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.

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, (MD), which restricts its internal motion, as a qualifier of the local dynamic structure. (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.

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, = exp(-) (, local potential), and associated conformational entropy, = -∫ (ln ) ─ln ∫d, 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) functions indicate "flexibility" ("rigidity"; the respective concepts are used below in this context).

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, = exp(-) (, local potential), of bond-vectors in proteins provide information on structural flexibility. The related conformational entropy, = -∫(ln )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 and from MD simulations, using the N-H bond as probe.

Slowly Relaxing Local Structure Analysis of N Relaxation from the Proteins p50 and Human Neutrophil Gelatinase-Associated Lipocalin: New Insights into the Dynamic Structure of β-Barrel Proteins.

Nuclear magnetic resonance relaxation analysis is a powerful method for studying the internal mobility of proteins. We have developed for analysis the slowly relaxing local structure (SRLS) approach. SRLS is general in its nature in several respects, including the tensorial representation of the physical quantities comprising the dynamic model.

Structural Dynamics by NMR in the Solid State: II. The MOMD Perspective of the Dynamic Structure of Metal-Organic Frameworks Comprising Several Mobile Components.

We describe the application of the microscopic-order-macroscopic-disorder (MOMD) approach, developed for the analysis of dynamic H NMR lineshapes in the solid state, to unravel interactions among the constituents of metal-organic frameworks (MOFs) that comprise mobile components. MOMD was applied recently to University of Windsor Dynamic Material (UWDM) MOFs with one mobile crown ether per cavity. In this work, we study UWDM-9-, which comprises a mobile H-labeled phenyl-ring residue along with an isotopically unlabeled 24C8 crown ether.

The N-Terminal Domain of Aβ-Amyloid Fibril: The MOMD Perspective of its Dynamic Structure from NMR Lineshape Analysis.

We have developed the stochastic microscopic-order-macroscopic-disorder (MOMD) approach for elucidating dynamic structures in the solid-state from H NMR lineshapes. In MOMD, the probe experiences an effective/collective motional mode. The latter is described by a potential, , which represents the local spatial-restrictions, a local-motional diffusion tensor, , and key features of local geometry.

Structural Dynamics from NMR Relaxation by SRLS Analysis: Local Geometry, Potential Energy Landscapes, and Spectral Densities.

We have developed the two-body coupled-rotator slowly relaxing local structure (SRLS) approach for elucidating protein dynamics by nuclear magnetic resonance (NMR) relaxation. The rotators are represented by diffusion tensors for overall protein tumbling and for locally ordered probe motion. and are coupled dynamically by a potential, , typically given by linear combinations of the Wigner functions and ( + ).

SRLS Analysis of N-H NMR Relaxation from the Protein S100A1: Dynamic Structure, Calcium Binding, and Related Changes in Conformational Entropy.

We report on amide (N-H) NMR relaxation from the protein S100A1 analyzed with the slowly relaxing local structure (SRLS) approach. S100A1 comprises two calcium-binding "EF-hands" (helix-loop-helix motifs) connected by a linker. The dynamic structure of this protein, in both calcium-free and calcium-bound form, is described as the restricted local N-H motion coupled to isotropic protein tumbling.

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, ∝ exp(-). By selecting a bond vector (e.

Structural Dynamics by NMR in the Solid State: The Unified MOMD Perspective Applied to Organic Frameworks with Interlocked Molecules.

The microscopic-order-macroscopic-disorder (MOMD) approach for NMR lineshape analysis has been applied to the University of Windsor Dynamic Materials (UWDM) of types 1, 2, α-3, β-3, and 5, which are metal-organic frameworks (MOFs) comprising mobile mechanically interlocked molecules (MIMs). The mobile MIM components are selectively deuterated crown ether macrocycles - 24C6, 22C6, and B24C6. Their motion is described in MOMD by an effective/collective dynamic mode characterized by a diffusion tensor, , a restricting/ordering potential, , expanded in the Wigner rotation matrix elements, , and features of local geometry.

Local ordering and dynamics in anisotropic media by magnetic resonance: from liquid crystals to proteins.

Magnetic resonance methods have been used extensively for over 50 years to elucidate molecular structure and dynamics of liquid crystals (LCs), providing information quite unique in its rigour and extent. The ESR- or NMR-active probe is often a solute molecule reporting on characteristics associated with the surrounding (LC) medium, which exerts the spatial restrictions on the probe. The theoretical approaches developed for LCs are applicable to anisotropic media in general.

Conformational Entropy from Restricted Bond-Vector Motion in Proteins: The Symmetry of the Local Restrictions and Relation to NMR Relaxation.

Locally mobile bond-vectors contribute to the conformational entropy of the protein, given by ≡ / = -∫( ln )dΩ - ln∫dΩ. The quantity = exp(-)/ is the orientational probability density, where is the partition function and is the spatially restricting potential exerted by the immediate internal protein surroundings at the site of the motion of the bond-vector. It is appropriate to expand the potential, , which restricts local rotational reorientation, in the basis set of the real combinations of the Wigner rotation matrix elements, .

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, , of the real combinations of the Wigner rotation matrix elements, , with = 1-4 and appropriate symmetry.

Local Ordering at Mobile Sites in Proteins: Combining Perspectives from NMR Relaxation and Molecular Dynamics.

We report on progress toward improving NMR relaxation analysis in proteins in terms of the slowly relaxing local structure (SRLS) approach by developing a method that combines SRLS with molecular dynamics (MD) simulations. N-H bonds from the Rho GTPase binding domain of plexin-B1 are used as test case. We focus on the locally restricting/ordering potential of mean force (POMF), u(θ,φ), at the N-H site (θ and φ specify the orientation of the N-H bond in the protein).

Phenyl-Ring Dynamics in Amyloid Fibrils and Proteins: The Microscopic-Order-Macroscopic-Disorder Perspective.

We have developed the microscopic-order-macroscopic-disorder (MOMD) approach for studying internal mobility in polycrystalline proteins with H lineshape analysis. The motion itself is expressed by a diffusion tensor, R, the local spatial restraints by a potential, u, and the "local geometry" by the relative orientation of the model-related and nuclear magnetic resonance-related tensors. Here, we apply MOMD to phenyl-ring dynamics in several Αβ-amyloid-fibrils, and the villin headpiece subdomain (HP36).

MOMD Analysis of NMR Line Shapes from Aβ-Amyloid Fibrils: A New Tool for Characterizing Molecular Environments in Protein Aggregates.

The microscopic-order-macroscopic-disorder (MOMD) approach for H NMR line shape analysis is applied to dry and hydrated 3-fold- and 2-fold-symmetric amyloid-Aβ fibrils and protofibrils of the D23N mutant. The methyl moieties of L17, L34, V36 (C-CD), and M35 (S-CD) serve as probes. Experimental H spectra acquired previously in the 147-310 K range are used.

Protein dynamics in the solid-state from H NMR lineshape analysis. III. MOMD in the presence of Magic Angle Spinning.

We report on a new approach to the analysis of dynamic NMR lineshapes from polycrystalline (i.e., macroscopically disordered) samples in the presence of Magic Angle Spinning (MAS).

Conformational Entropy from Slowly Relaxing Local Structure Analysis of N-H Relaxation in Proteins: Application to Pheromone Binding to MUP-I in the 283-308 K Temperature Range.

The slowly relaxing local structure (SRLS) approach is applied to N-H relaxation from the major urinary protein I (MUP-I), and its complex with pheromone 2-sec-butyl-4,5-dihydrothiazol. The objective is to elucidate dynamics, and binding-induced changes in conformational entropy. Experimental data acquired previously in the 283-308 K temperature range are used.

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. S (entropy in units of kT) is given by -∫(PlnP)dΩ, where P = exp(-u) is the probability density for probe orientation, and u the local potential.

Conformational Entropy from NMR Relaxation in Proteins: The SRLS Perspective.

Conformational entropy changes associated with bond-vector motions in proteins contribute to the free energy of ligand-binding. To derive such contributions, we apply the slowly relaxing local structure (SRLS) approach to NMR relaxation from N-H bonds or C-CDH moieties of several proteins in free and ligand-bound form. The spatial restraints on probe motion, which determine the extent of local order, are expressed in SRLS by a well-defined potential, u(θ).

An SRLS Study of H Methyl-Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLC1C SH2.

The two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for NMR relaxation in proteins is extended to derive conformational entropy, Ŝ. This version of SRLS is applied to deuterium relaxation from the C-CDH bonds of free and peptide-bound PLC1C SH2. Local C-CDH motion is described by a correlation time for local diffusion, τ, and a Maier-Saupe potential, u.

Local Ordering at Mobile Sites in Proteins from Nuclear Magnetic Resonance Relaxation: The Role of Site Symmetry.

Restricted motions in proteins (e.g., N-H bond dynamics) are studied effectively with NMR.

Polar Versus Non-polar Local Ordering at Mobile Sites in Proteins: Slowly Relaxing Local Structure Analysis of (15)N Relaxation in the Third Immunoglobulin-Binding Domain of Streptococcal Protein G.

We developed recently the slowly relaxing local structure (SRLS) approach for studying restricted motions in proteins by NMR. The spatial restrictions have been described by potentials comprising the traditional L = 2, K = 0, 2 spherical harmonics. However, the latter are associated with non-polar ordering whereas protein-anchored probes experience polar ordering, described by odd-L spherical harmonics.