Inferring the nature of the gene network connectivity

Dynamic modeling of gene expression dataNeal S. Holter, Amos Maritan, Marek Cieplak, Nina V. Fedoroff, and Jayanth R. Banavar

Topics in biophysics13.1.2009Effi 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 Mendel1822-1884

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 expressionGreen – 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

TUSVA

IUU T *

IVV T *

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

r

iiijj tXUtA

1, )()(

iXTSV

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

0

2

4

6

8

10

12

14

16

18

1234567891011index

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