Learning Regulatory Networks that Represent Regulator States and Roles

Keith Noto (noto@cs.wisc.edu) and Mark Craven

K. Noto and M. Craven, Learning Regulatory Network Models that Represent Regulator States and Roles. To appear in Lecture Notes in Bioinformatics.

Task• Given:

– Gene expression data– Other sources of data

• e.g. sequence data, transcription factor binding sites, transcription unit predictions

• Do:– Construct a model that captures regulatory

interactions in a cell

Effector

Key Ideas: States and Roles

CellularCondition

RegulatorExpression

RegulateeExpression

RegulateeExpression

RegulatorState

• Regulator states– Cannot be observed– Depend on more than

regulator expression– We use cellular conditions

as surrogates/predictors of regulation effectors

• Regulator roles– Is a regulator an activator or

a repressor?– We use sequence analysis

to predict these roles

Network Variables and Structure

Hidden Regulator States:“activated” or “inactivated”

Cellular Conditions:“stationary growth phase”, “heat shock”, ...

Regulatees: expression states represented as a mixture of Gaussians

Regulators: expression states represented as a mixture of Gaussians

Connect where we have evidence of regulation

Select relevant parents

Network Parameters: Hidden Nodes use CPD-Trees

GrowthMedium

HeatShock

metJ

metJstate

Growth Phase = Log Phase

GrowthPhase

Growth Phase

metJ

• Parents selected from regulator expression, cellular conditions

• May contain context-sensitive independence

metJ = Low expression metJ ≠ Low expression

Growth Phase ≠ Log

P(metJ state = activated): 0.001

P(metJ state = activated): 0.994P(metJ state = activated): 0.004

Initializing Roles

0.6 0.40.2 0.80.9 0.10.5 0.5

metA transcription unit

Transcription Start Site*-35

Upstream Downstream

DNA

metRstate

metJstate

metA

metJ state

P(Low) P(High)

activated activated

activated inactivated inactivated activatedInactivated inactivated

metR state

CPT for regulatee metA

Binding sites

(metR binds upstream;

considered an activator)

(metJ binds downstream; considered a

repressor)

*Predicted transcription start sites from Bockhorst et. al., ISMB ‘03

Training the Model

• Initialize the parameters– Activators tend to bind more upstream than

repressors

• Use an EM algorithm to set parameters– E-Step: Determine expected states of

regulators– M-Step: Update CPDs

• Repeat until convergence

Experimental Data and Procedure

• Expression measurements from Affymetrix microarrays (Fred Blattner’s lab, University of Wisconsin-Madison)

• Regulator binding site predictions from TRANSFAC, EcoCyc, cross-species comparison (McCue, et. al., Genome Research 12, 2002)

• Experimental data consists of:– 90 Experiments– 6 Cellular condition variables (between two and seven values)– 296 regulatees– 64 regulators

• Cross-fold validation– Microarrays held aside for testing– Conditions from test microarrays do not appear in training set

Log Likelihood

Average Squared

Error

Classification

Error Model

-12,0040.5113.34%Our Model(3 iterations of adding missing TFs)

-12,1930.5112.42%Baseline #2(No hidden nodes, using cellular conditions)

-13,3630.7522.16%Baseline #1(No hidden nodes, no cellular conditions)

-11,8930.5414.19%

Random Initialization(3 iterations of adding missing TFs)