1. Dynamic modeling of gene expression data
Neal S. Holter et. al.
PNAS vol.98, No4, 2000
Summarized by Jinsan Yang

2. 2002 SNU Biointelligence Lab.
Introduction
Assumptions
The expression levels of genes at a given time are postulated to be linear combinations of their levels of at a previous time
Common Goals
Describe the time evolution of gene expression levels by using a time translation matrix
Derive the time translation matrix by using characteristic modes of SVD (singular value decomposition)
2002 SNU Biointelligence Lab.

3. 2002 SNU Biointelligence Lab.
Introduction
Notes
Time translation matrix reflects the magnitude of the connectivities between genes
The number of genes g far exceeds the number of time points
(g x g equations are needed – ill posed problem)
Nonlinear interpolation scheme: speculative
Clustering genes: not clear
In this paper: Use characteristic modes from SVD
The casual links between the modes (hence for genes) involve just a few essential connections and any additional connections are redundant
2002 SNU Biointelligence Lab.

4. Singular Value Decomposition (SVD)
Singular value decomposition of an (n x m) matrix A :
m: gene number, n: time interval number
columns of U (gene coefficient vectors) form a orthogonal basis for the gene space
a columns of V (gene expression vectors) form an orthogonal basis for the expression (array) space
2002 SNU Biointelligence Lab.

5. Singular Value Decomposition (SVD)
Calculating SVD of A : from the eigen values of AA and AA
Smaller singular values correspond to ‘noise’, larger singular values correspond to principle directions in the data
The columns of U are determined by
The vectors (modes) are the first r rows of
the matrix where each column corresponds to the times at which the corresponding expression data are measured
The temporal variation of any gene j can be written exactly as a linear combination of these r characteristic modes as
2002 SNU Biointelligence Lab.

6. Singular Value Decomposition (SVD)
For any gene j :
The contribution of the first k modes to the temporal pattern of a gene j and its average over all genes :
2002 SNU Biointelligence Lab.

7. Singular Value Decomposition (SVD)
2002 SNU Biointelligence Lab.

8. 2002 SNU Biointelligence Lab.
Method
Expression levels of r modes at time t :
The linear model:
The gene expression data set can be reexpressed precisely by using the r specific coefficients for each gene, M, and the initial values of each of the r modes.
M can be derived by using simulated annealing methods
M(i,j) describes the influence of mode j on mode i
M(i,j) multiplied by the expression level of gene j at time t contributes to the expression level of gene i at time (t+t )
2002 SNU Biointelligence Lab.

9. 2002 SNU Biointelligence Lab.
Results
Datasets:
yeast cell cycle (CDC15) (15)
yeast sporulation (7)
Human fibroblast (13)
Reducing the number of modes:
from the matrix M
from r clusters of genes: six clusters of yeast sporulation data: Metabolic, early I, early II, middle, midlate, late
2002 SNU Biointelligence Lab.

10. 2002 SNU Biointelligence Lab.
Results
The expression of 6 clusters by six modes:
The interrelationships between the cluster expression patterns:
measured (o) and calculated (-)
expression profiles
2002 SNU Biointelligence Lab.

11. 2002 SNU Biointelligence Lab.
Results
For (2 x 2) M matrix
from the matrix M
using 2 most important modes
a: 2x2 translation matrix from initial values
b: linear combination of 2 modes
c: original data
2002 SNU Biointelligence Lab.

12. 2002 SNU Biointelligence Lab.
Results
2002 SNU Biointelligence Lab.

13. 2002 SNU Biointelligence Lab.
Results
2002 SNU Biointelligence Lab.