Structure and dynamics analysis on plexin-B1 Rho GTPase binding domain as a monomer and dimer

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

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, DL,K, belonging to the D2h point group. The D2h subgroups Ag and B2u are found to dominate u(simulated); the B1u subgroup contributes in some cases. The Ag (B2u) 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 Ag (rhombic Ag and B2u) contributions. Until now, the chain-segment [β3-L3-β4] and to some extent the α2-helix have been associated with GTPase binding. Here, we find that this process causes an increase (decrease) in the potential strength of β3 and β4 (the preceding L2 loop and the remote chain-segment [(α2-helix)-(α2/β5-turn)-(β5-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 [(α2-helix)-(α2/β5-turn)-(β5-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 force-field parameters.

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

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 D2h 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 Cα-Cα 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 Ag, B2u, and B1u (Ag and B2u) D2h 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.

Structure, dynamics and free energy studies on the effect of point mutations on SARS-CoV-2 spike protein binding with ACE2 receptor

The ongoing COVID-19 pandemic continues to infect people worldwide, and the virus continues to evolve in significant ways which can pose challenges to the efficiency of available vaccines and therapeutic drugs and cause future pandemic. Therefore, it is important to investigate the binding and interaction of ACE2 with different RBD variants. A comparative study using all-atom MD simulations was conducted on ACE2 binding with 8 different RBD variants, including N501Y, E484K, P479S, T478I, S477N, N439K, K417N and N501Y-E484K-K417N on RBD. Based on the RMSD, RMSF, and DSSP results, overall the binding of RBD variants with ACE2 is stable, and the secondary structure of RBD and ACE2 are consistent after the point mutation. Besides that, a similar buried surface area, a consistent binding interface and a similar amount of hydrogen bonds formed between RBD and ACE2 although the exact residue pairs on the binding interface were modified. The change of binding free energy from point mutation was predicted using the free energy perturbation (FEP) method. It is found that N501Y, N439K, and K417N can strengthen the binding of RBD with ACE2, while E484K and P479S weaken the binding, and S477N and T478I have negligible effect on the binding. Point mutations modified the dynamic correlation of residues in RBD based on the dihedral angle covariance matrix calculation. Doing dynamic network analysis, a common intrinsic network community extending from the tail of RBD to central, then to the binding interface region was found, which could communicate the dynamics in the binding interface region to the tail thus to the other sections of S protein. The result can supply unique methodology and molecular insight on studying the molecular structure and dynamics of possible future pandemics and design novel drugs.

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

Amide-bond equilibrium probability density, P_eq = exp(-u) (u, local potential), and associated conformational entropy, S_k = -∫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.

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

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.

Transient association between proteins elicits alteration of dynamics at sites far away from interfaces

Proteins are known to undergo structural changes upon binding to partner proteins. However, the prevalence, extent, location, and function of change in protein dynamics due to transient protein-protein interactions is not well documented. Here, we have analyzed a dataset of 58 protein-protein complexes of known three-dimensional structure and structures of their corresponding unbound forms to evaluate dynamics changes induced by binding. Fifty-five percent of cases showed significant dynamics change away from the interfaces. This change is not always accompanied by an observed structural change. Binding of protein partner is found to alter inter-residue communication within the tertiary structure in about 90% of cases. Also, residue motions accessible to proteins in unbound form were not always maintained in the bound form. Further analyses revealed functional roles for the distant site where dynamics change was observed. Overall, the results presented here strongly suggest that alteration of protein dynamics due to binding of a partner protein commonly occurs.

Conformational Entropy from Mobile Bond Vectors in Proteins: A Viewpoint that Unifies NMR Relaxation Theory and Molecular Dynamics Simulation Approaches

A new method for determining conformational entropy in proteins is reported. Proteins prevail as conformational ensembles, p ∝ exp(-u). By selecting a bond vector (e.g., N-H) as a conformation representative, molecular dynamics simulations can provide (relative to a reference structure) p as approximate Boltzmann probability density and u as N-H potential of mean force (POMF). The latter is as accurate as implied by the force field but statistical in character; this limits the insights it can provide and its utilization. Conformational entropy is given exclusively by u. Deriving it from POMFs renders it accurate but statistical in character. Previously, we devised explicit (i.e., analytical but not exact) potentials made of Wigner functions, D_0K^L, with L ≤ 4, which closely resemble the corresponding POMFs in form; hence, they also approach the latter in accuracy. Such potentials can be beneficially characterized/compared in terms of composition, symmetry, and associated order parameters. In this study, we develop a method for deriving conformational entropy from them, which also features the benefits specified above. The method developed is applied to the dimerization of the Rho GTPase-binding domain of plexin-B1. Insights into local ordering, entropy compensation, and features of allostery are gained. In previous work, we developed the slowly relaxing local structure (SRLS) approach for the analysis of NMR relaxation from restricted bond vector motion in proteins. SRLS comprises explicit (restricting) potentials of the kind developed here. It also comprises diffusion tensors describing the local motion and related features of local geometry. The complete model fits experimental data. In future work, the explicit potentials developed here will be inserted unchanged in SRLS-based data fitting, thereby improving the picture of structural dynamics. Given that SRLS is unique in featuring potentials that can closely approach the corresponding POMFs in accuracy, the present study is an important step toward generally improving protein dynamics by NMR relaxation.

Local Ordering at the N-H Sites of the Rho GTPase Binding Domain of Plexin-B1: Impact of Dimerization

We have developed a new molecular dynamics (MD) based method for describing analytically local potentials at mobile N-H sites in proteins. Here we apply it to the monomer and dimer of the Rho GTPase binding domain (RBD) of the transmembrane receptor plexin-B1 to gain insight into dimerization, which can compete with Rho GTPase binding. In our method, the local potential is given by linear combinations, u^(D_L,K), of the real combinations of the Wigner rotation matrix elements, D_L,K, with L = 1-4 and appropriate symmetry. The combination that "fits best" the corresponding MD potential of mean force, u^(MD), is the potential we are seeking, u^{(D_L,K - BEST)}. For practical reasons the fitting process involves probability distributions, P_eq ∝ exp(-u), instead of potentials, u. The symmetry of the potential, u^(D_L,K), may be related to the irreducible representations of the D_2h point group. The monomer (dimer) potentials have mostly A_g and B_2u (B_1u and B_2u) symmetry. For the monomer, the associated probability distributions are generally dispersed in space, shallow, and centered at the "reference N-H orientation" (defined in section 3.1. below); for the dimer many are more concentrated, deep and centered away from the "reference N-H orientation". The u^(D_L,K) functions provide a consistent description of the potential energy landscape at protein N-H sites. The L1-loop of the plexin-B1 RBD is not seen in the crystal structure, and many resonances of the L4 loop are missing in the NMR ¹⁵N-¹H HSQC spectrum of the dimer; we suggest reasons for these features. An allosteric signal transmission pathway was reported previously for the monomer. We find that it has shallow N-H potentials at its ends, which become deeper as one proceeds toward the middle, complementing structurally the previously derived dynamic picture. Prospects of this study include correlating u^{(D_L,K - BEST)} with MD force-fields, and using them without further adjustment in NMR relaxation analysis schemes.

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) + D_0-2²(Ω)) (D_0K^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.

Causality, transfer entropy, and allosteric communication landscapes in proteins with harmonic interactions

A fast and approximate method of generating allosteric communication landscapes in proteins is presented by using Schreiber's entropy transfer concept in combination with the Gaussian Network Model of proteins. Predictions of the model and the allosteric communication landscapes generated show that information transfer in proteins does not necessarily take place along a single path, but an ensemble of pathways is possible. The model emphasizes that knowledge of entropy only is not sufficient for determining allosteric communication and additional information based on time delayed correlations should be introduced, which leads to the presence of causality in proteins. The model provides a simple tool for mapping entropy sink-source relations into pairs of residues. By this approach, residues that should be manipulated to control protein activity may be determined. This should be of great importance for allosteric drug design and for understanding the effects of mutations on function. The model is applied to determine allosteric communication in three proteins, Ubiquitin, Pyruvate Kinase, and the PDZ domain. Predictions are in agreement with molecular dynamics simulations and experimental evidence. Proteins 2017; 85:1056-1064. © 2017 Wiley Periodicals, Inc.

Different dynamics and pathway of disulfide bonds reduction of two human defensins, a molecular dynamics simulation study

Human defensins are a class of antimicrobial peptides that are crucial components of the innate immune system. Both human α defensin type 5 (HD5) and human β defensin type 3 (hBD-3) have 6 cysteine residues which form 3 pairs of disulfide bonds in oxidizing condition. Disulfide bond linking is important to the protein structure stabilization, and the disulfide bond linking and breaking order have been shown to influence protein function. In this project, microsecond long molecular dynamics simulations were performed to study the structure and dynamics of HD5 and hBD-3 wildtype and analogs which have all 3 disulfide bonds released in reducing condition. The structure of hBD-3 was found to be more dynamic and flexible than HD5, based on RMSD, RMSF, and radius of gyration calculations. The disulfide bridge breaking order of HD5 and hBD-3 in reducing condition was predicted by two kinds of methods, which gave consistent results. It was found that the disulfide bonds breaking pathways for HD5 and hBD-3 are very different. The breaking of disulfide bonds can influence the dimer interface by making the dimer structure less stable for both kinds of defensin. In order to understand the difference in dynamics and disulfide bond breaking pathway, hydrophilic and hydrophobic accessible surface areas (ASA), buried surface area between cysteine pairs, entropy of cysteine pairs, and internal energy were calculated. Comparing to the wildtype, hBD-3 analog is more hydrophobic, while HD5 is more hydrophilic. For hBD-3, the disulfide breaking is mainly entropy driven, while other factors such as the solvation effects may take the major role in controlling HD5 disulfide breaking pathway. Proteins 2017; 85:665-681. © 2016 Wiley Periodicals, Inc.

Molecular Dynamics Simulations Reveal Isoform Specific Contact Dynamics between the Plexin Rho GTPase Binding Domain (RBD) and Small Rho GTPases Rac1 and Rnd1

The Plexin family of transmembrane receptors are unique in that their intracellular region interacts directly with small GTPases of the Rho family. The Rho GTPase binding domain of plexin (RBD)-which is responsible for these interactions-can bind with Rac1 as well as Rnd1 GTPases. GTPase complexes have been crystallized with the RBDs of plexinA1, -A2, and -B1. The protein association is thought to elicit different functional responses in a GTPase and plexin isoform specific manner, but the origin of this is unknown. In this project, we investigated complexes between several RBD and Rac1/Rnd1 GTPases using multimicrosecond length all atom molecular dynamics simulations, also with reference to the free forms of the RBDs and GTPases. In accord with the crystallographic data, the RBDs experience more structural changes than Rho-GTPases upon complex formation. Changes in protein dynamics and networks of correlated motions are revealed by analyzing dihedral angle fluctuations in the proteins. The extent of these changes differs between the different RBDs and also between the Rac1 and Rnd1 GTPases. While the RBDs in the free and bound states have similar-if not decreased-correlations, correlations within the GTPases are increased upon binding. Mapping highly correlated residues to the structures, it is found that the plexinA1, -B1, and -A2 RBDs all have similar communication pathways within the ubiquitin fold, but that different residues are involved. Dynamic network analyses indicate that plexinA1 and -B1 RBDs interact with small GTPases in a similar manner, whereas complexes with the plexinA2 RBD display different features. Importantly complexes with Rnd1 have a considerable number of dynamic correlations and network connections between the proteins, whereas such features are missing in the RBD-Rac1 complexes. Overall, the simulations suggest mechanisms that are consistent with the experimental data on plexinB1 and indicate RBD and GTPase isoform specific changes in protein dynamics upon complex formation.

Entropy Transfer between Residue Pairs and Allostery in Proteins: Quantifying Allosteric Communication in Ubiquitin

It has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we develop a computational method that can determine and quantify allosteric activity in any given protein. Based on Schreiber's transfer entropy formulation, our approach leads to an information transfer landscape for the protein that shows the presence of entropy sinks and sources and explains how pairs of residues communicate with each other using entropy transfer. The model can identify the residues that drive the fluctuations of others. We apply the model to Ubiquitin, whose allosteric activity has not been emphasized until recently, and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. We explain the complex formation propensities of Ubiquitin in terms of entropy transfer. Important residues taking part in allosteric communication in Ubiquitin predicted by our approach are in agreement with results of NMR relaxation dispersion experiments. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.