Microsecond MD Simulations of the Plexin-B1 RBD: N–H Probability Density as Descriptor of Structural Dynamics, Dimerization-Related Conformational Entropy, and Transient Dimer Asymmetry

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Orientational probability densities, P eq = exp(−u) (u, local potential), of bond-vectors in proteins provide information on structural flexibility. The related conformational entropy, S k = −∫P eq(ln P eq)dΩ – ln ∫dΩ, provides the entropic contribution to the free energy of the physical/biological process studied. We have developed a new method for deriving P eq and S k from MD simulations, using the N–H bond as probe. Recently we used it to study the dimerization of the Rho GTPase binding domain of Plexin-B1 (RBD). Here we use it to study RBD binding to the small GTPase Rac1. In both cases 1 μs MD simulations have been employed. The RBD has the ubiquitin fold with four mostly long loops. L3 is associated with GTPase binding, L4 with RBD dimerization, L2 participates in interdomain interactions, and L1 has not been associated with function. We find that RBD-Rac1 binding renders L1, L3, and L4 more rigid and the turns β2/α1 and α2/β5 more flexible. By comparison, RBD dimerization renders L4 more rigid, and the α-helices, the β-strands, and L2 more flexible. The rigidity of L1 in RBDRAC is consistent with L1–L3 contacts seen in previous MD simulations. The analysis of the L3-loop reveals two states of distinct flexibility which we associate with involvement in slow conformational exchange processes differing in their rates. Overall, the N–H bonds make an unfavorable entropic contribution of (5.9 ± 0.9) kJ/mol to the free energy of RBD-Rac1 binding; they were found to make a favorably contribution of (−7.0 ± 0.7) kJ/mol to the free energy of RBD dimerization. In summary, the present study provides a new perspective on the impact of Rac1 binding and dimerization on the flexibility characteristics of the RBD. Further studies are stimulated by the results of this work.

“… P eq functions for the α 2 /β 5 turn of (a) d1, which is monomer unit 1 of the RBD dimer (ref ) and (b) RBDRAC. Designations R1–R4 as in the captions of Figure .…”

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Section: Theoretical/computational Backgroundmentioning

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Section: Introductionmentioning

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Microsecond MD Simulations of the Plexin-B1 RBD: 2. N–H Probability Densities and Conformational Entropy in Ligand-Free, Rac1-Bound, and Dimer RBD

Mendelman

Pshetitsky

et al. 2022

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Local Structures in Proteins from Microsecond Molecular Dynamics Simulations: A Symmetry-Based Perspective

Pshetitsky,

Mendelman,

Buck

et al. 2024

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We report on a new method for the characterization of local structures in proteins based on extensive molecular dynamics (MD) simulations, here, 1 μs in length. The N−H bond of the Rho GTPase binding domain of plexin-B1 (RBD) serves as a probe and the potential, u(MD), which restricts its internal motion, as a qualifier of the local dynamic structure. u(MD) is derived from the MD trajectory as a function of the polar angles, (θ, φ), which specify the N−H orientation in the protein. u(MD) is statistical in character yielding empirical descriptions. To establish more insightful methodical descriptions, we develop a comprehensive method which approximates u(MD) by combinations of analytical Wigner functions that belong to the D 2h point group. These combinations, called u(simulated), make it possible to gain a new perspective of local dynamic structures in proteins based on explicit potentials/free energy surfaces and associated probability densities, entropy, and ordering. A simpler method was developed previously using 100 ns MD simulations. In that case, the traditional "perpendicular N−H ordering" setting centered at C α −C α with (θ, φ) = (90, 90) and generally, featuring positive φ, prevailed. u(MD) derived from 1 μs MD simulations is considerably more complex requiring substantial model enhancement. The enhanced method applies to the well-structured sections of the RBD. It only applies partly to its loops where u(MD) extends into the negative-φ region where we detect nonperpendicular N−H ordering. This arrangement requires devising new reference structures and making substantial algorithmic changes, to be performed in future work. Here, we focus on developing the comprehensive method and using it to investigate perpendicular ordering settings. We find that secondary structures (loops) exhibit varying (virtually invariant) potentials with A g , B 2u , and B 1u (A g and B 2u ) D 2h symmetry. Application to RBD dimerization and RBD binding to the GTPase Rac1 is described in the subsequent article. Applications to other probes, proteins, and biological functions, based on explicit local potentials, probability densities, entropy, and ordering, are possible. 2 D 2,2 , where D 2,0 and D 2,2 are the Wigner functions with D 2h symmetry, D L,K , with L = 2 and K = 0 and 2 (cf. the Supporting Information (SI)). The D L,K functions, hence u, are given in terms of the polar angles, θ and φ, which specify the orientation of the N−H bond in the protein. 12 More enhanced potential forms comprising additional D L,K functions could not be used in view

Local Structures in Proteins from Microsecond Molecular Dynamics Simulations: 2. The Role of Symmetry in GTPase Binding and Dimer Formation

Pshetitsky,

Buck,

Meirovitch

2024

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The Rho GTPase binding domain of Plexin-B1 (RBD) prevails in solution as dimer. Under appropriate circumstances, it binds the small GTPase Rac1 to yield the complex RBD-Rac1. Here, we study RBD dimerization and complex formation from a symmetry-based perspective using data derived from 1 μs long MD simulations. The quantities investigated are the local potentials, u(MD), prevailing at the N−H sites of the protein. These potentials are statistical in character providing an empirical description of the local structure. To establish more methodical description, a method for approximating them by explicit functions, u(simulated), was developed in the preceding article in this journal issue. These functions are combinations of analytical Wigner functions, D L,K , belonging to the D 2h point group. The D 2h subgroups A g and B 2u are found to dominate u(simulated); the B 1u subgroup contributes in some cases. The A g (B 2u ) functions have axial or rhombic symmetry. For the first time, local potentials in proteins can be quantitatively characterized in terms of their strength (rhombicity) evaluated by axial A g (rhombic A g and B 2u ) contributions. Until now, the chain-segment [β 3 -L3-β 4 ] and to some extent the α 2 -helix have been associated with GTPase binding. Here, we find that this process causes an increase (decrease) in the potential strength of β 3 and β 4 (the preceding L2 loop and the remote chain-segment [(α 2 -helix)-(α 2 /β 5 -turn)-(β 5 -strand)]), suggesting effects of counterbalancing and allostery. There is evidence for the L2 loop being associated with RBD-GTPase binding. Until now only the L4 loop has been associated with RBD dimerization. The latter process is found to cause an increase (decrease) in the potential strength and rhombicity of the L4 loop (the adjacent chain-segment [(α 2 -helix)-(α 2 /β 5 -turn)-(β 5 -strand)]), suggesting counterbalancing activity. On average, the RBD dimer features stronger local potentials than RBD-Rac1. The novel information inherent in these findings is mesoscopic in character. Prospects of interest include exploring relation to atomistic forcefield parameters.