Multiway Dependence in Exponential Family Conditional Distributions

Conditionally specified statistical models are frequently constructed from one-parameter exponential family conditional distributions. One way to formulate such a model is to specify the dependence structure among random variables through the use of a Markov random field (MRF). A common assumption on the Gibbsian form of the MRF model is that dependence is expressed only through pairs of random variables, which we refer to as the “pairwise-only dependence” assumption. Based on this assumption, J. Besag (1974, J. Roy. Statist. Soc. Ser. B36, 192–225) formulated exponential family “auto-models” and showed the form that one-parameter exponential family conditional densities must take in such models. We extend these results by relaxing the pairwise-only dependence assumption, and we give a necessary form that one-parameter exponential family conditional densities must take under more general conditions of multiway dependence. Data on the spatial distribution of the European corn borer larvae are fitted using a model with Bernoulli conditional distributions and several dependence structures, including pairwise-only, three-way, and four-way dependencies.     

Design of a new electrogenerated polyquinone film substituted with glutathione. Towards direct electrochemical biosensors

We developed a method to graft a tripeptide (glutathione) onto 5-hydroxy-1,4-naphthoquinone, an electropolymerizable molecule. The resulting thin conducting polymer presents a well-defined and stable electroactivity in neutral buffered solution, due to the embedded quinone group, and is able to covalently graft amino-modified DNA probe strands. It is shown that the bioelectrode presents positive current change following DNA hybridization. This makes a “signal-on” direct electrochemical DNA sensor. The results were obtained with low target concentration (50 nM) and the selectivity is excellent as a single-mismatch sequence can be discriminated from the full-complementary target.     

A Platform Approach to Cleavable Macrocycles for the Controlled Disassembly of Mechanically Caged Molecules

Inspired by interlocked oligonucleotides, peptides and knotted proteins, synthetic systems where a macrocycle cages a bioactive species that is “switched on” by breaking the mechanical bond have been reported. However, to date, each example uses a bespoke chemical design. Here we present a platform approach to mechanically caged structures wherein a single macrocycle precursor is diversified at a late stage to include a range of trigger units that control ring opening in response to enzymatic, chemical, or photochemical stimuli. We also demonstrate that our approach is applicable to other classes of macrocycles suitable for rotaxane and catenane formation.     

Assessment of quantum‐chemical methods for electronic properties and geometry of signaling biomolecules

A reasonable balance between accuracy and feasibility of quantum‐chemical methods depends on the complexity of the molecular system and the scientific goals. Six series of indole‐, naphthalene‐, phenol‐, benzoic‐, phenoxy‐, other auxin‐derivatives, and a test set of similar organic molecules have been chosen for an assessment of 13 density functional and semi‐empirical molecular orbital methods with respect to electronic and structural properties. The accuracy and precision of HOMO/LUMO calculations are determined by comparison with experimental ionization potentials and electron affinities. Further comparison was performed at atomic level by covariance analysis. The methods KMLYP, MSINDO, and PM3 are precise and accurate for the whole set of molecules. The method AM1 offers comparable accuracy with the exception of electron affinities of indole derivatives, where significant deviations from experiment were observed. Geometrical properties were best reproduced with the semi‐empirical method MSINDO. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

A Proof of a Conjecture of Ohba

We prove a conjecture of Ohba that says that every graph G on at most vertices satisfies .     

Mixing Homomorphisms,Recolorings, and Extending Circular Precolorings

This work brings together ideas of mixing graph colorings, discrete homotopy, and precoloring extension. A particular focus is circular colorings. We prove that all the ‐colorings of a graph G can be obtained by successively recoloring a single vertex provided along the lines of Cereceda, van den Heuvel, and Johnson's result for k‐colorings. We give various bounds for such mixing results and discuss their sharpness, including cases where the bounds for circular and classical colorings coincide. As a corollary, we obtain an Albertson‐type extension theorem for ‐precolorings of circular cliques. Such a result was first conjectured by Albertson and West. General results on homomorphism mixing are presented, including a characterization of graphs G for which the endomorphism monoid can be generated through the mixing process. As in similar work of Brightwell and Winkler, the concept of dismantlability plays a key role.     

Bi2O3 deposited on highly ordered mesoporous carbon for supercapacitors

A simple route has been employed to prepare nanosized Bi₂O₃ deposited on highly ordered mesoporous carbon. The electrochemical measurements reveal that, by loading only 10% Bi₂O₃ on the mesoporous carbon, the specific capacitance of the composite is improved by 62%, with the maximum value reaching 232 F g^?1 at a sweep rate of 5 mV s^?1. The specific capacitance of Bi₂O₃ is calculated and reaches 1305 F g^?1 at 1 mV s^?1. It is found that the mass transfer in the framework of the crystalline oxide is still difficult in spite of its nanosize, as evidenced by the decline of the specific capacitance of the Bi₂O₃ with the increase of the sweep rate. The cyclic life of composite materials is also measured and the capacitance only declines 21% after 1000 cycles.     

Effect of visible light on normal and P23H-3 transgenic rat retinas: characterization of a novel retinoic acid derivative present in the P23H-3 retina

Transgenic rats with the P23H mutation in rhodopsin exhibit increased susceptibility to light damage, compared with normal animals. It is known that light-induced retinal damage requires repetitive bleaching of rhodopsin and that photoreceptor cell loss is by apoptosis; however, the underlying molecular mechanism(s) leading to photoreceptor cell death are still unknown. Photoproducts, such as all-trans retinal or other retinoid metabolites, released by the extensive bleaching of rhodopsin could lead to activation of degenerative processes, especially in animals genetically predisposed to retinal degenerations. Using wild-type and transgenic rats carrying the P23H opsin mutation, we evaluated the effects of acute intense visible light on retinoid content, type and distribution in ocular tissues. Rats were exposed to green light (480-590 nm) for 0, 5, 10, 30 and 120 min. Following light treatment, rats were sacrificed and neural retinas were dissected free of the retinal pigment epithelium. Retinoids were extracted from retinal tissues and then subjected to HPLC and mass spectral analysis. We found that the light exposure affected relative levels of retinoids in the neural retina and retinal pigment epithelium of wild-type and P23H rat eyes similarly. In the P23H rat retina but not the wild-type rat retina, we found a retinoic acid-like compound with an absorbance maximum of 357 nm and a mass of 304 daltons. Production of this retinoic acid-like compound in transgenic rats is influenced by the age of the animals and the duration of light exposure. It is possible that this unique retinoid may be involved in the process of light-induced retinal degeneration.     

Density-functional geometry optimization of the 150,000-atom photosystem-I trimer

We present a linear-scaling method based on the use of density-functional theory (DFT) for the system-wide optimization of x-ray structural coordinates and apply it to optimize the 150,000 atoms of the photosystem-I (PS-I) trimer. The method is based on repetitive applications of a multilevel ONIOM procedure using the PW916-31G(d) DFT calculations for the high level and PM3 for the lower level; this method treats all atoms in the structure equivalently, a structure in which the majority of the atoms can be considered as part of some internal "active site." To obtain a realistic single structure, some changes to the original protein model were necessary but these are kept to a minimum in order that the optimized structure most closely resembles the original x-ray one. Optimization has profound effects on the perceived electronic properties of the cofactors, with, e.g., optimization lowering the internal energy of the chlorophylls by on average 53 kcal mol(-1) and eliminates the enormous 115 kcal mol(-1) energy spread depicted by the original x-ray heavy-atom coordinates. A highly precise structure for PS-I results that is suitable for analysis of device function. Significant qualitative features of the structure are also improved such as correction of an error in the stereochemistry of one of the chlorophylls in the "special pair" of the reaction center, as well as the replacement of a water molecule with a metal cation in a critical region on the C3 axis. The method also reveals other unusual features of the structure, leading both to suggestions concerning device functionality and possible mutations between gene sequencing and x-ray structure determination. The optimization scheme is thus shown to augment the molecular modeling schemes that are currently used to add medium-resolution structural information to the raw scattering data in order to obtain atomically resolved structures. System-wide optimization is now a feasible process and its use within protein x-ray data refinement should be considered.