Local Ordering at Mobile Sites in Proteins: Combining Perspectives from NMR Relaxation and Molecular Dynamics

We report on progress toward improving NMR relaxation analysis in proteins in terms of the slowly relaxing local structure (SRLS) approach by developing a method that combines SRLS with molecular dynamics (MD) simulations. ¹⁵N-H bonds from the Rho GTPase binding domain of plexin-B1 are used as test case. We focus on the locally restricting/ordering potential of mean force (POMF), u(θ,φ), at the N-H site (θ and φ specify the orientation of the N-H bond in the protein). In SRLS, u(θ,φ) is expanded in the basis set of the real linear combinations of the Wigner rotation matrix elements with M = 0, D _{L,| K|}(θ,φ). Because of limited data sensitivity, only the lowest ( L = 2) terms are preserved; this potential function is denoted by u^(SRLS). In MD, the force-field-parametrized POMF is the potential, u^(MD), defined in terms of the probability distribution, P_eq^(MD) ∝ exp(- u^(MD)). P_eq^(MD), and subsequently u^(MD), can be derived from the MD trajectory as histograms. One might contemplate utilizing u^(MD) instead of u^(SRLS); however, histograms cannot be used in SRLS analyses. Here, we approximate u(θ,φ) in terms of linear combinations of the D _{L,| K|} functions with L = 1-4 and appropriate symmetry, denoted by u^(DLK), and optimize the latter (via P_eq) against u^(MD). This yields for every N-H bond an analytical ordering potential, u^(DLK-BEST), which exceeds u^(SRLS) considerably in accuracy. u^(DLK-BEST) can be used fixed in SRLS data fitting, thereby enabling the determination of additional parameters. This yields a substantially improved picture of structural dynamics, which is a significant benefit. The primary achievement of this work is to have employed for the first time MD data to derive a suitable (in terms of composition and symmetry) approximation to the SRLS POMF.