Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins

Abstract

We present a new coarse-grained C_α-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Figure 1

Idea of the PID angles. The interaction between residues i and j involves angles Ψ_ij (defined by i – 1, i, i + 1, and j beads) and Ψ_ji (defined by j – 1, j, j + 1, and i beads).

Figure 2

Distributions of the PID angles in the contacts from the PDB survey that are only of one type (green histograms). Local i, i + 3 and i, i + 4 contacts are excluded. Each contact has two angles. Distribution of the first (Ψ_PID^ij) is on the top panels, and that of the second (Ψ_PID^ji) is on the bottom panels. Subdistributions made from contacts that obey the directional criteria defined in ref (37) are shown as red histograms. The potential resulting from the Boltzmann inversion procedure (blue dots; unit of energy, ε ≈ 1.5 kcal/mol) was fitted to an analytical function (purple line).

Figure 3

Two-dimensional distributions of contacts, where the PID angle Ψ_PID is on one axis, and the C_α–C_α distance r is on the other axis. The i, i + 3 and i, i + 4 contacts are excluded. The distributions include each contact obtained in the PDB survey where at least one residue in the pair was of the given amino acid type (PRO, GLY, ALA, and GLN). The PID angle Ψ_PID for each contact is the one associated with this residue (if both residues were the same amino acid, then it corresponds to two counts with two different PID angles).

Figure 4

Comparison between the simulated and measured radius of gyration for 23 IDPs. Panels (a)–(f) show simulation results obtained within six different models. The model names are specified in the panels and defined in the text. The value of the Pearson coefficient is also indicated in each panel. Colors indicate the number of residues constituting a given IDP.

Figure 5

Histogram test for the new model (P^– F MD_0.1 C) and previous model (A⁺ L ME₁ T) based on simulations of proteins his5, NRG1, and p53 at temperatures 0.35 and 0.4 ε/k_B. Insets show the energy histograms binned every 1 ε and used to construct the quantity log(p₁(E)/p₂(E)) shown on the main plots as a function of energy.

Figure 6

Physical time of 1 ns-simulation run on a single core for the new model (P^– F MD_0.1 C, squares) and previous model (A⁺ L ME₁ T, stars) as a function of the system size. The number of protein chains in the simulation is indicated by color. The system density of multichain simulations was set to 1 residue/nm³. Fitted lines have coefficients of 0.003 and 0.0005 s/residue, respectively, with a fit error in the order of 0.0001 s/residue.

Figure 7

Top seven variants of the PID model ranked by their Pearson coefficient.