High-Dimensional Mixed Graphical Models

While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models for datasets with both continuous and discrete variables (mixed data), which are common in many scientific applications. We propose a novel graphical model for mixed data, which is simple enough to be suitable for high-dimensional data, yet flexible enough to represent all possible graph structures. We develop a computationally efficient regression-based algorithm for fitting the model by focusing on the conditional log-likelihood of each variable given the rest. The parameters have a natural group structure, and sparsity in the fitted graph is attained by incorporating a group lasso penalty, approximated by a weighted lasso penalty for computational efficiency. We demonstrate the effectiveness of our method through an extensive simulation study and apply it to a music annotation dataset (CAL500), obtaining a sparse and interpretable graphical model relating the continuous features of the audio signal to binary variables such as genre, emotions, and usage associated with particular songs. While we focus on binary discrete variables for the main presentation, we also show that the proposed methodology can be easily extended to general discrete variables.     

Bionectriol A, a polyketide glycoside from the fungus Bionectria sp. associated with the fungus-growing ant, Apterostigma dentigerum

A new polyketide glycoside, bionectriol A (1), was produced by a fungal culture of Bionectria sp., which was isolated from a fungus garden of the fungus-growing ant Apterostigma dentigerum, in Costa Rica. The structure of bionectriol A was determined mainly through NMR and mass spectroscopic data, as well as UV and IR spectra. The relative configurations of the main chain, the pyranohexose, and the pentitol moiety were elucidated by ¹H–¹H coupling constants and ROESY NMR spectral analysis.     

Isoprenoid-chained lipid β-XylOC16+4—A novel molecule for in meso membrane protein crystallization

Here we report a successful use of a recently developed isoprenoid-chained lipid family for in meso crystallization of membrane proteins. The isoprenoid-chained lipid 1-O-(3,7,11,15-tetramethylhexadecyl)-β–d-xyloside (β-XylOC₁₆₊₄) used as a host lipid for in meso crystallization provided high quality bacteriorhodopsin (bR) crystals (P6₃ space group) diffracting to high resolution and characterized by low twinning ratio. β-XylOC₁₆₊₄ has an isoprenoid chain with methyl branches at each 4th position and a xylose group in the water-soluble part. These peculiarities make the lipid clearly distinguishable in the bR crystalline lattice and provides a unique opportunity to study the role of the host lipid in the in meso crystallization. We conclude that β-XylOC₁₆₊₄ may have a general application for in meso crystallization for a wide range of membrane proteins. The cubic phase of β-XylOC₁₆₊₄ is present over a wide range of temperatures and is stable at low temperature (down to about 8 °C). This opens up the possibility of using temperature as a tool for the optimization of in meso crystallization with additional advantages for the crystallization of membrane proteins at lower temperatures where the proteins of interest may be more stable.     

Partial estimation of covariance matrices

A classical approach to accurately estimating the covariance matrix Σ of a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. However, many modern applications operate with much smaller sample sizes, thus calling for estimation guarantees in the regime ${n \ll p}$ . We show that a sample of size n = O(m log⁶ p) is sufficient to accurately estimate in operator norm an arbitrary symmetric part of Σ consisting of m ≤ n nonzero entries per row. This follows from a general result on estimating Hadamard products M · Σ, where M is an arbitrary symmetric matrix.     

Cationic methyl complexes of rhodium(III): synthesis, structure, and some reactions

Cationic methyl complex of rhodium(III), trans-[Rh(Acac)(PPh₃)₂(CH₃)(CH₃CN)][BPh₄] (1) is prepared by interaction of trans-[Rh(Acac)(PPh₃)₂(CH₃)I] with AgBPh₄ in acetonitrile. Cationic methyl complexes of rhodium(III), cis-[Rh(Acac)(PPh₃)₂ (CH₃)(CH₃CN)][BPh₄] (2) and cis-[Rh(BA)(PPh₃)₂(CH₃)(CH₃CN)][BPh₄] (3) (Acac, BA are acetylacetonate and benzoylacetonate, respectively), are obtained by CH₃I oxidative addition to rhodium(I) complexes [Rh(Acac)(PPh₃)₂] and [Rh(BA)(PPh₃)₂] in acetonitrile in the presence of NaBPh₄. Complexes 2 and 3 react readily with NH₃ at room temperature to form cis-[Rh(Acac)(PPh₃)₂(CH₃)(NH₃)][BPh₄] (4) and cis-[Rh(BA)(PPh₃)₂(CH₃)(NH₃)][BPh₄] (5), respectively. Complexes 1-5 were characterized by elemental analysis, ¹H and ³¹P{¹H} NMR spectra. Complexes 1, 2, 3 and 4 were characterized by X-ray diffraction analysis. Complexes 2 and 3 in solutions (CH₂Cl₂, CHCl₃) are presented as mixtures of cis-(PPh₃)₂ isomers involved into a fluxional process. Complex 2 on heating in acetonitrile is converted into trans-isomer 1. In parallel with that isomerization, reductive elimination of methyl group with formation of [CH₃PPh₃][BPh₄] takes place. Replacement of CH₃CN in complexes 1 and 2 by anion I⁻ yields in both cases the neutral complex trans-[Rh(Acac)(PPh₃)₂(CH₃)I]. Strong trans influence of CH₃ ligand manifests itself in the elongation (in solid) and labilization (in solution) of rhodium-acetonitrile nitrogen bond.     

NanoFAST: structure-based design of a small fluorogen-activating protein with only 98 amino acids

One of the essential characteristics of any tag used in bioscience and medical applications is its size. The larger the label, the more it may affect the studied object, and the more it may distort its behavior. In this paper, using NMR spectroscopy and X-ray crystallography, we have studied the structure of fluorogen-activating protein FAST both in the apo form and in complex with the fluorogen. We showed that significant change in the protein occurs upon interaction with the ligand. While the protein is completely ordered in the complex, its apo form is characterized by higher mobility and disordering of its N-terminus. We used structural information to design the shortened FAST (which we named nanoFAST) by truncating 26 N-terminal residues. Thus, we created the shortest genetically encoded tag among all known fluorescent and fluorogen-activating proteins, which is composed of only 98 amino acids.

We solved the structure of a fluorogen-activating protein FAST and synthesized the library of potential fluorogens. Using these data, we designed the shortest genetically encoded fluorescent tag among all known.     

Comparative analysis of the quality of membrane protein bacteriorhodopsin crystals during crystallization in octylglucoside and octylthioglucoside

Crystallization of bacteriorhodopsin (bR) in the lipidic cubic phase using n-octyl-β-D-glucoside (OG) and its more stable and inexpensive analogue n-octyl-β-D-thioglucoside (OTG) was comparatively analyzed [1]. It was shown that bacteriorhodopsin is efficiently crystallized in OTG in the same detergent concentration range as in OG. However, x-ray diffraction analysis shows that bR crystals in OG are characterized by a better resolution (1.35 Å) than bR crystals in OTG (1.45 Å).