] to gain additional insight into folding kinetics. Examples of MD simulations using explicit solvent which yielded experimentally consistent rates were performed by Pande et al, who observed helix-coil transitions [133] and protein folding [34]. However, a potential drawback in the use of water models is that they are parameterized to a single temperature (~298 K), and thus may bias the dynamics in non-native temperature simulations.…”