Commuting Charges of the Quantum Korteweg-deVries and Boussinesq Theories from the Reduction of W(infinity) and W(1+infinity) Algebras

Integrability of the quantum Boussinesq equation for c=-2 is demonstrated by giving a recursive algorithm for generating explicit expressions for the infinite number of commuting charges based on a reduction of the W(infinity) algebra. These charges exist for all spins $s \geq 2$. Likewise, reductions of the W(infinity/2) and W((1+infinity)/2) algebras yield the commuting quantum charges for the quantum KdV equation at c=-2 and c=1/2, respectively.Comment: 11 pages, RevTe

Charged Vortex Dynamics in Ginzburg-Landau Theory of the Fractional Quantum Hall Effect

We write a Ginzburg-Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2+1 dimensions. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.Comment: 28 pages + 1 Figure, new phyzzx macro (included), MAD/TH-92-0

Comprehensive inventory of protein complexes in the Protein Data Bank from consistent classification of interfaces

<p>Abstract</p> <p>Background</p> <p>Protein-protein interactions are ubiquitous and essential for all cellular processes. High-resolution X-ray crystallographic structures of protein complexes can reveal the details of their function and provide a basis for many computational and experimental approaches. Differentiation between biological and non-biological contacts and reconstruction of the intact complex is a challenging computational problem. A successful solution can provide additional insights into the fundamental principles of biological recognition and reduce errors in many algorithms and databases utilizing interaction information extracted from the Protein Data Bank (PDB).</p> <p>Results</p> <p>We have developed a method for identifying protein complexes in the PDB X-ray structures by a four step procedure: (1) comprehensively collecting all protein-protein interfaces; (2) clustering similar protein-protein interfaces together; (3) estimating the probability that each cluster is relevant based on a diverse set of properties; and (4) combining these scores for each PDB entry in order to predict the complex structure. The resulting clusters of biologically relevant interfaces provide a reliable catalog of evolutionary conserved protein-protein interactions. These interfaces, as well as the predicted protein complexes, are available from the Protein Interface Server (PInS) website (see Availability and requirements section).</p> <p>Conclusion</p> <p>Our method demonstrates an almost two-fold reduction of the annotation error rate as evaluated on a large benchmark set of complexes validated from the literature. We also estimate relative contributions of each interface property to the accurate discrimination of biologically relevant interfaces and discuss possible directions for further improving the prediction method.</p

Ab initio prediction of peptide-MHC binding geometry for diverse class I MHC allotypes

ABSTRACT Since determining the crystallographic structure of all peptide-MHC complexes is infeasible, an accurate prediction of the conformation is a critical computational problem. These models can be useful for determining binding energetics, predicting the structures of specific ternary complexes with T-cell receptors, and designing new molecules interacting with these complexes. The main difficulties are (1) adequate sampling of the large number of conformational degrees of freedom for the flexible peptide, (2) predicting subtle changes in the MHC interface geometry upon binding, and (3) building models for numerous MHC allotypes without known structures. Whereas previous studies have approached the sampling problem by dividing the conformational variables into different sets and predicting them separately, we have refined the Biased-Probability Monte Carlo docking protocol in internal coordinates to optimize a physical energy function for all peptide variables simultaneously. We also imitated the induced fit by docking into a more permissive smooth grid representation of the MHC followed by refinement and reranking using an all-atom MHC model. Our method was tested by a comparison of the results of cross-docking 14 peptides into HLA-A*0201 and 9 peptides into H-2K b as well as docking peptides into homology models for five different HLA allotypes with a comprehensive set of experimental structures. The surprisingly accurate prediction (0.75 Å backbone RMSD) for cross-docking of a highly flexible decapeptide, dissimilar to the original bound peptide, as well as docking predictions using homology models for two allotypes with low average backbone RMSDs of less than 1.0 Å illustrate the method&apos;s effectiveness. Finally, energy terms calculated using the predicted structures were combined with supervised learning on a large data set to classify peptides as either HLA-A*0201 binders or nonbinders. In contrast with sequence-based prediction methods, this model was also able to predict the binding affinity for peptides to a different MHC allotype (H-2K b ), not used for training, with comparable prediction accuracy. Proteins 2006;63:512-526

Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators

One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also, potentials related by real transformation functions are shown to have the same spectrum generating algebra with Hermitian generators related by this operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte

Public Protests and the Risk of Novel Coronavirus Disease Hospitalizations: A County-Level Analysis from California

The objective of this study was to assess the relationship between public protests and county-level, novel coronavirus disease (COVID-19) hospitalization rates across California. Publicly available data were included in the analysis from 55 of 58 California state counties (29 March–14 October 2020). Mixed-effects negative binomial regression models were used to examine the relationship between daily county-level COVID-19 hospitalizations and two main exposure variables: any vs. no protests and 1 or \u3e1 protest vs. no protests on a given county-day. COVID-19 hospitalizations were used as a proxy for viral transmission since such rates are less sensitive to temporal changes in testing access/availability. Models included covariates for daily county mobility, county-level characteristics, and time trends. Models also included a county-population offset and a two-week lag for the association between exposure and outcome. No significant associations were observed between protest exposures and COVID-19 hospitalization rates among the 55 counties. We did not find evidence to suggest that public protests were associated with COVID-19 hospitalization within California counties. These findings support the notion that protesting during a pandemic may be safe, ostensibly, so long as evidence-based precautionary measures are taken

Predicting protein-protein binding sites in membrane proteins

<p>Abstract</p> <p>Background</p> <p>Many integral membrane proteins, like their non-membrane counterparts, form either transient or permanent multi-subunit complexes in order to carry out their biochemical function. Computational methods that provide structural details of these interactions are needed since, despite their importance, relatively few structures of membrane protein complexes are available.</p> <p>Results</p> <p>We present a method for predicting which residues are in protein-protein binding sites within the transmembrane regions of membrane proteins. The method uses a Random Forest classifier trained on residue type distributions and evolutionary conservation for individual surface residues, followed by spatial averaging of the residue scores. The prediction accuracy achieved for membrane proteins is comparable to that for non-membrane proteins. Also, like previous results for non-membrane proteins, the accuracy is significantly higher for residues distant from the binding site boundary. Furthermore, a predictor trained on non-membrane proteins was found to yield poor accuracy on membrane proteins, as expected from the different distribution of surface residue types between the two classes of proteins. Thus, although the same procedure can be used to predict binding sites in membrane and non-membrane proteins, separate predictors trained on each class of proteins are required. Finally, the contribution of each residue property to the overall prediction accuracy is analyzed and prediction examples are discussed.</p> <p>Conclusion</p> <p>Given a membrane protein structure and a multiple alignment of related sequences, the presented method gives a prioritized list of which surface residues participate in intramembrane protein-protein interactions. The method has potential applications in guiding the experimental verification of membrane protein interactions, structure-based drug discovery, and also in constraining the search space for computational methods, such as protein docking or threading, that predict membrane protein complex structures.</p

Smooth Bosonization as a Quantum Canonical Transformation

We consider a 1+1 dimensional field theory which contains both a complex fermion field and a real scalar field. We then construct a unitary operator that, by a similarity transformation, gives a continuum of equivalent theories which smoothly interpolate between the massive Thirring model and the sine-Gordon model. This provides an implementation of smooth bosonization proposed by Damgaard et al. as well as an example of a quantum canonical transformation for a quantum field theory.Comment: 20 pages, revte