Divergence Entropy-Based Evaluation of Hydrophobic Core in Aggressive and Resistant Forms of Transthyretin

The two forms of transthyretin differing slightly in the tertiary structure, despite the presence of five mutations, show radically different properties in terms of susceptibility to the amyloid transformation process. These two forms of transthyretin are the object of analysis. The search for the sources of these differences was carried out by means of a comparative analysis of the structure of these molecules in their native and early intermediate stage forms in the folding process. The criterion for assessing the degree of similarity and differences is the status of the hydrophobic core. The comparison of the level of arrangement of the hydrophobic core and its initial stages is possible thanks to the application of divergence entropy for the early intermediate stage and for the final forms. It was shown that the minimal differences observed in the structure of the hydrophobic core of the forms available in PDB, turned out to be significantly different in the early stage (ES) structure in folding process. The determined values of divergence entropy for both ES forms indicate the presence of the seed of hydrophobic core only in the form resistant to amyloid transformation. In the form of aggressively undergoing amyloid transformation, the structure lacking such a seed is revealed, being a stretched one with a high content of β-type structure. In the discussed case, the active presence of water in the structural transformation of proteins expressed in the fuzzy oil drop model (FOD) is of decisive importance for the generation of the final protein structure. It has been shown that the resistant form tends to generate a centric hydrophobic core with the possibility of creating a globular structure, i.e., a spherical micelle-like form. The aggressively transforming form reveals in the structure of its early intermediate, a tendency to form the ribbon-like micelle as observed in amyloid.     

Unboundedness properties of smoothness Morrey spaces of regular distributions on domains

We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R~n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R~n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).     

FT NIR Raman studies on gamma-irradiated bone

Exciting with the Nd:YAG laser line at 1064 nm allows to receive high-quality, fluorescence-free Raman spectra of biomaterials. The paper presents investigations of Raman scattering from the bone irradiated with gamma radiation up to the dose of 1000 kGy. Results of Raman spectra studies of gamma-irradiated bone allowed to show that inorganic component of the animal bone are more sensitive to gamma radiation than the organic component. The changes in the irradiated bone were evaluated on the basis of the changes in the intensities of line, changes in their position and changes in some important ratios. Independent determination of the protein content and the content of some important amino acids were compared with the data obtain in the Raman studies. The majority of the bands assigned to organic component of bone were affected by doses higher than 100 kGy.     

Conceptual Unification of Gravity and Quanta

We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra on the groupoid Γ=E×G where E is the total space of the frame bundle over spacetime, and G the Lorentz group. The differential geometry, based on derivations of , is constructed. The eigenvalue equation for the Einstein operator plays the role of the generalized Einstein’s equation. The algebra , when suitably represented in a bundle of Hilbert spaces, is a von Neumann algebra ℳ of random operators representing the quantum sector of the model. The Tomita–Takesaki theorem allows us to define the dynamics of random operators which depends on the state φ. The same state defines the noncommutative probability measure (in the sense of Voiculescu’s free probability theory). Moreover, the state φ satisfies the Kubo–Martin–Schwinger (KMS) condition, and can be interpreted as describing a generalized equilibrium state. By suitably averaging elements of the algebra , one recovers the standard geometry of spacetime. We show that any act of measurement, performed at a given spacetime point, makes the model to collapse to the standard quantum mechanics (on the group G). As an example we compute the noncommutative version of the closed Friedman world model. Generalized eigenvalues of the Einstein operator produce the correct components of the energy-momentum tensor. Dynamics of random operators does not “feel” singularities.     

Approximation algorithms for Hamming clustering problems

We study Hamming versions of two classical clustering problems. The Hamming radius p-clustering problem (HRC) for a set S of k binary strings, each of length n, is to find p binary strings of length n that minimize the maximum Hamming distance between a string in S and the closest of the p strings; this minimum value is termed the p-radius of S and is denoted by . The related Hamming diameter p-clustering problem (HDC) is to split S into p groups so that the maximum of the Hamming group diameters is minimized; this latter value is called the p-diameter of S.We provide an integer programming formulation of HRC which yields exact solutions in polynomial time whenever k is constant. We also observe that HDC admits straightforward polynomial-time solutions when k=O(logn) and p=O(1), or when p=2. Next, by reduction from the corresponding geometric p-clustering problems in the plane under the L₁ metric, we show that neither HRC nor HDC can be approximated within any constant factor smaller than two unless P=NP. We also prove that for any >0 it is NP-hard to split S into at most pk^1/7− clusters whose Hamming diameter does not exceed the p-diameter, and that solving HDC exactly is an NP-complete problem already for p=3. Furthermore, we note that by adapting Gonzalez' farthest-point clustering algorithm [T. Gonzalez, Theoret. Comput. Sci. 38 (1985) 293–306], HRC and HDC can be approximated within a factor of two in time O(pkn). Next, we describe a 2^O(p/)k^O(p/)n²-time (1+)-approximation algorithm for HRC. In particular, it runs in polynomial time when p=O(1) and =O(log(k+n)). Finally, we show how to find in

Full-size image

time a set L of O(plogk) strings of length n such that for each string in S there is at least one string in L within distance (1+), for any constant 0<<1.     

VoteDock: Consensus docking method for prediction of protein–ligand interactions

Molecular recognition plays a fundamental role in all biological processes, and that is why great efforts have been made to understand and predict protein–ligand interactions. Finding a molecule that can potentially bind to a target protein is particularly essential in drug discovery and still remains an expensive and time‐consuming task. In silico, tools are frequently used to screen molecular libraries to identify new lead compounds, and if protein structure is known, various protein–ligand docking programs can be used. The aim of docking procedure is to predict correct poses of ligand in the binding site of the protein as well as to score them according to the strength of interaction in a reasonable time frame. The purpose of our studies was to present the novel consensus approach to predict both protein–ligand complex structure and its corresponding binding affinity. Our method used as the input the results from seven docking programs (Surflex, LigandFit, Glide, GOLD, FlexX, eHiTS, and AutoDock) that are widely used for docking of ligands. We evaluated it on the extensive benchmark dataset of 1300 protein–ligands pairs from refined PDBbind database for which the structural and affinity data was available. We compared independently its ability of proper scoring and posing to the previously proposed methods. In most cases, our method is able to dock properly approximately 20% of pairs more than docking methods on average, and over 10% of pairs more than the best single program. The RMSD value of the predicted complex conformation versus its native one is reduced by a factor of 0.5 Å. Finally, we were able to increase the Pearson correlation of the predicted binding affinity in comparison with the experimental value up to 0.5. © 2010 Wiley Periodicals, Inc. J Comput Chem 32: 568–581, 2011     

Five isomers of monomeric cytosine and their interconversions induced by tunable UV laser light

Photoisomerization processes involving five isomers of cytosine were induced by narrowband tunable UV irradiation of matrix-isolated monomers of the compound. Irradiation of an argon matrix containing cytosine monomers with UV λ = 313 nm laser light resulted in syn?anti photoisomerizations between the two imino-oxo forms, whereas the substantially more populated amino-hydroxy and amino-oxo forms stayed intact. Subsequent irradiation with shorter-wavelength UV λ = 311 nm laser light led to two concomitant phototautomeric processes consuming the amino-oxo isomer: (i) an oxo → hydroxy hydrogen-atom transfer photoprocess converting the amino-oxo form into the amino-hydroxy tautomer; (ii) amino → imino hydrogen-atom transfer converting the amino-oxo form into the imino-oxo isomers. The UV-induced phototransformations, together with mutual conversions of the two amino-hydroxy conformers induced by irradiation with narrowband NIR light, allowed positive detection and identification of the five isomeric forms of monomeric cytosine. This is the first experimental observation of all five low-energy isomers of cytosine.     

1H, 13C, 15N NMR coordination shifts in Fe(II), Ru(II) and Os(II) cationic complexes with 2,2':6',2″-terpyridine

(1)H, (13)C and (15)N NMR studies of iron(II), ruthenium(II) and osmium(II) bis-chelated cationic complexes with 2,2':6',2″-terpyridine ([M(terpy)(2) ](2+) ; M = Fe, Ru, Os) were performed. Significant shielding of nitrogen-adjacent H(6) and deshielding of H(3'), H(4') protons were observed, both effects being mostly expressed for Fe(II) compounds. The metal-bonded nitrogens were shielded, this effect being much larger for the outer N(1), N(1″) than the inner N(1') atoms, and enhanced in the Fe(II) → Ru(II) → Os(II) series.