(15)N-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. Sk (entropy in units of kBT) is given by -∫(PeqlnPeq)dΩ, where Peq = exp(-u) is the probability density for probe orientation, and u the local potential. Previous slowly relaxing local structure (SRLS) analyses of (15)N-H relaxation in proteins determined linear combinations of D00(2)(Ω) and (D02(2)(Ω) + D0-2(2)(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, Sk is calculated. We find that in general Sk decreases, i.e., the local order increases, upon plexin-B1 RBD dimerization. The largest decrease in Sk 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 ΔSk = Sk(dimer) - Sk(monomer), a few peripheral outliers partly counterbalance the overall decrease in Sk, and the probability density function, Peq, has rhombic symmetry given that the underlying potential function, u, has rhombic symmetry, are interesting features. We also derive S(2) (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 ΔSk(MF) profiles are u-dependent and differ from ΔSk(SRLS). A method that provides consistent, general, and accurate Sk, atomistic/mesoscopic in nature, has been developed. Its ability to provide new insights in protein research has been illustrated.