Density functional theory study of small nickel clusters

The stable geometries and atomization energies for the clusters Ni _n (n = 2–5) are predicted with all-electron density functional theory (DFT), using the BMK hybrid functional and a Gaussian basis set. Possible isomers and several spin states of these nickel clusters are considered systematically. The ground spin state and the lowest energy isomers are identified for each cluster size. The results are compared to available experimental and other theoretical data. The molecular orbitals of the largest cluster are plotted for all spin states. The relative stabilities of these states are interpreted in terms of superatom orbitals and no-pair bonding.     

Ab Initio Calculations of the Structure and Properties of Large Atomic Clusters

Abstract

A discussion is given of the problems involved in computing the total energy, using local density functional methods, of a cluster of atoms with a real space basis set of Gaussian orbitals. Particular attention is given to the methods used to evaluate the Hartree and exhange-correlation energies and their potentials. Several applications are described: molecular structures and properties, the bond lengths and dynamic properties of bulk silicon and diamond, the local vibratory mode of carbon in silicon, and the structures of H and H related complexes in diamond and gallium arsenide.     

A Short Note on Short Dispersal Events

We study how the speed of spread for an integrodifference equation depends on the dispersal pattern of individuals. When the dispersal kernel has finite variance, the central limit theorem states that convolutions of the kernel with itself will approach a suitably chosen Gaussian distribution. Despite this fact, the speed of spread cannot be obtained from the Gaussian approximation. We give several examples and explanations for this fact. We then use the kurtosis of the kernel to derive an improved approximation that shows a very good fit to all the kernels tested. We apply the theory to one well-studied data set of dispersal of Drosophila pseudoobscura and to two one-parameter families of theoretical dispersal kernels. In particular, we find kernels that, despite having compact support, have a faster speed of spread than the Gaussian kernel.     

Modeling functional data with spatially heterogeneous shape characteristics

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent Gaussian process. We model the marginal distributions using the skew t family. The mean, variance, and shape parameters are modeled nonparametrically as functions of location. A computationally tractable inferential framework for estimating heterogeneous asymmetric or heavy-tailed marginal distributions is introduced. This framework provides a new set of tools for increasingly complex data collected in medical and public health studies. Our methods were motivated by and are illustrated with a state-of-the-art study of neuronal tracts in multiple sclerosis patients and healthy controls. Using the tools we have developed, we were able to find those locations along the tract most affected by the disease. However, our methods are general and highly relevant to many functional data sets. In addition to the application to one-dimensional tract profiles illustrated here, higher-dimensional extensions of the methodology could have direct applications to other biological data including functional and structural magnetic resonance imaging (MRI).     

Correction for Covariate Measurement Error in Nonparametric Longitudinal Regression

Summary We introduce a correction for covariate measurement error in nonparametric regression applied to longitudinal binary data arising from a study on human sleep. The data have been surveyed to investigate the association of some hormonal levels and the probability of being asleep. The hormonal effect is modeled flexibly while we account for the error‐prone measurement of its concentration in the blood and the longitudinal character of the data. We present a fully Bayesian treatment utilizing Markov chain Monte Carlo inference techniques, and also introduce block updating to improve sampling and computational performance in the binary case. Our model is partly inspired by the relevance vector machine with radial basis functions, where usually very few basis functions are automatically selected for fitting the data. In the proposed approach, we implement such data‐driven complexity regulation by adopting the idea of Bayesian model averaging. Besides the general theory and the detailed sampling scheme, we also provide a simulation study for the Gaussian and the binary cases by comparing our method to the naive analysis ignoring measurement error. The results demonstrate a clear gain when using the proposed correction method, particularly for the Gaussian case with medium and large measurement error variances, even if the covariate model is misspecified.     

Statistically based postprocessing of phylogenetic analysis by clustering

MOTIVATION: Phylogenetic analyses often produce thousands of candidate trees. Biologists resolve the conflict by computing the consensus of these trees. Single-tree consensus as postprocessing methods can be unsatisfactory due to their inherent limitations. RESULTS: In this paper we present an alternative approach by using clustering algorithms on the set of candidate trees. We propose bicriterion problems, in particular using the concept of information loss, and new consensus trees called characteristic trees that minimize the information loss. Our empirical study using four biological datasets shows that our approach provides a significant improvement in the information content, while adding only a small amount of complexity. Furthermore, the consensus trees we obtain for each of our large clusters are more resolved than the single-tree consensus trees. We also provide some initial progress on theoretical questions that arise in this context.     

BIPSPI+: Mining Type-Specific Datasets of Protein Complexes to Improve Protein Binding Site Prediction

Computational approaches for predicting protein-protein interfaces are extremely useful for understanding and modelling the quaternary structure of protein assemblies. In particular, partner-specific binding site prediction methods allow delineating the specific residues that compose the interface of protein complexes. In recent years, new machine learning and other algorithmic approaches have been proposed to solve this problem. However, little effort has been made in finding better training datasets to improve the performance of these methods. With the aim of vindicating the importance of the training set compilation procedure, in this work we present BIPSPI+, a new version of our original server trained on carefully curated datasets that outperforms our original predictor. We show how prediction performance can be improved by selecting specific datasets that better describe particular types of protein interactions and interfaces (e.g. homo/hetero). In addition, our upgraded web server offers a new set of functionalities such as the sequence-structure prediction mode, hetero- or homo-complex specialization and the guided docking tool that allows to compute 3D quaternary structure poses using the predicted interfaces. BIPSPI+ is freely available at https://bipspi.cnb.csic.es.     

Genomic prediction of dichotomous traits with Bayesian logistic models

Bayesian methods are a popular choice for genomic prediction of genotypic values. The methodology is well established for traits with approximately Gaussian phenotypic distribution. However, numerous important traits are of dichotomous nature and the phenotypic counts observed follow a Binomial distribution. The standard Gaussian generalized linear models (GLM) are not statistically valid for this type of data. Therefore, we implemented Binomial GLM with logit link function for the BayesB and Bayesian GBLUP genomic prediction methods. We compared these models with their standard Gaussian counterparts using two experimental data sets from plant breeding, one on female fertility in wheat and one on haploid induction in maize, as well as a simulated data set. With the aid of the simulated data referring to a bi-parental population of doubled haploid lines, we further investigated the influence of training set size (N), number of independent Bernoulli trials for trait evaluation (n _i ) and genetic architecture of the trait on genomic prediction accuracies and abilities in general and on the relative performance of our models. For BayesB, we in addition implemented finite mixture Binomial GLM to account for overdispersion. We found that prediction accuracies increased with increasing N and n _i . For the simulated and experimental data sets, we found Binomial GLM to be superior to Gaussian models for small n _i , but that for large n _i Gaussian models might be used as ad hoc approximations. We further show with simulated and real data sets that accounting for overdispersion in Binomial data can markedly increase the prediction accuracy.     

Assignment of the absolute configuration of [n]-ladderanes by TD-DFT optical rotation calculations

In this study, we report theoretical specific rotation values for a series of cis-/trans-alkylated-[5]-ladderanes and cis-/trans-methylated-[n]-ladderanes. Using time-dependent density functional response theory optical rotation calculations, we can assign (+) and (-) optical rotation signs to trans-(S)-alkyl-[5]-ladderane and trans-(R)-alkyl-[5]-ladderane configurations, respectively. In order to qualitatively validate our absolute configuration predictions, we computed optical rotation values at three different levels of theory--B3LYP, RI-BP86, and Hartree-Fock--using the aug-cc-pVDZ basis set. We observe a novel rung-parity-controlled oscillatory optical rotatory phenomenon in our computations, which, to the best of our knowledge, has never been reported or observed before. Furthermore, this preliminary analysis of optical rotation properties in this class of compounds should facilitate the correct absolute stereochemical assignment of natural and synthetic ladderanes, such as the trans-isomer of pentacyclic C(20)-fatty acid methyl ester (pentacycloanammoxic methyl ester), without the need for derivatization, in particular for cases where NMR or X-ray crystal structures are not readily available.     

Conformational studies on polynucleotide chains. I. Hartree-fock energies and description of nonbonded interactions with Lennard-Jones potentials

The sugar–phosphate–sugar complex C₁₀H₁₈O₈P, a unit of the polynucleotide chains, was analyzed, making use of 100 conformational energies computed in the Hartree-Fock approximation with a small basis set of Gaussian type orbitals. The geometry of the conformations [which corresponds to the C(2′)-endo deoxy system], the basis set, and the computed total energies are reported in this work. In addition, a number of attempts are presented where we searched for a computationally very simple analytical expression apt to fit, with reasonable accuracy, the computed energies. Lennard-Jones type potential seems to offer an appropriate form capable of reproducing the positions of the maxima and the minima resulting from ab initio computations, but neither the 6-12 nor other similar forms seem to be able to correctly reproduce the intensity of the barriers. Form a details analysis of the barriers to rotation about the bonds O(5′)—C(5′) and C(5′)—C(4′) in terms of nonboned interactions, we found that a substantial improvement in the fit of analytical to ab initio energies may be obtained by distinguishing between atoms characterized by the same atomic number but having different chemical characteristics, like the oxygen atoms of the phosphate group, on one hand, and the oxygen atoms of the sugar rings and the hydroxyl groups, on the other.     

An insight into the general relationship between the three dimensional structures of enzymes and their electronic wave functions: Implication for the prediction of functional sites of enzymes

In this study, we explored the general relationship between the three-dimensional (3D) structures of enzymes and their electronic wave functions. Furthermore, we developed a method for the prediction of their functionally important sites. For this purpose, we first performed linear-scaling molecular orbital calculations for 112 nonredundant, non-homologous enzymes with known structure and function. In consequence, we showed that the canonical molecular orbitals (MOs) of the enzymes could be classified into three groups according to the degree of electron delocalization: highly localized orbitals (Group A), highly delocalized orbitals whose electrons are distributed over almost the whole molecule (Group B), and moderately delocalized orbitals (Group C). The MOs belonging to Group A are located near the HOMO-LUMO band gap, and thereby include the frontier orbitals of a given enzyme. We inferred that the MOs of Group B play a role in stabilizing the 3D structure of the enzyme, while those of Group C contribute to constructing the covalent bond framework of the enzyme. Next, we investigated whether the frontier orbitals of enzymes could be used for identifying their potential functional sites. As a result, we found that the frontier orbitals of the 112 enzymes have a high propensity to be colocalized with the known functional sites, especially when the enzymes are hydrated. Such a propensity is shown to be remarkable when Glu or Asp is a functional site residue. On the basis of these results, we finally propose a protocol for the prediction of functional sites of enzymes.     

Stochastic models for X chromosome inactivation

Summary A multivariate Gaussian model for mammalian development is presented with the associated biological and mathematical assumptions. Many biological investigations use the female mammal X chromosome to test hypotheses and to estimate parameters of the developmental system. In particular, Lyon's (1961) hypotheses are used as a basis of the mathematical model. Experimental mouse data and three sets of human experimental data are analyzed using the hypothesized Gaussian model. The estimated biological parameters are consistent with some current biological theories.     

PCA-correlated SNPs for structure identification in worldwide human populations

Existing methods to ascertain small sets of markers for the identification of human population structure require prior knowledge of individual ancestry. Based on Principal Components Analysis (PCA), and recent results in theoretical computer science, we present a novel algorithm that, applied on genomewide data, selects small subsets of SNPs (PCA-correlated SNPs) to reproduce the structure found by PCA on the complete dataset, without use of ancestry information. Evaluating our method on a previously described dataset (10,805 SNPs, 11 populations), we demonstrate that a very small set of PCA-correlated SNPs can be effectively employed to assign individuals to particular continents or populations, using a simple clustering algorithm. We validate our methods on the HapMap populations and achieve perfect intercontinental differentiation with 14 PCA-correlated SNPs. The Chinese and Japanese populations can be easily differentiated using less than 100 PCA-correlated SNPs ascertained after evaluating 1.7 million SNPs from HapMap. We show that, in general, structure informative SNPs are not portable across geographic regions. However, we manage to identify a general set of 50 PCA-correlated SNPs that effectively assigns individuals to one of nine different populations. Compared to analysis with the measure of informativeness, our methods, although unsupervised, achieved similar results. We proceed to demonstrate that our algorithm can be effectively used for the analysis of admixed populations without having to trace the origin of individuals. Analyzing a Puerto Rican dataset (192 individuals, 7,257 SNPs), we show that PCA-correlated SNPs can be used to successfully predict structure and ancestry proportions. We subsequently validate these SNPs for structure identification in an independent Puerto Rican dataset. The algorithm that we introduce runs in seconds and can be easily applied on large genome-wide datasets, facilitating the identification of population substructure, stratification assessment in multi-stage whole-genome association studies, and the study of demographic history in human populations.     

The diffusion process approach to one-compartmental stochastic models: A mathematical note

We consider the one-dimension (one-compartment) exponential model using a diffusion process approach. In particular, we summarize the known results in the case where the stochastic component of the model is a Gaussian white noise process with mean zero and variance σ². Finally, we briefly illustrate a number of cases where similar forms of model arise.     

Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models

Summary This article introduces new methods for performing classification of complex, high‐dimensional functional data using the functional mixed model (FMM) framework. The FMM relates a functional response to a set of predictors through functional fixed and random effects, which allows it to account for various factors and between‐function correlations. The methods include training and prediction steps. In the training steps we train the FMM model by treating class designation as one of the fixed effects, and in the prediction steps we classify the new objects using posterior predictive probabilities of class. Through a Bayesian scheme, we are able to adjust for factors affecting both the functions and the class designations. While the methods can be used in any FMM framework, we provide details for two specific Bayesian approaches: the Gaussian, wavelet‐based FMM (G‐WFMM) and the robust, wavelet‐based FMM (R‐WFMM). Both methods perform modeling in the wavelet space, which yields parsimonious representations for the functions, and can naturally adapt to local features and complex nonstationarities in the functions. The R‐WFMM allows potentially heavier tails for features of the functions indexed by particular wavelet coefficients, leading to a down‐weighting of outliers that makes the method robust to outlying functions or regions of functions. The models are applied to a pancreatic cancer mass spectroscopy data set and compared with other recently developed functional classification methods.