Microsecond MD Simulations of the Plexin-B1 RBD: N-H Probability Density as Descriptor of Structural Dynamics,...

Amide-bond equilibrium probability density, P_eq = exp(-u) (u, local potential), and associated conformational entropy, S = -∫P_eq (ln P_eq) dΩ ─ln ∫dΩ, are derived for the Rho GTPase binding domain of Plexin-B1 (RBD) as monomer and dimer from 1 μs MD simulations. The objective is to elucidate the effect of dimerization on the dynamic structure of the RBD. Dispersed (peaked) P_eq functions indicate "flexibility" ("rigidity"; the respective concepts are used below in this context). The L1 and L3 loops are throughout highly flexible, the L2 loop and the secondary structure elements are generally rigid, and the L4 loop is flexible in the monomer and rigid in the dimer. Overall, many residues are more flexible in the dimer. These features, and their implications, are discussed. Unexpectedly, we find that monomer unit 1 of the dimer (in short, d1) is unusually flexible, whereas monomer unit 2 (in short, d2) is as rigid as the RBD monomer. This is revealed due to their engagement in slow-to-intermediate conformational exchange detected previously by ¹⁵N relaxation experiments. Such motions occur with rates on the order of 10³-10⁴ s^-1; hence, they cannot be completely sampled over the course of 1 μs simulation. However, the extent to which rigid d2 is affected is small enough to enable physically relevant analysis. The entropy difference between d2 and the monomer yields an entropic contribution of -7 ± 0.7 kJ/mol to the free energy of RBD dimerization. In previous work aimed at similar objectives we used 50-100 ns MD simulations. Those results and the present result differ considerably. In summary, bond-vector P_eq functions derived directly from long MD simulations are useful descriptors of protein structural dynamics and provide accurate conformational entropy. Within the scope of slow conformational exchange, they can be useful, even in the presence of incomplete sampling.