Multiscale denoising of biological data: a comparative analysis.

Measured microarray genomic and metabolic data are a rich source of information about the biological systems they represent. For example, time-series biological data can be used to construct dynamic genetic regulatory network models, which can be used to design intervention strategies to cure or manage major diseases. Also, copy number data can be used to determine the locations and extent of aberrations in chromosome sequences. Unfortunately, measured biological data are usually contaminated with errors that mask the important features in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. Wavelet-based multiscale filtering has been shown to be a powerful denoising tool. In this work, different batch as well as online multiscale filtering techniques are used to denoise biological data contaminated with white or colored noise. The performances of these techniques are demonstrated and compared to those of some conventional low-pass filters using two case studies. The first case study uses simulated dynamic metabolic data, while the second case study uses real copy number data. Simulation results show that significant improvement can be achieved using multiscale filtering over conventional filtering techniques.

Inference of Boolean networks under constraint on bidirectional gene relationships.

The coefficient of determination (CoD) has been used to infer Boolean networks (BNs) from steady-state data, in particular, to estimate the constituent BNs for a probabilistic BN. The advantage of the CoD method over design methods that emphasise graph topology or attractor structure is that the CoD produces a network based on strong predictive relationships between target genes and their predictor (parent) genes. The disadvantage is that spurious attractor cycles appear in the inferred network, so that there is poor inference relative to the attractor structure, that is, relative to the steady-state behaviour of the network. Given steady-state data, there should not be a significant amount of steady-state probability mass in the inferred network lying outside the mass of the data distribution; however, the existence of spurious attractor cycles creates a significant amount of steady-state probability mass not accounted for by the data. Using steady-state data hampers design because the lack of temporal data causes CoD design to suffer from a lack of directionality with regard to prediction. This results in spurious bidirectional relationships among genes in which two genes are among the predictors for each other, when actually only one of them should be a predictor of the other, thereby creating a spurious attractor cycle. This paper characterises the manner in which bidirectional relationships affect the attractor structure of a BN. Given this characterisation, the authors propose a constrained CoD inference algorithm that outperforms unconstrained CoD inference in avoiding the creation of spurious non-singleton attractor. Algorithm performances are compared using a melanoma-based network.

On approximate stochastic control in genetic regulatory networks.

The control of probabilistic Boolean networks as a model of genetic regulatory networks is formulated as an optimal stochastic control problem and has been solved using dynamic programming; however, the proposed methods fail when the number of genes in the network goes beyond a small number. There are two dimensionality problems. First, the complexity of optimal stochastic control exponentially increases with the number of genes. Second, the complexity of estimating the probability distributions specifying the model increases exponentially with the number of genes. We propose an approximate stochastic control method based on reinforcement learning that mitigates the curses of dimensionality and provides polynomial time complexity. Using a simulator, the proposed method eliminates the complexity of estimating the probability distributions and, because the method is a model-free method, it eliminates the impediment of model estimation. The method can be applied on networks for which dynamic programming cannot be used owing to computational limitations. Experimental results demonstrate that the performance of the method is close to optimal stochastic control.

Multi-class cancer classification using multinomial probit regression with Bayesian gene selection.

We consider the problems of multi-class cancer classification from gene expression data. After discussing the multinomial probit regression model with Bayesian gene selection, we propose two Bayesian gene selection schemes: one employs different strongest genes for different probit regressions; the other employs the same strongest genes for all regressions. Some fast implementation issues for Bayesian gene selection are discussed, including preselection of the strongest genes and recursive computation of the estimation errors using QR decomposition. The proposed gene selection techniques are applied to analyse real breast cancer data, small round blue-cell tumours, the national cancer institute's anti-cancer drug-screen data and acute leukaemia data. Compared with existing multi-class cancer classifications, our proposed methods can find which genes are the most important genes affecting which kind of cancer. Also, the strongest genes selected using our methods are consistent with the biological significance. The recognition accuracies are very high using our proposed methods.

Genomic profiles and predictive biological networks in oxidant-induced atherogenesis.

Atherogenic stimuli trigger complex responses in vascular smooth muscle cells (VSMCs) that culminate in activation/repression of overlapping signal transduction cascades involving oxidative stress. In the case of benzo[a]pyrene (BaP), a polycyclic aromatic hydrocarbon present in tobacco smoke, the atherogenic response involves interference with redox homeostasis by oxidative intermediates of BaP metabolism. The present studies were conducted to define genomic profiles and predictive gene biological networks associated with the atherogenic response of murine (aortic) VSMCs to BaP. A combined oxidant-antioxidant treatment regimen was used to identify redox-sensitive targets during the early course of the atherogenic response. Gene expression profiles were defined using cDNA microarrays coupled to analysis of variance and several clustering methodologies. A predictor algorithm was then applied to gain insight into critical gene-gene interactions during atherogenesis. Supervised and nonsupervised analyses identified clones highly regulated by BaP, unaffected by antioxidant, and neutralized by combined chemical treatments. Lymphocyte antigen-6 complex, histocompatibility class I component factors, secreted phosphoprotein, and several interferon-inducible proteins were identified as novel redox-regulated targets of BaP. Predictor analysis confirmed these relationships and identified immune-related genes as critical molecular targets of BaP. Redox-dependent patterns of gene deregulation indicate that oxidative stress plays a prominent role during the early stages of BaP-induced atherogenesis.

Small sample issues for microarray-based classification.

In order to study the molecular biological differences between normal and diseased tissues, it is desirable to perform classification among diseases and stages of disease using microarray-based gene-expression values. Owing to the limited number of microarrays typically used in these studies, serious issues arise with respect to the design, performance and analysis of classifiers based on microarray data. This paper reviews some fundamental issues facing small-sample classification: classification rules, constrained classifiers, error estimation and feature selection. It discusses both unconstrained and constrained classifier design from sample data, and the contributions to classifier error from constrained optimization and lack of optimality owing to design from sample data. The difficulty with estimating classifier error when confined to small samples is addressed, particularly estimating the error from training data. The impact of small samples on the ability to include more than a few variables as classifier features is explained.

General nonlinear framework for the analysis of gene interaction via multivariate expression arrays.

A cDNA microarray is a complex biochemical-optical system whose purpose is the simultaneous measurement of gene expression for thousands of genes. In this paper we propose a general statistical approach to finding associations between the expression patterns of genes via the coefficient of determination. This coefficient measures the degree to which the transcriptional levels of an observed gene set can be used to improve the prediction of the transcriptional state of a target gene relative to the best possible prediction in the absence of observations. The method allows incorporation of knowledge of other conditions relevant to the prediction, such as the application of particular stimuli or the presence of inactivating gene mutations, as predictive elements affecting the expression level of a given gene. Various aspects of the method are discussed: prediction quantification, unconstrained prediction, constrained prediction using ternary perceptrons, and design of predictors given small numbers of replicated microarrays. The method is applied to a set of genes undergoing genotoxic stress for validation according to the manner in which it points toward previously known and unknown relationships. The entire procedure is supported by software that can be applied to large gene sets, has a number of facilities to simplify data analysis, and provides graphics for visualizing experimental data, multiple gene interaction, and prediction logic.

Multivariate measurement of gene expression relationships.

The operational activities of cells are based on an awareness of their current state, coupled to a programmed response to internal and external cues in a context-dependent manner. One key goal of functional genomics is to develop analytical methods for delineating the ways in which the individual actions of genes are integrated into our understanding of the increasingly complex systems of organelle, cell, organ, and organism. This paper describes a novel approach to assess the codetermination of gene transcriptional states based upon statistical evaluation of reliably informative subsets of data derived from large-scale simultaneous gene expression measurements with cDNA microarrays. The method finds associations between the expression patterns of individual genes by determining whether knowledge of the transcriptional levels of a small gene set can be used to predict the associated transcriptional state of another gene. To test this approach for identification of the relevant contextual elements of cellular response, we have modeled our approach using data from known gene response pathways including ionizing radiation and downstream targets of inactivating gene mutations. This approach strongly suggests that evaluation of the transcriptional status of a given gene(s) can be combined with data from global expression analyses to predict the expression level of another gene. With data sets of the size currently available, this approach should be useful in finding sets of genes that participate in particular biological processes. As larger data sets and more computing power become available, the method can be extended to validating and ultimately identifying biologic (transcriptional) pathways based upon large-scale gene expression analysis.

Classification of trabecular structure in magnetic resonance images based on morphological granulometries.

A new method of detecting structured changes in trabecular bone, such as those associated with osteoporosis, was evaluated on magnetic resonance images of the wrist. The method was based on gray-scale morphological granulometries which classify image texture by iteratively filtering an image and measuring the rate of change of structural diminution in a filtered-image sequence. A classification scheme capable of distinguishing structural changes in trabecular bone starting from normal trabeculae through sclerotic, cystic, and grossly porotic bone is presented. Results of the application of this technique to the evaluation of high resolution magnetic resonance images of the wrist are presented.