An effective all-atom potential for proteins

We describe and test an implicit solvent all-atom potential for simulations of protein folding and aggregation. The potential is developed through studies of structural and thermodynamic properties of 17 peptides with diverse secondary structure. Results obtained using the final form of the potential are presented for all these peptides. The same model, with unchanged parameters, is furthermore applied to a heterodimeric coiled-coil system, a mixed alpha/beta protein and a three-helix-bundle protein, with very good results. The computational efficiency of the potential makes it possible to investigate the free-energy landscape of these 49–67-residue systems with high statistical accuracy, using only modest computational resources by today’s standards.

💡 Research Summary

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The paper introduces an implicit‑solvent all‑atom force field specifically designed for efficient exploration of protein free‑energy landscapes. Unlike conventional force fields such as AMBER, CHARMM, or OPLS, which contain many detailed terms, this model deliberately reduces complexity while retaining the ability to reproduce the thermodynamics of whole protein chains. The total potential energy is expressed as

E = E_loc + E_ev + E_hb + E_sc

where each term addresses a distinct physical contribution.

Local interactions (E_loc) are split into three sub‑terms. The first (E_loc^(1)) accounts for electrostatic interactions between neighboring peptide units using fixed partial charges (±0.42 e on carbonyl O/C and ±0.20 e on amide N/H) and a dielectric scaling factor κ^(1)_loc = 6 eu (≈ ε_r = 41). The second term (E_loc^(2)) adds an O–O and H–H repulsion for adjacent units, with a special penalty for glycine ψ angles that are rarely observed in the PDB. The third term (E_loc^(3)) is an explicit torsional potential for side‑chain χ angles, grouped into four classes with different force constants and periodicities, reflecting steric preferences observed for residues such as Asn, Asp, Glu, Gln, and aromatic side chains.

Excluded‑volume (E_ev) employs a 12‑12 Lennard‑Jones‑type repulsion (κ_ev = 0.10 eu) with atom‑type radii (σ_S, σ_C, σ_N, σ_O, σ_H) and a scaling factor λ_ij that distinguishes three‑bond neighbors (λ = 1) from all other pairs (λ = 0.75). A cutoff of 4.3 λ_ij Å accelerates computation.

Hydrogen‑bonding (E_hb) treats only NH–CO interactions, either backbone‑backbone or side‑chain‑backbone. Two strength parameters, ε^(1)_hb = 3.0 eu and ε^(2)_hb = 2.3 eu, differentiate the two classes. The distance‑dependent term u(r) follows a 12‑10 Lennard‑Jones form with σ_hb = 2.0 Å and a 4.5 Å cutoff, while the angular term v(α,β) enforces proper N–H–O and H–O–C geometry (non‑zero only when both angles exceed 90°).

Side‑chain interactions (E_sc) consist of a hydrophobic term (E_hp) and a charge‑charge term (E_ch). Ten residues (Met, Lys, Val, Ile, Leu, Pro, Tyr, Phe, Trp, and the “Trp‑like” group) are assigned hydrophobicity parameters m_i ranging from 0.3 to 1.6 eu. Pairwise hydrophobic contact energy is taken as the additive sum M_hp(I,J) = m_I + m_J, reduced by a factor of 2 for next‑nearest neighbors and set to zero for directly bonded residues. Contact measures C_hp(I,J) are computed from predefined atom sets A_hp(I) using a distance‑based step function g(x) that transitions between 0 and 1 over 3.7–4.5 Å. A scaling factor γ_IJ (1 or 0.75) modulates the maximum contact fraction, reducing over‑packing for aromatic and branched aliphatic residues.

Charged residues (Asp, Glu, Lys, Arg) interact via a simple Coulombic term E_ch = –1.5 eu · s_I · s_J, where s = ±1 denotes charge sign. Contact measures for charges use atom sets A_ch(I) listed in the paper.

Chain termini are treated as charged groups unless capped with acetyl or succinyl moieties; capped groups contribute reduced hydrogen‑bond strength (factor ½).

Parameter calibration was performed on a training set of 17 peptides spanning α‑helices, β‑hairpins, mixed sheets, and small three‑strand bundles. For each peptide, extensive Monte‑Carlo (MC) simulations using Simulated Tempering (ST) with seven temperatures (279–367 K) were run ten times, accumulating 10⁹–10⁹⁺ steps per system. The conversion factor from the internal “eu” unit to kcal mol⁻¹ was fixed by matching the experimental melting temperature of the Trp‑cage peptide.

Validation on larger systems: The same, unmodified parameter set was applied to three larger proteins: (i) a heterodimeric leucine‑zipper (α‑helical coiled‑coil, 30 + 30 residues), (ii) the mixed α/β Top7‑CFr (49 residues), and (iii) a three‑helix bundle (67 residues). Parallel Tempering (PT) with 16 temperatures and four‑fold multiplexing (64 replicas) was used, yielding 2.4–3.5 × 10⁹ MC steps per replica. The model reproduced native structures with RMSDs typically below 2 Å and captured correct secondary‑structure content, demonstrating transferability from short peptides to medium‑size proteins.

Computational efficiency: Implemented in the open‑source C++ package PROFASI, the force field requires only modest CPU resources (tens of cores) to achieve statistically converged free‑energy profiles for 50–70‑residue systems, a task that would be prohibitive with explicit‑solvent all‑atom simulations.

Implications: By calibrating directly against whole‑chain thermodynamics rather than static crystal structures, the model balances competing minima (α vs. β) without bias, making it suitable for studies of folding pathways, aggregation, and conformational transitions where multiple basins are relevant. Its simplicity also facilitates integration with enhanced‑sampling schemes and could be extended to investigate mutant effects, ligand binding, or protein‑protein interfaces.

In summary, the authors present a rigorously tested, computationally tractable all‑atom implicit‑solvent potential that successfully folds a diverse set of peptides and scales to larger proteins while maintaining a single, transferable parameter set. This work provides a valuable tool for the biophysical community seeking high‑throughput, accurate exploration of protein free‑energy landscapes.