Multi-scale simulation reveals that an amino acid substitution increases photosensitizing reaction inputs in Rhodopsins

Evaluating the availability of molecular oxygen (O₂) and energy of excited states in the retinal binding site of rhodopsin is a crucial challenging first step to understand photosensitizing reactions in wild-type (WT) and mutant rhodopsins by absorbing visible light. In the present work, energies of the ground and excited states related to 11-cis-retinal and the O₂ accessibility to the β-ionone ring are evaluated inside WT and human M207R mutant rhodopsins. Putative O₂ pathways within rhodopsins are identified by using molecular dynamics simulations, Voronoi-diagram analysis, and implicit ligand sampling while retinal energetic properties are investigated through density functional theory, and quantum mechanical/molecular mechanical methods. Here, the predictions reveal that an amino acid substitution can lead to enough energy and O₂ accessibility in the core hosting retinal of mutant rhodopsins to favor the photosensitized singlet oxygen generation, which can be useful in understanding retinal degeneration mechanisms and in designing blue-lighting-absorbing proteic photosensitizers.     

A Review of Fractional Order Entropies

Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful.     

Discrete and selective absorption in crystalline molecular nanofilms

Recent research in nano-optical engineering and in nanomedicine as well, seeks for methods of construction of various types of nano-markers, nano-carriers, and ways to deliver drugs to the exactly determined regions of body. In this process it is important to find methods of recognition of certain types of molecules. It is obvious that optical recognition would be the easiest and the most effective way to do it. Our research presents a model of a molecular ultrathin crystalline film and generated exciton system inside it and corresponding methodology of analysis of their optical characteristics. Properties of these spatially very restricted structures are very sensitive to their surrounding surfaces. Using the two-time Green’s functions adapted for crystalline structures with symmetry breaking, and graphical-numerical software, we have calculated the energy spectra and possible exciton states. We have shown that the appearance and the presence of localized states on the surfaces and in the boundary layers of the film depend on the thickness of the film and the film surroundings, presented through the perturbation of parameters on surfaces. Optical properties in these structures demonstrate discrete and very selective resonant absorption spectra, depending on the perturbation on their surfaces.     

“Locus” and “Trace” in Cabrigéomètre: relationships between geometric and functional aspects in a study of transformations

The present text describes and characterises the tools “Locus” and “Trace” of Cabri-géomètre II, in relations to a study of geometric transformation, more precisely, the passage from the notion of transformation of figures to the notion of applications¹ that map points on the plane onto the plane itself. In particular it discusses how the conception of image of a figure under a transformation can evolve—through interaction in a “milieu” organised around Cabri-géomètre—such that students move from views of figure-images as undecomposible entities to see them as sets of image-points. Moreover, the study allowed the identification that the notion of trajectory (in a dynamic interpretation) has an important role in this conceptually difficult passage and that dynamic geometry environment renovate this notion.     

Interplay of Antiferromagnetic Coupling and Spin Crossover in Dinuclear Iron(II) Complexes

This article reports on the study of the interplay between magnetic coupling and spin transition in 2,2′-bipyrimidine (bpym)-bridged iron(II) dinuclear compounds. Coexistence of both phenomena has been observed in [Fe(bpym)(NCS)₂]₂bpym, [Fe(bpym)(NCSe)₂]₂bpym and [Fe(bt)(NCS)₂]₂bpym (bpym = 2,2′-bipyrimidine, bt = 2,2′-bithiazoline) by the action of external physical factors namely pressure or electromagnetic radiation. Competition between magnetic exchange and spin crossover has been studied in [Fe(bpym)(NCS)₂]₂bpym at 6.3 kbar. LIESST experiments carried out in [Fe(bpym)(NCSe)₂]₂bpym and [Fe(bt)(NCS)₂]₂bpym at 4.2 K have shown that is possible to achieve dinuclear molecules with different spin states in this class of compounds. This revised version was published online in August 2006 with corrections to the Cover Date.     

Presmoothing the transition probabilities in the illness-death model

One major goal in clinical applications of multi-state models is the estimation of transition probabilities. In a recent paper, Meira-Machado et al. (2006) introduce a substitute for the Aalen-Johansen estimator in the case of a non-Markov illness-death model. The idea behind their estimator is to weight the data by the Kaplan-Meier weights pertaining to the distribution of the total survival time of the process. In this paper we propose a modification of Meira-Machado et al. (2006) estimator based on presmoothing. Consistency is established. We investigate the finite sample performance of the new estimator through simulations. Data from a study on colon cancer are used for illustration purposes.     

Bayesian modeling of financial returns: A relationship between volatility and trading volume

The modified mixture model with Markov switching volatility specification is introduced to analyze the relationship between stock return volatility and trading volume. We propose to construct an algorithm based on Markov chain Monte Carlo simulation methods to estimate all the parameters in the model using a Bayesian approach. The series of returns and trading volume of the British Petroleum stock will be analyzed. Copyright © 2009 John Wiley & Sons, Ltd.     

Self-inverse Sheffer sequences and Riordan involutions

In this short note, we focus on self-inverse Sheffer sequences and involutions in the Riordan group. We translate the results of Brown and Kuczma on self-inverse sequences of Sheffer polynomials to describe all involutions in the Riordan group.     

A remark on a maximal function over a Cantor set of directions

LetM _e ⁰ be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL ². We consider a sequence of operators over finite sets of directions converging toM _e ⁰ . We improve the previous estimate for the (L ²,L ²)-norm of these particular operators. We also prove thatM _e ⁰ is bounded from some subsets ofL ² toL ². These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip. Partially supported by Spanish DGICYT grant no. PB90-0187.