Characterization, Modeling, and Characterization, Modeling, and - - PowerPoint PPT Presentation

Characterization, Modeling, and Characterization, Modeling, and Simulation Simulation

• f Mouse
• f Mouse Microarray

Microarray Data Data

David S. Lalush Bioinformatics Research Center

North Carolina State University

Acknowledgments

• Assistance from:

– Jeff Tucker (NIEHS) – Pierre Bushel (NIEHS) – Bruce Weir (NCSU)

• Funded by K01 HG02428, National Human

Genome Research Institute

Outline

• Microarray Simulation Project
• Characterization of Microarray Images
• Results of Characterization
• Simulations
• Conclusion

Outline

• Microarray Simulation Project
• Characterization of Microarray Images
• Results of Characterization
• Simulations
• Conclusion

Microarray in Diagnosis

Type I tumors Type II tumors Gene expression pattern Gene expression pattern Microarray Microarray

Microarray in Diagnosis

Unknown tumor Gene expression pattern Microarray Type I or type II? Probability of misclassification?

Research Focus

• Evaluating classification methods
• Studying variability in microarray data

Problems:

• Many replications are required to evaluate error rates.
• Microarray experiments are expensive.
• True patterns are unknown in real data.

Microarray Simulation

• Creating a realistic simulation of microarray

data

• Accounting for various sources of variability

in the system

Advantages:

• Generates many replications cheaply.
• True patterns are known.
• Can control sources of variability.

Microarray System

Slide Printing Sample Preparation Hybridization Scanning Image Processing Data Analysis

Simulation Model

Sample Slide Pin Array Printing And Hybridization Scanning

Simulation Model

Sample Slide Pin Array Printing And Hybridization Scanning

• Gene expression variation modeled

as multivariate normal

• Global expression variations

modeled as normal

Simulation Model

Sample Slide Pin Array Printing And Hybridization Scanning

• Background level modeled as

normal (dye-dependent)

• Defects modeled as 2D causal

Markov random field

Simulation Model

Sample Slide Pin Array Printing And Hybridization Scanning

• Spot size, shape, and orientation

modeled as normal

• Spot defects modeled with 2D causal

Markov random field

Simulation Model

Sample Slide Pin Array Printing And Hybridization Scanning

• Instantiates spots based on properties

from sample, slide, and pin

Simulation Model

Sample Slide Pin Array Printing And Hybridization Scanning

• Creates discretized image based on

spots, SNR, gain, resolution, and blur parameters

Characterization

• Characterization of existing microarray

images

– Spot properties (size, shape, uniformity) – Pin properties (spot uniformity) – Slide properties (background, signal-to-noise) – Gene properties (mean, variance, covariance)

Outline

• Microarray Simulation Project
• Characterization of Microarray Images
• Results of Characterization
• Simulations
• Conclusion

Characterization

• Characterization of mouse kidney dataset

– Six mice – Four slides each (2x2 fluor flip) – 24 slides in all – 5520 spots in 16 blocks, 4x4 block pattern

Characterization of Spots

• Step 1: Spot Detection

Characterization of Spots

• Step 2: Spot Morphology Measures

Cast rays from centroid Radius Area Eccentricity

Characterization of Spots

• Step 3: Spot Intensity Measures

– Mean and standard deviation of spot pixels – Mean and standard deviation of background pixels

Characterization of Spots

• Step 4: Secondary Intensity Measures

2 2

) (

background signal

background signal σ σ + −

Separability

Characterization of Spots

• Step 4: Secondary Intensity Measures

signal

signal

σ

Spot Uniformity

Characterization of Spot Defects

• Spots often exhibit characteristic

nonuniformities

– Low center – Spot breaks

Characterization of Spot Defects

Normal region Defect region

Consider each spot to have two regions

Characterization of Spot Defects

State 0: N State 1: D

Each region acts as a hidden state. Each state has its own distribution of emitted intensities.

Characterization of Spot Defects

The probability of a pixel being in a given state depends on its neighbors. N N D D X P(X | N,N,D,D)

Characterization of Spot Defects

State 0: N State 1: D

Region Model (2D causal MRF):

• 16 parameters for state transition
• 2 parameters for intensity of D region pixels

relative to N region (mean, s.d.)

Characterization of Spot Defects

State 0: N State 1: D

Applying the Region Model

Pixel is in D region if:

• It is in the spot
• It is below the spot average intensity in BOTH channels

Characterization of Spot Defects

State 0: N State 1: D

Applying the Region Model

• Smooth region boundary
• Compute the 18 parameters for each spot

Characterization of Background

• Base level and variation

– Modeled as stationary across slide

• Background defects

– Marks, scratches, bright spots, other features – Modeled with 2D Markov random field

Characterization of Background

• Classify all background pixels as normal or defect

– Defect is 2σ above background mean

• Compute statistics on normal background
• Apply 2D MRF to model defect state

– Similar to region model – Intensities are modeled as beta distribution

• Measures taken only by slide

0.1 0.2 0.3 0.4 0.5 0.6 0.7

0.01 0.02 0.03 0.04 0.05

Relative Defect Intensity

Probability

Characterization of Gene Expression

• Multivariate normal distribution for each

sample (test or reference)

– Mean vector – Covariance matrix

• Linear model to account for global effects

from slide to slide and dye effects

Sample = (mean gene expression) + slope * (slide perturbation) + (variable expression)

Characterization of Gene Expression

• Problem: Covariance matrix is BIG (5200x5200)

– In simulation, we will have to diagonalize it.

• Model the most significant correlations

– Compute correlations between each pair of genes on each slide – Cluster genes by correlation distance – Each gene in a cluster has greater than .48 absolute correlation with every other gene in the cluster

Analyzing Characterization Data

• Two-way ANOVA

– By slide (fixed) – By pin (random)

• Which properties varied more?

– By slide – By pin – By spot

Analyzing Characterization Data

• Spot morphology measures
• Spot secondary intensity measures
• Spot defect model parameters
• Background defect model parameters (by

slide measurement only - no ANOVA)

Only spots with separability > 1 used in ANOVA

Outline

• Microarray Simulation Project
• Characterization of Microarray Images
• Results of Characterization
• Simulations
• Conclusion

Results

Sometimes the images have their own story to tell.

Results: Spot Morphology

• Most variation (75% for size measures) was

attributed to variation by spot

• Pins behaved similarly (mostly)
• Slides showed some differences in last eight

slides (mice five and six)

Results: Spot Morphology

1 2 3 4 5 6 7 8 9

Pin Number Radius (pixels)

Spot size vs. Pin Number

Results: Spot Morphology

Spot size vs. Slide Number

1 2 3 4 5 6 7 8 9 Slide Number Radius (pixels)

Mouse 1 Mouse 2 Mouse 3 Mouse 4 Mouse 5 Mouse 6

Results: Spot Intensities

• Most variation in separability (83-90%) was

attributed to variation by spot

• Spot uniformity varied considerably by

slide, mostly due to last eight slides

Results: Spot Intensities

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Slide Number Uniformity (532 nm)

Mouse 1 Mouse 2 Mouse 3 Mouse 4 Mouse 5 Mouse 6

Spot uniformity (532nm) vs. Slide Number

Results: Spot Defect MRF

• The 16 region transition probability

parameters varied by pin

– Model the MRF as a property of a pin, not a slide

• The mean intensity of defect region was

strongly dependent on the pin.

• Mean intensity of defect region varied

considerably by slide.

Results: Spot Defect MRF

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Slide Number Low region mean intensity relative to normal region mean

Mouse 1 Mouse 2 Mouse 3 Mouse 4 Mouse 5 Mouse 6

Defect region intensity vs. Slide Number

Results: Background MRF

• Last eight slides had more intense

background defects

• Last eight also had higher probabilities of

generating a defect

Results: Background MRF

0.1 0.2 0.3 0.4 0.5 Slide Number Intensity of Background Defects Relative to Background Mean

Mouse 1 Mouse 2 Mouse 3 Mouse 4 Mouse 5 Mouse 6

Background defect intensity vs. Slide Number

Results: General

• Slide-pin interactions were small (<5% of

variance in all cases)

• Therefore, modeling of slide and pin effects

separately is justified.

Results: Summary

• Characterization shows differences in the

properties of slides for mice five and six:

– Spots were more likely to be broken. – Spot breaks were more severe. – Background defects were more numerous. – Background defects were more intense.

Did this impact the estimated mouse-to-mouse variation?

Results

Slide 2 (Mouse 1) Slide 19 (Mouse 5)

Outline

• Microarray Simulation Project
• Characterization of Microarray Images
• Results of Characterization
• Simulations
• Conclusion

Simulations

From mouse 1-4 properties Slide 2 (Mouse 1) Simulation

Simulations

From mouse 1-4 properties Slide 2 (Mouse 1) Simulation

Simulations

From mouse 5,6 properties Slide 19 (Mouse 5) Simulation

Simulations

From mouse 5,6 properties Slide 19 (Mouse 5) Simulation

Outline

• Microarray Simulation Project
• Characterization of Microarray Images
• Results of Characterization
• Simulations
• Conclusion

Conclusions

• Characterization of microarray images can

reveal important effects

– In the mouse kidney set, the slides from two mice may have been handled differently.

• Realistic simulation of microarray images

may allow us to estimate the effects of variations due to parts of the microarray system.

To Do List

• Noncausal MRF for spot and background

defects

• Multiscale modeling of large defects
• Simulation study to estimate effects of spot

uniformity and background defects