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. <i>S</i>_k (entropy in units of <i>k</i>_B<i>T</i>) is given by –∫(<i>P</i>_eqln<i>P</i>_eq)<i>d</i>Ω, where <i>P</i>_eq = exp­(−<i>u</i>) is the probability density for probe orientation, and <i>u</i> the local potential. Previous slowly relaxing local structure (SRLS) analyses of ¹⁵N–H relaxation in proteins determined linear combinations of <i>D</i>₀₀²(Ω) and (<i>D</i>₀₂²(Ω) + <i>D</i>_0–2²(Ω)) (<i>D</i>_0<i>K</i>^L(Ω) represents a Wigner rotation matrix element in uniaxial local medium) as “best-fit” form of <i>u</i>. 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 <i>u</i> thus in hand, <i>S</i>_k is calculated. We find that in general <i>S</i>_k decreases, i.e., the local order increases, upon plexin-B1 RBD dimerization. The largest decrease in <i>S</i>_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 Δ<i>S</i>_k = <i>S</i>_k(dimer) – <i>S</i>_k(monomer), a few peripheral outliers partly counterbalance the overall decrease in <i>S</i>_k, and the probability density function, <i>P</i>_eq, has rhombic symmetry given that the underlying potential function, <i>u</i>, has rhombic symmetry, are interesting features. We also derive <i>S</i>² (the proxy of <i>u</i> 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 <i>u</i>. Ensuing Δ<i>S</i>_k(MF) profiles are <i>u</i>-dependent and differ from Δ<i>S</i>_k(SRLS). A method that provides consistent, general, and accurate <i>S</i>_k, atomistic/mesoscopic in nature, has been developed. Its ability to provide new insights in protein research has been illustrated

Analysis of Velocity Autocorrelation Functions from Molecular Dynamics Simulations of a Small Peptide by the Generalized Langevin Equation with a Power-Law Kernel

Internal motions play an essential role in the biological functions of proteins and have been the subject of numerous theoretical and spectroscopic studies. Such complex environments are associated with anomalous diffusion where, in contrast to the classical Brownian motion, the relevant correlation functions have power law decays with time. In this work, we investigate the presence of long memory stochastic processes through the analysis of atomic velocity autocorrelation functions. Analytical expressions of the velocity autocorrelation function spectrum obtained through a Mori–Zwanzig projection approach were shown to be compatible with molecular dynamics simulations of a small helical peptide (8-polyalanine)

Stochastic Modeling of Flexible Biomolecules Applied to NMR Relaxation. 2. Interpretation of Complex Dynamics in Linear Oligosaccharides

A computational stochastic approach is applied to the description of flexible molecules. By combining (i) molecular dynamics simulations, (ii) hydrodynamics approaches, and (iii) a multidimensional diffusive description for internal and global dynamics, it is possible to build an efficient integrated approach to the interpretation of relaxation processes in flexible systems. In particular, the model is applied to the interpretation of nuclear magnetic relaxation measurements of linear oligosaccharides, namely a mannose-containing trisaccharide and the pentasaccharide LNF-1. Experimental data are reproduced with sufficient accuracy without free model parameters

Analysis of ¹⁵N–¹H NMR Relaxation in Proteins by a Combined Experimental and Molecular Dynamics Simulation Approach: Picosecond–Nanosecond Dynamics of the Rho GTPase Binding Domain of Plexin-B1 in the Dimeric State Indicates Allosteric Pathways

We investigate picosecond–nanosecond dynamics of the Rho-GTPase Binding Domain (RBD) of plexin-B1, which plays a key role in plexin-mediated cell signaling. Backbone ¹⁵N relaxation data of the dimeric RBD are analyzed with the model-free (MF) method, and with the slowly relaxing local structure/molecular dynamics (SRLS-MD) approach. Independent analysis of the MD trajectories, based on the MF paradigm, is also carried out. MF is a widely popular and simple method, SRLS is a general approach, and SRLS-MD is an integrated approach we developed recently. Corresponding parameters from the RBD dimer, a previously studied RBD monomer mutant, and the previously studied complex of the latter with the GTPase Rac1, are compared. The L₂, L₃, and L₄ loops of the plexin-B1 RBD are involved in interactions with other plexin domains, GTPase binding, and RBD dimerization, respectively. Peptide groups in the loops of both the monomeric and dimeric RBD are found to experience weak and moderately asymmetric local ordering centered approximately at the C_<i>i</i>–1^α–C_<i>i</i>^α axes, and nanosecond backbone motion. Peptide groups in the α-helices and the β-strands of the dimer (the β-strands of the monomer) experience strong and highly asymmetric local ordering centered approximately at the C_<i>i</i>–1^α–C_<i>i</i>^α axes (N–H bonds). N–H fluctuations occur on the picosecond time scale. An allosteric pathway for GTPase binding, providing new insights into plexin function, is delineated

Photoresponsive Supramolecular Architectures Based on Polypeptide Hybrids

Self-aggregation has recently emerged as an efficient tool for the production of well-ordered supramolecular structures at the nanometric scale. In this framework, peptides offer important advantages as building blocks because of their biocompatibility and 3D-structural/functional diversities. The chemical diversity of peptides may be further expanded by use of noncoded amino acids. In the present work, we focused our attention on two known photoswitchable azobenzene-containing α-amino acids and used them as initiators for the reversible modulation of the <i>cis</i>/<i>trans</i> conformational states of two poly­(γ-benzyl-l-glutamate)-based hybrid molecules with either <i>C</i>₂ or <i>C</i>₃ symmetry. The microscopic photoresponsive self-assembly of these compounds was examined in detail. Moreover, these hybrids were exploited in the construction of macroscopic supramolecular architectures via the electrospinning technique. Finally, after appropriate thiol functionalization, we fabricated and characterized dimeric and trimeric gold nanoparticle/polypeptide hybrid systems

Integrated Computational Approach to the Electron Paramagnetic Resonance Characterization of Rigid 3₁₀-Helical Peptides with TOAC Nitroxide Spin Labels

We address the interpretation, via an integrated computational approach, of the experimental continuous-wave electron paramagnetic resonance (cw-EPR) spectra of a complete set of conformationally highly restricted, stable 3₁₀-helical peptides from hexa- to nonamers, each bis-labeled with nitroxide radical-containing TOAC (4-amino-1-oxyl-2,2,6,6-tetramethylpiperidine-4-carboxylic acid) residues. The usefulness of TOAC for this type of analysis has been shown already to be due to its cyclic piperidine side chain, which is rigidly connected to the peptide backbone α-carbon. The TOAC α-amino acids are separated by two, three, four, and five intervening residues. This set of compounds has allowed us to modulate both the radical···radical distance and the relative orientation parameters. To further validate our conclusion, a comparative analysis has been carried out on three singly TOAC-labeled peptides of similar main-chain length