¹⁵N-H-Related Conformational Entropy Changes Entailed by Plexin-B1 RBD Dimerization: Combined Molecular Dynamics/NMR Relaxation Approach

We report on a new method for determining function-related conformational entropy changes in proteins. Plexin-B1 RBD dimerization serves as example, and internally mobile N-H bonds serve as probes. S_k (entropy in units of k_BT) is given by -∫(P_eqlnP_eq)dΩ, where P_eq = exp(-u) is the probability density for probe orientation, and u the local potential. Previous slowly relaxing local structure (SRLS) analyses of ¹⁵N-H relaxation in proteins determined linear combinations of D00²(Ω) and (D02₂(Ω) + D0-2²(Ω)) (D0K_L(Ω) represents a Wigner rotation matrix element in uniaxial local medium) as "best-fit" form of u. SRLS also determined the "best-fit" orientation of the related ordering tensor. On the basis of this information the coefficients (in the linear combination) of the terms specified above are determined with molecular dynamics (MD) simulations. With the explicit expression for u thus in hand, S_k is calculated. We find that in general S_k decreases, i.e., the local order increases, upon plexin-B1 RBD dimerization. The largest decrease in S_k occurs in the helices α₁ and α₂, followed by the α₂/β₆ turn. Only the relatively small peripheral β₂ strand, β₂/α₁ turn, and L3 loop become more disordered. That α-helices dominate ΔS_k = S_k(dimer) - S_k(monomer), a few peripheral outliers partly counterbalance the overall decrease in S_k, and the probability density function, P_eq, has rhombic symmetry given that the underlying potential function, u, has rhombic symmetry, are interesting features. We also derive S² (the proxy of u in the simple "model-free (MF)" limit of SRLS) with MD. Its conversion into a potential requires assumptions and adopting a simple axial form of u. Ensuing ΔS_k(MF) profiles are u-dependent and differ from ΔS_k(SRLS). A method that provides consistent, general, and accurate S_k, atomistic/mesoscopic in nature, has been developed. Its ability to provide new insights in protein research has been illustrated.