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Microarray analysis techniques are used in interpreting the data generated from experiments on DNA (Gene chip analysis), RNA, and protein
microarray A microarray is a multiplex (assay), multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of biological interactions. It is a two-dimensional array on a Substrate (materials science), solid substrate—usu ...
s, which allow researchers to investigate the expression state of a large number of genesin many cases, an organism's entire
genome A genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding genes, other functional regions of the genome such as ...
in a single experiment. Such experiments can generate very large amounts of data, allowing researchers to assess the overall state of a cell or organism. Data in such large quantities is difficultif not impossibleto analyze without the help of computer programs.


Introduction

Microarray data analysis is the final step in reading and processing data produced by a microarray chip. Samples undergo various processes including purification and scanning using the microchip, which then produces a large amount of data that requires processing via computer software. It involves several distinct steps, as outlined in the image below. Changing any one of the steps will change the outcome of the analysis, so the MAQC Project was created to identify a set of standard strategies. Companies exist that use the MAQC protocols to perform a complete analysis.


Techniques

Most microarray manufacturers, such as
Affymetrix Affymetrix is now Applied Biosystems, a brand of DNA microarray products sold by Thermo Fisher Scientific that originated with an American biotechnology research and development and manufacturing company of the same name. The Santa Clara, Calif ...
and Agilent, provide commercial data analysis software alongside their microarray products. There are also open source options that utilize a variety of methods for analyzing microarray data.


Aggregation and normalization

Comparing two different arrays or two different samples hybridized to the same array generally involves making adjustments for systematic errors introduced by differences in procedures and dye intensity effects. Dye normalization for two color arrays is often achieved by
local regression Local regression or local polynomial regression, also known as moving regression, is a generalization of the moving average and polynomial regression. Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally ...
. LIMMA provides a set of tools for background correction and scaling, as well as an option to average on-slide duplicate spots. A common method for evaluating how well normalized an array is, is to plot an MA plot of the data. MA plots can be produced using programs and languages such as R and MATLAB. Raw Affy data contains about twenty probes for the same RNA target. Half of these are "mismatch spots", which do not precisely match the target sequence. These can theoretically measure the amount of nonspecific binding for a given target. Robust Multi-array Average (RMA) is a normalization approach that does not take advantage of these mismatch spots but still must summarize the perfect matches through median polish. The median polish algorithm, although robust, behaves differently depending on the number of samples analyzed. Quantile normalization, also part of RMA, is one sensible approach to normalize a batch of arrays in order to make further comparisons meaningful. The current Affymetrix MAS5 algorithm, which uses both perfect match and mismatch probes, continues to enjoy popularity and do well in head to head tests.
Factor analysis Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observe ...
for Robust Microarray Summarization (FARMS) is a model-based technique for summarizing array data at perfect match probe level. It is based on a factor analysis model for which a Bayesian maximum a posteriori method optimizes the model parameters under the assumption of Gaussian measurement noise. According to the Affycomp benchmark FARMS outperformed all other summarizations methods with respect to sensitivity and specificity.


Identification of significant differential expression

Many strategies exist to identify array probes that show an unusual level of over-expression or under-expression. The simplest one is to call "significant" any probe that differs by an average of at least twofold between treatment groups. More sophisticated approaches are often related to
t-test Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is Statistical significance, statistically significant or not. It is any statistical hypothesis testing, statistical hypothesis test ...
s or other mechanisms that take both
effect size In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the ...
and variability into account. Curiously, the p-values associated with particular genes do not reproduce well between replicate experiments, and lists generated by straight fold change perform much better. This represents an extremely important observation, since the point of performing experiments has to do with predicting general behavior. The MAQC group recommends using a fold change assessment plus a non-stringent
p-value In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...
cutoff, further pointing out that changes in the background correction and scaling process have only a minimal impact on the rank order of fold change differences, but a substantial impact on p-values.


Clustering

Clustering is a data mining technique used to group genes having similar expression patterns.
Hierarchical clustering In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two ...
, and
k-means clustering ''k''-means clustering is a method of vector quantization, originally from signal processing, that aims to partition of a set, partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster (statistics), cluste ...
are widely used techniques in microarray analysis.


Hierarchical clustering

Hierarchical clustering is a statistical method for finding relatively
homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image. A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, i ...
clusters. Hierarchical clustering consists of two separate phases. Initially, a
distance matrix In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. Depending upon the application involved, the ''dist ...
containing all the pairwise distances between the genes is calculated. Pearson's correlation and Spearman's correlation are often used as dissimilarity estimates, but other methods, like
Manhattan distance Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two point (geometry), points is instead defined to be the sum of the absolute differences of their respective Cartesian ...
or
Euclidean distance In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is o ...
, can also be applied. Given the number of distance measures available and their influence in the clustering algorithm results, several studies have compared and evaluated different distance measures for the clustering of microarray data, considering their intrinsic properties and robustness to noise. After calculation of the initial distance matrix, the hierarchical clustering algorithm either (A) joins iteratively the two closest clusters starting from single data points (agglomerative, bottom-up approach, which is fairly more commonly used), or (B) partitions clusters iteratively starting from the complete set (divisive, top-down approach). After each step, a new distance matrix between the newly formed clusters and the other clusters is recalculated. Hierarchical
cluster analysis Cluster analysis or clustering is the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more Similarity measure, similar (in some specific sense defined by the ...
methods include: * Single linkage (minimum method, nearest neighbor) * Average linkage (
UPGMA UPGMA (unweighted pair group method with arithmetic mean) is a simple agglomerative (bottom-up) hierarchical clustering method. It also has a weighted variant, WPGMA, and they are generally attributed to Sokal and Michener. Note that the unwei ...
) * Complete linkage (maximum method, furthest neighbor) Different studies have already shown empirically that the Single linkage clustering algorithm produces poor results when employed to gene expression microarray data and thus should be avoided.


K-means clustering

K-means clustering is an algorithm for grouping genes or samples based on pattern into ''K'' groups. Grouping is done by minimizing the sum of the squares of distances between the data and the corresponding cluster
centroid In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the figure. The same definition extends to any object in n-d ...
. Thus the purpose of K-means clustering is to classify data based on similar expression. K-means clustering algorithm and some of its variants (including
k-medoids -medoids is a classical partitioning technique of clustering that splits the data set of objects into clusters, where the number of clusters assumed known ''a priori'' (which implies that the programmer must specify k before the execution of a - ...
) have been shown to produce good results for gene expression data (at least better than hierarchical clustering methods). Empirical comparisons of
k-means ''k''-means clustering is a method of vector quantization, originally from signal processing, that aims to partition of a set, partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster (statistics), cluste ...
,
k-medoids -medoids is a classical partitioning technique of clustering that splits the data set of objects into clusters, where the number of clusters assumed known ''a priori'' (which implies that the programmer must specify k before the execution of a - ...
, hierarchical methods and, different distance measures can be found in the literature.


Pattern recognition

Commercial systems for gene network analysis such as Ingenuity and Pathway studio create visual representations of differentially expressed genes based on current scientific literature. Non-commercial tools such as FunRich, GenMAPP and Moksiskaan also aid in organizing and visualizing gene network data procured from one or several microarray experiments. A wide variety of microarray analysis tools are available through Bioconductor written in the
R programming language R is a programming language for statistical computing and data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of so ...
. The frequently cited SAM module and other microarray tools are available through Stanford University. Another set is available from Harvard and MIT. Specialized software tools for statistical analysis to determine the extent of over- or under-expression of a gene in a microarray experiment relative to a reference state have also been developed to aid in identifying genes or gene sets associated with particular
phenotype In genetics, the phenotype () is the set of observable characteristics or traits of an organism. The term covers the organism's morphology (physical form and structure), its developmental processes, its biochemical and physiological propert ...
s. One such method of analysis, known as
Gene Set Enrichment Gene set enrichment analysis (GSEA) (also called functional enrichment analysis or pathway enrichment analysis) is a method to identify classes of genes or proteins that are over-represented in a large set of genes or proteins, and may have an a ...
Analysis (GSEA), uses a Kolmogorov-Smirnov-style statistic to identify groups of genes that are regulated together. This third-party statistics package offers the user information on the genes or gene sets of interest, including links to entries in databases such as NCBI's
GenBank The GenBank sequence database is an open access, annotated collection of all publicly available nucleotide sequences and their protein translations. It is produced and maintained by the National Center for Biotechnology Information (NCBI; a par ...
and curated databases such as Biocarta and
Gene Ontology The Gene Ontology (GO) is a major bioinformatics initiative to unify the representation of gene and gene product attributes across all species. More specifically, the project aims to: 1) maintain and develop its controlled vocabulary of gene and ...
. Protein complex enrichment analysis tool (COMPLEAT) provides similar enrichment analysis at the level of protein complexes. The tool can identify the dynamic protein complex regulation under different condition or time points. Related system, PAINT and SCOPE performs a statistical analysis on gene promoter regions, identifying over and under representation of previously identified
transcription factor In molecular biology, a transcription factor (TF) (or sequence-specific DNA-binding factor) is a protein that controls the rate of transcription (genetics), transcription of genetics, genetic information from DNA to messenger RNA, by binding t ...
response elements. Another statistical analysis tool is Rank Sum Statistics for Gene Set Collections (RssGsc), which uses rank sum probability distribution functions to find gene sets that explain experimental data. A further approach is contextual meta-analysis, i.e. finding out how a gene cluster responds to a variety of experimental contexts.
Genevestigator Genevestigator is an application consisting of a gene expression database and tools to analyse the data. It exists in two versions, biomedical and plant, depending on the species of the underlying DNA microarray, microarray and RNAseq as well as si ...
is a public tool to perform contextual meta-analysis across contexts such as anatomical parts, stages of development, and response to diseases, chemicals, stresses, and
neoplasms A neoplasm () is a type of abnormal and excessive growth of tissue (biology), tissue. The process that occurs to form or produce a neoplasm is called neoplasia. The growth of a neoplasm is uncoordinated with that of the normal surrounding tiss ...
.


Significance analysis of microarrays (SAM)

Significance analysis of microarrays (SAM) is a
statistical technique A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis. A statistical hypothesis test typically involves a calculation of a test statistic. T ...
, established in 2001 by Virginia Tusher, Robert Tibshirani and Gilbert Chu, for determining whether changes in
gene expression Gene expression is the process (including its Regulation of gene expression, regulation) by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, proteins or non-coding RNA, ...
are statistically significant. With the advent of
DNA microarray A DNA microarray (also commonly known as a DNA chip or biochip) is a collection of microscopic DNA spots attached to a solid surface. Scientists use DNA microarrays to measure the expression levels of large numbers of genes simultaneously or t ...
s, it is now possible to measure the expression of thousands of genes in a single hybridization experiment. The data generated is considerable, and a method for sorting out what is significant and what isn't is essential. SAM is distributed by
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
in an R-package. SAM identifies statistically significant genes by carrying out gene specific
t-tests Student's ''t''-test is a statistical test used to test whether the difference between the response of two groups is statistically significant or not. It is any statistical hypothesis test in which the test statistic follows a Student's ''t''-dis ...
and computes a statistic ''dj'' for each gene ''j'', which measures the strength of the relationship between gene expression and a response variable.Chu, G., Narasimhan, B, Tibshirani, R, Tusher, V. "SAM "Significance Analysis of Microarrays" Users Guide and technical document."

/ref> This analysis uses
non-parametric statistics Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric s ...
, since the data may not follow a
normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...
. The response variable describes and groups the data based on experimental conditions. In this method, repeated
permutations In mathematics, a permutation of a Set (mathematics), set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example ...
of the data are used to determine if the expression of any gene is significant related to the response. The use of permutation-based analysis accounts for correlations in genes and avoids parametric assumptions about the distribution of individual genes. This is an advantage over other techniques (e.g.,
ANOVA Analysis of variance (ANOVA) is a family of statistical methods used to compare the means of two or more groups by analyzing variance. Specifically, ANOVA compares the amount of variation ''between'' the group means to the amount of variation ''w ...
and Bonferroni), which assume equal variance and/or independence of genes.


Basic protocol

* Perform
microarray A microarray is a multiplex (assay), multiplex lab-on-a-chip. Its purpose is to simultaneously detect the expression of thousands of biological interactions. It is a two-dimensional array on a Substrate (materials science), solid substrate—usu ...
experiments — DNA microarray with oligo and cDNA primers, SNP arrays, protein arrays, etc. * Input Expression Analysis in Microsoft Excel — see below * Run SAM as a Microsoft Excel Add-Ins * Adjust the Delta tuning parameter to get a significant # of genes along with an acceptable false discovery rate (FDR)) and Assess Sample Size by calculating the mean difference in expression in the SAM Plot Controller * List Differentially Expressed Genes (Positively and Negatively Expressed Genes)


Running SAM

* SAM is available for download online at http://www-stat.stanford.edu/~tibs/SAM/ for academic and non-academic users after completion of a registration step. * SAM is run as an Excel Add-In, and the SAM Plot Controller allows Customization of the False Discovery Rate and Delta, while the SAM Plot and SAM Output functionality generate a List of Significant Genes, Delta Table, and Assessment of Sample Sizes *
Permutations In mathematics, a permutation of a Set (mathematics), set can mean one of two different things: * an arrangement of its members in a sequence or linear order, or * the act or process of changing the linear order of an ordered set. An example ...
are calculated based on the number of samples * Block Permutations ** Blocks are batches of microarrays; for example for eight samples split into two groups (control and affected) there are 4!=24 permutations for each block and the total number of permutations is (24)(24)= 576. A minimum of 1000 permutations are recommended; the number of permutations is set by the user when imputing correct values for the data set to run SAM


Response formats

Types: * Quantitative — real-valued (such as heart rate) * One class — tests whether the mean gene expression differs from zero * Two class — two sets of measurements ** Unpaired — measurement units are different in the two groups; e.g. control and treatment groups with samples from different patients ** Paired — same experimental units are measured in the two groups; e.g. samples before and after treatment from the same patients * Multiclass — more than two groups with each containing different experimental units; generalization of two class unpaired type * Survival — data of a time until an event (for example death or relapse) * Time course — each experimental units is measured at more than one time point; experimental units fall into a one or two class design * Pattern discovery — no explicit response parameter is specified; the user specifies eigengene (principal component) of the expression data and treats it as a quantitative response


Algorithm

SAM calculates a test statistic for relative difference in gene expression based on permutation analysis of expression data and calculates a false discovery rate. The principal calculations of the program are illustrated below. The ''s''o constant is chosen to minimize the coefficient of variation of ''di''. r''i'' is equal to the expression levels (x) for gene ''i'' under y experimental conditions. \mathrm Fold changes (t) are specified to guarantee genes called significant change at least a pre-specified amount. This means that the absolute value of the average expression levels of a gene under each of two conditions must be greater than the fold change (t) to be called positive and less than the inverse of the fold change (t) to be called negative. The SAM algorithm can be stated as: # Order test statistics according to magnitude # For each permutation compute the ordered null (unaffected) scores # Plot the ordered test statistic against the expected null scores # Call each gene significant if the absolute value of the test statistic for that gene minus the mean test statistic for that gene is greater than a stated threshold # Estimate the false discovery rate based on expected versus observed values


Output

* Significant gene sets ** Positive gene set — higher expression of most genes in the gene set correlates with higher values of the phenotype ** Negative gene set — lower expression of most genes in the gene set correlates with higher values of the phenotype


SAM features

* Data from Oligo or cDNA arrays, SNP array, protein arrays, etc. can be utilized in SAM * Correlates expression data to clinical parameters * Correlates expression data with time * Uses data permutation to estimates False Discovery Rate for multiple testing * Reports local false discovery rate (the FDR for genes having a similar di as that gene) and miss rates * Can work with blocked design for when treatments are applied within different batches of arrays * Can adjust threshold determining number of gene called significant


Error correction and quality control


Quality control

Entire arrays may have obvious flaws detectable by visual inspection, pairwise comparisons to arrays in the same experimental group, or by analysis of RNA degradation. Results may improve by removing these arrays from the analysis entirely.


Background correction

Depending on the type of array, signal related to nonspecific binding of the fluorophore can be subtracted to achieve better results. One approach involves subtracting the average signal intensity of the area between spots. A variety of tools for background correction and further analysis are available from TIGR, Agilent ( GeneSpring), and Ocimum Bio Solutions (Genowiz).


Spot filtering

Visual identification of local artifacts, such as printing or washing defects, may likewise suggest the removal of individual spots. This can take a substantial amount of time depending on the quality of array manufacture. In addition, some procedures call for the elimination of all spots with an expression value below a certain intensity threshold.


See also

*
Microarray databases A microarray database is a repository containing microarray gene expression data. The key uses of a microarray database are to store the measurement data, manage a searchable index, and make the data available to other applications for analysis and ...
* Significance analysis of microarrays *
Transcriptomics Transcriptomics technologies are the techniques used to study an organism's transcriptome, the sum of all of its RNA, RNA transcripts. The information content of an organism is recorded in the DNA of its genome and Gene expression, expressed throu ...
*
Proteomics Proteomics is the large-scale study of proteins. Proteins are vital macromolecules of all living organisms, with many functions such as the formation of structural fibers of muscle tissue, enzymatic digestion of food, or synthesis and replicatio ...


References

{{reflist, refs= {{cite journal , last1 = Tusher , first1 = V. G. , last2 = Tibshirani , first2 = R. , display-authors =et al , year = 2001 , title = Significance analysis of microarrays applied to the ionizing radiation response , url = http://www-stat.stanford.edu/~tibs/SAM/pnassam.pdf , journal = Proceedings of the National Academy of Sciences , volume = 98 , issue = 9, pages = 5116–5121 , doi=10.1073/pnas.091062498, pmid = 11309499 , pmc = 33173 , bibcode = 2001PNAS...98.5116G , doi-access = free {{cite journal , last1 = Zang , first1 = S. , last2 = Guo , first2 = R. , display-authors = et al , year = 2007 , title = Integration of statistical inference methods and a novel control measure to improve sensitivity and specificity of data analysis in expression profiling studies , journal = Journal of Biomedical Informatics , volume = 40 , issue = 5, pages = 552–560 , doi=10.1016/j.jbi.2007.01.002, pmid = 17317331 , doi-access = free


External links


ArrayExplorer - Compare microarray side by side to find the one that best suits your research needs


—software * ttp://statsarray.com/ StatsArray - Online Microarray Analysis Services—software
ArrayMining.net - web-application for online analysis of microarray data
—software
FunRich - Perform gene set enrichment analysis
—software
Comparative Transcriptomics Analysis
i
Reference Module in Life Sciences



GeneChip® Expression Analysis-Data Analysis Fundamentals
(by Affymetrix)
Duke data_analysis_fundamentals_manual
Microarrays Bioinformatics algorithms