Protein-Protein Interaction Network

1
Protein-Protein Interaction Network

• Gautam Chaurasia
• 08.07.04

2
Overview

• Introduction.
• Three Different Models
• Structure of the protein-protein interaction
  network.
• Non-power law.
• Evolutoin of the network.
• Power Law Random Graphs.
• Detection of functional modules from protein
  interaction networks.
• Clustering algorithm

3
Introduction

• The network is viewed as a graph whose nodes
  correspond to proteins. Two proteins are
  connected by an edge if they interact.
• The collection of all interactions between the
  proteins of an organism is called interactome.
• The Y2H system (yeast-two-hybrid) is used to
  yield a comprehensive map of protein-protein
  interaction network.
• The network resembles a random graph in that it
  consists of many small subnets (groups of
  proteins that interact with each other but do not
  interact with any other protein) and one large
  connected subnet comprising more than half of all
  interacting proteins.

4
Structure of PPI Network

• Yeast protein interaction network. (Uetz et al.
  2000)
• A A two-dimensional drawing of the entire
  network.
• B The giant (hub) component of this graph
  consists of 466 proteins.
• C A small section of the hub component, with
  gene or open reading frame names shown next to
  each node.

5
Structure of PPI Network

• Degree
• Described by the connectivity k of the node,
  which tells us how many links the node has to
  other nodes.
• Degree distribution
• The degree distribution p(k), gives the
  probability that a selected node has exactly k
  links.
• P(k) is obtained by

6
ER Random Graph

• ER Random Graphs
• An ER random graph consists of n nodes and k
  edges, where any pair of nodes is equally likely
  to be connected by one of the k edges.
• Start with a given number of nodes and add links
  randomly.
• which creates a graph with approximately
  pN(N1)/2 randomly placed links.
• The node degrees follow a Poisson distribution.

7
Scale-Free Network

• Scale-free networks Rich getter richer.
• Scale-free networks are characterized by a
  power-law degree distribution the probability
  that a node has x links follows,
• where ? gt 0, so that a plot of log(degree) by
  log(frequency) shows a decreasing linear trend.

8
Model-I Non-Power Law-I

• The essence of this model is to observe that
  parts of proteins, called domains, contains sites
  into which complementary parts of other protein
  can bind.
• These complementary parts are referred to as
  positive and negative aspects of domain.
• Bipartite sub-graph-graphs comprising two
  disjointed sets of nodes in which each node in
  one set is connected to every node in the other
  set.

Fig 2 In this figure, a particular domain for
which the positive form is present in three
proteins A, B, and C, and whose negative form is
in four proteins W, X, Y, Z.
9
Model-I Non-Power Law-II

• We assume that there are n proteins and m domains
  with a negative and positive form.
• A domains may be any of the 2m types 1, 1-, 2,
  2-,....,m, m-.
• Each of the n proteins contains each of the 2m
  possible domains with constant probability p.
• Let Xi be the number of domains that the ith
  protein has is distributed binomially
• All the Xi are independent and identically
  distributed.
• Thus, the average number of sites per protein l
  2mp.

10
Model-I Non-Power Law-III

• Let Yi be the number of interactions of the ith
  protein.
• So the probability that any other protein j will
  not connect to i only if it does not contain any
  of the x complementary domain aspects.
• Since there are n-1 such proteins, we have
• Where q (1-p). Hence, the unconditional
  distribution of Yi is a binomial mixture of
  binomials

11
Model-I Non-Power Law-IV

• By Using Inclusion-Exclusion property-type
  expression we get
• Binomial distribution An experiment with a fixed
  number of independent trials, each of which can
  only have two possible outcomes.
• For example Tossing a coin 20 times to see how
  many tails occur.
• Inclusion-Exclusion Let A denote a finite set
  and let P1, ...,Pn be any given properties. We
  want to express the number of elements of A which
  have none of these properties in terms of numbers
  of elements which have some of these properties.

12
Log-log plot of the distribution

• f(y) is plotted for n6000 proteins, m1000
  domains and
• ? 1,2.
• The resulting graph shows clear non-linearity.

Fig Loglog plot of the distribution of vertex
degrees in the modelled interactome with 6000
proteins, 1000 domains and an average of 1 or 2
domains per protein, shown as solid and dotted
lines respectively
13
Degree distribution of sampled sub-graphs

• A total of 450 proteins were sampled at random.
• The mean number of neighbors for each protein in
  this sample was 5.
• The resulting graph has approximately the same
  number of vertices and edges as the Uetz
  datasets.

FigThe Ito and Uetz datasets are plotted in
black and blue, respectively. A straight line
(power law) fit is shown as a dotted line. The
distribution is obtained by sampling from this
model with 6000 proteins, 1000 domains and an
average of 1 domain per protein is plotted in
red.
14
Degree distribution of sampled sub-graphs

• A total of 1500 proteins were sampled at random.
• The resulting graph shows the fit of this model
  to datais better than power law.

• Fig The DIP dataset is plotted in black. The
  distribution obtained by sampling from this model
  with 6000 proteins, 1000 domains and an average
  of 2 domains per protein is plotted in red. A
  straight line (power law) fit is shown as a
  dotted line.

15
Conclusions

• The degree distribution predicted by this model
  fit the data better than do power law
  distribution.
• This model fits better to the subnet as compared
  to the power law

16
Example

• This model can be used to infer the existence of
  interactions not yet detected experimentally, by
  using the predicted bipartite structure of
  sub-graphs.

In this figure strongly suggests that o-Raf1,
PLC-, RALGDS, AF-6, RLF and SUR-8 contain a motif
that interacts with a complementary motif in
R-Ras, Rap1A, KRAS2B, RIN, RIBB, N-Ras and H-Ras.
This would imply that for instance RLF and AF-6
should interact with Rap1A and R-Ras in order to
complete the bipartite graph.
17
Model-II

• The Yeast Protein Interaction Network Evolves
  Rapidly and Contains Few Redundant Duplicate
  Genes.

18
Evolution of Function

• Examples
• Partially redundant duplicates
• CLN1/2/3 Involves in regulation of activity of
  yeast cyclin dependent kinase. Ks 2.4, over
  200 Myr.
• TPK1/2/3 Catalytic subunits of yeast cyclic
  AMP-dependent protein kinase. Ks 1.31
• Diverged gene function
• EDN vs. ECP EDN has high RNAse activity, act as
  antivetroviral agent,
• whereas ECP is an antibacterial toxin exertings.
• dopa carboxylase and amd Duplicates are
  expressed in different parts of the cell,
  therefore having different biological functions.

19
Objective

• Two main questions are addressed in this model
  are
• At what rate does functional divergence occur
  after gene duplication for a large sample of
  duplicated gene in genome?
• Which effects have the products of the duplicated
  genes in the protein-protein interaction network?

20
Data for Analysis

• The required information on protein-protein
  interaction data comes from a large experiment
  (Uetz et al. 2000) using the yeast two-hybrid
  system (Field and Song 1989).
• 985 proteins, 899 interactions.
• 45 self intearctions.
• Data for duplicated genes were obtained from the
  University of Oregon and described by using the
  fraction Ks .
• Ks is the measure of the similarity between two
  genes.
• Only those genes pairs were considered for
  further analysis whose Ks lt 5 cutoff.
• There were such 9,059 pairs among 6,000 genes
  with Ks lt 5.

21
Power Law Random Graphs-I

• PL random graphs are random graphs whose degree
  probability distribution P(d) is proportional to
  d-t for some constant t.
• First, n 6279 isolated nodes were generated,
  and a random integer d gt 0 was assinged to these
  node.
• This random number d was generated in the
  following way,
• where r is a random real number uniformly
  distributed in the interval (0, 1), and g gt 0 ,
  is a constant.

22
Power Law Random Graphs-II

• Second, this number d was accepted with
  probability d-t.
• The resulting distribution of d is a Power law
  with an weighing function.
• If d was discarded, a new d was generated
  according to same prescription, and this process
  was repeated untill a d was accepted
• Once d was accepted, it was assigned to the
  randomly chosen node.

23
Power Law Random Graphs-III

• Another node was chosen at random (without
  replacement of the previous chosen node), an
  integer d was assigned to it in same way, and
  this process was repeated untill the sum S of
  all the integers assigned to the chosen nodes
  first exceed 2k, where k is the number of edges.
• The integer assigned to each node correspond to
  the nodes degree.
• Nodes were connected as per the number of edges
  and this was done untill the number of edges is
  S/2 k.

24
Interaction Network vs. Random Graph

• Comparison of protein contact network (n 985
  nodes, k 899 edges) with random graphs.
• The PPI network has an excess of proteins with
  degree 1, but fewer proteins with a higher
  degree than the ER Random graph.
• Whereas degree distribution of PPI network is
  consistent with the Power Law Random graph.

25
Duplications and Interactions

• This figure illustrate the effect of gene
  duplication on gene products involved in protein
  interactions.

26
Divergence of Interactions

• 20 of duplicate gene pairs share an interaction
  partner with 0.5 lt Ks lt 1.0, whereas 80 of genes
  have no common interaction partner with their
  duplicates approximately 100 Myr after
  duplication.
• Ks gt 2 approaches the value expected for
  randomly chosen gene pairs.

• The histogram of the fraction of duplicates genes
  whose products have at least one interacting
  protein in common as a function of Ks.

200-300 myr
Intercation turn over every 200-300 Myr
27
Divergence of Interactions

• Only 57 of the most closely related duplicate
  gene pairs (0ltKslt.5) for which both genes
  interact with other proteins share any protein
  interaction partner in the same subnet.
• For 380 gene pairs with Ks gt 0.5 the fraction of
  duplicate partners with shared interaction is lt
  20.
• Ks gt 1.5 is close to the random expected value.

28
The Rate of Interaction Loss

• The divergence in protein interaction after gene
  duplication is largely due to interaction loss.
• 127 pairs with KS lt 2, where both duplicates
  engage in protein-protein interaction network.
• 920 interactions were present after duplication.
• 429 of which have been lost since at the rate of
  2.3e-3/Myr.
• Is this estimate low or high?
• interaction data noise leads to overestimates.
• young pairs and double-losses lead to
  underestimates.

29
Divergence of Self-interactions

• Loss or gain of interactions between a pair of
  paralogs due to self-interaction.

Self-Interactions and interactions between
products of duplicate genes.
30
Divergence of Self-interactions

• Total of 25 paralogs.
• Only few conserved self-interactions was found.
• New interactions
• 13/25 new interactions at the rate of 2.88 x 10-6
  /Myr per pair Ks 1 corresponds to 100 Myr.

31
Conclusions

• Protein-protein interaction network shows a
  power-law degree distribution.
• Total 6280 ORF in yeast genome with 1.97 x 107
  possible pair- wise interactions.
• New interactions forming at slow rates/pair, and
  evolved at a rate of 2.88x10-6 per protein pair
  per million year.
• Extrapolating the above estimate to entire yeast
  proteome would thus yield (1.97 x 107 x
  2.88x10-6) 57 newly evolved interaction per
  million years.

32
Model-III- Cluster Analysis
Detection of Functional Modules from Protein
Interaction Networks of S.cerevisiae.
33
Cluster Analysis

• CA is an obvious choice of methodology for the
  extraction of functional modules from protein
  interaction networks.
• Clustering is defined as the grouping of objects
  based on their sharing discrete, measureable
  properties.
• In functional genomics, clustering algorithm have
  been devised for multiple tasks, such as mRNA
  expression analysis and the detection of protein
  families.
• The aim of this model is to detect biologically
  meaningfull patterns in the entire known protein
  interaction network of S.cerevisiae.

34
Clustering Algorithm

• The protein interaction data were obtained from
  DIP database.
• The network of proteins is first transformed into
  a weighted graph.
• The weights attributed to each intearaction
  reflect the degree of confidence level,
  represented by the number of experiments that
  support the interactions.
• The score of 3.0 was assigned for the first
  instance of interaction, and increased by 1 if
  the interaction supported by another method or
  0.25 if the interaction had already been observed
  by that method.

35
Clustering Algorithm

• The resulting graph is weighted network of
  proteins connected by edges.
• Now this weighted graph is converted into a line
  graph L(G), in which edegs now represent nodes
  and nodes represent edges.

36
Clustering Algorithm

• The scores for the original constituent
  interaction are then averaged and assigned to
  each edge.
• The TribeMCL software, an algorithm for
  clustering graph, was used to cluster the
  interaction network and recover cluster of
  associated interactions.
• These clusters range in size from 2 to 292
  components (average size is 8.05), and form a
  scale-free protein network.

37
Results

• Total of 1046 clusters were obtained.
• In this analysis, each protein was on average
  present in 2.1 clusters.
• Only 76 interactions and 146 proteins (represent
  only lt 1 of total data), which were weakly
  connected to the main interaction network, were
  discarded by the clustering method.
• The found Clusters were classified in three
  categories according to the functional
  involvement of proteins in different machanism.
• KEGG regulatory and metabolic classifications
  (20).
• GQFC Genequiz automatic functional
  classification (45).
• MIPS Cellular localization (48).

38
Validation of the Clustering Method-I

• Scoring the cluster Cluaters are validated by
  assesing the consistency of protein
  classification within an individual cluster.
• This is measured, for each of three
  classifiaction schemes, by calculating the
  redundancy of each cluster j
• Rj redundancy (Rj) of each cluster j.
• n represents the number of classes in the
  classification scheme,
• Ps represents the relative frequency of the
  class in cluster j,
• The numerator represents the information content
  in bits given by entropy (H),
• The denominator is a normalizing factor
  representing the maximum entropy for the cluster
  j (Hmax).

39
Validation of the Clustering Method-II
Fig. Module validation using biological
classification schemes
40
Validation of the Clustering Method-III

Fig. Module validation using biological
classification schemes
41
Validation of the Clustering Method-IV
Fig. Module validation using biological
classification schemes
42
Example-I Cluster 55

• Here, cluster 55 recovers a set of protein
  interactions (inset) that are involved in vaculor
  transport and fusion from ER via pre- vacuolar
  compartment.

43
Examples-II clusters 32 and 86

• Recovery of signal transduction pathway
  controlling cell wall biogenesis, from the
  membrane protein (Fks1) to the trancription
  factors activated by this pathway (Swi4, Swi6 and
  Rlm1).Pathway was recovered as a set of two
  clusters connected by two proteins (Pkc1p and
  Smd3p), shows one-to-many relationship.

44
Network of functional modules

• This graph shows the connection between 40
  functional modules connected by shared proteins.

45
Conclusions

• This model can be used to predict poorly
  characterized proteins into their functional
  context according to their interacting partners
  within a module.
• The predictve power of this model allows us to
  examine the organization and coordination of
  multiple complex cellular processes and determine
  how they are organized into pathways.
• One-to-many relationship can be used for pathway
  discovery.

46
References

• On the structure of proteinprotein interaction
  Networks A. Thomas, R. Cannings, N.A.M. Monk, and
  C. Cannings. Biochemical Society Transactions
  (2003) Volume 31, part 6.
• The Yeast Protein Interaction Network Evolves
  Rapidly and Contains Few Redundant Duplicate
  Genes. Andreas Wagner Mol. Biol. Evol.
  18(7)12831292. 2001.
• Detection of Functional Modules From Protein
  Interaction Networks Jose B. Pereira-Leal,1
  Anton J. Enright,2 and Christos A. Ouzounis1
  PROTEINS Structure, Function, and Bioinformatics
  544957 (2004).