Multidimensional integration through Markovian sampling under steered function morphing: A physical guise from statistical mechanics

Abstract We present a computational strategy for the evaluation of multidimensional integrals on hyper-rectangles based on Markovian stochastic exploration of the integration domain while the integrand is being morphed by starting from an initial appropriate profile. Thanks to an abstract reformulation of Jarzynski’s equality applied in stochastic thermodynamics to evaluate the free-energy profiles along selected reaction coordinates via non-equilibrium transformations, it is possible to cast the orig... Title of program: JEMDI Catalogue Id: AEWO_v1_0 Nature of problem Integration of general functions of many variables Versions of this program held in the CPC repository in Mendeley Data AEWO_v1_0; JEMDI; 10.1016/j.cpc.2015.04.010 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018

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)

Simulation of electron spin resonance spectroscopy in diverse environments: An integrated approach

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract We discuss in this work a new software tool, named E-SpiReS (Electron Spin Resonance Simulations), aimed at the interpretation of dynamical properties of molecules in fluids from electron spin resonance (ESR) measurements. The code implements an integrated computational approach (ICA) for the calculation of relevant molecular properties that are needed in order to obtain spectral lines. The protocol encompasses information from atomistic level (quantum mechanical) to coarse grained level (hyd... Title of program: E-SpiReS Catalogue Id: AEEM_v1_0 Nature of problem ab initio simulation of cw-ESR spectra of radicals in solution Versions of this program held in the CPC repository in Mendeley Data AEEM_v1_0; E-SpiReS; 10.1016/j.cpc.2009.06.01

Stochastic Modeling of CW-ESR Spectroscopy of [60]Fulleropyrrolidine Bisadducts with Nitroxide Probes

In this work, we address the interpretation of continuous wave electron spin resonance (CW-ESR) spectra of fulleropyrrolidine bisadducts with nitroxide addends. Our approach is based on a definition of the spin Hamiltonian which includes exchange and dipolar interactions and on a complete numerical solution of the resulting stochastic Liouville equation, with inclusion of diffusive rotational dynamics. CW-ESR spectra are simulated for a series of C60 bisadducts made up of four trans isomers and the equatorial isomer. A nonlinear least-squares fitting procedure allows extraction directly from the available experimental spectra of a wide range of parameters, namely interprobe relative distances, diffusion tensors, and values of the exchange parameter J. Results are in good agreement with previous, more phenomenological estimates, proving that the combination of sensitive ESR spectroscopy based on multiple spin labeling with nitroxide radicals and sophisticated modeling can be highly helpful in providing structural and dynamic information on molecular systems

Stochastic Modeling of Flexible Biomolecules Applied to NMR Relaxation. I. Internal Dynamics of Cyclodextrins: γ‑Cyclodextrin as a Case Study

In this work, we address the description of the dynamics of cyclodextrins in relation with nuclear magnetic resonance (NMR) relaxation data collected for hydroxymethyl groups. We define an integrated computational approach based on the definition and parametrization of a stochastic equation able to describe the relevant degrees of freedom affecting the NMR observables. The computational protocol merges molecular dynamics simulations and hydrodynamics approaches for the evaluation of most of the molecular parameters entering the stochastic description of the system. We apply the method to the interpretation of the 13C NMR relaxation of the −CH2OH group of cyclodextrins. We use γ-cyclodextrin as a case study. Results are in agreement with quantitative and qualitative analyses performed in the past with simpler models and molecular dynamics simulations. The element of novelty in our approach is in the treatment of the coupling of the relevant internal (glucopyranose ring twisting/tilting and hydroxymethyl group jumps) and global (molecular tumbling) degrees of freedom

Development and Validation of an Integrated Computational Approach for the Modeling of cw-ESR Spectra of Free Radicals in Solution: <i>p</i>-(Methylthio)phenyl Nitronylnitroxide in Toluene as a Case Study

In this work we address the interpretation, via an ab initio integrated computational approach, of continuous wave electron spin resonance (cw-ESR) spectra of p-(methylthio)phenyl nitronylnitroxide (MTPNN) dissolved in toluene. Our approach is based on the determination of the spin Hamiltonian, averaged with respect to fast vibrational motions, with magnetic tensor parameters (Zeeman and hyperfine tensors) characterized by quantum mechanical density functional calculations. The system is then described by a stochastic Liouville equation, with inclusion of diffusive rotational dynamics. Parametrization of diffusion rotational tensor is provided by a hydrodynamic model. Cw-ESR spectra of MTPNN are simulated for a wide range of temperatures (155−292 K) with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing structural and dynamic information on molecular systems

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

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