Inferring the nature of the gene network connectivity Dynamic modeling of gene expression data Neal S. Holter, Amos Maritan, Marek Cieplak, Nina V. Fedoroff, and Jayanth R. Banavar Topics in biophysics Effi Kenigbserg

Outline Gene networks  basics  what can be measured microarray technology - the explosion of dataset Holter’s paper – trying to simplify the problem

Once upon a time “the father of genetics“ Gene : the basic unit of heredity in a living organism Gregor Mendel

From DNA to Protein - the flow of information Across different tissues conditions and cell phase: DNA sequence is (almost) identical Number of mRNA and protein copies is highly variable

Cells within the same tissues and conditions show similar gene expression profiles Proteins are crucial functional units of the living cell Cells that function similarly express similar protein profiles How is protein abundance regulated?

The key variables Abundance (concentration) of proteins –high throughput measurement hasn’t been done yet. mRNA expression - a fair predictor of protein abundance (r ~ 0.7 in yeast ). Before 1995, it was not practical. Now days it is relatively easy How is mRNA expression measured?

Microarray technology Allows detection of thousands of DNA molecules simultaneously Two competing array type:  Gene chip (DNA chip, Affymetrix chip)  cDNA chip DNA microarray, two-channel array)

Affymetrix chip Consists of an arrayed series of thousands of microscopic spots of DNA oligonucleotide probe Target

Making a labeled DNA from mRNA sample Extract mRNA from the cell Convert mRNA into colored cDNA (complementary fluorescently labeled DNA) Hybridize cDNA with array Each cDNA sequence hybridizes (attaches) specifically with the corresponding gene sequence in the array Wash unhybridized cDNA off

Scanning the array The laser excited array is being scanned. The scanned result for a given gene is the average over all probes which correspond to this gene.

Analyzing the array scans SCHENA, Brown, et al.

Data Explosion! Hundred of thousands (or maybe millions?) microarray experiments are conducted every year Will we ever understand this data?

Usage of mRNA expression data How do gene expression levels at time t can describe gene expression levels at time t+Δ?

5–10 micrometers doubling time of ~2 hours ~4800 genes The budding yeast - Saccharomyces cerevisiae (sugar fungi of beer)

Cell cycle in budding yeast A succession of events whereby a cell grows and divides into two daughter cells that each contain the information and machinery necessary to repeat the process

S. cerevisiae regulatory network Less than 100 genes Ananko et al. 2002

The dataset (yeast cell cycle) 800 genes 12 equally spaced time points (12 microarrays) Two cell cycles long genes t Red – high mRNA expression Green – low mRNA expression (relative to a control)

The linear interaction model the expression levels of the n genes at a given time are postulated to be linear combinations of their levels at a previous time In order to learn n² gene interactions, n equations (time points) are needed

Simplifying gene interactions using SVD Singular Value Decomposition Let A be our dataset (n * m matrix). Then there exists a factorization of the form: where:  U is a n x n unitary matrix  S is a n x m diagonal matrix, with positive values on the diagonal  V is a m x m unitary matrix

S Wikipedia’s SVD example The singular values

Using SVD The modes: the first r rows of the matrix, i = 1..r r=number of singular values Expression of each gene is a linear combination of the modes

How do modes effect each other? Time translation matrix, M, represents the interactions between modes When r = #(singular values), M can be calculated directly

Cell cycle singular values Complexity may be reduced by using only the modes corresponding to the highest singular values index Value

Gene expression profile is well reconstructed using only 2 modes The first two characteristic modes for the cell cycle data o measured - approximated Mode 1 Mode 2

Simplify gene interactions using clustering Clustering genes by similarity and learning the interactions between clusters may simplify the problem Spellman et al. Alon, Barkai et al. 1999

Conclusions Gene connectivity networks are highly redundant It is possible to describe some of variability of huge biological datasets by simple interaction models There is a lot of biological data out there