Multi‐Resolution Simulation of Biomolecular Systems: A Review of Methodological Issues

Theoretical‐computational modeling with an eye to explaining experimental observations in regard to a particular chemical phenomenon or process requires choices concerning essential degrees of freedom and types of interactions and the generation of a Boltzmann ensemble or trajectories of configurations. Depending on the degrees of freedom that are essential to the process of interest, for example, electronic or nuclear versus atomic, molecular or supra‐molecular, quantum‐ or classical‐mechanical equations of motion are to be used. In multi‐resolution simulation, various levels of resolution, for example, electronic, atomic, supra‐atomic or supra‐molecular, are combined in one model. This allows an enhancement of the computational efficiency, while maintaining sufficient detail with respect to particular degrees of freedom. The basic challenges and choices with respect to multi‐resolution modeling are reviewed and as an illustration the differential catalytic properties of two enzymes with similar folds but different substrates with respect to these substrates are explored using multi‐resolution simulation at the electronic, atomic and supra‐molecular levels of resolution.     

Deriving Structural Information from Experimentally Measured Data on Biomolecules

During the past half century, the number and accuracy of experimental techniques that can deliver values of observables for biomolecular systems have been steadily increasing. The conversion of a measured value Q^exp of an observable quantity Q into structural information is, however, a task beset with theoretical and practical problems: 1) insufficient or inaccurate values of Q^exp, 2) inaccuracies in the function used to relate the quantity Q to structure , 3) how to account for the averaging inherent in the measurement of Q^exp, 4) how to handle the possible multiple‐valuedness of the inverse of the function , to mention a few. These apply to a variety of observable quantities Q and measurement techniques such as X‐ray and neutron diffraction, small‐angle and wide‐angle X‐ray scattering, free‐electron laser imaging, cryo‐electron microscopy, nuclear magnetic resonance, electron paramagnetic resonance, infrared and Raman spectroscopy, circular dichroism, Förster resonance energy transfer, atomic force microscopy and ion‐mobility mass spectrometry. The process of deriving structural information from measured data is reviewed with an eye to non‐experts and newcomers in the field using examples from the literature of the effect of the various choices and approximations involved in the process. A list of choices to be avoided is provided.     

13C GIAO DFT calculation as a tool for configuration prediction of N–O group in saturated heterocyclic N‐oxides

Tropane, tropinone, pseudopelletierine and cocaine were oxidized in situ in a nuclear magnetic resonance (NMR) tube providing mixtures of exo/endo N‐oxides. Observed ¹³C chemical shifts were correlated with values calculated by gauge‐including atomic orbitals density functional theory (DFT) OPBE/6‐31G* method using DFT B3LYP/6‐31G* optimized geometries. The same method of ¹³C chemical shift calculation was applied on series of methyl‐substituted 1‐methylpiperidines and their epimeric N‐oxides described in literature. The results show that using this undemanding calculation method enables assignment of configuration of N–O group in N‐epimeric saturated heterocyclic N‐oxides. The approach enables assigning of the configuration with high degree of certainty even if NMR data of only one isomer are available. An improved method of in situ oxidation of starting amines in an NMR tube is also described. Copyright © 2012 John Wiley & Sons, Ltd.     

Low molecular mass organogel from mesomorphic N‐(4‐hexyloxybenzoyl)‐N′‐(4′‐nitrobenzoyl)hydrazine

The mesomorphic compound N‐(4‐hexyloxybenzoyl)‐N′‐(4′‐nitrobenzoyl)hydrazine (C6‐NO₂), containing a dihydrazide unit in the rigid core, exhibited a highly stable SmA₁ phase (between 172.2 and 259.5°C) and strong gelation ability in chloroform and other non‐protonic organic solvents. Both SEM observations and X‐ray diffraction data indicated that the molecules self‐assembled into fibrous aggregates with a diameter of about 50 nm, and retained a head‐to‐tail configuration within layers. FTIR and ¹H NMR studies confirmed that intermolecular hydrogen bonding played a key role in the formation of the supra‐structures, and this was considered to be the driving force. Additionally, aggregation‐induced enhanced emission was observed in the organogels, and this was attributed to aggregation induced planarization and J‐aggregate formation.     

Correlated Coordination and Redox Activity of a Hemilabile Noninnocent Ligand in Nickel Complexes

The compound [Ni(Q_M)₂], Q_M=4,6‐di‐tert‐butyl‐N‐(2‐methylthiomethylphenyl)‐o‐iminobenzoquinone, is a singlet diradical species with approximately planar configuration at the tetracoordinate metal atom and without any Ni?S bonding interaction. One‐electron oxidation results in additional twofold Ni?S coordination (d_Ni?S≈2.38 Å) to produce a complex cation of [Ni(Q_M)₂](PF₆) with hexacoordinate Ni^II and two distinctly different mer‐configurated tridentate ligands. The O,O′‐trans arrangement in the neutral precursor is changed to an O,O′‐cis configuration in the cation. The EPR signal of [Ni(Q_M)₂](PF₆) has a very large g anisotropy and the magnetic measurements indicate an S=3/2 state. The dication was structurally characterized as [Ni(Q_M)₂](ClO₄)₂ to exhibit a similar NiN₂O₂S₂ framework as the monocation. However, the two tridentate (O,N,S) ligands are now equivalent according to the formulation [Ni^II(Q_M⁰)₂]²⁺. Cyclic voltammetry reflects the qualitative structure change on the first, but not on the second oxidation of [Ni(Q_M)₂], and spectroelectrochemistry reveals a pronounced dependence of the 800–900 nm absorption on the solvent and counterion. Reduction of the neutral form occurs in an electrochemically reversible step to yield an anion with an intense near‐infrared absorption at 1345 nm (ε=10400 M ^?1 cm^?1) and a conventional g factor splitting for a largely metal‐based spin (S=1/2), suggesting a [(Q_M ^{. ?})Ni^II(Q_M^2?)]^? configuration with a tetracoordinate metal atom with antiferromagnetic Ni^II–(Q_M ^{. ?}) interactions and symmetry‐allowed ligand‐to‐ligand intervalence charge transfer (LLIVCT). Calculations are used to understand the Ni?S binding activity as induced by remote electron transfer at the iminobenzoquinone redox system.     

Monte Carlo Simulation of the Topology and Conformational Behavior of Hyperbranched Molecules: Pd–Diimine‐Catalyzed Polyethylene

A kinetic Monte Carlo model was developed to simulate the polymerization of ethylene with palladium–α‐diimine catalyst wherein hyperbranched molecules are formed through a chain‐walking mechanism. The total degree of branching and the distribution of short branches obtained with the model agree well with reported ¹³C NMR experimental results. Different chain topologies were generated by varying the probability of chain walking, P_w , which controls the competition between chain‐walking and monomer insertion. Molecular Monte Carlo simulations were subsequently conducted to study the conformations of isolated molecules (created by the kinetic Monte Carlo scheme) to relate molecular shape and topology. Our results provide evidence that the topology varies from predominantly linear with many short branches at low P_w to a densely branched, globular structure at high P_w . In contrast to experimental observations, our results for the molecular weight (N) dependence of the radius of gyration (R_g ∝ N^v) indicate that the branching topology has an effect on this relation, i. e., high‐P_w molecules have a smaller scaling exponent v. The simulated N‐dependence of the second virial coefficient exhibits a similar behavior. We also discuss the unusual conformational behavior of highly branched polymers obtained when P_w → 1.     

Theoretical Study on Co^3＋ in Aqueous Solution in Terms of ABEEM/MM Model

A detailed theoretical investigation on Co^3＋ hydration in aqueous solution has been carded out by means of molecular dynamics （MD） simulations based on the atom-bond electronegativity equalization method fused into molecular mechanics （ABEEM/MM）. The effective Co^3＋ ion-water potential has been constructed by fitting to ab initio structures and binding energies for ionic clusters. And then the ion-water interaction potential was applied in combination with the ABEEM-7P water model to molecular dynamics simulations of single Co^3＋（aq.） solution, managing to reproduce many experimental structural and dynamical properties of the solution. Here, not only the common properties （radial distribution function, angular distribution function and solvation energy） obtained for Co^3＋ in ABEEM-7P water solution were in good agreement with those from the experimental methods and other molecular dynamics simulations but also very interesting properties of charge distributions, geometries of water molecules, hydrogen bond, diffusion coefficients, vibrational spectra are investigated by ABEEM/MM model.     

Using the QSPR Approach for Estimating the Density of Azole‐based Energetic Compounds

The relationship between density of energetic azole‐based compounds and their molecular structure is investigated through quantitative structure‐property relationship (QSPR) approach. The methodology of this work introduces a new model, which related density of azole‐based energetic compounds to the optimum elemental composition, the degree of unsaturation (DoU) of the compounds, presence of nitroimino group in the structural formula, as well as several non‐additive structural parameters. The presence of nitroimino functional group and also increasing the value of n_O/n_N in the formula of these compounds can enhance their density. The correlation is derived on the basis of experimental density values of 100 azole‐based energetic compounds with different molecular structure as training set. The determination coefficient of the new correlation is 0.923. Also, it has the root mean square deviation (RMSD) and the average absolute deviation (AAD) of 0.038 and 0.030 g · cm^–3, respectively. In addition, the correlation gives good predictions for further 25 azole‐based energetic compounds as test set (Q²_EXT = 0.901). The predictive ability of the correlation is checked using a cross validation method (Q²_LMO = 0.918). The proposed method can also apply for designing novel azole‐based energetic compounds.     

Ln3Q9 as a Molecular Framework for Ion‐Size‐Driven Assembly of Heterolanthanide (Nd,Er, Yb) Multiple Near‐Infrared Emitters

A unique example of discrete molecular entity Nd_yEr_xYb_3?(x+y)Q₉ ( 1 ) (Q=quinolinolato) containing three different lanthanides simultaneously emitting in three different spectral regions in the NIR, ranging from 900 to 1600 nm, has been synthesized and fully chararacterized. A simple molecular strategy based on tuning metal composition in the Ln₃Q₉ framework, which contains inequivalent central and terminal coordination sites, has allowed a satisfactory ion‐size‐driven control of molecular speciation close to 90 %. In 1 the central position of the larger Nd ion is well distinguished from the terminal ones of the smaller Yb³⁺ and Er³⁺, which are almost “vicariants” as found in the heterobimetallic Er_xYb_3?xQ₉ ( 2 ). The Ln₃Q₉ molecular architecture, which allows communication between the ions, has proved to afford multiple NIR emission in 1 and 2 , and is promising to develop a variety of multifunctional materials through the variation of the Ln composition.     

Novel high‐performance polymer memory devices containing (OMe)2tetraphenyl‐p‐phenylenediamine moieties

The functional polyimide (OMe)₂TPPA‐6FPI ( PI ) and the polyamide (OMe)₂TPPA‐6FPA ( PA ) consisting of electron‐donating N,N′‐bis(4‐aminophenyl)‐N,N′‐di(4‐methoxylphenyl)1,4‐phenylenediamine [(OMe)₂TPPA‐diamine] for memory application were prepared in this study. These polyimide and polyamide memory devices were fabricated with the sandwich configuration of indium tin oxide (ITO)/polymer/Al, and could be switched from the initial low‐conductivity (OFF) state to the high‐conductivity (ON) state with high ON/OFF current ratios of 10⁷ and 10⁹, respectively. PI exhibited dynamic random access memory (DRAM) performance, whereas PA showed static random access memory (SRAM) behavior. To get more insight into the memory behaviors of these two different types of polymer memory devices, molecular simulation on the basic unit was carried out. Furthermore, the differences of highest occupied molecular orbital (HOMO) energy level, lowest unoccupied molecular orbital (LUMO) charge density isosurfaces, dipole moment, and linkage conformation between PI and PA were found to affect the volatile memory behavior. Both polymer memory devices revealed excellent stability with long operation time of 10⁴ s at continuous applied voltage of ‐2 V. The effect of polymer thickness on the volatile memory behavior of PA was also investigated in this study. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Four‐Center Oxidation State Combinations and Near‐Infrared Absorption in [Ru(pap)(Q)2]n (Q=3,5‐Di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine,pap=2‐Phenylazopyridine)

The complex series [Ru(pap)(Q)₂]ⁿ ([ 1 ]ⁿ–[ 4 ]ⁿ; n=+2, +1, 0, ?1, ?2) contains four redox non‐innocent entities: one ruthenium ion, 2‐phenylazopyridine (pap), and two o‐iminoquinone moieties, Q=3,5‐di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine (aryl=C₆H₅ ( 1⁺ ); m‐(Cl)₂C₆H₃ ( 2⁺ ); m‐(OCH₃)₂C₆H₃ ( 3⁺ ); m‐(tBu)₂C₆H₃ ( 4 ⁺)). A crystal structure determination of the representative compound, [ 1 ]ClO₄, established the crystallization of the ctt‐isomeric form, that is, cis and trans with respect to the mutual orientations of O and N donors of two Q ligands, and the coordinating azo N atom trans to the O donor of Q. The sensitive C? O (average: 1.299(3) Å), C? N (average: 1.346(4) Å) and intra‐ring C? C (meta; average: 1.373(4) Å) bond lengths of the coordinated iminoquinone moieties in corroboration with the N?N length (1.292(3) Å) of pap in 1 ⁺ establish [Ru^III(pap⁰)(Q^.?)₂]⁺ as the most appropriate electronic structural form. The coupling of three spins from one low‐spin ruthenium(III) (t_2g⁵) and two Q^.? radicals in 1 ⁺– 4 ⁺ gives a ground state with one unpaired electron on Q^.?, as evident from g=1.995 radical‐type EPR signals for 1 ⁺– 4 ⁺. Accordingly, the DFT‐calculated Mulliken spin densities of 1 ⁺ (1.152 for two Q, Ru: ?0.179, pap: 0.031) confirm Q‐based spin. Complex ions 1 ⁺– 4 ⁺ exhibit two near‐IR absorption bands at about λ=2000 and 920 nm in addition to intense multiple transitions covering the visible to UV regions; compounds [ 1 ]ClO₄–[ 4 ]ClO₄ undergo one oxidation and three separate reduction processes within ±2.0 V versus SCE. The crystal structure of the neutral (one‐electron reduced) state ( 2 ) was determined to show metal‐based reduction and an EPR signal at g=1.996. The electronic transitions of the complexes 1 ⁿ– 4 ⁿ (n=+2, +1, 0, ?1, ?2) in the UV, visible, and NIR regions, as determined by using spectroelectrochemistry, have been analyzed by TD‐DFT calculations and reveal significant low‐energy absorbance (λ_max>1000 nm) for cations, anions, and neutral forms. The experimental studies in combination with DFT calculations suggest the dominant valence configurations of 1 ⁿ– 4 ⁿ in the accessible redox states to be [Ru^III(pap⁰)(Q^.?)(Q⁰)]²⁺ ( 1 ²⁺– 4 ²⁺)→[Ru^III(pap⁰)(Q^.?)₂]⁺ ( 1 ⁺– 4 ⁺)→[Ru^II(pap⁰)(Q^.?)₂] ( 1 – 4 )→[Ru^II(pap^.?)(Q^.?)₂]^? ( 1 ^?– 4 ^?)→[Ru^III(pap^.?)(Q^2?)₂]^2? ( 1 ^2?– 4 ^2?).     

Associative block copolymers comprising poly(N‐isopropylacrylamide) and poly(ethylene oxide) end‐functionalized with a fluorophilic or hydrophilic group. Synthesis and aqueous solution properties

A series of block copolymers comprising poly(N‐isopropylacrylamide) (PNIPAM) and poly(ethylene oxide) (PEO) end‐functionalized with a quaternary ammonium group (R_Q) was synthesized by free‐radical polymerization of N‐isopropylacrylamide with well‐defined R_QPEO macroazoinitiators. The radical termination occurred mainly by disproportionation, as confirmed by combining the data from size exclusion chromatography (SEC) and rheology measurements. The copolymers denoted R_QE_xN_y differ in type of the terminal group [F_Q = C₈F₁₇(CH₃)₂N⁺ or M_Q = (CH₃)₃N⁺] and in the length of the PEO (E_x; x = 4, 6, or 10 K) and PNIPAM (N_y; y = 7 or 17–19 K) blocks. The type of the terminal group determined the behavior of the block copolymers in the dilute and semidilute regime. Self‐assembled species formed by both F_Q and M_Q modified block copolymers were detected by static light scattering measurements at 25 °C and above the lower critical solution temperature (LCST). The LCST of the block copolymers depended on the type of the R_Q group and the length of the blocks. F_Q‐modified copolymers form elastic gels below and above the LCST. It was inferred that the F_Q groups and the PNIPAM blocks form segregated microdomains that serve as junctions to maintain a viscoelastic network. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5736–5744, 2004     

Anharmonicity of a molecular oscillator

The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d³E/d Q ³ ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )_N = 0 and λ = (?k/?N) _Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Novel Dinuclear Redox‐isomeric Complexes with a Tetrapodal Pyridine‐based Ligand

Tris‐o‐semiquinonato cobalt complexes react with a tetrapodal pyridine‐derived ligand to form dinuclear cobalt compounds of general formula (OMP)[CoQ₂]₂, where OMP = 2,2′‐(pyridine‐2,6‐diyl)bis(N¹,N¹,N³,N³‐tetramethylpropane‐1,3‐diamine), Q = mono‐ or dianion of 3,6‐di‐tert‐butyl‐o‐benzoquinone (complex 1 ) and it derivatives: 3,6‐di‐tert‐butyl‐4,5‐N,N′‐piperazino‐o‐benzoquinone (complex 2 ), and 3,6‐di‐tert‐butyl‐4‐Cl‐o‐benzoquinone (complex 3 ). Single crystal X‐ray crystallography of 1 and 3 indicates two bis‐quinonato cobalt units bound by an OMP ligand, which acts as a bridge. Each central cobalt atom is chelated by one N¹,N¹,N³,N³‐tetramethylpropane‐1,3‐diamine and two o‐quinonato fragments. The nitrogen atom of the pyridine ring is uncoordinated. All complexes were characterized by NIR‐IR and EPR spectroscopy, precise adiabatic vacuum calorimetry, and by variable‐temperature magnetic susceptibility measurements. All data indicate a reversible thermally driven redox‐isomeric (valence tautomeric) transformation in the solid state for all complexes.     

Analysis of Nascent Rotational Energy Distributions and Reaction Mechanisms of the Gas‐Phase Radical–Radical Reaction O(3P)+(CH3)2CH→C3H6+OH

This paper reports on the gas‐phase radical–radical dynamics of the reaction of ground‐state atomic oxygen [O(³P), from the photodissociation of NO₂] with secondary isopropyl radicals [(CH₃)₂CH, from the supersonic flash pyrolysis of isopropyl bromide]. The major reaction channel, O(³P)+(CH₃)₂CH→C₃H₆ (propene)+OH, is examined by high‐resolution laser‐induced fluorescence spectroscopy in crossed‐beam configuration. Population analysis shows bimodal nascent rotational distributions of OH (X²Π) products with low‐ and high‐N′′ components in a ratio of 1.25:1. No significant spin–orbit or Λ‐doublet propensities are exhibited in the ground vibrational state. Ab initio computations at the CBS‐QB3 theory level and comparison with prior theory show that the statistical method is not suitable for describing the main reaction channel at the molecular level. Two competing mechanisms are predicted to exist on the lowest doublet potential‐energy surface: direct abstraction, giving the dominant low‐N′′ components, and formation of short‐lived addition complexes that result in hot rotational distributions, giving the high‐N′′ components. The observed competing mechanisms contrast with previous bulk kinetic experiments conducted in a fast‐flow system with photoionization mass spectrometry, which suggested a single abstraction pathway. In addition, comparison of the reactions of O(³P) with primary and tertiary hydrocarbon radicals allows molecular‐level discussion of the reactivity and mechanism of the title reaction.     

ONIOM and FMO‐EDA study of metabotropic glutamate receptor 1: Quantum insights into the allosteric binding site

The crystal structure of metabotropic glutamate receptor 1 (mGluR1) complexed with 4‐fluoro‐N‐(4‐(6‐(isopropylamino)pyrimidin‐4‐yl)thiazol‐2‐yl)‐N‐methylbenzamide (FITM, a negative allosteric modulator) and its twelve close structural analogs with a broad spectrum of affinities (2.4 nM < IC₅₀ > 10 000 nM) were investigated using quantum mechanical methods. The our own N‐layered integrated molecular orbital and molecular mechanics (ONIOM) was used to optimize the molecular geometries of the receptor with complexed ligands, which were then used to perform the ab initio calculations using the fragment molecular orbitals method with energy decomposition analysis (FMO‐EDA). The results clearly showed that residues Q660^3.28 and/or Y805^6.55 were the anchoring points for all the studied analogs of FITM, while the H‐bond with T815^7.38 determined only the orientation of very active molecules containing an amino substituent in the pyrimidine moiety (e.g., FITM). The orientation of the other parts of ligands resulted from hydrophobic interactions mainly with L757^5.44, F801^6.51, or W798^6.48. The applied ONIOM/FMO–EDA approach facilitated the study of effects related to very small changes in the ligand structure and led to conclusions regarding the significance of individual interactions in the allosteric binding pocket of mGluR1.     

异丁烯在不同硅铝比的NanZSM-5型分子筛中的吸附：分子模拟研究

Frameworks of NanZSM-5 type zeolites with various Si/A1 ratios have been constructed and optimized with molecular dynamic quench simulation. The results show that the structure parameters of NanZSM-5 type zeolite, including the bond length and atomic charges, are consistent with those predicted by ab initio cluster calculations. It was also observed that atomic charges of Si atoms were shifted to higher field in NanZSM-5 type zeolite with lower Si/Al ratio. Then, the adsorption of isobutene on NanZSM-5 with various Si/Al ratios has been investigated using grand canonical ensemble Monte Carlo simulation and Cvff-300-1.01 forcefield. The simulated adsorption amount was in good agreement with the experimental data. Based on these facts, the effects of Si/Al ratio on the adsorption amount and adsorption isotherms of isobutene on NanZSM-5 were predicted. The results indicated that Si/Al ratio was important for the adsorption of isobutene and the adsorption amount was decreased as the Si/Al ratio was increased, which can be explained that the atomic charge of Na^＋ cation would influence greatly the π electrons of the isobutene double bond due to the Coulomb force. In addition, the adsorption sites of isobutene and interaction energy of isobutene with NanZSM-5 were also discussed.