1. Systems Biology Course Name: Conducted by- Shigehiko kanaya &
Md. Altaf-Ul-Amin

2. Dates of Lectures: October 9, 15, 16, 22, 23, 30 November
5, 6, 12, 13, 19, 20, 26, 27
Lecture Time: Mondays &Tuesdays 11:00-12:30
Website

3. Syllabus
Introduction to Graphs/Networks, Different network models, Properties of Protein-Protein Interaction Networks, Different centrality measures
Protein Function prediction using network concepts, Application of network concepts in DNA sequencing, Line graphs
Concept and types of metric, Hierarchical Clustering, Finding clusters in undirected simple graphs: application to protein complex detection
Introduction to KNApSAcK database, Metabolic Reaction system as ordinary differential equations, Metabolic Reaction system as stochastic process
Metabolic network and stoichiometric matrix, Information contained in stoichiometric matrix, Elementary flux modes and extreme pathways
Graph spectral analysis/Graph spectral clustering and its application to metabolic networks
Normalization procedures for gene expression data, Tests for differential expression of genes, Multiple testing and FDR, Reverse Engineering of genetic networks
Finding Biclusters in Bipartite Graphs, Properties of transcriptional/gene regulatory networks, Introduction to software package Expander
Introduction to signaling pathways, Selected biological processes: Glycolytic oscillations, Sustained oscillation in signaling cascades

4. Central dogma of molecular biology

5. The crowded Environment inside the cell
Some of the physical characteristics are as follows:
Viscosity > 100 × μ H20
Osmotic pressure < 150 atm
Electrical gradient ~ V/cm
Near crystalline state
The osmotic pressure of ocean water is about 27 atm and that of blood is 7.7 atm at 25oC
Without a complicated regulatory system all the processes inside the cell cannot be controlled properly.
Source: Systems biology by Bernhard O. Palsson

6. From Genome to Phenome Metabolites (Bio-chemical molecules)
(Dynamic)
Phenotype X
Phenome
Metabolites (Bio-chemical molecules)
Metabolome
Proteins-Amino Acid Sequences
Proteome
mRNA and other RNAs - Nucleotide sequence-Single Stranded
Transcriptome
Genome (Gene set)
DNA –Nucleotide sequence- ATCTGAT……Double Helix
(Statiic)
Progressing genome projects: many kinds of “–omics” works have progressed such as genomics, transcriptomics, proteomics, metabolomics ….
These are dynamic information reflecting to Phenome.

7. Bioinofomatics Understanding organism as a system (Systems Biology)
Genome:
Integration of omics
to define elements
(genome, mRNAs,
Proteins, metabolites)
Understanding organism as a system
(Systems Biology)
Understanding species-species relations
(Survival Strategy) 5’ 3’ b c h i k m 3’ 5’ a d e f g j l
Transcriptome：
Activation (+) 5’ A 3’ b c h i k m 3’ G 5’ a d e f g j l
Repression (-) G
Proteome, Interactome
Protein A B C D E F G H I J K L M
Function
Unit A B C D E G H K I L M J F
Metabolome
FT-MS
comprehensive and global analysis of diverse metabolites produced in cells and organisms B C I L
Metabolite 1
Metabolite 2
Metabolite 3
Metabolite 5 D E F
Metabolic Pathway H K
Metabolite 4
Metabolite 6

8. Introduction to Graphs/Networks Representing as a network often helps to understand a system

9. Konigsberg bridge problem
Konigsberg was a city in present day Germany encompassing two islands and the banks of Pregel River. The city was connected by 7 bridges.
Problem: Start at any point, walk over each bridge exactly once and return to the same point. Possible?

10. Konigsberg bridge problem
Konigsberg was a city in present day Germany including two islands and the banks of Pregel River. The city was connected by 7 bridges.
Problem: Start at any point, walk over each bridge exactly once and return to the same point. Possible?

11. Konigsberg bridge problem
Konigsberg was a city in present day Germany including two islands and the banks of Pregel River. The city was connected by 7 bridges.
Problem: Start at any point, walk over each bridge exactly once and return to the same point. Possible?

12. Konigsberg bridge problem
Problem: Start at any point, walk over each bridge exactly once and return to the same point. Possible?
This problem was solved by Leonhard Eular in 1736 by means of a graph.

13. Konigsberg bridge problem
Problem: Start at any point, walk over each bridge exactly once and return to the same point. Possible?
This problem was solved by Leonhard Eular in 1736 by means of a graph. A B C D

14. Konigsberg bridge problem
Problem: Start at any point, walk over each bridge exactly once and return to the same point. Possible? A B C D
A, B, C, D circles represent land masses and each line represent a bridge
The necessary condition for the existence of the desired route is that each land mass be connected to an even number of bridges.
The graph of Konigsberg bridge problem does not hold the necessary condition and hence there is no solution of the above problem.
This notion has been used in solving DNA sequencing problem

15. Definition
A graph G=(V,E) consists of a set of vertices V={v1, v2,…) and a set of edges E={e1,e2, …..) such that each edge ek is identified by a pair of vertices (vi, vj) which are called end vertices of ek.
A graph is an abstract representation of almost any physical situation involving discrete objects and a relationship between them.

16. Both these graphs are the same
It is immaterial whether the vertices are drawn rectangular or circular or the edges are drawn staright or curved, long or short. A A B C D B D C
Both these graphs are the same

17. Many systems in nature can be represented as networks
The internet is a network of computers

18. Many systems in nature can be represented as networks
Air route Network
Road Network
No such node exists
Very high degree node

19. Many systems in nature can be represented as networks
Printed circuit boards are networks
Network theory is extensively used to design the wiring and placement of components in electronic circuits

20. Many systems in nature can be represented as networks
Protein-protein interaction network of e.coli

21. Some Basic Concepts regarding networks:
Average Path length
Diameter
Eccentricity
Clustering Coefficient
Degree distribution

22. Average Path length
Distance between node u and v called d(u,v) is the least length of a path from u to v.
d(a,e) = ? a c d b f e

23. Average Path length
Distance between node u and v called d(u,v) is the least distance of a path from u to v.
d(a,e) = ?
Length of a-b-c-d-f-e path is 5 a c d b f e

24. Average Path length
Distance between node u and v called d(u,v) is the least distance of a path from u to v.
d(a,e) = ?
Length of a-b-c-d-f-e path is 5
Length of a-c-d-f-e path is 4 a c d b f e

25. Average Path length
Distance between node u and v called d(u,v) is the least length of a path from u to v
d(a,e) = ?
Length of a-b-c-d-f-e path is 5
Length of a-c-d-f-e path is 4
Length of a-c-d-e path is 3 a c d b f e
The minimum length of a path from a to e is 3 and therefore
d(a,e) = 3.

26. Average Path length
Average path length L of a network is defined as the mean distance between all pairs of nodes. a c
There are 6 nodes and
6C2 = (6!)/(2!)(4!)=15 distinct pairs for example (a,b), (a,c)…..(e,f). d b f e
We have to calculate distance between each of these 15 pairs and average them

27. Average Path length
Average path length L of a network is defined as the mean distance between all pairs of nodes.
a to b 1
a to c 1
a to d 2
a to e 3
a to f 3
____________________
15 pairs 27(total length) a c d b f e
L=27/15=1.8
Average path length of most real complex network is small

28. Average Path length
Finding average path length is not easy when the network is big enough. Even finding shortest path between any two pair is not easy.
A well known algorithm is as follows:
Dijkstra E.W., A note on two problems in connection with Graphs”, Numerische Mathematik, Vol. 1, 1959,
Dijkstra’s algorithm can be found in almost every book of graph theory.
There are other algorithms for finding shortest paths between all pairs of nodes.

29. Diameter
Distance between node u and v called d(u,v) is the least length of a path from u to v.
The longest of the distances between any two node is called Diameter
a to b 1
a to c 1
a to d 2
a to e 3
a to f 3
15 pairs a c d b f e
Diameter of this graph is 3

30. Eccentricity And Radius
Eccentricity of a node u is the maximum of the distances of any other node in the graph from u.
The radius of a graph is the minimum of the eccentricity values among all the nodes of the graph.
a to b 1
a to c 1
a to d 2
a to e 3
a to f 3
Therefore eccentricity of node a is 3 3 2 a c d b f 3 e
Radius of this graph is 2

31. Degree Distribution
The degree distribution is the probability distribution function P(k), which shows the probability that the degree of a randomly selected node is k.

32. Degree Distribution
# of nodes having degree k 10 1 2 3 4
Degree

33. Degree Distribution
P(k) 1 1 2 3 4
Degree
Any randomness in the network will broaden the shape of this peak

34. Degree Distribution
# of nodes having degree k 4 2 1 2 3 4
Degree

35. Degree Distribution
P(k)
0.5
0.25 1 2 3 4
Degree

36. Degree Distribution
Poisson’s Distribution
e = , the Base of natural Logarithms
Degree distribution of random graphs follow Poisson’s distribution

37. P(k) ~ k-γ Degree Distribution P(k) Power Law Distribution
Connectivity k
P(k)
Degree Distribution
P(k) ~ k-γ
Power Law Distribution
Degree distribution of many biological networks follow Power Law distribution
Power Law Distribution on log-log plot is a straight line

38. Clustering coefficient
ki = # of neighbors of node i
Ei = # of edges among the neighbors of node i a c d b f e

39. Clustering coefficient
Ca=2*1/2*1= 1
ki = # of neighbors of node i
Ei = # of edges among the neighbors of node i a c d b f e

40. Clustering coefficient
Ca=2*1/2*1= 1
Cb=2*1/2*1= 1
Cc=2*1/3*2= 0.333
Cd=2*1/3*2= 0.333
Ce=2*1/2*1= 1
Cf=2*1/2*1= 1
Total = 4.666
C =4.666/6=
ki = # of neighbors of node i
Ei = # of edges among the neighbors of node i a c d b f e

41. Clustering coefficient
By studying the average clustering C(k) of nodes with a given degree k, information about the actual modular organization can be extracted.
Ca=2*1/2*1= 1
Cb=2*1/2*1= 1
Cc=2*1/3*2= 0.333
Cd=2*1/3*2= 0.333
Ce=2*1/2*1= 1
Cf=2*1/2*1= 1 a c d b
C(1)=0
C(2)=(Ca+Cb+Ce+Cf)/4=1
C(3)=(Cc+Cd)/2=0.333 f e

42. C(k) ~ k-γ Clustering coefficient
By studying the average clustering C(k) of nodes with a given degree k, information about the actual modular organization can be extracted.
For most of the known metabolic networks the average clustering follows the power-law.
C(k) ~ k-γ
Power Law Distribution

43. Subgraphs
Consider a graph G=(V,E). The graph G'=(V',E') is a subgraph of G if V' and E' are respectively subsets of V and E. a c b
Subgraph of G a c d c b f d f
Subgraph of G e
Graph G

44. Induced Subgraphs
An induced subgraph on a graph G on a subset S of nodes of G is obtained by taking S and all edges of G having both end-points in S. a c b
Induced subgraph of G for S={a, b, c} a c d c b f d f
Induced subgraph of G for S={c, d, f} e
Graph G

45. Graphlets are non-isomprphic induced subgraphs of large networks
T. Milenkovic, J. Lai, and N. Przulj, GraphCrunch: A Tool for Large Network Analyses, BMC Bioinformatics, 9:70, January 30, 2008.

46. Partial subgraphs/Motifs
A partial subgraph on a graph G on a subset S of nodes of G is obtained by taking S and some of the edges in G having both end-points in S. They are sometimes called edge subgraphs. a c b a c
Partial subgraph of G
For S={a, b, c} d b f e
Graph G

47. Partial subgraphs/Motifs
Genomic analysis of regulatory network dynamics reveals large topological changes
Nicholas M. Luscombe, M. Madan Babu, Haiyuan Yu, Michael Snyder, Sarah A. Teichmann & Mark Gerstein, NATURE | VOL 431| 2004
SIM=Single input motif
MIM= Multiple input motif
FFL=Feed forward loop
This paper searched for these motifs in transcriptional regulatory network of Saccharomyces cerevisiae

48. Partial subgraphs/Motifs
Genomic analysis of regulatory network dynamics reveals large topological changes
Nicholas M. Luscombe, M. Madan Babu, Haiyuan Yu, Michael Snyder, Sarah A. Teichmann & Mark Gerstein, NATURE | VOL 431| 2004