Bayes factors for detection of Quantitative Trait Loci

A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor.     

Conformational space comparison of GnRH and lGnRH-III using molecular dynamics, cluster analysis and Monte Carlo thermodynamic integration

The conformational space available to GnRH and lGnRH-III was compared using 5.2 ns constant temperature and pressure molecular dynamics simulations with explicit TIP3P solvation and the AMBER v. 5.0 force field. Cluster analysis of both trajectories resulted in two groups of conformations. Results of free energy calculations, in agreement with previous experimental data, indicate that a conformation with a turn from residues 5 through 8 is preferred for GnRH in an aqueous environment. By contrast, a conformation with a helix from residues 2 through 7 with a bend from residues 6 through 10 is preferred for lGnRH-III in an aqueous environment. The side chains of His2 and Trp3 in lGnRH-III occupy different regions of phase space and participate in weakly polar interactions different from those in GnRH. The unique conformational properties of lGnRH-III may account for its specific anti cancer activity.     

Predicting the effects of basepair mutations in DNA-protein complexes by thermodynamic integration

Thermodynamically rigorous free energy methods in principle allow the exact computation of binding free energies in biological systems. Here, we use thermodynamic integration together with molecular dynamics simulations of a DNA-protein complex to compute relative binding free energies of a series of mutants of a protein-binding DNA operator sequence. A guanine-cytosine basepair that interacts strongly with the DNA-binding protein is mutated into adenine-thymine, cytosine-guanine, and thymine-adenine. It is shown that basepair mutations can be performed using a conservative protocol that gives error estimates of ∼10% of the change in free energy of binding. Despite the high CPU-time requirements, this work opens the exciting opportunity of being able to perform basepair scans to investigate protein-DNA binding specificity in great detail computationally.     

Computing free energies using nested sampling-based approaches

Abstract

Nested sampling (NS) has emerged as a powerful statistical mechanical sampling technique to compute the partition function of atomic and molecular systems. From the partition function all thermodynamic quantities can be calculated in absolute terms, including absolute free energies and entropies. In this article, we provide a brief overview of NS within a Bayesian context, as well as overviews of how NS is used to compute the partition functions and thermodynamic quantities in the canonical and isothermal-isobaric ensembles. Then we introduce a new scheme, Coupling Parameter Path Nested Sampling, to estimate the free energy difference between two systems with different potential energy functions. The method uses a NS simulation to traverse the same path through phase space as would be covered in traditional coupling parameter-based methods such as thermodynamic integration and perturbation approaches. We demonstrate the new method with two case studies and confirm its accuracy by comparison to conventional methods, including Widom test particle insertion and thermodynamic integration. The proposed method provides a powerful alternative to traditional coupling parameter-based free energy simulation methods.     

Computing factors of safety against wind-induced tree stem damage

The drag forces, bending moments and stresses acting on stems differing in size and location within the mechanical infrastructure of a large wild cherry (Prunus serotina Ehrh.) tree are estimated and used to calculate the factor of safety against wind-induced mechanical failure based on the mean breaking stress of intact stems and samples of wood drawn from this tree. The drag forces acting on stems are calculated based on stem projected areas and field measurements of wind speed taken within the canopy and along the length of the trunk. The bending moments and stresses resulting from these forces are shown to increase basipetally in a nearly log-log linear fashion toward the base of the tree. The factor of safety, however, varies in a sinusoidal manner such that the most distal stems have the highest factors of safety, whereas stems of intermediate location and portions of the trunk near ground level have equivalent and much lower factors of safety. This pattern of variation is interpreted to indicate that, as a course of normal growth and development, trees similar to the one examined in this study maintain a cadre of stems prone to wind-induced mechanical damage that can reduce the probability of catastrophic tree failure by reducing the drag forces acting on older portions of the tree. Comparisons among real and hypothetical stems with different taper experiencing different vertical wind speed profiles show that geometrically self-similar stems have larger factors of safety than stems tapering according to elastic or stress self-similarity, and that safety factors are less significantly influenced by the 'geometry' of the wind-profile.     

Adjusting batch effects in microarray expression data using empirical Bayes methods

Non-biological experimental variation or "batch effects" are commonly observed across multiple batches of microarray experiments, often rendering the task of combining data from these batches difficult. The ability to combine microarray data sets is advantageous to researchers to increase statistical power to detect biological phenomena from studies where logistical considerations restrict sample size or in studies that require the sequential hybridization of arrays. In general, it is inappropriate to combine data sets without adjusting for batch effects. Methods have been proposed to filter batch effects from data, but these are often complicated and require large batch sizes ( > 25) to implement. Because the majority of microarray studies are conducted using much smaller sample sizes, existing methods are not sufficient. We propose parametric and non-parametric empirical Bayes frameworks for adjusting data for batch effects that is robust to outliers in small sample sizes and performs comparable to existing methods for large samples. We illustrate our methods using two example data sets and show that our methods are justifiable, easy to apply, and useful in practice. Software for our method is freely available at: http://biosun1.harvard.edu/complab/batch/.     

Prediction of antisense oligonucleotides using structural and thermodynamic motifs

Specific gene expression regulation strategy using antisense oligonucleotides occupy significant space in recent clinical trials. The therapeutical potential of oligos lies in the identification and prediction of accurate oligonucleotides against specific target mRNA. In this work we present a computational method that is built on Artificial Neural Network (ANN) which could recognize and predict oligonucleotides effectively. In this study first we identified 11 major parameters associated with oligo:mRNA duplex linkage. A feed forward multilayer perceptron ANN classifier is trained with a set of experimentally proven feature vectors. The classifier gives an exact prediction of the input sequences under 2 classes – oligo or non-oligo. On validation, our tool showed comparatively significant accuracy of 92.48% with 91.7% sensitivity and 92.09% specificity. This study was also able to reveal the relative impact of individual parameters we considered on antisense oligonucleotide predictions.