The bond-algebraic approach to dualities

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature (strong-coupling)/high temperature (weak-coupling) dualities of classical statistical mechanics (or (Euclidean) path integrals). Its range of applications includes discrete lattice, continuum field and gauge theories. Dualities are revealed to be local, structure-preserving mappings between model-specific bond algebras that can be implemented as unitary transformations, or partial isometries if gauge symmetries are involved. This characterization permits us to search systematically for dualities and self-dualities in quantum models of arbitrary system size, dimensionality and complexity, and any classical model admitting a transfer matrix or operator representation. In particular, special dualities such as exact dimensional reduction, emergent and gauge-reducing dualities that solve gauge constraints can be easily understood in terms of mappings of bond algebras. As a new example, we show that the ?₂ Higgs model is dual to the extended toric code model in any number of dimensions. Non-local transformations such as dual variables and Jordan–Wigner dictionaries are algorithmically derived from the local mappings of bond algebras. This permits us to establish a precise connection between quantum dual and classical disorder variables. Our bond-algebraic approach goes beyond the standard approach to classical dualities, and could help resolve the long-standing problem of obtaining duality transformations for lattice non-Abelian models. As an illustration, we present new dualities in any spatial dimension for the quantum Heisenberg model. Finally, we discuss various applications including location of phase boundaries, spectral behavior and, notably, we show how bond-algebraic dualities help constrain and realize fermionization in an arbitrary number of spatial dimensions.     

Disordered proteins and network disorder in network descriptions of protein structure, dynamics and function: hypotheses and a comprehensive review

During the last decade, network approaches became a powerful tool to describe protein structure and dynamics. Here we review the links between disordered proteins and the associated networks, and describe the consequences of local, mesoscopic and global network disorder on changes in protein structure and dynamics. We introduce a new classification of protein networks into 'cumulus-type', i.e., those similar to puffy (white) clouds, and 'stratus-type', i.e., those similar to flat, dense (dark) low-lying clouds, and relate these network types to protein disorder dynamics and to differences in energy transmission processes. In the first class, there is limited overlap between the modules, which implies higher rigidity of the individual units; there the conformational changes can be described by an 'energy transfer' mechanism. In the second class, the topology presents a compact structure with significant overlap between the modules; there the conformational changes can be described by 'multi-trajectories'; that is, multiple highly populated pathways. We further propose that disordered protein regions evolved to help other protein segments reach 'rarely visited' but functionally-related states. We also show the role of disorder in 'spatial games' of amino acids; highlight the effects of intrinsically disordered proteins (IDPs) on cellular networks and list some possible studies linking protein disorder and protein structure networks.     

Conformational profile of a proline-arginine hybrid

The intrinsic conformational preferences of a new nonproteinogenic amino acid have been explored by computational methods. This tailored molecule, named ((β)Pro)Arg, is conceived as a replacement for arginine in bioactive peptides when the stabilization of folded turn-like conformations is required. The new residue features a proline skeleton that bears the guanidilated side chain of arginine at the C(β) position of the five-membered pyrrolidine ring, in either a cis or a trans orientation with respect to the carboxylic acid. The conformational profiles of the N-acetyl-N'-methylamide derivatives of the cis and trans isomers of ((β)Pro)Arg have been examined in the gas phase and in solution by B3LYP/6-31+G(d,p) calculations and molecular dynamics simulations. The main conformational features of both isomers represent a balance between geometric restrictions imposed by the five-membered pyrrolidine ring and the ability of the guanidilated side chain to interact with the backbone through hydrogen bonds. Thus, both cis- and trans-((β)Pro)Arg exhibit a preference for the α(L) conformation as a consequence of the interactions established between the guanidinium moiety and the main-chain amide groups.     

Homoleptic Ti[ONO]2 type complexes of amino-acid-tethered phenolato Schiff-base ligands: Synthesis,characterization, time-resolved fluorescence spectroscopy,and cytotoxicity against ovarian and colon cancer cells

Six homoleptic Ti (IV) compounds of dianionic tridentate ONO Schiff base ligands with various substitutions were prepared from chiral amino acids, 2-hydroxybenzaldehyde, which were generated in situ, and Ti (OⁱPr)₄. The compounds were spectroscopically characterized and the molecular geometries of five complexes were established by X-ray crystallography; for two structures, two independent molecules compose the asymmetric units. The di-anionic, tridentate ligands coordinate the titanium centers via the carboxylate-O-, imine-N- and phenoxide-O atoms to form five- and six-membered chelate rings. The molecules are based on a trans-N₂O₄ donor with each carboxylate-O atom trans to a phenoxide-O atom. For the smallest derivative with Me substitution, racemization occurs during repeated recrystallization. Photophysical profiles of the titanium compounds in the solid phase and in solution are discussed. Marked cytotoxicities were recorded toward human ovarian A2780 and colon HT-29 cancer cells with IC₅₀ values ranging between 23 ± 2 and 103 ± 3 μM. Comparative hydrolytic stability of the complexes were studied by NMR in 10% D₂O solutions which provided t_1/2 values of up to 15 ± 2 hr.     

Engineering Aqueous Fiber Assembly into Silk‐Elastin‐Like Protein Polymers

Self‐assembled peptide/protein nanofibers are valuable 1D building blocks for creating complex structures with designed properties and functions. It is reported that the self‐assembly of silk‐elastin‐like protein polymers into nanofibers or globular aggregates in aqueous solutions can be modulated by tuning the temperature of the protein solutions, the size of the silk blocks, and the charge of the elastin blocks. A core‐sheath model is proposed for nanofiber formation, with the silk blocks in the cores and the hydrated elastin blocks in the sheaths. The folding of the silk blocks into stable cores—affected by the size of the silk blocks and the charge of the elastin blocks—plays a critical role in the assembly of silk‐elastin nanofibers. Furthermore, enhanced hydrophobic interactions between the elastin blocks at elevated temperatures greatly influence the nanoscale features of silk‐elastin nanofibers.

     

Direct gaugino mediation

We describe renormalizable supersymmetric four-dimensional theories which lead to gaugino mediation and various generalizations thereof. Even though these models are strongly coupled, we can demonstrate the parametric suppression of soft scalar masses via Seiberg duality. We show that our models have a parameter which continuously interpolates between suppressed soft scalar masses and their conventional gauge mediated contribution. The main physical effect which we utilize is the general relation between massive deformations in one frame and the Higgs mechanism in the dual frame. Some compelling and relatively unexplored phenomenological scenarios arise naturally in this framework. We offer preliminary comments on various aspects of the phenomenology and outline several of the outstanding open problems.     

The unique Alzheimer's β-amyloid triangular fibril has a cavity along the fibril axis under physiological conditions

Elucidating the structure of Aβ(1-40) fibrils is of interest in Alzheimer's disease research because it is required for designing therapeutics that target Aβ(1-40) fibril formation at an early stage of the disease. M35 is a crucial residue because of its potential oxidation and its strong interactions across β-strands and across β-sheets in Aβ fibrils. Experimentally, data for the three-fold symmetry structure of the Aβ(9-40) fibril suggest formation of tight hydrophobic core through M35 interactions across the fibril axis and strong I31-V39 interactions between different cross-β units. Herein, on the basis of experimental data, we probe conformers with three-fold symmetry of the full-length Aβ(1-40). Our all-atom molecular dynamics simulations in explicit solvent of conformers based on the ssNMR data reproduced experimental observations of M35-M35 and I31-V39 distances. Our interpretation of the experimental data suggests that the observed ～5-7 ? M35-M35 distance in the fibril three-fold symmetry structure is likely to relate to M35 interactions along the fibril axis, rather than across the fibril axis, since our measured M35-M35 distances across the fibril axis are consistently above 15 ?. Consequently, we revealed that the unique Aβ(1-40) triangular structure has a large cavity along the fibril axis and that the N-termini can assist in the stabilization of the fibril by interacting with the U-turn domains or with the C-termini domains. Our findings, together with the recent cyroEM characterization of the hollow core in Aβ(1-42) fibrils, point to the relevance of a cavity in Aβ(1-40/1-42) oligomers which should be considered when targeting oligomer toxicity.