Robust Clustering Using Exponential Power Mixtures

Summary Clustering is a widely used method in extracting useful information from gene expression data, where unknown correlation structures in genes are believed to persist even after normalization. Such correlation structures pose a great challenge on the conventional clustering methods, such as the Gaussian mixture (GM) model, k‐means (KM), and partitioning around medoids (PAM), which are not robust against general dependence within data. Here we use the exponential power mixture model to increase the robustness of clustering against general dependence and nonnormality of the data. An expectation–conditional maximization algorithm is developed to calculate the maximum likelihood estimators (MLEs) of the unknown parameters in these mixtures. The Bayesian information criterion is then employed to determine the numbers of components of the mixture. The MLEs are shown to be consistent under sparse dependence. Our numerical results indicate that the proposed procedure outperforms GM, KM, and PAM when there are strong correlations or non‐Gaussian components in the data.     

Bayesian dynamic modeling of latent trait distributions

Studies of latent traits often collect data for multiple items measuring different aspects of the trait. For such data, it is common to consider models in which the different items are manifestations of a normal latent variable, which depends on covariates through a linear regression model. This article proposes a flexible Bayesian alternative in which the unknown latent variable density can change dynamically in location and shape across levels of a predictor. Scale mixtures of underlying normals are used in order to model flexibly the measurement errors and allow mixed categorical and continuous scales. A dynamic mixture of Dirichlet processes is used to characterize the latent response distributions. Posterior computation proceeds via a Markov chain Monte Carlo algorithm, with predictive densities used as a basis for inferences and evaluation of model fit. The methods are illustrated using data from a study of DNA damage in response to oxidative stress.     

New possibilities for the mathematical modeling of turbulent transport processes in plasma

A new mathematical model is proposed for the probability distributions of the characteristics of the processes observed in turbulent plasmas. The model is based on formal theoretical considerations related to probabilistic limit theorems for a nonhomogeneous random walk and has the form of a finite mixture of Gaussian distributions. The reliability of the model is confirmed by the results of a statistical analysis of the experimental data on density fluctuations in high-temperature plasmas of the L-2M, LHD, and TJ-II stellarators and the local fluctuating flux in the TAU-1 linear device and in the edge plasma of the L-2M stellarator with the use of the estimation-maximization algorithm. It is shown that low-frequency structural turbulence in a magnetized plasma is related to non-Brownian transport, which is determined by the characteristic temporal and spatial scales of the ensembles of stochastic plasma structures. Mechanisms that could be responsible for the random nature of time samples of the local turbulent flux in TAU-1 are indicated. A new physical concept of the intermittence of plasma turbulent pulsations is developed on the basis of the statistical separation of mixtures in terms of the model proposed. The intermittence of plasma pulsations is shown to be associated with the generation of plasma structures (solitons and vortices) and their nonlinear interaction, as well as with their damping and drift.     

Identification by microscopically controlled comet assay of peritoneal macrophages in a mixture of peritoneal exudate for DNA strand break analysis

A simple modification of the alkaline comet assay allows the study of DNA damage in a specific cell type in a mixture of primary cells. Peritoneal macrophages from mice are selected from other peritoneal exudate cells without complex preparation and separation steps by their size and shape of the nuclei and their comets. The DNA damage can be well characterised by the manually monitored parameter 'tail length'. Complex measurement of the 'tail moment', often used for characterising DNA damage is not required, a fact which further simplifies the protocol. The distribution of tail length within one sample is symmetric and can be described by a Gaussian distribution and the mean tail length. As a first application, UV-A sensitivity of resident and stimulated macrophages was studied. The resident macrophages were more sensitive to UV-A than the stimulated ones. DNA damage repair follows the same simple monoexponential time course for both cell types. The simplicity of results, i.e., applicability of tail lengths and Gaussian statistics as well as monoexponential kinetics, suggest that microscopically controlled comet assay is well suited to study elementary processes of DNA damage induction and repair.     

Mathematical evaluation of two parameter flow cytometric histograms

A general procedure was developed to evaluate two-parameter flow cytometric data. These data usually show overlapping distributions representing different subpopulations. To calculate the fractions of cells in the various subpopulations, the maximum likelihood method is used, assuming an unknown number of Gaussian distributions with constant coefficient of variation in the histogram. A test on simulated data shows that Gaussians can be separated clearly by the procedure if the distance between their mean values is larger than twice the maximum standard deviation. The analysis of different measurements of double-stained (DNA/protein) cultured cells out of the same pool yield the same fractions in the phases of the cell cycle with acceptable error rates. To simulate samples with different fractions in the phases of the cell cycle, defined mixtures of proliferating and resting cells of the same type were prepared and measured for DNA and cell size. The calculated fractions are consistent with the expected variation of G1, S and G2 + M fractions depending on the mixture ratio.     

Statistical Analysis of the Comet Assay Using a Mixture of Gamma Distributions

Tail moments in the single cell gel electrophoresis (comet) assay usually do not follow a normal distribution, making the statistical analysis complicated. Researchers have used a wide variety of statistical techniques in an attempt to overcome this problem. In many cases, the tail moments follow a bimodal distribution that can be modeled with a mixture of gamma distributions. This bimodality may be due to cells being in two different stages of the cell cycle at the time of treatment. Maximum likelihood, modified to accommodate censored data, can be used to estimate the five parameters of the gamma mixture distribution for each slide. A weighted analysis of variance on the parameter estimates for the gamma mixtures can be performed to determine differences in DNA damage between treatments. These methods were applied to an experiment on the effect of thymidine kinase in DNA damage and repair. Analysis based on the mixture of gamma distributions was found to be more statistically valid, more powerful, and more informative than analysis based on log-transformed tail moments.     

Detection of two-component mixtures of lognormal distributions in grouped, doubly truncated data: analysis of red blood cell volume distributions

We have examined the statistical requirements for the detection of mixtures of two lognormal distributions in doubly truncated data when the sample size is large. The expectation-maximization algorithm was used for parameter estimation. A bootstrap approach was used to test for a mixture of distributions using the likelihood ratio statistic. Analysis of computer simulated mixtures showed that as the ratio of the difference between the means to the minimum standard deviation increases, the power for detection also increases and the accuracy of parameter estimates improves. These procedures were used to examine the distribution of red blood cell volume in blood samples. Each distribution was doubly truncated to eliminate artifactual frequency counts and tested for best fit to a single lognormal distribution or a mixture of two lognormal distributions. A single population was found in samples obtained from 60 healthy individuals. Two subpopulations of cells were detected in 25 of 27 mixtures of blood prepared in vitro. Analyses of mixtures of blood from 40 patients treated for iron-deficiency anemia showed that subpopulations could be detected in all by 6 weeks after onset of treatment. To determine if two-component mixtures could be detected, distributions were examined from untransfused patients with refractory anemia. In two patients with inherited sideroblastic anemia a mixture of microcytic and normocytic cells was found, while in the third patient a single population of microcytic cells was identified. In two family members previously identified as carriers of inherited sideroblastic anemia, mixtures of microcytic and normocytic subpopulations were found. Twenty-five patients with acquired myelodysplastic anemia were examined. A good fit to a mixture of subpopulations containing abnormal microcytic or macrocytic cells was found in two. We have demonstrated that with large sample sizes, mixtures of distributions can be detected even when distributions appear to be unimodal. These statistical techniques provide a means to characterize and quantify alterations in erythrocyte subpopulations in anemia but could also be applied to any set of grouped, doubly truncated data to test for the presence of a mixture of two lognormal distributions.     

The Fanconi anemia/BRCA pathway: a coordinator of cross-link repair

Fanconi anemia (FA) is a rare inherited disease characterized by genomic instability and markedly increased cancer risk. Efforts to elucidate the molecular basis of FA have unearthed a novel DNA damage response pathway, the integrity of which is critical for cellular resistance to DNA cross-linking agents. Despite significant progress in uncovering the molecular events underlying FA, the precise function of this pathway in DNA repair is unknown. This article will review evidence implicating FA proteins in multiple aspects of DNA cross-link repair and propose a model to explain the selectivity of the FA pathway toward DNA cross-linking agents.     

USP7S-dependent inactivation of Mule regulates DNA damage signalling and repair

The E3 ubiquitin ligase Mule/ARF-BP1 plays an important role in the cellular DNA damage response by controlling base excision repair and p53 protein levels. However, how the activity of Mule is regulated in response to DNA damage is currently unknown. Here, we report that the Ser18-containing isoform of the USP7 deubiquitylation enzyme (USP7S) controls Mule stability by preventing its self-ubiquitylation and subsequent proteasomal degradation. We find that in response to DNA damage, downregulation of USP7S leads to self-ubiquitylation and proteasomal degradation of Mule, which eventually leads to p53 accumulation. Cells that are unable to downregulate Mule show reduced ability to upregulate p53 levels in response to DNA damage. We also find that, as Mule inactivation is required for stabilization of base excision repair enzymes, the failure of cells to downregulate Mule after DNA damage results in deficient DNA repair. Our data describe a novel mechanism by which Mule is regulated in response to DNA damage and coordinates cellular DNA damage responses and DNA repair.     

DNA interstrand crosslink repair in mammalian cells

DNA damage by agents crosslinking the strands presents a formidable challenge to the cell to repair for survival and to repair accurately for maintenance of genetic information. It appears that repair of DNA crosslinks occurs in a path involving double strand breaks (DSBs) in the DNA. Mammalian cells have multiple systems involved in the repair response to such damage, including the Fanconi anemia pathway that appears to be directly involved, although the mechanisms and site of action remain elusive. A particular finding relating to deficiency of the Fanconi anemia pathway is the observation of chromosomal radial formations after ICL damage. The basis of formation of such chromosomal aberrations is unknown although they appear secondarily to DSBs. Here we review the processes involved in response to DNA interstrand crosslinks which might lead to radial formation and the role of the nucleotide excision repair gene, ERCC1, which is required for a normal response, not just to DNA crosslinks, but also for DSBs at collapsed replication forks caused by substrate depletion. J. Cell. Physiol. 220: 569–573, 2009. © 2009 Wiley‐Liss, Inc.     

Chromatin dynamics after DNA damage: The legacy of the access–repair–restore model

Eukaryotic genomes are packaged into chromatin, which is the physiological substrate for all DNA transactions, including DNA damage and repair. Chromatin organization imposes major constraints on DNA damage repair and thus undergoes critical rearrangements during the repair process. These rearrangements have been integrated into the “access–repair–restore” (ARR) model, which provides a molecular framework for chromatin dynamics in response to DNA damage. Here, we take a historical perspective on the elaboration of this model and describe the molecular players involved in damaged chromatin reorganization in human cells. In particular, we present our current knowledge of chromatin assembly coupled to DNA damage repair, focusing on the role of histone variants and their dedicated chaperones. Finally, we discuss the impact of chromatin rearrangements after DNA damage on chromatin function and epigenome maintenance.     

The Metagenomic Telescope

Next generation sequencing technologies led to the discovery of numerous new microbe species in diverse environmental samples. Some of the new species contain genes never encountered before. Some of these genes encode proteins with novel functions, and some of these genes encode proteins that perform some well-known function in a novel way. A tool, named the Metagenomic Telescope, is described here that applies artificial intelligence methods, and seems to be capable of identifying new protein functions even in the well-studied model organisms. As a proof-of-principle demonstration of the Metagenomic Telescope, we considered DNA repair enzymes in the present work. First we identified proteins in DNA repair in well–known organisms (i.e., proteins in base excision repair, nucleotide excision repair, mismatch repair and DNA break repair); next we applied multiple alignments and then built hidden Markov profiles for each protein separately, across well–researched organisms; next, using public depositories of metagenomes, originating from extreme environments, we identified DNA repair genes in the samples. While the phylogenetic classification of the metagenomic samples are not typically available, we hypothesized that some very special DNA repair strategies need to be applied in bacteria and Archaea living in those extreme circumstances. It is a difficult task to evaluate the results obtained from mostly unknown species; therefore we applied again the hidden Markov profiling: for the identified DNA repair genes in the extreme metagenomes, we prepared new hidden Markov profiles (for each genes separately, subsequent to a cluster analysis); and we searched for similarities to those profiles in model organisms. We have found well known DNA repair proteins, numerous proteins with unknown functions, and also proteins with known, but different functions in the model organisms.     

Joint modeling of DNA sequence and physical properties to improve eukaryotic promoter recognition

We present an approach to integrate physical properties of DNA, such as DNA bendability or GC content, into our probabilistic promoter recognition system McPROMOTER. In the new model, a promoter is represented as a sequence of consecutive segments represented by joint likelihoods for DNA sequence and profiles of physical properties. Sequence likelihoods are modeled with interpolated Markov chains, physical properties with Gaussian distributions. The background uses two joint sequence/profile models for coding and non-coding sequences, each consisting of a mixture of a sense and an anti-sense submodel. On a large Drosophila test set, we achieved a reduction of about 30% of false positives when compared with a model solely based on sequence likelihoods.     

The role of chromatin proteins in DNA damage recognition and repair Mini-review

The structure of chromatin is the major factor determining the rate and efficiency of DNA repair. Chromatin remodeling events such as rearrangement of nucleosomes and higher order chromatin structures are indispensable features of repair processes. During the last decade numerous chromatin proteins have been identified that preferentially bind to different types of DNA damage. The HMGB proteins, which preferentially interact with DNA intrastrand crosslinks induced by cisplatin, are the archetypal example of such proteins. Several hypothetical models have been proposed describing the role of such damage-binding chromatin proteins. The damage shielding model postulates that binding of chromatin proteins to damaged DNA might disturb damage recognition by repair factors and impair its removal. Alternatively, the damage-recognition/signaling model proposes that the binding of specific chromatin proteins to damaged DNA could serve as a hallmark to be recognized by repair proteins. Additionally, the binding of specific chromatin proteins to damaged DNA could induce chromatin remodeling at the damage site and indirectly affect its repair. This paper aims to critically review current experimental data in relation to such possible roles of chromatin proteins.     

Probits of mixtures

The tolerances of individuals (insects, parasites) in a population have a frequency or probability distribution called a tolerance distribution. Many tolerance distributions in bioassay studies can be the result of a rather heterogeneous population of individuals and can often be modelled as a mixture of a number of standard unimodal distributions. A probit analysis can be generalized to the case where the tolerance distribution is a mixture of location and scale parameter distributions. In this article, the existence and determination of the maximum likelihood estimates are investigated. An expectation-maximization (EM) algorithm for probits of mixtures is developed and it is shown that by application of the EM algorithm, the problem of probits of mixtures can be separated into a series of probits of individual component tolerance distributions.     

DNA damage alters nuclear mechanics through chromatin reorganization

DNA double-strand breaks drive genomic instability. However, it remains unknown how these processes may affect the biomechanical properties of the nucleus and what role nuclear mechanics play in DNA damage and repair efficiency. Here, we have used Atomic Force Microscopy to investigate nuclear mechanical changes, arising from externally induced DNA damage. We found that nuclear stiffness is significantly reduced after cisplatin treatment, as a consequence of DNA damage signalling. This softening was linked to global chromatin decondensation, which improves molecular diffusion within the organelle. We propose that this can increase recruitment for repair factors. Interestingly, we also found that reduction of nuclear tension, through cytoskeletal relaxation, has a protective role to the cell and reduces accumulation of DNA damage. Overall, these changes protect against further genomic instability and promote DNA repair. We propose that these processes may underpin the development of drug resistance.     

Detection of oxidative DNA damage in isolated marine bivalve hemocytes using the comet assay and formamidopyrimidine glycosylase (Fpg)

Organisms in polluted areas can be exposed to complex mixtures of chemicals; however, exposure to genotoxic contaminants can be particularly devastating. DNA damage can lead to necrosis, apoptosis, or heritable mutations, and therefore has the potential to impact populations as well as individuals. Single cell gel electrophoresis (the comet assay) is a simple and sensitive technique used to examine DNA damage in single cells. The lesion-specific DNA repair enzyme formamidopyrimidine glycoslyase (Fpg) can be used in conjunction with the comet assay to detect 8-oxoguanine and other damaged bases, which are products of oxidative damage. Fpg was used to detect oxidative DNA damage in experiments where isolated oyster (Crassostrea virginica) and clam (Mercenaria mercenaria) hemocytes were exposed to hydrogen peroxide. Standard enzyme buffers used with Fpg and the comet assay produced unacceptably high amounts of DNA damage in the marine bivalve hemocytes used in this study necessitating a modification of existing methods. A sodium chloride based reaction buffer was successfully used. Oxidative DNA damage can be detected in isolated oyster and clam hemocytes using Fpg and the comet assay when the sodium chloride reaction buffer and protocols outlined here are employed. The use of DNA repair enzymes, such as Fpg, in conjunction with the comet assay expands the usefulness and sensitivity of this assay, and provides important insights into the mechanisms of DNA damage.