Evolutionary Boussinesq model with nonmonotone friction and heat flux boundary conditions

In this paper we prove the existence and regularity of a solution to a two-dimensional system of evolutionary hemivariational inequalities which describes the Boussinesq model with nonmonotone friction and heat flux. We use the time retardation and regularization technique, combined with a regularized Galerkin method, and recent results from the theory of hemivariational inequalities.     

Photophysics of Fluorescent Contact Sensors Based on the Dicyanodihydrofuran Motif

Fluorescent molecular rotors have been used for measurements of local mobility on molecular length scales, for example to determine viscosity, and for the visualization of contact between two surfaces. In the present work, we deepen our insight into the excited-state deactivation kinetics and mechanics of dicyanodihydrofuran-based molecular rotors. We extend the scope of the use of this class of rotors for contact sensing with a red-shifted member of the family. This allows for contact detection with a range of excitation wavelengths up to ∼600 nm. Steady-state fluorescence shows that the fluorescence quantum yield of these rotors depends not only on the rigidity of their environment, but – under certain conditions – also on its polarity. While excited state decay via rotation about the exocyclic double bond is rapid in nonpolar solvents and twisting of a single bond allows for fast decay in polar solvents, the barriers for both processes are significant in solvents of intermediate polarity. This effect may also occur in other molecular rotors, and it should be considered when applying such molecules as local mobility probes.     

Nucleic acid reactivity: Challenges for next‐generation semiempirical quantum models

Semiempirical quantum models are routinely used to study mechanisms of RNA catalysis and phosphoryl transfer reactions using combined quantum mechanical (QM)/molecular mechanical methods. Herein, we provide a broad assessment of the performance of existing semiempirical quantum models to describe nucleic acid structure and reactivity to quantify their limitations and guide the development of next‐generation quantum models with improved accuracy. Neglect of diatomic differential overlap and self‐consistent density‐functional tight‐binding semiempirical models are evaluated against high‐level QM benchmark calculations for seven biologically important datasets. The datasets include: proton affinities, polarizabilities, nucleobase dimer interactions, dimethyl phosphate anion, nucleoside sugar and glycosidic torsion conformations, and RNA phosphoryl transfer model reactions. As an additional baseline, comparisons are made with several commonly used density‐functional models, including M062X and B3LYP (in some cases with dispersion corrections). The results show that, among the semiempirical models examined, the AM1/d‐PhoT model is the most robust at predicting proton affinities. AM1/d‐PhoT and DFTB3‐3ob/OPhyd reproduce the MP2 potential energy surfaces of 6 associative RNA phosphoryl transfer model reactions reasonably well. Further, a recently developed linear‐scaling “modified divide‐and‐conquer” model exhibits the most accurate results for binding energies of both hydrogen bonded and stacked nucleobase dimers. The semiempirical models considered here are shown to underestimate the isotropic polarizabilities of neutral molecules by approximately 30%. The semiempirical models also fail to adequately describe torsion profiles for the dimethyl phosphate anion, the nucleoside sugar ring puckers, and the rotations about the nucleoside glycosidic bond. The modeling of pentavalent phosphorus, particularly with thio substitutions often used experimentally as mechanistic probes, was problematic for all of the models considered. Analysis of the strengths and weakness of the models suggests that the creation of robust next‐generation models should emphasize the improvement of relative conformational energies and barriers, and nonbonded interactions. © 2015 Wiley Periodicals, Inc.     

QM/MM modeling of the hydroxylation of the androstenedione substrate catalyzed by cytochrome P450 aromatase (CYP19A1)

CYP19A1 aromatase is a member of the Cytochrome P450 family of hemeproteins, and is the enzyme responsible for the final step of the androgens conversion into the corresponding estrogens, via a three‐step oxidative process. For this reason, the inhibition of this enzyme plays an important role in the treatment of hormone‐dependent breast cancer. The first catalytic subcycle, corresponding to the hydroxilation of androstenedione, has been proposed to occur through a first hydrogen abstraction and a subsequent oxygen rebound step. In present work, we have studied the mechanism of the first catalytic subcycle by means of hybrid quantum mechanics/molecular mechanics methods. The inclusion of the protein flexibility has been achieved by means of Free Energy Perturbation techniques, giving rise to a free energy of activation for the hydrogen abstraction step of 13.5 kcal/mol. The subsequent oxygen rebound step, characterized by a small free energy barrier (1.5 kcal/mol), leads to the hydroxylated products through a highly exergonic reaction. In addition, an analysis of the primary deuterium kinetic isotopic effects, calculated for the hydrogen abstraction step, reveals values (～10) overpassing the semiclassical limit for the C? H, indicating the presence of a substantial tunnel effect. Finally, a decomposition analysis of the interaction energy for the substrate and cofactor in the active site is also discussed. According to our results, the role of the enzymatic environment consists of a transition state stabilization by means of dispersive and polarization effects. © 2015 Wiley Periodicals, Inc.     

Mechanism of proteolysis in matrix metalloproteinase‐2 revealed by QM/MM modeling

The mechanism of enzymatic peptide hydrolysis in matrix metalloproteinase‐2 (MMP‐2) was studied at atomic resolution through quantum mechanics/molecular mechanics (QM/MM) simulations. An all‐atom three‐dimensional molecular model was constructed on the basis of a crystal structure from the Protein Data Bank (ID: 1QIB), and the oligopeptide Ace‐Gln‐Gly～Ile‐Ala‐Gly‐Nme was considered as the substrate. Two QM/MM software packages and several computational protocols were employed to calculate QM/MM energy profiles for a four‐step mechanism involving an initial nucleophilic attack followed by hydrogen bond rearrangement, proton transfer, and C? N bond cleavage. These QM/MM calculations consistently yield rather low overall barriers for the chemical steps, in the range of 5–10 kcal/mol, for diverse QM treatments (PBE0, B3LYP, and BB1K density functionals as well as local coupled cluster treatments) and two MM force fields (CHARMM and AMBER). It, thus, seems likely that product release is the rate‐limiting step in MMP‐2 catalysis. This is supported by an exploration of various release channels through QM/MM reaction path calculations and steered molecular dynamics simulations. © 2015 Wiley Periodicals, Inc.     

Multiscale Modeling of the Active Site of [Fe] Hydrogenase: The H2 Binding Site in Open and Closed Protein Conformations

A series of QM/MM optimizations of the full protein of [Fe] hydrogenase were performed. The FeGP cofactor has been optimized in the water‐bound resting state ( 1 ), with a side‐on bound dihydrogen ( 2 ), or as a hydride intermediate ( 3 ). For inclusion of H₄ MPT in the closed structure, advanced multiscale modeling appears to be necessary, especially to obtain reliable distances between CH‐H₄MPT⁺ and the dihydrogen (H₂) or hydride (H^?) ligand in the FeGP cofactor. Inclusion of the full protein is further important for the relative energies of the two intermediates 2 and 3 . We finally find that hydride transfer from 3 has a significantly higher barrier than found in previous studies neglecting the full protein environment.     

计算材料科学中桥域多尺度方法的若干进展

材料科学中存在固有的多尺度特性,桥域多尺度方法是在宏观尺度(如连续介质力学)中引入不同的细微观尺度的计算区域,乃至纳米尺度的分子动力学、量子力学计算区域,将不同尺度的研究方法通过一定的数学模型耦合在一起。该方法既能节约计算成本,又能保证所研究问题的物理特性。本文对多尺度方法的基本概念、跨尺度桥域多尺度方法的发展、基本原理、耦合方法和离散方程进行了讨论,给出了几个应用算例,并在最后进行了总结,展望了今后的可能发展方向。     

弹性力学混合状态方程的小波解法

应用小波理论求解弹性力学混合状态方程，讨论了解的收敛性。从文中的数值算例不难看出，该方法不失为混合状态方程一种新的求解途径。