Challenges in protein folding simulations: Timescale, representation, and analysis

Abstract

Experimental studies of protein folding processes are frequently hampered by the fact that only low resolution structural data can be obtained with sufficient temporal resolution. Molecular dynamics simulations offer a complementary approach, providing extremely high resolution spatial and temporal data on folding processes. The effectiveness of such simulations is currently hampered by continuing questions regarding the ability of molecular dynamics force fields to reproduce the true potential energy surfaces of proteins, and ongoing difficulties with obtaining sufficient sampling to meaningfully comment on folding mechanisms. We review recent progress in the simulation of three common model systems for protein folding, and discuss how recent advances in technology and theory are allowing protein folding simulations to address their current shortcomings.

Figure 1

Cartoon representations of proteins discussed in this review. Secondary structures are assigned using STRIDE (97): α helix (purple), β sheet (yellow), turn (cyan), coil (white), or 3₁₀ helix (blue). a) Trpcage (PDB code 1L2Y). b) Villin (PDB code 1YRI). c) WW domain (PDB code 2F21). d) λ repressor (PDB code 1LMB). Secondary structure elements for villin and the WW domain are labeled matching discussion in the text.

Figure 2

Representative snapshots of the trajectory followed by villin headpiece from the pre-folded intermediate to the native state, with labels corresponding to the discussion in the text. Protein coloring runs blue to red from N terminus to C terminus; the crystal structure is shown as a transparent gray cartoon for comparison. Reprinted from Biophysical Journal 97; Lydia Freddolino and Klaus Schulten; Common structural transitions in explicit-solvent simulations of villin headpiece folding; 2338–2347; Copyright 2009, with permission from Elsevier.

Figure 3

Projections of a villin folding trajectory (corresponding to WT-FOLD1 in Fig. 2) onto two-dimensional surfaces. a) Projection onto Q/C_α-RMSD space; Q represents the fraction of native contacts formed, and is defined as in (98). b) Embedding of the trajectory into a two-dimensional space chosen via nMDS (58) based on the dihedral angles of the protein. In both cases frames prior to the intial hydrophobic collapse are omitted for clarity; the earlier frames are very low Q, high C_α-RMSD, and are scattered randomly in nMDS space. Two arrows are drawn showing the path taken between the 5315 ns, 5384 ns, and 5458 ns time points (c.f. Fig. 2); this path corresponds to the crossing of the putative free energy barrier identified in (30).

Figure 4

Directionality of hydrogen bonding in folding simulations. a) Illustration of the hydrogen-acceptor-acceptor antecedent angle Ψ in a protein backbone hydrogen bond. b) Normalized histogram of Ψ angles present in MD simulations of a misfolded helical state (Helix) or the native state (Sheet) of the WW domain (39). A survey of the PDB indicated that both should peak between 155 and 160 degrees (80). Part (b) reprinted from supplementary material of Biophysical Journal 96; Lydia Freddolino, Sanghyun Park, Benoît Roux, and Klaus Schulten; Force field bias in protein folding simulations; 3772–3780; Copyright 2009, with permission from Elsevier.