Statistical methods for efficiency adjusted real-time PCR quantification

The statistical treatment for hypothesis testing using real-time PCR data is a challenge for quantification of gene expression. One has to consider two key factors in precise statistical analysis of real-time PCR data: a well-defined statistical model and the integration of amplification efficiency (AE) into the model. Previous publications in real-time PCR data analysis often fall short in integrating the AE into the model. Novel, user-friendly, and universal AE-integrated statistical methods were developed for real-time PCR data analysis with four goals. First, we addressed the definition of AE, introduced the concept of efficiency-adjusted Delta Delta Ct, and developed a general mathematical method for its calculation. Second, we developed several linear combination approaches for the estimation of efficiency adjusted Delta Delta Ct and statistical significance for hypothesis testing based on different mathematical formulae and experimental designs. Statistical methods were also adopted to estimate the AE and its equivalence among the samples. A weighted Delta Delta Ct method was introduced to analyze the data with multiple internal controls. Third, we implemented the linear models with SAS programs and analyzed a set of data for each model. In order to allow other researchers to use and compare different approaches, SAS programs are included in the Supporting Information. Fourth, the results from analysis of different statistical models were compared and discussed. Our results underline the differences between the efficiency adjusted Delta Delta Ct methods and previously published methods, thereby better identifying and controlling the source of errors introduced by real-time PCR data analysis.     

Statistical analysis of real-time PCR data

Background  

Even though real-time PCR has been broadly applied in biomedical sciences, data processing procedures for the analysis of quantitative real-time PCR are still lacking; specifically in the realm of appropriate statistical treatment. Confidence interval and statistical significance considerations are not explicit in many of the current data analysis approaches. Based on the standard curve method and other useful data analysis methods, we present and compare four statistical approaches and models for the analysis of real-time PCR data.     

Blast2GO: a universal tool for annotation, visualization and analysis in functional genomics research

SUMMARY: We present here Blast2GO (B2G), a research tool designed with the main purpose of enabling Gene Ontology (GO) based data mining on sequence data for which no GO annotation is yet available. B2G joints in one application GO annotation based on similarity searches with statistical analysis and highlighted visualization on directed acyclic graphs. This tool offers a suitable platform for functional genomics research in non-model species. B2G is an intuitive and interactive desktop application that allows monitoring and comprehension of the whole annotation and analysis process. AVAILABILITY: Blast2GO is freely available via Java Web Start at http://www.blast2go.de. SUPPLEMENTARY MATERIAL: http://www.blast2go.de -> Evaluation.     

Processing of gene expression data generated by quantitative real-time RT-PCR

Quantitative real-time PCR represents a highly sensitive and powerful technique for the quantitation of nucleic acids. It has a tremendous potential for the high-throughput analysis of gene expression in research and routine diagnostics. However, the major hurdle is not the practical performance of the experiments themselves but rather the efficient evaluation and the mathematical and statistical analysis of the enormous amount of data gained by this technology, as these functions are not included in the software provided by the manufacturers of the detection systems. In this work, we focus on the mathematical evaluation and analysis of the data generated by quantitative real-time PCR, the calculation of the final results, the propagation of experimental variation of the measured values to the final results, and the statistical analysis. We developed a Microsoft Excel-based software application coded in Visual Basic for Applications, called Q-Gene, which addresses these points. Q-Gene manages and expedites the planning, performance, and evaluation of quantitative real-time PCR experiments, as well as the mathematical and statistical analysis, storage, and graphical presentation of the data. The Q-Gene software application is a tool to cope with complex quantitative real-time PCR experiments at a high-throughput scale and considerably expedites and rationalizes the experimental setup, data analysis, and data management while ensuring highest reproducibility.     

SelSim: a program to simulate population genetic data with natural selection and recombination

SUMMARY: SelSim is a program for Monte Carlo simulation of DNA polymorphism data for a recombining region within which a single bi-allelic site has experienced natural selection. SelSim allows simulation from either a fully stochastic model of, or deterministic approximations to, natural selection within a coalescent framework. A number of different mutation models are available for simulating surrounding neutral variation. The package enables a detailed exploration of the effects of different models and strengths of selection on patterns of diversity. This provides a tool for the statistical analysis of both empirical data and methods designed to detect natural selection. AVAILABILITY: http://www.stats.ox.ac.uk/mathgen/software.html. SUPPLEMENTARY INFORMATION: http://www.stats.ox.ac.uk/mathgen/software.html.     

An error model for protein quantification

MOTIVATION: Quantitative experimental data is the critical bottleneck in the modeling of dynamic cellular processes in systems biology. Here, we present statistical approaches improving reproducibility of protein quantification by immunoprecipitation and immunoblotting. RESULTS: Based on a large data set with more than 3600 data points, we unravel that the main sources of biological variability and experimental noise are multiplicative and log-normally distributed. Therefore, we suggest a log-transformation of the data to obtain additive normally distributed noise. After this transformation, common statistical procedures can be applied to analyze the data. An error model is introduced to account for technical as well as biological variability. Elimination of these systematic errors decrease variability of measurements and allow for a more precise estimation of underlying dynamics of protein concentrations in cellular signaling. The proposed error model is relevant for simulation studies, parameter estimation and model selection, basic tools of systems biology. AVAILABILITY: Matlab and R code is available from the authors on request. The data can be downloaded from our website www.fdm.uni-freiburg.de/~ckreutz/data.     

A CART-based approach to discover emerging patterns in microarray data

MOTIVATION: Cancer diagnosis using gene expression profiles requires supervised learning and gene selection methods. Of the many suggested approaches, the method of emerging patterns (EPs) has the particular advantage of explicitly modeling interactions among genes, which improves classification accuracy. However, finding useful (i.e. short and statistically significant) EP is typically very hard. METHODS: Here we introduce a CART-based approach to discover EPs in microarray data. The method is based on growing decision trees from which the EPs are extracted. This approach combines pattern search with a statistical procedure based on Fisher's exact test to assess the significance of each EP. Subsequently, sample classification based on the inferred EPs is performed using maximum-likelihood linear discriminant analysis. RESULTS: Using simulated data as well as gene expression data from colon and leukemia cancer experiments we assessed the performance of our pattern search algorithm and classification procedure. In the simulations, our method recovers a large proportion of known EPs while for real data it is comparable in classification accuracy with three top-performing alternative classification algorithms. In addition, it assigns statistical significance to the inferred EPs and allows to rank the patterns while simultaneously avoiding overfit of the data. The new approach therefore provides a versatile and computationally fast tool for elucidating local gene interactions as well as for classification. AVAILABILITY: A computer program written in the statistical language R implementing the new approach is freely available from the web page http://www.stat.uni-muenchen.de/~socher/     

MACAT--microarray chromosome analysis tool

SUMMARY: By linking differential gene expression to the chromosomal localization of genes, one can investigate microarray data for characteristic patterns of expression phenomena involving sizeable parts of specific chromosomes. We have implemented a statistical approach for identifying significantly differentially expressed chromosome regions. We demonstrate the applicability of the approach on a publicly available data set on acute lymphocytic leukemia. AVAILABILITY: The R-package MACAT can be obtained from http://www.compdiag.molgen.mpg.de/software/macat.shtml SUPPLEMENTARY INFORMATION: http://www.compdiag.molgen.mpg.de/software/macat.shtml.     

Application of quantitative real-time PCR for monitoring the process of enrichment of clones on in vitro protein selection

In vitro selection of proteins from cDNA libraries using display technologies, such as the in vitro virus method, is a powerful means for the discovery of novel protein interactions. After iterative screening, selected proteins are usually identified and evaluated by cloning and sequencing analysis. Previously we applied real-time PCR for evaluation of the sequences obtained on in vitro virus screening. Here, we have presented additional data regarding monitoring of the process of enrichment of selected clones in each round of selection and elimination of false positives by real-time PCR, and have also discussed the utility of the novel method. This approach should also be applicable to other display technologies.     

Q-Gene: processing quantitative real-time RT-PCR data

SUMMARY: Q-Gene is an application for the processing of quantitative real-time RT-PCR data. It offers the user the possibility to freely choose between two principally different procedures to calculate normalized gene expressions as either means of Normalized Expressions or Mean Normalized Expressions. In this contribution it will be shown that the calculation of Mean Normalized Expressions has to be used for processing simplex PCR data, while multiplex PCR data should preferably be processed by calculating Normalized Expressions. The two procedures, which are currently in widespread use and regarded as more or less equivalent alternatives, should therefore specifically be applied according to the quantification procedure used. AVAILABILITY: Web access to this program is provided at http://www.biotechniques.com/softlib/qgene.html     

USAGE: a web-based approach towards the analysis of SAGE data. Serial Analysis of Gene Expression

MOTIVATION: SAGE enables the determination of genome-wide mRNA expression profiles. A comprehensive analysis of SAGE data requires software, which integrates (statistical) data analysis methods with a database system. Furthermore, to facilitate data sharing between users, the application should reside on a central server and be accessed via the internet. Since such an application was not available we developed the USAGE package. RESULTS: USAGE is a web-based application that comprises an integrated set of tools, which offers many functions for analysing and comparing SAGE data. Additionally, USAGE includes a statistical method for the planning of new SAGE experiments. USAGE is available in a multi-user environment giving users the option of sharing data. USAGE is interfaced to a relational database to store data and analysis results. The USAGE query editor allows the composition of queries for searching this database. Several database functions have been included which enable the selection and combination of data. USAGE provides the biologist increased functionality and flexibility for analysing SAGE data. AVAILABILITY: USAGE is freely accessible for academic institutions at http://www.cmbi.kun.nl/usage/. The source code of USAGE is freely available for academic institutions on request from the first author.     

Standardisation of data from real-time quantitative PCR methods – evaluation of outliers and comparison of calibration curves

Background  

As real-time quantitative PCR (RT-QPCR) is increasingly being relied upon for the enforcement of legislation and regulations dependent upon the trace detection of DNA, focus has increased on the quality issues related to the technique. Recent work has focused on the identification of factors that contribute towards significant measurement uncertainty in the real-time quantitative PCR technique, through investigation of the experimental design and operating procedure. However, measurement uncertainty contributions made during the data analysis procedure have not been studied in detail. This paper presents two additional approaches for standardising data analysis through the novel application of statistical methods to RT-QPCR, in order to minimise potential uncertainty in results.     

A comparative genome approach to marker ordering

MOTIVATION: Genome maps are fundamental to the study of an organism and essential in the process of genome sequencing which in turn provides the ultimate map of the genome. The increased number of genomes being sequenced offers new opportunities for the mapping of closely related organisms. We propose here an algorithmic formalization of a genome comparison approach to marker ordering. RESULTS: In order to integrate a comparative mapping approach in the algorithmic process of map construction and selection, we propose to extend the usual statistical model describing the experimental data, here radiation hybrids (RH) data, in a statistical framework that models additionally the evolutionary relationships between a proposed map and a reference map: an existing map of the corresponding orthologous genes or markers in a closely related organism. This has concretely the effect of exploiting, in the process of map selection, the information of marker adjacencies in the related genome when the information provided by the experimental data is not conclusive for the purpose of ordering. In order to compute efficiently the map, we proceed to a reduction of the maximum likelihood estimation to the Traveling Salesman Problem. Experiments on simulated RH datasets as well as on a real RH dataset from the canine RH project show that maps produced using the likelihood defined by the new model are significantly better than maps built using the traditional RH model. AVAILABILITY: The comparative mapping approach is available in the last version of de Givry,S. et al. [(2004) Bioinformatics, 21, 1703-1704, www.inra.fr/mia/T/CarthaGene], a free (the LKH part is free for academic use only) mapping software in C++, including LKH (Helsgaun,K. (2000) Eur. J. Oper. Res., 126, 106-130, www.dat.ruc.dk/keld/research/LKH) for maximum likelihood computation.     

Mayday--a microarray data analysis workbench

Mayday is a workbench for visualization, analysis and storage of microarray data. It features a graphical user interface and supports the development and integration of existing and new analysis methods. Besides the infrastructural core functionality, Mayday offers a variety of plug-ins, such as various interactive viewers, a connection to the R statistical environment, a connection to SQL-based databases and different data mining methods, including WEKA-library based methods for classification and various clustering methods. In addition, so-called meta information objects are provided for annotation of the microarray data allowing integration of data from different sources, which is a feature that, for instance, is employed in the enhanced heatmap visualization. Supplementary information: The software and more detailed information including screenshots and a user guide as well as test data can be found on the Mayday home page http://www.zbit.uni-tuebingen.de/pas/mayday. The core is published under the GPL (GNU Public License) and the associated plug-ins under the LGPL (Lesser GNU Public License).     

In silico analysis of complete bacterial genomes: PCR, AFLP-PCR and endonuclease restriction

We have developed a website, www.in-silico.com, which runs a software program that performs three basic tasks in completely sequenced bacterial genomes by in silico analysis: PCR amplification, amplified fragment length polymorphism (AFLP-PCR) and endonuclease restriction. For PCR, after selection of the genome and introduction of primers, fragment size, DNA sequence and corresponding open reading frame (ORF) identity of the resulting PCR product is computed. Plasmids of sequenced species may be included in the analysis. Theoretical AFLP-PCR analyzes similar parameters, and includes a suggestion tool providing a list of commercial restriction enzyme pairs yielding up to 50 amplicons in the selected genome. Endonuclease restriction analysis of complete genomes and plasmids calculates the number of restriction sites for endonucleases in a given genome. If the number of fragments is 50 or fewer, pulsed field gel electrophoresis image and restriction maps are illustrated. Other tools that have been included in this site are ORF search by name and DNA to protein translation as well as restriction digestion of user-defined DNA sequences. AVAILABILITY: This is a new molecular biology resource freely available over the Internet at http://www.in-silico.com