Modeling sequence dependence of microarray probe signals

Li Zhang

Department of Biostatistics and Applied Mathematics

MD Anderson Cancer Center

Wide use of short oligonucleotide microarrays

• Gene expression assay

• Genotyping (SNP detection)

• Comparative genome hybridization

• DNA methylation detection

• Gene structure discovery

• Genome reseqeuncing

Protocol of a microarray experiment

Affymetrix GeneChip® Probe Arrays

24µm

Each probe cell or feature containsmillions of copies of a specificoligonucleotide probe

Image of Hybridized Probe Array

Over 250,000 different probes complementary to geneticinformation of interest

Single stranded, fluorescentlylabeled DNA target

Oligonucleotide probe

**

**

*

1.28cm

GeneChip Probe Array

Hybridized Probe Cell

*

Double helix on microarrays

The probe is a 25-mer DNA oligo:

ATCAGCATACGAGAGAATGATGGAT|||||||||||||||||||||||||

AAUAGUCGUAUGCUCUCUUACUACCUAGC

cRNA fragment from solution

ATCAGCATACGACAGAATGATGGAT

Average distance between probes is 80Å

Technical factors affecting gene expression measurements

• Interaction between base pairs (stacking)

• Interaction with microarray surface

• Interaction with unintended targets (cross hybridization)

• Kinetic process (equilibration & washing)

• Physical properties of RNA sample Degradation (missing 5’ ends)

Alternative splicing (missing exons)Secondary structure (RNA hairpins & loops)Biotinylation

Technical factors affecting gene expression measurements

• Interaction between base pairs (stacking)Nearest-neighbor model

• Interaction with microarray surfacePositional dependant weights for stacking energies

• Interaction with unintended targets (cross hybridization)PDNN; mean field theory

• Kinetic process (equilibration & washing)Langmuir and Sips model

• Physical properties of RNA sample Degradation (missing 5’ ends)

Alternative splicing (missing exons)Secondary structure (RNA hairpins & loops)Biotinylation

Assumption: two types of binding

1. Gene-specific binding: 25 n.t. exact complementary sequences (binding with the intended target).

2. Non-specific binding: Many (>5) mismatches or short stretches (binding with unintended targets).

Gene-specific binding energy:

Non-specific binding energy:

Weighted sum base-pair stacking energies:

Positional Dependant Nearest-Neighbor (PDNN) model of molecular interactions

),( 1 iiibb

),(*** 1 iii bb

PDNN model of probe signals

2, )ln(ln ijobsij IIT

Be

N

e

NI

ijij EE

j

ij

*1

*

1

Minimization of T •Energy parameters•B, N*, Nj

•N*, B are the same on a microarray; •Nj is the same in a probe set.

Probe Signal:

Fitness:

Constraints:

Software available at: http://odin.mdacc.tmc.edu/~zhangli/PerfectMatch

Fitting PDNN modelln

(si

gnal

)

Probe index

Energy parameters in PDNN model

Weight factors Stacking energy terms

-0.8

-0.4

0.0

0.4

0.8

1.2

aa ac ag at ca cc cg ct ga gc gg gt ta tc tg tt

Dinucleotide

Sta

ckin

g e

ner

gy

GenomeTiling

Expr_U133A

SNP_50k

-0.2

0.2

0.6

1.0

1.4

1.8

1 3 5 7 9 11 13 15 17 19 21 23

Dinucleotide position on probe

Wei

gh

t

GenomeTiling

Expr_U133A

SNP_50k

Baseline of non-specific binding

Non-specific binding energy

Effects of Mismatches

•A Mismatch disrupts the double helix formation.•Energetically, it is unfavorable for binding.•It depends on the context of DNA sequences.

-3

-2

-1

0

1

2

3

Middle 3 bases of PM probe

< ln(PM/MM) >

E*(PM)-E*(MM)

A

C

G

T

Effect of mismatch at base13 depends on the nearest-neighbors

AA

C

G

T

Sequence dependence of free energy cost of single mismatch in DNA duplexes

R2 = 0.35

1

2

3

4

5

6

0.5 1 1.5 2

microarray mismatch G

So

luti

on

mis

mat

ch

G

Pattern of cross hybridization: MM and PM probes bind to different molecules

Var(ln PM)

Var

(ln

MM

)

Data source: Affymetrix HG-U133 spike-in data set. Large variation indicates resonse to spike-ins. Number of arrays: 42. Number of probes on an array: ~ 0.5 million.

Microarray surface effects

• DNA and RNA are negatively charged.

• Glass surface also charged

• Repulsion

Pattern of cross hybridization: bias towards the 5’ end

0

0.25

0.5

0 10 20

Nucleotide position on the probe

wei

gh

t

5’ end

Sense and antisense

• Upon binding, sense and antisense probes form the same double helix structure.

• The same interactions should lead to the same binding energy.

• The observed data contradict with this prediction.

Contrast of sense and antisense probe signals

• Ŷ = -0.17 + 0.05 Nt – 0.05 Na + 0.02 NgR2 = 0.67; Sample size=875.

predict

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-1.5 -1 -0.5 0 0.5 1 1.5

Ln (sense probe signal / antisense probe signal)

Mod

el fi

tted

Summary

•Binding on array surface: Probe binding free energy can be approximated by a weighted sum of base-pair stacking energies, with the probe ends having less contributions.

•Mismatches: Mismatches disrupt hybridization, especially in cross hybridization. The effects of mismatches depend on sequences. The surface also an effect.

•Surface effects: Cross hybridization is biased towards the 5’ end of the probes. Repulsion of surface depends on nucleotides.