1. Biological Network Analysis
Kimberly Glass
BIO508 April 9, 2014

2. Outline Network models Network properties Network paths Network motifs
Information flow
Graph clustering
Biological networks
Relational networks
Correlative networks
Causative/regulatory networks
Applications
Biological data integration
Function prediction
Resources and tools

3. Outline Network models Network properties Network paths Network motifs
Information flow
Graph clustering
Biological networks
Relational networks
Correlative networks
Causative/regulatory networks
Applications
Biological data integration
Function prediction
Resources and tools

4. The Internet colored by IP address

5. Co-authorship of scientific articles

6. Networks in Molecular Biology
Protein-Protein interactions
Protein-DNA interactions
Genetic interactions
Metabolic reactions
Co-expression interactions
Text mining interactions
Association Networks
Etc.
Barabasi & Oltvai, Nature Reviews, 2004

7. Graphs Graph G=(V,E) is a set of vertices V and edges E
V = {v1, v2, v3, v4, v5}
E = {(v1, v2), (v1, v3), (v2, v4), (v2, v5) , (v3, v5)}
A subgraph G’ of G is induced by some V’  V and E’  E
For example, V’ = {v1, v2, v3} and E’ = {(v1, v2), (v1, v3)}
Graph properties:
Directed vs. undirected
Weighted vs. unweighted
Cyclic vs. acyclic
Connectivity (node degree, paths) v2 v5 v3 v1 v2 v3

8. Networks and Graphs: Terminology
Formally, a network is a graph is…
G = (V, E), an ordered tuple of two sets
V = {v1, …, vn}, a set of unique nodes, and
E = {(vi, vj), …}, a set of (un)ordered node tuples
Bipartite
Cyclic
Multigraph
Acyclic
(DAG)
Weighted
0.5
1.2 6 -2
Loops (Self-connections)
Undirected
Directed

9. Sparse vs Dense
G(V, E) where |V|=n, |E|=m the number of vertices and edges
Graph is sparse if m~n
Graph is dense if m~n2
Complete graph when m=n2

10. Connected Components
G(V,E)
|V| = 69
|E| = 71

11. Connected Components
G(V,E)
|V| = 69
|E| = 71
6 connected components

12. Paths
A path is a sequence {x1, x2,…, xn} such that (x1,x2), (x2,x3), …, (xn-1,xn) are edges of the graph.
A closed path xn=x1 on a graph is called a graph cycle or circuit.

13. Shortest-Path between nodes

14. Shortest-Path between nodes

15. Longest Shortest-Path

16. Network paths and diameter
Shortest path:
Connect two nodes by as few edges as possible
Network diameter:
The longest shortest path in the network
The network diameter is often very short: ‘Small world network’

17. Network Motifs: Simple Building Blocks
of Complex Networks
Milo, Alon, et. al. Science Oct 25;298(5594):824-7

18. Network Motifs Feedback Positive auto-regulation
Negative auto-regulation
memory
delay
speed + stability
Coherent feed-forward
Bi-fan
filter
Incoherent feed-forward
Whole Genome Duplication
and evolvability
pulse

19. Network Motifs: Simple Building Blocks
of Complex Networks
Milo, Alon, et. al. Science Oct 25;298(5594):824-7

20. Network Motifs: Simple Building Blocks
of Complex Networks
Shen-Orr, Alon et.al. Nature Genetics, 2002 May;31(1):64-8.

21. Degree or connectivity

22. Random vs scale-free networks
P(k) is probability of each degree k, i.e fraction of nodes having that degree.
For random networks, P(k) is normally distributed.
For real networks the distribution is often a power-law:
P(k) ~ k-g
Such networks are said to be scale-free

23. Knock-out lethality and connectivity

24. Clustering coefficient
The density of the network surrounding node I, characterized as the number of triangles through I. Related to network modularity
k: neighbors of I
nI: edges between node I’s neighbors
The center node has 8 (grey) neighbors
There are 4 edges between the neighbors
C = 2*4 /(8*(8-1)) = 8/56 = 1/7

25. Mixing Properties of Networks
Assortative Network
Nodes tend to connect to other nodes of similar degree
Disassortative Network
Nodes tend to connect to other nodes of dissimilar degree

26. Network Structure: Hubs, Bottlenecks, and Information Flow26

27. Network Structure: Cliques and Clusters
Clique: fully connected subgraph
Quasi-clique: near-miss
k-clique: clique of size exactly k
Maximal clique: largest clique in graph

28. Outline Networks as a model Network properties Network paths
Network motifs
Information flow
Graph clustering
Biological networks
Relational networks
Correlative networks
Causative/regulatory networks
Applications
Biological data integration
Function prediction
Resources and tools

29. How is biological data represented in networks?
High
Correlation
Low
Gene expression
Physical PPIs
Genetic interactions
Colocalization
Sequence
Protein domains
Regulatory binding sites … + =

30. Building and Interpreting Biological Networks
How we build a biological network depends on what data we have AND what we want the edges in the network to represent.
The meaning of the edges in a biological network depend on the method used to generate those edges.
Influences how we interpret the interactions in a network.
node:
an object in the network (e.g. genes)
edge:
indicates relationship between two nodes

31. Interpreting the “edges” in Biological Networks
Relational Networks
Generally Undirected (non-causal relationships)
Nodes all of same “type”
Generally no “signs” on edges
Example: Protein A is a dimerization partner with protein B. A B
Correlation Network
Undirected (non-causal relationships)
Nodes all of same “type”
Edges can have “signs”
Example: When the expression of Gene A changes, so does the expression for Gene B. A B
*Correlation is not causation.
Regulatory Network
Directed Network (causal relationships)
Can have “types” of nodes
Edges can have “signs”
Example: TF A regulates
Gene B. A B

32. Types of Protein Interactions
Physical Protein Interactions
Edge between proteins if they physically interact
Wild Type
Viable
Cell Death X
Synthetic Lethality
Edge between proteins if mutating both causes lethality

33. Functional Associations Between Processes
Edges
Associations between processes
Very
Strong
Moderately
Gene Ontology: structured as a directed acyclic graph (DAG)
Ashburger et al. Gene Ontology: tool for the unification of biology. Nature Genetics 2000.

34. Functional Associations Between Genes
Level of shared function between genes
Edge between two genes if they are involved in many of the same biological processes

35. Interpreting the “edges” in Biological Networks
Relational Networks
Generally Undirected (non-causal relationships)
Nodes all of same “type”
Generally no “signs” on edges
Example: Protein A is a dimerization partner with protein B. A B
Correlation Network
Undirected (non-causal relationships)
Nodes all of same “type”
Edges can have “signs”
Example: When the expression of Gene A changes, so does the expression for Gene B. A B
*Correlation is not causation.
Regulatory Network
Directed Network (causal relationships)
Can have “types” of nodes
Edges can have “signs”
Example: TF A regulates
Gene B. A B

36. Network inference from expression data
Margolin and Califano, Ann. N.Y. Acad. Sci. 1115: 51–72 (2007).
Differential equations
Boolean Networks
Linear Regression
Bayesian networks
Information theoretic models
Latent variable networks
conditions
genes
Focusing on gene expression is a simplification. But let’s us to put our hand on it.

37. Correlation is the simplest metric for co-expression
genes
genes
conditions
genes

38. Mutual Information is a Measure of Non-linear Correlation
Pearson correlation value
Source:

39. Mutual Information (MI)
Definition
Properties
Measures how much knowing one of these variables reduces uncertainty about the other
Positive and symmetric
Invariant under nonlinear transformation
Network Reconstruction Algorithms that use MI:
ARACNE
CLR

40. (Algorithm for the Reconstruction of Accurate Cellular Networks)
ARACNe
(Algorithm for the Reconstruction of Accurate Cellular Networks)
Margolin, Califano et al. BMC Bioinformatics Mar 20;7 Suppl 1:S7.

41. (Algorithm for the Reconstruction of Accurate Cellular Networks)
ARACNe
(Algorithm for the Reconstruction of Accurate Cellular Networks)
Margolin, Califano et al. BMC Bioinformatics Mar 20;7 Suppl 1:S7.
Key Idea: Remove indirect relationships.

42. CLR (Context Likelihood of Relatedness)
Faith, Gardner et al. PLoS Biol Jan;5(1):e8.

43. CLR (Context Likelihood of Relatedness)
Faith, Gardner et al. PLoS Biol Jan;5(1):e8.
Key Idea: Normalize the MI for each gene pair against its corresponding background.

44. Interpreting the “edges” in Biological Networks
Relational Networks
Generally Undirected (non-causal relationships)
Nodes all of same “type”
Generally no “signs” on edges
Example: Protein A is a dimerization partner with protein B. A B
Correlation Network
Undirected (non-causal relationships)
Nodes all of same “type”
Edges can have “signs”
Example: When the expression of Gene A changes, so does the expression for Gene B. A B
*Correlation is not causation.
Regulatory Network
Directed Network (causal relationships)
Can have “types” of nodes
Edges can have “signs”
Example: TF A regulates
Gene B. A B

45. Thinking of Gene Regulation As a Network
Nodes are genes, edges indicate causal relationships between genes (“TF A regulates gene B”)
Networks are directed, from transcription factors to target genes (some of which are also transcription factors)
Edges in gene regulatory networks can have signs corresponding to target gene activation (increased transcription) and gene repression (prevention of transcription)
note that edge signs are hard to measure in practice.
Transcription Factor
Target Gene
TF A activates gene B
Transcription Factor
Target Gene
TF A represses gene B

46. How Can We Model GRNs in Human Systems? TF1 TF2 TF3
TF-Gene Regulation Data
Two main ways to produce this type of network: G1
TF1
Experimentally
Computationally
Technique: ChIP-chip
Technique: DNA sequence scan for TF binding sites
Limitations: very expensive, limited number of ChIP antibodies
Limitations: only know recognitions sequences for 10-20% of TFs, prone to false positives, not environment-specific
Strength: High quality, environment-specific
Strengths: cheap G2 G3
TF2 G4 G5
TF3
TF4 G6

47. Outline Networks as a model Network properties Network paths
Network motifs
Information flow
Graph clustering
Biological networks
Relational networks
Correlative networks
Causative/regulatory networks
Applications
Biological data integration
Function prediction
Resources and tools

48. Incorporating Epigenetic Information With TF Sequence-motif Data
All potential interactions
Motif found within gene’s promoter
Interactions with Epigenetic Evidence
Motif found in gene’s promoter and located in region of open chromatin
Epigenetic data
motif
TF1  Gene1
Gene1
Gene2
Gene3
Gene4
Open Chromatin
(DNase hypersensitivity site)

49. Relationship between Expression Information and Gene Regulation
Experimental (ChIP-chip)
Computational (motif)
Gene Expression
Limited antibodies (sparse)
Quality of PWM
Large amount of data
Environment specific
Not environment specific
Non-functional targets
Non-functional sequences
Correlation is not causation
“Good quality, sparse, expensive”
“Poor quality, dense, cheap”
Regulatory Network
combination

50. Relationship between Expression Information and Gene Regulation
Correlation of expression might occur when:
One gene regulates another
Two genes are regulated by the same TF.
Gene Expression
Large amount of data
Environment specific
Correlation is not causation TF
TF is expressed
Sometime later…..
genes are expressed
Correlation in two genes’ expression patterns is actually more often a measure of co-regulation

51. Relationship between Expression Information and Gene Regulation?
TF1 G2 G1
Correlated expression
Example: G2
The expression of G1 and G2 is highly correlated
Since TF1 targets G1, there is a higher possibility that TF1 also regulated G2.

52. Protein Interaction Is Related to Regulation
Some transcription factors don’t bind a particular DNA sequence.
TFs can regulate a gene:
Through direct interaction with the control (promoter) region of that gene.
By forming a complex with other TFs which directly interact with the promoter region of that gene.
We can model protein interactions as a network.

53. Protein-Protein Interaction Data TF-Gene Regulation Data
Relationship between Protein Interaction Information and Gene Regulation
Protein-Protein Interaction Data
TF-Gene Regulation Data G1
TF1
TF1
TF4 G2 G3
TF5
TF2
TF2 G4 G5
TF3
TF3
TF4
Know recognition sequence

54. Protein-Protein Interaction Data TF-Gene Regulation Data
Relationship between Protein Interaction Information and Gene Regulation
Protein-Protein Interaction Data
TF-Gene Regulation Data G1
TF1
TF1
TF4 G2 G3
TF5
TF2
TF2 G4 G5
TF3
TF3
TF4

55. Relationship between Protein Interaction Information and Gene Regulation
Integrated Network
Example: G3
TF1 and TF2 are potential regulators.
Since TF5 interacts with both TF1 and TF2, there is higher possibility that TF5 is also involved in the regulation of G3. G1
TF1 G2 G3
TF5
TF2 G4 G5
TF3
TF4
TF-Gene Regulation
Protein-Protein Interaction

56. Outline Networks as a model Network properties Network paths
Network motifs
Information flow
Graph clustering
Biological networks
Relational networks
Correlative networks
Causative/regulatory networks
Applications
Biological data integration
Function prediction
Resources and tools

57. Functional mapping: mining biological networks
Predicted relationships between genes
High
Confidence
Low
The strength of these relationships indicates how cohesive a process is.
Cell cycle genes

58. Functional mapping: mining biological networks
Predicted relationships between genes
High
Confidence
Low
Cell cycle genes

59. Functional mapping: mining biological networks
Predicted relationships between genes
High
Confidence
Low
The strength of these relationships indicates how associated two processes are.
Cell cycle genes
DNA replication genes

60. Predicting gene function
Predicted relationships between genes
High
Confidence
Low
Cell cycle genes

61. Predicting gene function
Predicted relationships between genes
High
Confidence
Low
Cell cycle genes

62. Predicting gene function
Predicted relationships between genes
High
Confidence
Low
These edges provide a measure of how likely a gene is to specifically participate in the process of interest.
Cell cycle genes

63. Outline Networks as a model Network properties Network paths
Network motifs
Information flow
Graph clustering
Biological networks
Relational networks
Correlative networks
Causative/regulatory networks
Applications
Biological data integration
Function prediction
Resources and tools

64. Known Gene Regulatory Network: E. coli
E. coli is a single-celled organism with a circular DNA structure encoding approximately 4000 genes (about 2500 “operons”)
Probably has with most complete experimentally-constructed gene regulatory network.
Used for many early investigations into GRN structure.

65. Human Regulatory Information: ENCODE

66. Protein Interaction Information: StringDB

67. Pathway Information http://www.biocarta.com/

68. Network Analysis and Visualization