The ideal trefoil knot

The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed.Comment: 11 pages, 8 figure

Optimal shapes of compact strings

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice. This simply stated problem has had a profound impact in many areas, ranging from the crystallization and melting of atomic systems, to optimal packing of objects and subdivision of space. Here we study an analogous problem--that of determining the optimal shapes of closely packed compact strings. This problem is a mathematical idealization of situations commonly encountered in biology, chemistry and physics, involving the optimal structure of folded polymeric chains. We find that, in cases where boundary effects are not dominant, helices with a particular pitch-radius ratio are selected. Interestingly, the same geometry is observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure

Finding class C GPCR subtype-discriminating n-grams through feature selection

G protein-coupled receptors (GPCRs) are a large and heterogeneous superfamily of receptors that are key cell players for their role as extracellular signal transmitters. Class C GPCRs, in particular, are of great interest in pharmacology. The lack of knowledge about their full 3-D structure prompts the use of their primary amino acid sequences for the construction of robust classifiers, capable of discriminating their different subtypes. In this paper, we describe the use of feature selection techniques to build Support Vector Machine (SVM)-based classification models from selected receptor subsequences described as n-grams. We show that this approach to classification is useful for finding class C GPCR subtype-specific motifs.Peer ReviewedPostprint (author’s final draft

Harnessing ion-binding sites for GPCR pharmacology

Endogenous ions play important roles in the function and pharmacology of G-protein coupled receptors (GPCRs). Historically the evidence for ionic modulation ofGPCRfunction dates to 1973 with studies of opioid receptors, where it was demonstrated that physiologic concentrations of sodium allosterically attenuated agonist binding. This Na+-selective effect was distinct from effects of other monovalent and divalent cations, with the latter usually counteracting sodium’s negative allosteric modulation of binding. Since then, numerous studies documenting the effects of mono- and divalent ions on GPCR function have been published. While ions can act selectively and nonselectively at many sites in different receptors, the discovery of the conserved sodium ion site in class A GPCR structures in 2012 revealed the unique nature of Na+ site, which has emerged as a near-universal site for allosteric modulation of class A GPCR structure and function. In this review, we synthesize and highlight recent advances in the functional, biophysical, and structural characterization of ions bound to GPCRs. Taken together, these findings provide a molecular understanding of the unique roles of Na+ and other ions as GPCR allosteric modulators. Wewill also discuss how this knowledge can be applied to the redesign of receptors and ligand probes for desired functional and pharmacological profiles. © 2019, American Society for Pharmacology and Experimental Therapy. All rights reserved

Energy Bounds of Linked Vortex States

Energy bounds of knotted and linked vortex states in a charged two-component system are considered. It is shown that a set of local minima of free energy contains new classes of universality. When the mutual linking number of vector order parameter vortex lines is less than the Hopf invariant, these states have lower-lying energies.Comment: 4 pages, Latex2

A model of glueballs

We model the observed glueball mass spectrum in terms of energies for tightly knotted and linked QCD flux tubes. The data is fit well with one parameter. We predict additional glueball masses.Comment: 11 pages, 3 figures, 1 table; minor changes, comments added, typos correcte

Advances in GPCR Modeling Evaluated by the GPCR Dock 2013 Assessment: Meeting New Challenges

Despite tremendous successes of GPCR crystallography, the receptors with available structures represent only a small fraction of human GPCRs. An important role of the modeling community is to maximize structural insights for the remaining receptors and complexes. The community-wide GPCR Dock assessment was established to stimulate and monitor the progress in molecular modeling and ligand docking for GPCRs. The four targets in the present third assessment round presented new and diverse challenges for modelers, including prediction of allosteric ligand interaction and activation states in 5-hydroxytryptamine receptors 1B and 2B, and modeling by extremely distant homology for smoothened receptor. Forty-four modeling groups participated in the assessment. State-of-the-art modeling approaches achieved close-to-experimental accuracy for small rigid orthosteric ligands and models built by close homology, and they correctly predicted protein fold for distant homology targets. Predictions of long loops and GPCR activation states remain unsolved problems

Pocketome: an encyclopedia of small-molecule binding sites in 4D

The importance of binding site plasticity in protein–ligand interactions is well-recognized, and so are the difficulties in predicting the nature and the degree of this plasticity by computational means. To assist in understanding the flexible protein–ligand interactions, we constructed the Pocketome, an encyclopedia of about one thousand experimentally solved conformational ensembles of druggable binding sites in proteins, grouped by location and consistent chain/cofactor composition. The multiplicity of pockets within the ensembles adds an extra, fourth dimension to the Pocketome entry data. Within each ensemble, the pockets were carefully classified by the degree of their pairwise similarity and compatibility with different ligands. The core of the Pocketome is derived regularly and automatically from the current releases of the Protein Data Bank and the Uniprot Knowledgebase; this core is complemented by entries built from manually provided seed ligand locations. The Pocketome website (www.pocketome.org) allows searching for the sites of interest, analysis of conformational clusters, important residues, binding compatibility matrices and interactive visualization of the ensembles using the ActiveICM web browser plugin. The Pocketome collection can be used to build multi-conformational docking and 3D activity models as well as to design cross-docking and virtual ligand screening benchmarks

Fluctuating Filaments I: Statistical Mechanics of Helices

We examine the effects of thermal fluctuations on thin elastic filaments with non-circular cross-section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies non-monotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix ``melts'' and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross--section leads to resonant dependence of the persistence length on the twist rate.Comment: 5 figure

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure