Refining the macromolecular model – achieving the best agreement with the data from X-ray diffraction experiment

ABSTRACT

Refinement of macromolecular X-ray crystal structures involves using complex software with hundreds of different settings. The complexity of underlying concepts and the sheer amount of instructions may make it difficult for less experienced crystallographers to achieve optimal results in their refinements. This tutorial review offers guidelines for choosing the best settings for the reciprocal-space refinement of macromolecular models and provides practical tips for manual model correction. To help aspiring crystallographers navigate the process, some of the most practically important concepts of protein structure refinement are described. Among the topics covered are the use and purpose of R-free, geometrical restraints, restraints on atomic displacement parameters (ADPs), refinement weights, various parametrizations of ADPs (full anisotropic refinement and TLS), and omit maps. We also give practical tips for manual model correction in Coot, modelling of side-chains with poor or missing density, and ligand identification, fitting, and refinement.     

Grain Size Effects on Mine Water Quality and Acid/Neutral Rock Drainage Production in Kinetic Testing Using Recsk Porphyry Skarn Cu–Zn Deposit Rocks

The quality of mine drainage from sulphide-containing waste rock dumps is controlled by several factors. To characterize the effects of grain size on acid/neutral rock drainage production, kinetic tests were performed on samples from the Recsk porphyry skarn Cu–Zn deposit in Hungary, an area known to generate ARD. Five columns were used, each containing specific grain size ranges (1–2, 2–4, 4–8, 8–16, and 16–32 mm). Prior to the kinetic tests, a static test was performed for each grain size range to obtain total and available neutralizing potential (NP) and acid potential (AP). Total NP and AP values were roughly similar for all grain size ranges, while available NP increased as grain size decreased. The neutralization potential ratio for all grain size ranges was <1, which suggests a potentially acid-producing material. The kinetic tests, however, had contrasting results; a grain size of 1–4 mm produced a circumneutral pH, while grain size groups >4 mm produced pHs from 5.1 down to 3.6. Higher alkalinity values in the leach water were linked to the finer grain samples, primarily producing circumneutral pH. Grain size correlated with the sulphate release rate during the stable release period: the sulphate release rate was less at larger grain sizes. In contrast, sulphide oxidation calculated from oxygen consumption was highest for the intermediate grain size range, followed by the coarser and then the finer grains. The leaching of metals established an increasing concentration with increasing acidity without a very clear relationship to grain size. The established concept of increased metal mobility with decreasing pH applies, regardless of grain size.     

Photoactive epichlorohydrin, 2. Photoinitiated free-radical and promoted cationic polymerization by using polyepichlorohydrin with benzoin terminal groups

The photoinitiated free-radical polymerization of methyl methacrylate (MMA) and the radical-promoted cationic polymerization of cyclohexene oxide (CHO) in the presence of low-molecular-weight polyepichlorohydrin terminated with groups containing benzoin derivatives were studied. Benzoin-terminated polyepichlorohydrin was prepared by Activated Monomer (AM) polymerization. Upon photolysis. polymer-bound alkoxy benzyl radicals were generated, initiating the radical polymerization of MMA. In the case of radical-promoted cationic polymerization of CHO, the cationic initiating species were formed by the oxidation of photochemically generated polymeric radicals by N-ethoxy-2-methylpyridinium hexafluorophosphate.     

Data assimilation and sampling in Banach spaces

This paper studies the problem of approximating a function f in a Banach space \(\mathcal{X}\) from measurements \(l_j(f)\), \(j=1,\ldots ,m\), where the \(l_j\) are linear functionals from \(\mathcal{X}^*\). Quantitative results for such recovery problems require additional information about the sought after function f. These additional assumptions take the form of assuming that f is in a certain model class \(K\subset \mathcal{X}\). Since there are generally infinitely many functions in K which share these same measurements, the best approximation is the center of the smallest ball B, called the Chebyshev ball, which contains the set \(\bar{K}\) of all f in K with these measurements. Therefore, the problem is reduced to analytically or numerically approximating this Chebyshev ball. Most results study this problem for classical Banach spaces \(\mathcal{X}\) such as the \(L_p\) spaces, \(1\le p\le \infty \), and for K the unit ball of a smoothness space in \(\mathcal{X}\). Our interest in this paper is in the model classes \(K=\mathcal{K}(\varepsilon ,V)\), with \(\varepsilon >0\) and V a finite dimensional subspace of \(\mathcal{X}\), which consists of all \(f\in \mathcal{X}\) such that \(\mathrm{dist}(f,V)_\mathcal{X}\le \varepsilon \). These model classes, called approximation sets, arise naturally in application domains such as parametric partial differential equations, uncertainty quantification, and signal processing. A general theory for the recovery of approximation sets in a Banach space is given. This theory includes tight a priori bounds on optimal performance and algorithms for finding near optimal approximations. It builds on the initial analysis given in Maday et al. (Int J Numer Method Eng 102:933–965, 2015) for the case when \(\mathcal{X}\) is a Hilbert space, and further studied in Binev et al. (SIAM UQ, 2015). It is shown how the recovery problem for approximation sets is connected with well-studied concepts in Banach space theory such as liftings and the angle between spaces. Examples are given that show how this theory can be used to recover several recent results on sampling and data assimilation.     

Bacterial cell killing properties of silver-loaded polysiloxane microspheres

Cross-linked polysiloxane microspheres containing a large number of SiOH groups were modified by introduction of organic thiol groups, which were further used for the functionalization of the microspheres with silver thiolate groups. The microspheres were characterized by ²⁹Si MAS NMR, ¹³C MAS NMR, SEM, XPS and elemental analysis. They were tested as biocides against selected Gram-positive and Gram-negative bacteria strains and exhibited high bactericidal activity. Separately, linear polysiloxane polymers equipped with organothiol groups and loaded with silver were synthesized. Their antibacterial activity was compared with that of silver thiolate-functionalized microspheres. Different shape of particles and a different form of silver explained somewhat lower activity of polymers.     

String Art: Towards Computational Fabrication of String Images

In this paper we propose a novel method for the automatic computation and digital fabrication of artistic string images. String art is a technique used by artists for the creation of abstracted images which are composed of straight lines of strings tensioned between pins distributed on a frame. Together the strings fuse to a perceptible image. Traditionally, artists craft such images manually in a highly sophisticated and tedious design process. To achieve this goal fully automatically we propose a computational setup driven by a discrete optimization algorithm which takes an ordinary picture as input and converts it into a connected graph of strings that tries to reassemble the input image best possibly. Furthermore, we propose a hardware setup for automatic digital fabrication of these images using an industrial robot that spans the strings. Finally, we demonstrate the applicability of our approach by generating and fabricating a set of real string art images.     

Strength of silicon wafers: fracture mechanics approach

This paper describes a model to predict mechanical strength distribution of silicon wafers. A generalized expression, based on a multimodal Weibull distribution, is proposed to describe the strength of a brittle material with surface, edge, and bulk flaws. The specific case of a cast, unpolished photovoltaic (PV) wafer is further analyzed. Assuming that surface microcracks constitute the dominant mechanism of wafer breakage, this model predicts the strength distribution of PV silicon that matches well the experimental results available in the literature.     

A new approach to BER estimation for ISI corrupted baseband transmission systems

This paper derives two new formulae for BER estimation when the transmission system is subject to both intersymbol interference and additive Gaussian noise. The approach undertaken here was oriented to find a simple formula giving close estimation of the true BER, which may be useful for the transmission system designer for rapid evaluation of system performance. The obtained results are compared with commonly used BER estimations. Copyright © 2001 John Wiley & Sons, Ltd.     

Hologram-like transmission of pictures

A new digital representation of pictures is proposed. The main feature of this representation is: Given a string of data Z representing a picture with full resolution, various substrings of Z represent the same picture with appropriately lower resolution. This is analogous to a well-known property of holograms. The new representation is based on a particular picture traversal algorithm and uses overlapping sampling areas. The paper presents the principle of this representation, analyzes its overhead, and provides examples of picture reconstruction. An application of the hologram-like representation to the transmission of pictures with progressive resolution is indicated.