Presentation on theme: "4. Functional Genomics and Microarray Analysis (1)"— Presentation transcript:
14. Functional Genomics and Microarray Analysis (1)
2Background Functional Genomics Systematic analysis of gene activity in healthy and diseased tissues.Obtaining an overall picture of genome functions, including the expression profiles at the mRNA level and the protein level.Functional Genome Analysis:used to understand the functions of genes and proteins in an organism. This is typically known as genome annotation.used in integrative biology and systems biology studies aiming to understand health and disease states (e.g. cancer, obesity, …etc)Used as an important step in the search for new target molecules in the drug discovery process. (which genes, proteins to target and how)
3What is…? Gene Expression: Microarrays: determinesDNA sequence(split into genes)Amino AcidSequenceProtein3DStructureFunctionCellActivitycodes forfolds intodictateshasWhat is…?Gene Expression:The process by which the information encoded in a gene is converted into an observable phenotype (most commonly production of a protein).The degree to which a gene is active in a certain tissue of the body, measured by the amount of mRNA in the tissue.Microarrays:Tools used to measure the presence and abundance of gene expression (measure as mRNA) in tissue.microarray technologies provide a powerful tool by which the expression patterns of thousands of genes can be monitored simultaneously and measured quantitatively
4Applications of Microarray Technology Applications covered only as example contexts, emphasis is on analysis methodsIdentify Genes expressed in different cell types (e.g. Liver vs Kidney)Learn how expression levels change in different developmental stages (embryo vs. adult)Learn how expression levels change in disease development (cancerous vs non-cancerous)Learn how groups of genes inter-relate (gene-gene interactions)Identify cellular processes that genes participate in (structure, repair, metabolism, replication, … etc)
5Microarrays Basic Idea Affymetrix Inc. is the leading provider of Microarray technology (GeneChip® )Microarrays Basic IdeaA Microarray is a device that detects the presence and abundance of labelled nucleic acids in a biological sample.In the majority of experiments, the labelled nucleic acids are derived from the mRNA of a sample or tissue.The Microarray consists of a solid surface onto which known DNA molecules have been chemically bonded at special locations.Each array location is typically known as a probe and contains many replicates of the same molecule.The molecules in each array location are carefully chosen so as to hybridise only with mRNA molecules corresponding to a single gene.
6Several companies sell equipment to make DNA chips, including spotters to deposit the DNA on the surface and scanners to detect the fluorescent or radioactive signals.Basic IdeaA Microarray works by exploiting the ability of a given mRNA molecule to bind specifically to, or hybridize to, the DNA template from which it originated.By using an array containing many DNA samples, scientists can determine, in a single experiment, the expression levels of hundreds or thousands of genes within a cell by measuring the amount of mRNA bound to each site on the array.With the aid of a computer, the amount of mRNA bound to the spots on the Microarray is precisely measured, generating a profile of gene expression in the cell.
7Microarray ProcessThe molecules in the target biological sample are labelled using a fluorescent dye before sample is applied to arrayIf a gene is expressed in the sample, the corresponding mRNA hybridises with the molecules on a given probe (array location).If a gene is not expressed, no hybridisation occurs on the corresponding probe.Reading the array outputAfter the sample is applied, a laser light source is applied to the array.The fluorescent label enables the detection of which probes have hybridised (presence) via the light emitted from the probe.If gene is highly expressed, more mRNA exists and thus more mRNA hybridises to the probe molecules (abundance) via the intensity of the light emitted.
8The array Chemistry Basics: Surface Chemistry is used to attach the probe molecules to the glass substrate.Chemical reactions are used to attach the florescent dyes to the target moleculesProbe and Target hybridise to form a double helix
9Affymetrix GeneChip Example of Single Label Chips Hundreds of thousands of oligonucleotide probes packed at extremely high densities. The probes designed to maximize sensitivity, specificity, and reproducibility, allowing consistent discrimination between specific and background signals, and between closely related target sequences.RNA labeled and scanned in a single “color” one sample per chip
10From Microarray images to Gene Expression Matrices SamplesGenesGene expression levelsFinal dataGene Expression MatrixRaw dataArray scansImagesSpotsSpot/Image quantiationsIntermediate data
11Steps of a Microarray Experiment Biological questionSample AttributesExperimental designPlatform ChoiceMicroarray experiment16-bit TIFF FilesImage analysisQuantify the DotsNormalizationClusteringStatistical AnalysisData MiningPattern DiscoveryClassificationBiological verificationand interpretation
12Qualitative Interpretation of Reads GREEN represents High Control hybridization RED represents High Sample hybridization YELLOW represents a combination of Control and Sample where both hybridized equally. BLACK represents areas where neither the Control nor Sample hybridized.Main issue is to quantify the results:How green is green?What is the ratio of the signal to background noise?How to compare multiple experiments using different chips?How to quantify cross hybridization (if any)?
13NormalizationNormalisation is a general term for a collection of methods that are directed at reasoning about and resolving the systematic errors and bias introduced by microarray experimental platformsNormalisation methods stand in contrast with the data analysis methods described in other lectures (e.g. differential gene expression analysis, classification and clustering).Our overall aim is to be able to quantify measured/calculated variability, differentials and similarity:Are they biologically significant or just side effects of the experimental platforms and conditions?
14Why Normalization Sources of Microarray Data Variability The measured gene expression in any experiment includes true gene expression,together with contributions from many sources of variabilityWhy Normalization Sources of Microarray Data VariabilityThere are several levels of variability in measured gene expression of a feature.At the highest level, there is biological variability in the population from which the sample derives.At an experimental level, there isvariability between preparations and labelling of the sample,variability between hybridisations of the same sample to different arrays, andvariability between the signal on replicate features on the same array.Variability between IndividualsTrue gene expression of individualVariability between sample preparationsVariability between arrays and hybridisationsVariability between replicate featuresMeasured gene expression
15Normalisation Examples Probe Intensity Value Typical Problem: Usually more variability at low intensityNormalisation Examples Probe Intensity ValueThe raw intensities of signal from each spot on the array are not directly comparable. Depending on the types of experiments done, a number of different approaches to normalization may be needed. Not all types of normalization are appropriate in all experiments. Some experiments may use more than one type of normalization.Reasonable Assumption: intensities of fluorescent molecules reflect the abundance of the mRNA molecules – generally true but could be problematicExample:intensity of gene A spot is 100 units in normal-tissue arrayintensity of gene A spot is 50 units in cancer-tissue arrayConclusion: gene A’s expression level in normal issue is significantly higher than in cancer tissue
16Normalisation Examples Probe Intensity Value Images showing examples of how background intensity can be calculatedProblem? What if the overall background intensity of the normal-tissue array is 95 units while the background intensity of cancer-tissue array is 10 units?Solutions:Subtract background intensity valueTake ratio of spot intensity to background intensity (preferable)In both cases have to decide where to measure background intensity (e.g. local to spot or globally per chip)In general, There could be many factors contributing to the background intensity of a microarray chipTo compare microarray data across different chips, data (intensity levels) need to be normalized to the “same” level
17Differential Gene Expression Analysis Consider a microarray experimentthat measures gene expression in two groups of rat tissue (>5000 genes in each experiment).The rat tissues come from two groups:WT: Wild-Type rat tissue,KO: Knock Out Treatment rat tissueGene expression for each group measured under similar conditionsQuestion: Which genes are affected by the treatment? How significant is the effect? How big is the effect?
18Calculating Expression Ratios In Differential Gene Expression Analysis, we are interested in identifying genes with different expression across two states, e.g.:Tumour cell lines vs. Normal cell linesTreated tissue vs. diseased tissueDifferent tissues, same organismSame tissue, different organismsSame tissue, same organismTime course experimentsWe can quantify the difference (effect) by taking a ratioi.e. for gene k, this is the ratio between expression in state a compared to expression in state bThis provides a relative value of change (e.g. expression has doubled)If expression level has not changed ratio is 1
19Fold change (Fold ratio) A gene is up-regulated in state 2 compared to state 1 if it has a higher value in state 2A gene is down-regulated in state 2 compared to state 1 if it has a lower value in state 2Fold change (Fold ratio)Ratios are troublesome sinceUp-regulated & Down-regulated genes treated differentlyGenes up-regulated by a factor of 2 have a ratio of 2Genes down-regulated by same factor (2) have a ratio of 0.5As a resultdown regulated genes are compressed between 1 and 0up-regulated genes expand between 1 and infinityUsing a logarithmic transform to the base 2 rectifies problem, this is typically known as the fold change
20Examples of fold change A, B and D are down regulatedC is up-regulatedE has no changeExamples of fold changeGene IDExpression in state 1Expression in state 2RatioFold ChangeA1005021B105C0.5-1D2007.65EYou can calculate Fold change between pairs of expression values:e.g. Between State 1 vs State 2 for gene AOr Between mean values of all measurements for a gene in the WT/KO experimentsmean(WT1..WT4) vs mean (KO1..KO4)
21Statistics Significance of Fold Change For our problem we can calculate an average fold ratio for each gene (each row)This will give us an average effect value for each gene2, 1.7, 10, 100, etcQuestion which of these values are significant?Can use a threshold, but what threshold value should we set?Use statistical techniques based on number of members in each group, type of measurements, etc -> significance testing.
22Statistics Unpaired statistical experiments ConditionGroup 1 membersGroup 2 membersStatistics Unpaired statistical experimentsOverall setting: 2 groups of 4 individuals eachGroup1: Imperial studentsGroup2: UCL studentsExperiment 1:We measure the height of all studentsWe want to establish if members of one group are consistently (or on average) taller than members of the other, and if the measured difference is significantExperiment 2:We measure the weight of all studentsWe want to establish if members of one group are consistently (or on average) heavier than the other, and if the measured difference is significantExperiment 3:………
23Statistics Unpaired statistical experiments ConditionGroup 1 membersGroup 2 membersStatistics Unpaired statistical experimentsIn unpaired experiments, you typically have two groups of people that are not related to one another, and measure some property for each member of each groupe.g. you want to test whether a new drug is effective or not, you divide similar patients in two groups:One groups takes the drugAnother groups takes a placeboYou measure (quantify) effect of both groups some time laterYou want to establish whether there is a significant difference between both groups at that later pointThe WT/KO example is an unpaired experiment if the rats in the experiments are different !
24Statistics Unpaired statistical experiments The WT/KO example is an unpaired experiment if the rats in the experiments are different!Experiment for WT Rats for Gene 96608_atRat #WT gene expressionWT1100WT2WT3200WT4300Experiment for KO Rats for Gene 96608_atRat #KO gene expressionKO1150KO2300KO3100KO4
25Statistics Unpaired statistical experiments How do we address the problem?Compare two sets of results (alternatively calculate mean for each group and compare means)Graphically:Scatter PlotsBox plots, etcCompare StatisticallyUse unpaired t-testAre these two series significantly different?Are these two series significantly different?
26Statistics Paired statistical experiments Group membersCondition 1Condition 2Statistics Paired statistical experimentsIn paired experiments, you typically have one group of people, you typically measure some property for each member before and after a particular event (so measurement come in pairs of before and after)e.g. you want to test the effectiveness of a new cream for tanningYou measure the tan in each individual before the cream is appliedYou measure the tan in each individual after the cream is appliedYou want to establish whether the there is a significant difference between measurements before and after applying the cream for the group as a whole
27Statistics Paired statistical experiments The WT/KO example is a paired experiment if the rats in the experiments are the same!Experiments for Gene 96608_atRat #WT gene expressionKO gene expressionRat1100200Rat2300Rat3400Rat4500
28Statistics Paired statistical experiments How do we address the problem?Calculate difference for each pairCompare differences to zeroAlternatively (compare average difference to zero)Graphically:Scatter Plot of differenceBox plots, etcStatisticallyUse unpaired t-testAre differences close to Zero?
29Statistics Significance testing In both cases (paired and unpaired) you want to establish whether the difference is significantSignificance testing is a statistical term and refers to estimating (numerically) the probability of a measurement occurring by chance.To do this, you need to review some basic statisticsNormal distributions: mean, standard deviations, etcHypothesis Testingt-distributionst-tests and p-values
30Mean and standard deviation 68% of dist.1 s.d.xMean and standard deviationMean and standard deviation tell you the basic features of a distributionmean = average value of all members of the groupu = (x1+x2+x3 ….+xN)/Nstandard deviation = a measure of how much the values of individual members vary in relation to the meanThe normal distribution is symmetrical about the mean 68% of the normal distribution lies within 1 s.d. of the mean
31Note on s.d. calculationThrough the following slides and in the tutorials, I use the following formula for calculating standard deviationSome people use the unbiased form below (for good reasons)Please use the simple form if you want the answers to add up at the end
32The Normal Distribution Many continuous variables follow a normal distribution, and it plays a special role in the statistical tests we are interested in;68% of dist.1 s.d.xThe x-axis represents the values of a particular variableThe y-axis represents the proportion of members of the population that have each value of the variableThe area under the curve represents probability – i.e. area under the curve between two values on the x-axis represents the probability of an individual having a value in that range
33Hypothesis Testing: Are two data sets different We use z-test (normal distribution) if the standard deviations of two populations from which the data sets came are known (and are the same)We pose a null hypothesis that the means are equalWe try to refute the hypothesis using the curves to calculate the probability that the null hypothesis is true (both means are equal)if probability is low (low p) reject the null hypothesis and accept the alternative hypothesis (both means are different)If probability is high (high p) accept null hypothesis (both means are equal)HoPopulation 1Population 2HaPopulation 1Population 2If standard deviation known use z test, else use t-test
34Comparing Two Samples Graphical interpretation To compare two groups you can compare the mean of one group graphically.The graphical comparison allows you to visually see the distribution of the two groups.If the p-value is low, chances are there will be little overlap between the two distributions. If the p-value is not low, there will be a fair amount of overlap between the two groups.We can set a critical value for the x-axis based on the threshold of p-value
35t-test terminologyt-test: Used to compare the mean of a sample to a known numberAssumptions: Subjects are randomly drawn from a population and the distribution of the mean being tested is normal.Test: The hypotheses for a single sample t-test are:Ho: u = u0Ha: u < > u0p-value: probability of error in rejecting the hypothesis of no difference between the two groups.(where u0 denotes the hypothesized value to which you are comparing a population mean)
37t-test terminology Unpaired vs. paired t-test Same as before !! Depends on your experimentUnpaired t-Test: The hypotheses for the comparison of two independent groups are:Ho: u1 = u2 (means of the two groups are equal)Ha: u1 <> u2 (means of the two group are not equal)Paired t-test: The hypothesis of paired measurements in same individualsHo: D = 0 (the difference between the two observations is 0)Ha: D <> 0 (the difference is not 0)
38Calculating t-test (t statistic) Remember these formulae !!Calculating t-test (t statistic)First calculate t statistic value and then calculate p valueFor the paired t-test, t is calculated using the following formula:And n is the number of pairs being tested.For an unpaired (independent group) t-test, the following formula is used:Where σ (x) is the standard deviation of x and n (x) is the number of elements in x.Where d is calculated by
39Calculating p-value for t-test When carrying out a test, a P-value can be calculated based on the t-value and the ‘Degrees of freedom’.There are three methods for calculating P:One Tailed >:One Tailed <:Two Tailed:Where p(t,v) is looked up from the t-distribution tableThe number of degrees (v) of freedom is calculated as:UnPaired: n (x) +n (y) -2Paired: n- 1 (where n is the number of pairs.)
40p-valuesResults of the t-test: If the p-value associated with the t-test is small (usually set at p < 0.05), there is evidence to reject the null hypothesis in favour of the alternative.In other words, there is evidence that the mean is significantly different than the hypothesized value. If the p-value associated with the t-test is not small (p > 0.05), there is not enough evidence to reject the null hypothesis, and you conclude that there is evidence that the mean is not different from the hypothesized value.
41t-value and p-valueGiven a t-value, and degrees of freedom, you can look-up a p-valueAlternatively, if you know what p-value you need (e.g. 0.05) and degrees of freedom you can set the threshold for critical t
42Finding a critical t A = .05 -tc A = .05 tc The table provides the t values (tc) for which P(tx > tc) = AFinding a critical tA= .05-tcA= .05tc=-1.812=1.812t.100t.05t.025t.01t.005
43Meaning of t-value High t-value Take Gene A, assuming paired test:For Either type of testAverage Difference is = 100, SD. = 0t value is near infinity,p is extremely low
44Consider Gene M for a paired experiment Where d is calculated byConsider Gene M for a paired experimentAverage Difference is = 0t value is zero, what does this mean?
45Consider Gene T for a paired experiment Where d is calculated byConsider Gene T for a paired experiment
46Hypothesis Testing Uses hypothesis testing methodology. For each Gene (>5,000)Pose Null Hypothesis (Ho) that gene is not affectedPose Alternative Hypothesis (Ha) that gene is affectedUse statistical techniques to calculate the probability of rejecting the hypothesis (p-value)If p-value < some critical value reject Ho and Accept HaThe issues:Large number of genes (or experiments)Need quick way to filter out significant genes that have high fold changeNeed also to sort genes by fold change and significance
47Volcano Plots A visual approach Volcano plots are a graphical means for visualising results of large numbers of t-tests allowing us to plot both the Effect and significance of each test in an easy to interpret wayFor each gene calculate the significance of the change(t-test, p-value)For each gene compare the value of the effect between population WT vs. KO(fold change)Identify Genes with high effect and high significanceVolcano Plot
48Volcano plots In a volcano plot: X-axis represents effect measured as fold change:y-axis represents the number of zeroes in the p-valueEffect = log(WT) – log(KO)2= log(WT / KO)2If WT = WO, Effect Fold Change = 0 , If WT = 2 WO, Effect Fold Change = 1...
49Numerical Interpretation (Significance) (2 decimal places)p< 0.1(1 decimal place)Using log10 for Y axis: