Presented by Laur Tooming Bioinformatics journal club 28 Oct 2009 Gene network reconstruction from transcriptional dynamics under kinetic model uncertainty: a case for the second derivative Presented by Laur Tooming Bioinformatics journal club 28 Oct 2009

Terminology Gene regulation network Kinetic model AB: gene A encodes a transcription factor that regulates the transcription of gene B Kinetic model Differential equations modeling how the concentration of molecules in a cell changes in time

Basic idea of article Given: “gene expression measured at four or more points separated by equal intervals of time” Want to find out which genes regulate other genes Method: “we apply Bayes’s theorem to a well studied class of kinetic models”

Transcriptional network models First order model: Second order model: “Classical” Bayesian network models (static and dynamic): x_i(t): transcript abundance of i-th gene at time t β_ij: strength of influence of j-th gene on i-th (positive: activation, negative: repression) We know x_i(t) ≈ y_i(t) (expression data) and we want to estimate β_ij.

Transcriptional network models First order model: Second order model: The article tries to compare the first order model, the second order model and a combined model (assigning prior probability ½ to both models)

Key ideas Replace differential equation with difference equation Introduce α_ij, which is 1 or 0 depending on whether β_ij is nonzero. In first order case: What we want: P(α_ij | y)

Statistical methods Keywords: Bayes factor (BF) Bayesian information criterion (BIC)

P(α_ij | y) First order model: Second order model: Mixed (average) model:

Generalisations The model can handle missing gene expression data (m’<m, m’: number of genes with expression measurements, m: number of potentially regulating genes) The model can handle replication (repeated measures, n individual organisms). Information about which genes encode TF-s can be incorporated into prior probabilities.

Validation Two yeast datasets (Spellman, de Lichtenberg) Two bacteria datasets (Kao, Bansal) (plus maize cell culture data in supplementary data) For each gene i, find gene j with highest P(α_ij | y) ROC AUC

AUC scores

Conclusion of the article The second-order model is better than the first-order one (hence the title)