EE150a Genomic Signal and Information Processing On DNA Microarrays Technology October 12, 2004 Recall the information flow in cells Replication of DNA {A,C,G,T} to {A, C, G,T} Transcription of DNA to mRNA {A,C,G,T} to {A, C, G,U} Translation of mRNA to proteins {A,C,G,U} to {20 amino-acids} Interrupt the information flow and measure gene expression levels! Gene Microarrays A medium for matching known and unknown sequences of nucleotides based on hybridization (base-pairing: A-T, C-G) Applications identification of a sequence (gene or gene mutation) determination of expression level (abundance) of genes verification of computationally determined genes Enables massively parallel gene expression studies Two types of molecules take part in the experiments: probes, orderly arranged on an array targets, the unknown samples to be detected Microarray Technologies Oligonucleotide arrays (Affymetrix GeneChips) probes are photo-etched on a chip (20-80 nucleotides) dye-labeled mRNA is hybridized to the chip laser scanning is used to detect gene expression levels (i.e., amount of mRNA) cDNA arrays complementary DNA (cDNA) sequences spotted on arrays ( nucleotides) dye-labeled mRNA is hybridized to the chip (2 types!) laser scanning is used to detect gene expression levels There are various hybrids of the two technologies above Oligonucleotide arrays Source: Affymetrix website GeneChip Architecture Source: Affymetrix website Hybridization Source: Affymetrix website Laser Scanning Source: Affymetrix website Sample Image Source: The Paterson Institute for Cancer Research Competing Microarray Technologies So far considered oligonucleotide arrays: automated, on-chip design light dispersion may cause problems short probes, cDNA microarrays are another technology: longer probes obtained via PCR, polymerase chain reaction [sidenote: what is optimal length?] probes grown in a lab, robot printing two types of targets control and test cDNA Microarrays Sample cDNA Microarray Image Some Design Issues Photo-etching based design: unwanted light exposure border minimization the probes are long Hybridization: binding of a target to its perfect complement However, when a probe differs from a target by a small number of bases, it still may bind This non-specific binding (cross-hybridization) is a source of measurement noise In special cases (e.g., arrays for gene detection), designer has a lot of control over the landscape of the probes on the array Dealing with Measurement Noise Recent models of microarray noise measurements reveal signal-dependent noise (i.e., shot-noise) as the major component additional Gaussian-like noise due to sample preparation, image scanning, etc. Image processing assumes image background noise attempts to subtract it sets up thresholds Lack of models of processes on microarrays Probabilistic DNA Microarray Model Consider an m m DNA microarray, with m 2 unique types of nucleotide probes A total of N molecules of n different types of cDNA targets with concentrations c 1,,c n, is applied to the microarray Measurement is taken after the system reached chemical equilibrium Our goal: from the scanned image, estimate the concentrations DNA Microarray Model Contd Each target may hybridize to only one type of probe There are k non-specific bindings Model diffusion of unbound molecules by random walk; distribution of unbound molecules uniform on the array justified by reported experimental results Assume known probabilities of hybridization and cross- hybridization Theoretically: from melting temperature Experimentally: measurements (e.g., from control target samples) Markov Chain Model Modeling transition between possible states of a target: one specific binding state k=2 non-specific bindings p n =1-kp c -p h is probability that an unbound molecule remains free Measurement is taken after the system reached state of chemical equlibrium need to find steady state Markov Chain Model Contd Let i =[ i,1 i,2 i,k+2 ] T be a vector whose components are numbers of the type i targets that are in one of the k+2 states of the Markov chain i,1 is the # of hybridized molecules i,j, 2 < j k+2 is # of cross-hybrid. Note that k=1 k+2 i,k =c i for every i. Stationary State of the Markov Chain In equilibrium, we want to find i such that where the transition matrix P i is given by Clearly, in the stationary state we have Finally, ratio i /c i gives stationary state probabilities Linear Microarray Model Let matrix Q collect the previously obtained probabilities The microarray measurement model can be written as Vector w describes inherent fluctuations in the measured signal due to hybridization (shot-noise) Binding of the j-type target to the i-type probe is the Bernoulli random variable with variance q i,j (1-q i,j ) hence the variance of w i is given by Vector v is comprised of iid Gaussian entries Detection of Gene Expression Levels A simple estimate is obtained via pseudo-inverse, Maximize a posteriori probability p(s|c), which is equivalent to where the matrix is given by Optimization above readily simplifies to Simulation Results Consider an 8 8 array (m=8) Apply n=6 types of targets Concentrations: [1e5 2e5 2e5 2e5 1e5 2e5] (N=1e6) Assume the following probabilities: hybridization 0.8 cross-hybridization 0.1 release 0.02 Let k=3 (number of non-specific bindings) Free molecules perform random walk on the array Simulation Results: Readout Data Simulation Results: Estimate Some Comments Adopt mean-square error for a measure of performance As expected, we observe significant improvement over raw measurements (improvement in terms of MSE) Things to do: investigate how to incorporate control sample measurements modification of the technique for very large microarrays is needed (matrix inversion may be unstable) Experimental verification! Why is this Estimation Problem Important? Microarrays measure expression levels of thousands of gene simultaneously Assume that we are taking samples at different times during a biological process Cluster data in the expression level space relatedness in biological function often implies similarity in expression behavior (and vice versa) similar expression behavior indicates co-expression Clustering of expression level data heavily depends on the measurements better estimation may lead to different functionality conclusions Summary Microarray technologies are becoming of great importance for medicine and biology understanding how the cell functions, effects on organism towards diagnostics, personalized medicine Plenty of interesting problems combinatorial design techniques statistical analysis of the data signal processing / estimation