A benchmark of optimally folded protein structures using integer programming and the 3D-HP-SC model

The Protein Structure Prediction (PSP) problem comprises, among other issues, forecasting the three-dimensional native structure of proteins using only their primary structure information. Most computational studies in this area use synthetic data instead of real biological data. However, the closer to the real-world, the more the impact of results and their applicability. This work presents 17 real protein sequences extracted from the Protein Data Bank for a benchmark to the PSP problem using the tri-dimensional Hydrophobic-Polar with Side-Chains model (3D-HP-SC). The native structure of these proteins was found by maximizing the number of hydrophobic contacts between the side-chains of amino acids. The problem was treated as an optimization problem and solved by means of an Integer Programming approach. Although the method optimally solves the problem, the processing time has an exponential trend. Therefore, due to computational limitations, the method is a proof-of-concept and it is not applicable to large sequences. For unknown sequences, an upper bound of the number of hydrophobic contacts (using this model) can be found, due to a linear relationship with the number of hydrophobic residues. The comparison between the predicted and the biological structures showed that the highest similarity between them was found with distance thresholds around 5.2–8.2 Å. Both the dataset and the programs developed will be freely available to foster further research in the area.     

Spectral analysis of Pk Finite Element matrices in the case of Friedrichs–Keller triangulations via Generalized Locally Toeplitz technology

In the present article, we consider a class of elliptic partial differential equations with Dirichlet boundary conditions and where the operator is div(?a( x )?·), with a continuous and positive over $\stackrel{￣}{\mathrm{\Omega }}$, Ω being an open and bounded subset of ${\mathbb{R}}^d$, d≥1. For the numerical approximation, we consider the classical ${\mathbb{P}}_k$ Finite Elements, in the case of Friedrichs–Keller triangulations, leading, as usual, to sequences of matrices of increasing size. The new results concern the spectral analysis of the resulting matrix‐sequences in the direction of the global distribution in the Weyl sense, with a concise overview on localization, clustering, extremal eigenvalues, and asymptotic conditioning. We study in detail the case of constant coefficients on Ω=(0,1)² and we give a brief account in the more involved case of variable coefficients and more general domains. Tools are drawn from the Toeplitz technology and from the rather new theory of Generalized Locally Toeplitz sequences. Numerical results are shown for a practical evidence of the theoretical findings.     

Stability and bonding of carbon(0)-iron−N2 complexes relevant to nitrogenase co-factor: EDA-NOCV analyses

The factors/structural features which are responsible for the binding, activation and reduction of N₂ to NH₃ by FeMoco of nitrogenase have not been completely understood well. Several relevant model complexes by Holland et al. and Peters et al. have been synthesized, characterized and studied by theoretical calculations. For a matter of fact, those complexes are much different than real active N₂-binding Fe-sites of FeMoco, which possesses a central C(4-) ion having an eight valence electrons as an μ₆-bridge. Here, a series of [(S₃C(0))Fe(II/I/0)-N₂]^n- complexes in different charged/spin states containing a coordinated σ- and π-donor C(0)-atom which possesses eight outer shell electrons [carbone, (Ph₃P)₂C(0); Ph₃P→C(0)←PPh₃] and three S-donor sites (i.e. ^-S-Ar), have been studied by DFT, QTAIM, and EDA-NOCV calculations. The effect of the weak field ligand on Fe-centres and the subsequent N₂-binding has been studied by EDA-NOCV analysis. The role of the oxidation state of Fe and N₂-binding in different charged and spin states of the complex have been investigated by EDA-NOCV analyses. The intrinsic interaction energies of the Fe−N₂ bond are in the range from −42/−35 to −67 kcal/mol in their corresponding ground states. The S₃C(0) donor set is argued here to be closer to the actual coordination environment of one of the six Fe-centres of nitrogenase. In comparison, the captivating model complexes reported by Holland et al. and Peter et al. possess a stronger π-acceptor C-ring (S₂C_ring donor, π-C donor) and stronger donor set like CP₃ (σ-C donor) ligands, respectively.     

Comparison of structural,thermodynamic, kinetic and mass transport properties of Mg2+ ion models commonly used in biomolecular simulations

The prevalence of Mg²⁺ ions in biology and their essential role in nucleic acid structure and function has motivated the development of various Mg²⁺ ion models for use in molecular simulations. Currently, the most widely used models in biomolecular simulations represent a nonbonded metal ion as an ion‐centered point charge surrounded by a nonelectrostatic pairwise potential that takes into account dispersion interactions and exchange effects that give rise to the ion's excluded volume. One strategy toward developing improved models for biomolecular simulations is to first identify a Mg²⁺ model that is consistent with the simulation force fields that closely reproduces a range of properties in aqueous solution, and then, in a second step, balance the ion–water and ion–solute interactions by tuning parameters in a pairwise fashion where necessary. The present work addresses the first step in which we compare 17 different nonbonded single‐site Mg²⁺ ion models with respect to their ability to simultaneously reproduce structural, thermodynamic, kinetic and mass transport properties in aqueous solution. None of the models based on a 12‐6 nonelectrostatic nonbonded potential was able to reproduce the experimental radial distribution function, solvation free energy, exchange barrier and diffusion constant. The models based on a 12‐6‐4 potential offered improvement, and one model in particular, in conjunction with the SPC/E water model, performed exceptionally well for all properties. The results reported here establish useful benchmark calculations for Mg²⁺ ion models that provide insight into the origin of the behavior in aqueous solution, and may aid in the development of next‐generation models that target specific binding sites in biomolecules. © 2015 Wiley Periodicals, Inc.     

Oligo-Quinolylene–Vinylene Foldamers

Quinoline based aromatic amide foldamers are known to adopt stable folded conformations. We have developed a synthetic approach to produce similar oligomers where all amide bonds, or part of them, have been replaced by an isosteric vinylene group. The results of solution and solid state structural studies show that oligomers exclusively containing vinylene linkages are not well folded, and adopt predominantly flat conformations. In contrast, a vinylene segment flanked by helical oligoamides also folds in a helix, albeit with a slightly lower curvature. The presence of vinylene functions also result in an extension of π-conjugation across the oligomer that may change charge transport properties. Altogether, these results pave the way to foldamers in which both structural control and specific electronic properties may be engineered.     

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In this paper, by using central limit theorem of ND sequences and probability inequality, the precise asymptotics for partial sums of nonstationary ND sequences is investigated, and the same results with it under that of NA sequences are obtained.     

On null sequences for Banach operator ideals,trace duality and approximation properties

Let be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of ‐null sequences of Carl and Stephani on X , , from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when is right‐accessible for , behaves much alike . When this is the case we give a geometric tensor product representation of . On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of . We apply our results to study some problems related with the ‐approximation property giving a trace condition which is used to solve the remaining case () of a problem posed by Kim (2015). Namely, we prove that if a dual space has the ‐approximation property then the space has the ‐approximation property.     

伽罗瓦环上的一类No序列的构造

近年来,伽罗瓦环上的序列理论成为人们研究的热点问题.有限域上的No序列是一类伪随机序列,它在序列密码中占具十分重要的角色.本文利用伽罗瓦环上的置换,构造了伽罗瓦环Z_(p~e)上的一类新的No序列,并且研究了其线性复杂度.研究的结果表明此类No序列具有相当大的线性复杂度.