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!

http://www-stat.stanford.edu/~susan/courses/s166/central.gif

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 (500-1000 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, 20-80

• 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

http://pcf1.chembio.ntnu.no/~bka/images/MicroArrays.jpg

cDNA Microarrays

Sample cDNA Microarray Image

Some Design Issues

• Photo-etching based design: unwanted light exposure

– border minimization

– the probes are 20-80 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 m2 unique types of

nucleotide probes

• A total of N molecules of n different types of cDNA targets

with concentrations c1,…,cn,

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 Cont’d

• 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

• pn=1-kpc-ph 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 Cont’d

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=1k+2i,k=ci for every i.

Stationary State of the Markov Chain

• In equilibrium, we want to find i such that

where the transition matrix Pi is given by

• Clearly, in the stationary state we have

• Finally, ratio i/ci 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 qi,j(1-qi,j)

– hence the variance of wi 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