In this article, we develop a quantitative comparison method for two arbitrary protein structures. This method uses a root-mean-square deviation characterization and employs a series expansion of the protein's shape function in terms of the Wigner-D functions to define a new criterion, which is called a "similarity value." We further demonstrate that the expansion coefficients for the shape function obtained with the help of the Wigner-D functions correspond to structure factors. Our method addresses the common problem of comparing two proteins with different numbers of atoms. We illustrate it with a worked example.

We consider particles transport in the Sinai billiard with infinite horizon. The simulation shows that the transport is superdiffusive in both continuous and discrete time. Also, it is shown that the moments do not converge to the Gaussian moments even in the logarithmically renormalized time scale, at least for a fairly long computational time. These results are discussed with respect to the existent rigorous theorems. Similar results are obtained for the stadium billiard.

BackgroundThis paper provides a simple and rapid method for a protein-clustering strategy. The basic idea implemented here is to use computational geometry methods to predict and characterize ligand-binding pockets of a given protein structure. In addition to geometrical characteristics of the protein structure, we consider some simple biochemical properties that help recognize the best candidates for pockets in a protein’s active site.ResultsOur results are shown to produce good agreement with known empirical results.ConclusionsThe method presented in this paper is a low-cost rapid computational method that could be used to classify proteins and other biomolecules, and furthermore could be useful in reducing the cost and time of drug discovery.

In this paper, we use the time-super-operator formalism and the two-level Friedrichs model to obtain a phenomenological model of mesons decay. Our approach provides a fairly good estimation of the CP-symmetry violation parameter in the case of K, B and D mesons.

The Hamiltonian Friedrichs model [1] describing the evolution of a two-level system coupled to a continuum is used in order to modelize the decay of the kaon states K1, K2. Using different cut-off functions of the continuous degrees of freedom, we show that this model leads to a CP violation that qualitatively fits with experimental data improving previous numerical estimates. We also discuss the relation of our model to other models of open systems.