Mirror-image Pairs Research Articles

Electromagnetic Enantiomer: Chiral Nanophotonic Cavities for Inducing Chemical Asymmetry.

Chiral molecules, a cornerstone of chemical sciences with applications ranging from pharmaceuticals to molecular electronics, come in mirror-image pairs called enantiomers. However, their synthesis often requires complex control of their molecular geometry. We propose a strategy called "electromagnetic enantiomers" for inducing chirality in molecules located within engineered nanocavities using light, eliminating the need for intricate molecular design. This approach works by exploiting the strong coupling between a nonchiral molecule and a chiral mode within a nanocavity. We provide evidence for this strong coupling through angular emission patterns verified by numerical simulations and with complementary evidence provided by luminescence lifetime measurements. In simpler terms, our hypothesis suggests that chiral properties can be conveyed on to a molecule with a suitable chromophore by placing it within a specially designed chiral nanocavity that is significantly larger (hundreds of nanometers) than the molecule itself. To demonstrate this concept, we showcase an application in display technology, achieving efficient emission of circularly polarized light from a nonchiral molecule. The electromagnetic enantiomer concept offers a simpler approach to chiral control, potentially opening doors for asymmetric synthesis.

A decoupling method for analyzing foldover designs

AbstractFoldover designs often have attractive properties. Among these is that the effects can be divided into two orthogonal subspaces, one for odd effects and one for even effects. In this paper, we introduce a new method for analyzing foldover designs called the decoupling method that exploits this trait. Utilizing mirror image pair runs, two new responses are created, where each of them is only affected by effects in one of the orthogonal subspaces. Thereby the analysis of odd and even effects can be performed in two independent steps, enabling use of standard statistical procedures and formal testing of the presence of higher‐order interactions. The method is demonstrated on real data from a foldover of a 12‐run Plackett‐Burman (PB) design, and further evaluated through a simulation study, in which the decoupling method is compared to existing analysis methods. To get a thorough understanding of the properties, both a PB design and an OMARS design are used, and different design sizes and heredity scenarios considered. The method is especially suited for screening, as it yields high power for detecting the active effects.

Antisymmetry and Externalization

Abstract There are no mirror-image pairs of languages. This restriction on the otherwise vast set of possible languages must be accounted for, and puts boundary conditions on any theory of the human language faculty. There are implications for externalization and in the longer run for the evolution of the language faculty. Antisymmetric linear/temporal order is part of core syntax. Temporal order is partly (though not fully) integrated into core syntax via Merge itself. When two elements X and Y are merged, a relative linear/temporal order is assigned to them. At the same time, that instance of Merge assigns no relative order to the subparts of X and Y. Core syntax can explicitly have X precede Y without having any subpart of X precede any subpart of Y.

Catalyst-controlled doubly enantioconvergent coupling of racemic alkyl nucleophiles and electrophiles

Stereochemical control in the construction of carbon-carbon bonds between an alkyl electrophile and an alkyl nucleophile is a persistent challenge in organic synthesis. Classical substitution reactions via SN1 and SN2 pathways are limited in their ability to generate carbon-carbon bonds (inadequate scope, due to side reactions such as rearrangements and eliminations) and to control stereochemistry when beginning with readily available racemic starting materials (racemic products). Here, we report a chiral nickel catalyst that couples racemic electrophiles (propargylic halides) with racemic nucleophiles (β-zincated amides) to form carbon-carbon bonds in doubly stereoconvergent processes, affording a single stereoisomer of the product from two stereochemical mixtures of reactants.

Mirror image pairs of cyclic hexapeptides have different oral bioavailabilities and metabolic stabilities.

Rule-of-five parameters and membrane permeabilities have been routinely used to guide development of orally bioavailabile drugs. Here we compare enantiomeric pairs of cyclic hexapeptides with identical rule-of-five parameters and membrane permeabilities. For each enantiomeric pair, the isomer with more l- than d-amino acids is much more orally bioavailable in rats, more metabolically stable to rat liver microsomes, and cleared more slowly in vivo.

Constructing Two-Level Designs by Concatenation of Strength-3 Orthogonal Arrays

ABSTRACTTwo-level orthogonal arrays of N runs, k factors, and a strength of 3 provide suitable fractional factorial designs in situations where many of the main effects are expected to be active, as well as some two-factor interactions. If they consist of N/2 mirror image pairs, these designs are fold-over designs. They are called even and provide at most N/2 − 1 degrees of freedom to estimate interactions. For k < N/3 factors, there exist strength-3 designs that are not fold-over designs. They are called even-odd designs and they provide many more degrees of freedom to estimate interactions. For N ⩽ 48, attractive even-odd designs can be extracted from complete catalogs of strength-3 orthogonal arrays. However, for larger run sizes, no complete catalogs exist. To construct even-odd designs with N > 48, we develop an algorithm for an optimal concatenation of strength-3 designs involving N/2 runs. Our approach involves column permutations of one of the concatenated designs, as well as sign switches of the elements of one or more columns of that design. We illustrate the potential of the algorithm by generating two-level even-odd designs with 64 and 128 runs involving up to 33 factors, because this allows a comparison with benchmark designs from the literature. With a few exceptions, our even-odd designs outperform or are competitive with the benchmark designs in terms of the aliasing of two-factor interactions and in terms of the available degrees of freedom to estimate two-factor interactions. Supplementary materials for the article are available online.

The added value of small-molecule chirality in technological applications

Chirality is a fundamental symmetry property; chiral objects, such as chiral small molecules, exist as a pair of non-superimposable mirror images. Although small-molecule chirality is routinely considered in biologically focused application areas (such as drug discovery and chemical biology), other areas of scientific development have not considered small-molecule chirality to be central to their approach. In this Review, we highlight recent research in which chirality has enabled advancement in technological applications. We showcase examples in which the presence of small-molecule chirality is exploited in ways beyond the simple interaction of two different chiral molecules; this can enable the detection and emission of chiral light, help to control molecular motion, or provide a means to control electron spin and bulk charge transport. Thus, we demonstrate that small-molecule chirality is a highly promising avenue for a wide range of technologically oriented scientific endeavours. Although it is a fundamental property of many small molecules, chirality is not widely exploited in materials applications as its benefits are not widely recognized — indeed, the need for stereoselective synthesis may be seen as a disadvantage. In this Review, we highlight recent research in which chirality has had an enabling impact in technological applications.

The Life Story of Hydrogen Peroxide III: Chirality and Physical Effects at the Dawn of Life.

It is a remarkable observed fact that all life on Earth is homochiral, its biology using exclusively the D-enantiomer of ribose, the sugar moiety of the ribonucleic acids, and the L-enantiomers of the chiral amino acids. Motivated by concurrent work that elaborates further the role of hydrogen peroxide in providing an oscillatory drive for the RNA world (Ball & Brindley 2015a, J. R. Soc. Interface 12, 20150366, and Ball & Brindley 2015b, this journal, in press), we reappraise the structure and physical properties of this small molecule within this context. Hydrogen peroxide is the smallest, simplest molecule to exist as a pair of non-superimposable mirror images, or enantiomers, a fact which leads us to develop the hypothesis that its enantiospecific interactions with ribonucleic acids led to enantioselective outcomes. We propose a mechanism by which these chiral interactions may have led to amplification of D-ribonucleic acids and extinction of L-ribonucleic acids.

Experiments for Multi-Stage Processes

Multi-stage processes are very common in both process and manufacturing industries. In this article we present a methodology for designing experiments for multi-stage processes. Typically in these situations the design is expected to involve many factors from different stages. To minimize the required number of experimental runs, we suggest using mirror image pairs of experiments at each stage following the first. As the design criterion, we consider their projectivity and mainly focus on projectivity P > 3 designs. We provide the methodology for generating these designs for processes with any number of stages and also show how to identify and estimate the effects. Both regular and non-regular designs are considered as base designs in generating the overall design.

Electronic helix theory-guided rational design of kinetic resolutions by means of the Sharpless asymmetric dihydroxylation reactions

Kinetic resolution represents a key chemical reaction strategy for asymmetric synthesis of optically enriched compounds, and it originates from a simple phenomenon that a pair of mirror images (enantiomers) of a racemate can react with different rates under a chiral environment. While highly efficient catalytic kinetic resolutions by means of the classical Sharpless asymmetric epoxidation (AE) reactions are well established in modern organic synthesis, such systems based on the arguably more versatile Sharpless asymmetric dihydroxylation (AD) processes, although long pursued and widely attempted, remain largely underexplored. With insights gained from a new electronic helix theory we recently developed for molecular chirality and chiral interactions, we were able to advance a proposal suggesting why this problem is challenging and how it might be solved. Guided by a new design concept aimed at identifying complimentary catalyst–substrate electronic interactions, we reported herein that not only can such elusive systems be generally feasible, but efficiencies well reach the highest levels known to date with chemical or enzymatic kinetic resolutions of any type.

Split-plot designs with mirror image pairs as sub-plots

In this article we investigate two-level split-plot designs where the sub-plots consist of only two mirror image trials. Assuming third and higher order interactions negligible, we show that these designs divide the estimated effects into two orthogonal sub-spaces, separating sub-plot main effects and sub-plot by whole-plot interactions from the rest. Further we show how to construct split-plot designs of projectivity P≥3. We also introduce a new class of split-plot designs with mirror image pairs constructed from non-geometric Plackett–Burman designs. The design properties of such designs are very appealing with effects of major interest free from full aliasing assuming that 3rd and higher order interactions are negligible.

Cambrothyra ampulliformis, an unusual coeloscleritophoran from the Lower Cambrian of Shaanxi Province, China

Cambrothyra ampulliformisQian and Zhang, 1983, is a jar- or vase-shaped fossil known from the Lower Cambrian of Shaanxi and Hubei provinces, China. It has been interpreted as a protistan test or cyst or a metazoan sclerite. A large collection of specimens from the Xihaoping Member of the Dengying Formation in southern Shaanxi Province permits its detailed redescription. These fossils are highly variable in shape but this variation is continuous and does not support the current recognition of multiple species for this material. They were originally hollow with a restricted basal foramen and a calcareous wall probably composed of fibrous aragonite. All of these features support the identification ofCambrothyraas sclerites of a coeloscleritophoran, a problematic group of Cambrian scleritome-bearing metazoans. Furthermore, the walls ofCambrothyrasclerites contain numerous pores, a feature shared with other coeloscleritophorans.Cambrothyraresembles chancelloriids in particular due to the shared presence of a verruculose texture around the foramen and the absence of mirror-image pairs of asymmetric sclerites. However, unlike chancelloriids, which have rosette-like compound sclerites, the scleritome ofCambrothyrawas dominated by isolated sclerites, with only a few pairs and clusters of sclerites and twin sclerites. Consequently, we hypothesize thatCambrothyraforms a clade with other chancelloriids, but represents a basal lineage that plesiomorphically retained isolated sclerites. The morphology ofCambrothyrasclerites, which shares features with both chancelloriids and halkieriids, thus supports the hypothesis that all coeloscleritophorans form a natural group.

Thermodynamic mechanism for solution phase chiral amplification via a lattice model

We formulate a two-dimensional lattice model to study the equilibrium phase behavior of a ternary mixture composed of two enantiomeric forms of a chiral molecule and a nonchiral liquid solvent. Numerical solution of the model invoking the mean-field approximation of statistical mechanics allows the calculation of a ternary phase diagram. A prominent feature of the phase diagram is the appearance of a mirror-image pair of triple points involving coexistence of a liquid phase enriched in one of the enantiomers with two solid phases: a racemic and an enantiopure crystal. Thus, over broad ranges of initial composition, including liquid mixtures containing almost equal amounts of the two enantiomers, the equilibrium state of the system produces liquid-phase chiral amplification. The calculations predict that chiral amplification is favored at low temperatures, and by strengthening those molecular interactions that stabilize the racemic crystal. The phase behavior that we obtain is qualitatively identical to that reported in a recent experimental study of solutions of amino acids, aimed at probing the liquid-phase control of asymmetric catalysis. Those results, and the present calculations that provide molecular-level insight into their underlying causes, suggest a possible thermodynamic scenario for the liquid-phase emergence of chiral imbalance in a prebiotic and presumably nearly racemic world.

A mirror image pair of bisphosphonate analogs further demonstrates the mode of binding of the bisphosphonates in farnesyl pyrophosphate synthase

A mirror image pair of bisphosphonate analogs further demonstrates the mode of binding of the bisphosphonates in farnesyl pyrophosphate synthase

Switching of electrical and magnetic resonances in Omega structures by a reflection operation experimental studies

AbstractOmega shaped metallization on a dielectric substrate if appropriately designed will exhibit plasmonic resonances when excited by microwaves. We present experimental results for the complex S‐parameters for four types of metamaterial slabs constructed with discrete omega shapes in a rectangular lattice. A double layer of omega shapes in a rectangular lattice is obtained by reflecting the pattern of one strip by +180° (Omega A), the third sample is realized by reflecting one strip by −180° (Omega B) and the fourth sample (Omega C) is realized by an alternate arrangement of the Omega A and Omega B samples in a rectangular lattice. The single layer sample is asymmetric (S11 ≠ S22), the two mirror image pair samples are perfectly symmetric with S11 = S22. Plasmonic resonances and band gaps were observed. The complex S‐parameters were used to extract the complex permittivity and permeability of the symmetric samples by inverting Fresnel formulae for the reflection and transmission coefficients of a planar slab normally illuminated by a plane wave. The data of the asymmetric sample was inverted with this procedure to obtain two sets of data, one set using S11 and S21 and another set using S22 and S12 for the extraction of complex parameters. A reflection operation on the Omega geometry by ±180° results in the switching of the electric and magnetic properties in certain frequency ranges. Band gaps have been observed for both Omega A and Omega B that coincide with short circuit regions for the real part of the impedance. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2624–2629, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21984

Analysis of Split‐plot Designs with Mirror Image Pairs as Sub‐plots

AbstractIn this article we present a procedure to analyze split‐plot experiments with mirror image pairs as sub‐plots when third‐ and higher‐order interactions can be assumed negligible. Although performing a design in a split‐plot manner induces correlation among observations, we show that with such designs the essential search for potentially active factors can be done in two steps using ordinary least squares. The suggested procedure is tested out on a real example and on two simulated screening examples; one with a split‐plot design based on a geometric design and one with a split‐plot design based on a non‐geometric Plackett and Burman design. The examples also illustrate the advantage of using non‐geometric designs where the effects are partially aliased instead of being fully aliased as in highly fractionated fractional factorials. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Vulva morphogenesis involves attraction of plexin 1-expressing primordial vulva cells to semaphorin 1a sequentially expressed at the vulva midline

Vulva development in C. elegans involves cell fate specification followed by a morphogenesis phase in which homologous mirror image pairs within a linear array of primordial vulva cells form a crescent shape as they move sequentially towards a midline position within the array. The homologous pairs from opposite half vulvae in fixed sequence fuse with one another at their leading tips to form ring-shaped (toroidal) cells stacked in precise alignment one atop the other. Here, we show that the semaphorin 1a SMP-1, and its plexin receptor PLX-1, are required for the movement of homologous pairs of vulva cells towards this midline position. SMP-1 is upregulated on the lumen membrane of each primordial vulva cell as it enters the forming vulva and apparently attracts the next flanking homologous PLX-1-expressing vulva cells towards the lumen surface of the ring. Consequently, a new ring-shaped cell forms immediately ventral to the previously formed ring. This smp-1- and plx-1-dependent process repeats until seven rings are stacked along the dorsoventral axis, creating a common vulva lumen. Ectopic expression of SMP-1 suggests it has an instructive role in vulva cell migration. At least two parallel acting pathways are required for vulva formation: one requires SMP-1, PLX-1 and CED-10; and another requires the MIG-2 Rac GTPase and its putative activator UNC-73.

Discrimination in racemates of small chiral molecules

A comparison of similar chiral molecules provides information about the impact of molecular characteristics on selectivity. In this article, the intermolecular structure in racemic fluids is the basis for comparing the molecules: the radial distribution between atoms on identical molecules is compared with the corresponding distribution for atoms from a mirror-image pair. A difference in these distributions signals an enantiomeric imbalance in the local distribution of molecules. The structure in the racemic fluids is explored using Monte Carlo (MC) simulations and the integral equation theory of Chandler, Silbey and Ladanyi (CSL) [1982, Molec. Phys., 46, 1335]. Racemic fluids are examined for several categories of chiral molecules. First, symmetrically shaped molecules have been considered in order to isolate local excesses attributable to energetic contributions. Second, racemates of hard chiral molecules have been examined. Here, enantiomeric imbalances can only originate from asymmetry in the molecular shape. Finally, both the molecular shape and the interaction strengths have been varied in order to explore the competition between steric and energetic effects. Within each category, the number of chiral molecules is large and a selection mechanism is required to identify those molecules which are expected to show large local excesses. An appropriate selection criterion (chirality index) has been defined and evaluated for 400 000 chiral molecules. Based on the results of this assessment, 24 racemates have been chosen for detailed examination by MC simulations and integral equation theories.

Strand-specific loading of DnaB helicase by DnaA to a substrate mimicking unwound oriC.

We analysed the enzymatic activity (strand dis-placement) of the Escherichia coli DnaB helicase on a mirror-image pair of oligonucleotide-based substrates mimicking the unwound replication origin oriC. Loading of the helicase complex occurred exclusively to the single-stranded 'lower strand' part of the substrates. Full helicase activity required DnaA bound to the double-stranded part of the substrates (oriC DnaA box R1) and to their single-stranded 'upper strand' part. We assume that in vivo DnaA also loads the first of two helicase complexes - required for the assembly of two replication forks - to the lower strand of oriC during initiation of bidirectional chromosome replication in E. coli.

Coordination of carbonyl and carboxyl oxygen atoms with phosphorus in the presence of hydrogen bonding. P-O donor action.

A series of phosphorus compounds 1-5 containing carbonyl or carboxyl groups was obtained and subjected to X-ray analysis. Syntheses of the phosphoranes 1 and 5 were effected by oxidation reactions using potassium permaganate, while the phosphine oxide 2 was obtained by oxidation with hydrogen peroxide. The readily available phosphines 3 and 4 were included in the study. The structures revealed that P-O coordination occurred for 1-3 in the presence of extensive hydrogen bonding and led to trigonal bipyramidal geometries. A similar structure was observed for 4 in the absence of hydrogen bonding. (31)P chemical shifts indicate retention of the basic coordination geometries in solution. Consideration of the chirality of the phosphoranes 1 and 5 leads to a pair of mirror images that are possible in solution but exist in preferred isomeric forms in the crystalline state. Evaluation of the energies of two competing bonding types indicated a range for P-O coordination above and below the hydrogen bond energy. The results suggest that phosphoryl transfer enzyme mechanisms should benefit by taking into account donor interactions to phosphorus by residues at active sites in addition to the inclusion of hydrogen bonding interactions.