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Topics in biophysics 13.1.2009 Effi Kenigbserg

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 13.1.2009 Effi Kenigbserg. Outline. Gene networks basics what can be measured

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Topics in biophysics 13.1.2009 Effi Kenigbserg

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  1. Inferring the nature of the gene network connectivityDynamic modeling of gene expression dataNeal S. Holter, Amos Maritan, Marek Cieplak, Nina V. Fedoroff, and Jayanth R. Banavar Topics in biophysics 13.1.2009 Effi Kenigbserg

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

  3. Once upon a time • “the father of genetics“ • Gene : the basic unit of heredity in a living organism Gregor Mendel 1822-1884

  4. 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

  5. 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?

  6. 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?

  7. 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)

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

  9. 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

  10. 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.

  11. Analyzing the array scans SCHENA, Brown, et al.

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

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

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

  15. 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

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

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

  18. 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

  19. 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

  20. The singular values S Wikipedia’s SVD example

  21. 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

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

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

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

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

  26. 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

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