Variational method and duality in the 2D square Potts model

The ferromagnetic q-state Potts model on a square lattice is analyzed, for q>4, through an elaborate version of the operatorial variational method. In the variational approach proposed in the paper, the duality relations are exactly satisfied, involving at a more fundamental level, a duality relationship between variational parameters. Besides some exact predictions, the approach is very effective in the numerical estimates over the whole range of temperature and can be systematically improved.Comment: 20 pages, 5 EPS figure

Topological Landau-Ginzburg Theory for Vortices in Superfluid 4^4He

We propose a new Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid $^4$He. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the total vorticity manifest. The topological term gives rise to the Berry phase term in the vortex mechanical actions.Comment: LATEX, 9 page

Spectroscopic variability of two Oe stars

The Oe stars HD45314 and HD60848 have recently been found to exhibit very different X-ray properties: whilst HD60848 has an X-ray spectrum and emission level typical of most OB stars, HD45314 features a much harder and brighter X-ray emission, making it a so-called gamma Cas analogue. Monitoring the optical spectra could provide hints towards the origin of these very different behaviours. We analyse a large set of spectroscopic observations of HD45314 and HD60848, extending over 20 years. We further attempt to fit the H-alpha line profiles of both stars with a simple model of emission line formation in a Keplerian disk. Strong variations in the strengths of the H-alpha, H-beta, and He I 5876 emission lines are observed for both stars. In the case of HD60848, we find a time lag between the variations in the equivalent widths of these lines. The emission lines are double peaked with nearly identical strengths of the violet and red peaks. The H-alpha profile of this star can be successfully reproduced by our model of a disk seen under an inclination of 30 degrees. In the case of HD45314, the emission lines are highly asymmetric and display strong line profile variations. We find a major change in behaviour between the 2002 outburst and the one observed in 2013. This concerns both the relationship between the equivalent widths of the various lines and their morphologies at maximum strength (double-peaked in 2002 versus single-peaked in 2013). Our simple disk model fails to reproduce the observed H-alpha line profiles of HD45314. Our results further support the interpretation that Oe stars do have decretion disks similar to those of Be stars. Whilst the emission lines of HD60848 are explained by a disk with a Keplerian velocity field, the disk of HD45314 seems to have a significantly more complex velocity field that could be related to the phenomenon that produces its peculiar X-ray emission.Comment: Accepted for Publication in A&

Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point.Comment: 11 pages, RevTeX, 6 PostScript figures included. Manuscript substantially extended, details on the analytical and numerical calculations added. To appear in Phys. Rev.

Corner Exponents in the Two-Dimensional Potts Model

The critical behavior at a corner in two-dimensional Ising and three-state Potts models is studied numerically on the square lattice using transfer operator techniques. The local critical exponents for the magnetization and the energy density for various opening angles are deduced from finite-size scaling results at the critical point for isotropic or anisotropic couplings. The scaling dimensions compare quite well with the values expected from conformal invariance, provided the opening angle is replaced by an effective one in anisotropic systems.Comment: 11 pages, 2 eps-figures, uses LaTex and eps

Polycation-π Interactions Are a Driving Force for Molecular Recognition by an Intrinsically Disordered Oncoprotein Family

Molecular recognition by intrinsically disordered proteins (IDPs) commonly involves specific localized contacts and target-induced disorder to order transitions. However, some IDPs remain disordered in the bound state, a phenomenon coined "fuzziness", often characterized by IDP polyvalency, sequence-insensitivity and a dynamic ensemble of disordered bound-state conformations. Besides the above general features, specific biophysical models for fuzzy interactions are mostly lacking. The transcriptional activation domain of the Ewing's Sarcoma oncoprotein family (EAD) is an IDP that exhibits many features of fuzziness, with multiple EAD aromatic side chains driving molecular recognition. Considering the prevalent role of cation-π interactions at various protein-protein interfaces, we hypothesized that EAD-target binding involves polycation- π contacts between a disordered EAD and basic residues on the target. Herein we evaluated the polycation-π hypothesis via functional and theoretical interrogation of EAD variants. The experimental effects of a range of EAD sequence variations, including aromatic number, aromatic density and charge perturbations, all support the cation-π model. Moreover, the activity trends observed are well captured by a coarse-grained EAD chain model and a corresponding analytical model based on interaction between EAD aromatics and surface cations of a generic globular target. EAD-target binding, in the context of pathological Ewing's Sarcoma oncoproteins, is thus seen to be driven by a balance between EAD conformational entropy and favorable EAD-target cation-π contacts. Such a highly versatile mode of molecular recognition offers a general conceptual framework for promiscuous target recognition by polyvalent IDPs. © 2013 Song et al

Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

Specialized dynamical properties of promiscuous residues revealed by simulated conformational ensembles

The ability to interact with different partners is one of the most important features in proteins. Proteins that bind a large number of partners (hubs) have been often associated with intrinsic disorder. However, many examples exist of hubs with an ordered structure, and evidence of a general mechanism promoting promiscuity in ordered proteins is still elusive. An intriguing hypothesis is that promiscuous binding sites have specific dynamical properties, distinct from the rest of the interface and pre-existing in the protein isolated state. Here, we present the first comprehensive study of the intrinsic dynamics of promiscuous residues in a large protein data set. Different computational methods, from coarse-grained elastic models to geometry-based sampling methods and to full-atom Molecular Dynamics simulations, were used to generate conformational ensembles for the isolated proteins. The flexibility and dynamic correlations of interface residues with a different degree of binding promiscuity were calculated and compared considering side chain and backbone motions, the latter both on a local and on a global scale. The study revealed that (a) promiscuous residues tend to be more flexible than nonpromiscuous ones, (b) this additional flexibility has a higher degree of organization, and (c) evolutionary conservation and binding promiscuity have opposite effects on intrinsic dynamics. Findings on simulated ensembles were also validated on ensembles of experimental structures extracted from the Protein Data Bank (PDB). Additionally, the low occurrence of single nucleotide polymorphisms observed for promiscuous residues indicated a tendency to preserve binding diversity at these positions. A case study on two ubiquitin-like proteins exemplifies how binding promiscuity in evolutionary related proteins can be modulated by the fine-tuning of the interface dynamics. The interplay between promiscuity and flexibility highlighted here can inspire new directions in protein-protein interaction prediction and design methods. © 2013 American Chemical Society

Functional Diversity and Structural Disorder in the Human Ubiquitination Pathway

The ubiquitin-proteasome system plays a central role in cellular regulation and protein quality control (PQC). The system is built as a pyramid of increasing complexity, with two E1 (ubiquitin activating), few dozen E2 (ubiquitin conjugating) and several hundred E3 (ubiquitin ligase) enzymes. By collecting and analyzing E3 sequences from the KEGG BRITE database and literature, we assembled a coherent dataset of 563 human E3s and analyzed their various physical features. We found an increase in structural disorder of the system with multiple disorder predictors (IUPred - E1: 5.97%, E2: 17.74%, E3: 20.03%). E3s that can bind E2 and substrate simultaneously (single subunit E3, ssE3) have significantly higher disorder (22.98%) than E3s in which E2 binding (multi RING-finger, mRF, 0.62%), scaffolding (6.01%) and substrate binding (adaptor/substrate recognition subunits, 17.33%) functions are separated. In ssE3s, the disorder was localized in the substrate/adaptor binding domains, whereas the E2-binding RING/HECT-domains were structured. To demonstrate the involvement of disorder in E3 function, we applied normal modes and molecular dynamics analyses to show how a disordered and highly flexible linker in human CBL (an E3 that acts as a regulator of several tyrosine kinase-mediated signalling pathways) facilitates long-range conformational changes bringing substrate and E2-binding domains towards each other and thus assisting in ubiquitin transfer. E3s with multiple interaction partners (as evidenced by data in STRING) also possess elevated levels of disorder (hubs, 22.90% vs. non-hubs, 18.36%). Furthermore, a search in PDB uncovered 21 distinct human E3 interactions, in 7 of which the disordered region of E3s undergoes induced folding (or mutual induced folding) in the presence of the partner. In conclusion, our data highlights the primary role of structural disorder in the functions of E3 ligases that manifests itself in the substrate/adaptor binding functions as well as the mechanism of ubiquitin transfer by long-range conformational transitions. © 2013 Bhowmick et al