MCMC for hidden Markov models incorporating aggregation of states and filtering

This paper is concerned with the statistical analysis of single ion channel records. Single channels are modelled by using hidden Markov models and a combination of Bayesian statistics and Markov chain Monte Carlo methods. The techniques presented here provide a straightforward generalization to those in Rosales et al. (2001, Biophys. J., 80, 1088–1103), allowing to consider constraints imposed by a gating mechanism such as the aggregation of states into classes. This paper also presents an extension that allows to consider correlated background noise and filtered data, extending the scope of the analysis toward real experimental conditions. The methods described here are based on a solid probabilistic basis and are less computationally intensive than alternative Bayesian treatments or frequentist approaches that consider correlated data.     

Characterization of single channel currents using digital signal processing techniques based on Hidden Markov Models.

Techniques for extracting small, single channel ion currents from background noise are described and tested. It is assumed that single channel currents are generated by a first-order, finite-state, discrete-time, Markov process to which is added 'white' background noise from the recording apparatus (electrode, amplifiers, etc). Given the observations and the statistics of the background noise, the techniques described here yield a posteriori estimates of the most likely signal statistics, including the Markov model state transition probabilities, duration (open- and closed-time) probabilities, histograms, signal levels, and the most likely state sequence. Using variations of several algorithms previously developed for solving digital estimation problems, we have demonstrated that: (1) artificial, small, first-order, finite-state, Markov model signals embedded in simulated noise can be extracted with a high degree of accuracy, (2) processing can detect signals that do not conform to a first-order Markov model but the method is less accurate when the background noise is not white, and (3) the techniques can be used to extract from the baseline noise single channel currents in neuronal membranes. Some studies have been included to test the validity of assuming a first-order Markov model for biological signals. This method can be used to obtain directly from digitized data, channel characteristics such as amplitude distributions, transition matrices and open- and closed-time durations.     

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

Background

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics.

Results

Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes.

Conclusions

Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.     

Sequence organization of the human genome

The organization of three sequence classes—single copy, repetitive, and inverted repeated sequences—within the human genome has been studied by renaturation techniques, hydroxylapatite binding methods, and DNA hyperchromism. Repetitive sequence classes are distributed throughout 80% or more of the genome. Slightly more than half of the genome consists of short single copy sequences, with a length of about 2 kb interspersed with repetitive sequences. The average length of the repetitive sequences is also small and approximates the length of these sequences found in other organisms. The sequence organization of the human genome therefore resembles the sequence organization found in Xenopus and sea urchin. The inverted repeats are essentially randomly positioned with respect to both sequence class and sequence arrangement, so that all three sequence classes are found to be mutually interspersed in a portion of the genome.     

Markovian analysis of cervical cell images.

Markovian analysis is a method to measure optical texture based on gray-level transition probabilities in digitized images. Experiments are described that investigate that classification performance of parameters generated by Markovian analysis. Results using Markov texture parameters show that the selection of a Markov step size strongly affects classification error rates and the number of parameters required to achieve the maximum correct classification rates. Markov texture parameters are shown to achieve high rates of correct classification in discriminating images of normal from abnormal cervical cell nuclei.     

Trace metal imaging with high spatial resolution: applications in biomedicine

New generations of analytical techniques for imaging of metals are pushing hitherto boundaries of spatial resolution and quantitative analysis in biology. Because of this, the application of these imaging techniques described herein to the study of the organization and dynamics of metal cations and metal-containing biomolecules in biological cell and tissue is becoming an important issue in biomedical research. In the current review, three common metal imaging techniques in biomedical research are introduced, including synchrotron X-ray fluorescence (SXRF) microscopy, secondary ion mass spectrometry (SIMS), and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). These are exemplified by a demonstration of the dopamine-Fe complexes, by assessment of boron distribution in a boron neutron capture therapy cell model, by mapping Cu and Zn in human brain cancer and a rat brain tumor model, and by the analysis of metal topography within neuromelanin. These studies have provided solid evidence that demonstrates that the sensitivity, spatial resolution, specificity, and quantification ability of metal imaging techniques is suitable and highly desirable for biomedical research. Moreover, these novel studies on the nanometre scale (e.g., of individual single cells or cell organelles) will lead to a better understanding of metal processes in cells and tissues.     

Foraging Behavior of Nightingales (Luscinia Supergenus): An Experimental Study

Biology Bulletin - Abstract—Foraging techniques influence the morphological peculiarities and ecological specialization of species, also determining their organization in a community. The...     

Fast probabilistic analysis of sequence function using scoring matrices

MOTIVATION: We present techniques for increasing the speed of sequence analysis using scoring matrices. Our techniques are based on calculating, for a given scoring matrix, the quantile function, which assigns a probability, or p, value to each segmental score. Our techniques also permit the user to specify a p threshold to indicate the desired trade-off between sensitivity and speed for a particular sequence analysis. The resulting increase in speed should allow scoring matrices to be used more widely in large-scale sequencing and annotation projects. RESULTS: We develop three techniques for increasing the speed of sequence analysis: probability filtering, lookahead scoring, and permuted lookahead scoring. In probability filtering, we compute the score threshold that corresponds to the user-specified p threshold. We use the score threshold to limit the number of segments that are retained in the search process. In lookahead scoring, we test intermediate scores to determine whether they will possibly exceed the score threshold. In permuted lookahead scoring, we score each segment in a particular order designed to maximize the likelihood of early termination. Our two lookahead scoring techniques reduce substantially the number of residues that must be examined. The fraction of residues examined ranges from 62 to 6%, depending on the p threshold chosen by the user. These techniques permit sequence analysis with scoring matrices at speeds that are several times faster than existing programs. On a database of 12 177 alignment blocks, our techniques permit sequence analysis at a speed of 225 residues/s for a p threshold of 10-6, and 541 residues/s for a p threshold of 10-20. In order to compute the quantile function, we may use either an independence assumption or a Markov assumption. We measure the effect of first- and second-order Markov assumptions and find that they tend to raise the p value of segments, when compared with the independence assumption, by average ratios of 1.30 and 1.69, respectively. We also compare our technique with the empirical 99. 5th percentile scores compiled in the BLOCKSPLUS database, and find that they correspond on average to a p value of 1.5 x 10-5. AVAILABILITY: The techniques described above are implemented in a software package called EMATRIX. This package is available from the authors for free academic use or for licensed commercial use. The EMATRIX set of programs is also available on the Internet at http://motif.stanford.edu/ematrix.     

Rapid,sensitive and specific electron capture—gas chromatographic method for the quantitation of 6-chloro-2-(1-piperazinyl)pyrazine in biological fluids

A highly specific and sensitive gas chromatographic method for the determination of 6-chloro-2-(1-piperazinyl)pyrazine (MK-212), a central serotonin-like agent, in biological fluids is described. MK-212 and a related internal standard are extracted into benzene from an alkaline solution, back-extracted into acid and then re-extracted into benzene at an alkaline pH. The amines are converted to the trifluoroacetyl derivatives (characterized by gas—liquid chromatography—mass spectrometry), chromatographed and detected with a ⁶³Ni electron capture detector. The sensitivity of the method is such that 10 ng of drug can be measured per aliquot of biological fluid. The precision and accuracy of the method are well within acceptable limits. Specificity of analysis was established by gas—liquid chromatography—mass spectrometry techniques.     

In vivo plasma membrane organization: results of biophysical approaches

In the last two decades, various biophysical techniques have been used to investigate the organization of the plasma membrane in live cells. This review describes some of the most important experimental findings and summarizes the characteristics and limitations of a few frequently used biophysical techniques. In addition, the current knowledge about three membrane organizational elements: the membrane-associated cytoskeleton, caveolae and lipid microdomains, is described in detail. Unresolved issues, experimental contradictions and future directions to integrate the variety of experimental data into a revised model of the plasma membrane of eukaryotic cells are discussed in the last section.     

In vivo plasma membrane organization: results of biophysical approaches

In the last two decades, various biophysical techniques have been used to investigate the organization of the plasma membrane in live cells. This review describes some of the most important experimental findings and summarizes the characteristics and limitations of a few frequently used biophysical techniques. In addition, the current knowledge about three membrane organizational elements: the membrane-associated cytoskeleton, caveolae and lipid microdomains, is described in detail. Unresolved issues, experimental contradictions and future directions to integrate the variety of experimental data into a revised model of the plasma membrane of eukaryotic cells are discussed in the last section.     

Non-homogeneous Markov processes for biomedical data analysis

Some time ago, the Markov processes were introduced in biomedical sciences in order to study disease history events. Homogeneous and Non-homogeneous Markov processes are an important field of research into stochastic processes, especially when exact transition times are unknown and interval-censored observations are present in the analysis. Non-homogeneous Markov process should be used when the homogeneous assumption is too strong. However these sorts of models increase the complexity of the analysis and standard software is limited. In this paper, some methods for fitting non-homogeneous Markov models are reviewed and an algorithm is proposed for biomedical data analysis. The method has been applied to analyse breast cancer data. Specific software for this purpose has been implemented.     

Bayesian selection of markov models for symbol sequences: application to microsaccadic eye movements

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.     

Markov and Semi‐Markov Switching Linear Mixed Models Used to Identify Forest Tree Growth Components

Summary Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time‐varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi‐Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi‐Markovian manner. The underlying semi‐Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi‐Markov chain represent—in the corresponding growth phase—both the influence of time‐varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi‐Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation–maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates.     

Approaches to messenger RNA detection - comparison of methods

Detection of messenger RNA is an important part of current biomedical research, although utilized for decades. This communication endeavors to compare three most commonly used techniques of mRNA detection, i.e. Northern blot, ribonuclease protection assay (RPA), and real-time polymerase chain reaction (RT-PCR). Principles and general procedures of these methods are described, and advantages and weaknesses of each are discussed in terms of their specificity, sensitivity, difficulty, time and material demands as well as health and environmental risks. We conclude that choice of any method discussed depends on particular purpose, experience of the researcher, and on laboratory equipment and organization.     

Inferring speciation rates from phylogenies

Abstract It is possible to estimate the rate of diversification of clades from phylogenies with a temporal dimension. First, I present several methods for constructing confidence intervals for the speciation rate under the simple assumption of a pure birth process. I discuss the relationships among these methods in the hope of clarifying some fundamental theory in this area. Their performances are compared in a simulation study and one is recommended for use as a result. A variety of other questions that may, in fact, be the questions of primary interest (e.g., Has the rate of cladogenesis been declining?) are then recast as biological variants of the purely statistical question—Is the birth process model appropriate for my data? Seen in this way, a preexisting arsenal of statistical techniques is opened up for use in this area: in particular, techniques developed for the analysis of Poisson processes and the analysis of survival data. These two approaches start from different representations of the data—the branch lengths in the tree—and I explicitly relate the two. Aiming for a synoptic account of useful theory in this area, I briefly discuss some important results from the analysis of two distinct birth‐death processes: the one introduced into this area by Hey (1992) is refitted with some powerful statistical tools.     

A Multi-stage Representation of Cell Proliferation as a Markov Process

The stochastic simulation algorithm commonly known as Gillespie’s algorithm (originally derived for modelling well-mixed systems of chemical reactions) is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular level it is often reasonable to assume that times between successive reaction/interaction events are exponentially distributed and can be appropriately modelled as a Markov process and hence simulated by the Gillespie algorithm. However, Gillespie’s algorithm is routinely applied to model biological systems for which it was never intended. In particular, processes in which cell proliferation is important (e.g. embryonic development, cancer formation) should not be simulated naively using the Gillespie algorithm since the history-dependent nature of the cell cycle breaks the Markov process. The variance in experimentally measured cell cycle times is far less than in an exponential cell cycle time distribution with the same mean.Here we suggest a method of modelling the cell cycle that restores the memoryless property to the system and is therefore consistent with simulation via the Gillespie algorithm. By breaking the cell cycle into a number of independent exponentially distributed stages, we can restore the Markov property at the same time as more accurately approximating the appropriate cell cycle time distributions. The consequences of our revised mathematical model are explored analytically as far as possible. We demonstrate the importance of employing the correct cell cycle time distribution by recapitulating the results from two models incorporating cellular proliferation (one spatial and one non-spatial) and demonstrating that changing the cell cycle time distribution makes quantitative and qualitative differences to the outcome of the models. Our adaptation will allow modellers and experimentalists alike to appropriately represent cellular proliferation—vital to the accurate modelling of many biological processes—whilst still being able to take advantage of the power and efficiency of the popular Gillespie algorithm.