Peptide-Plane Dynamics in Protein Loops from Microsecond Molecular Dynamics: A Symmetry-Based Perspective

We present a new description of large-scale peptide-plane dynamics occurring primarily in protein loops, based on established symmetry principles. As model system we analyze molecular dynamics (MD) simulations of the Rho GTPase-binding domain of plexin-B1 (RBD). From the MD trajectories, we derive statistical local peptide-plane-related potentials, u(θ, φ), and corresponding probability distributions, P(θ, φ) = exp[−u(θ, φ)]. The polar angles, (θ, φ), describe the orientation of the probe in the protein. The time series of the peptide-plane-flanking dihedrals, (Ψ, Φ), are also derived. Earlier 50–100 ns RBD simulations yielded positive-φ free-energy surfaces, u(positive)(θ, φ), spanning the 0 ≤ (θ, φ) ≤ 180° range. To extract maximal information from these statistical functions, we explicitly approximated them by combinations of real Wigner functions, DL,K, which, like the peptide plane, exhibit D2h symmetry. Nonpolar Ag and uniquely polar-vector B2u terms were found to make the dominant contributions. Here we use 1 μs RBD simulations. Along with the previously observed u(positive)(θ, φ) component, a negative-φ component, u(negative)(θ, φ), spanning the θ′ = 180° – θ and φ′ = – φ range, also appears. Within the overall potential, u(combined)(θ, φ), the two components relate by inversion and rarely interconvert, pointing phenomenologically to slow motion on the 1 μs time scale. This behavior is also evident in the time series of the peptide-plane-flanking dihedrals. The overall potential, u(combined)(θ, φ), is analyzed empirically. We show that Ag and B2u D2h symmetry elements are inherent to its structure. Based on the results obtained here and in the accompanying article in this issue, we establish a new symmetry-based framework for analyzing local peptide-plane dynamics, grounded in the effective D2h symmetry of the peptide plane. Actual motions are exemplified by the canonical type II → type I β-turn crankshaft flips executed by the peptide plane K50–G51 of the L2 loop of the RBD. Broader applications involving diverse peptide-plane restructuring mechanisms are presented in the accompanying article.