Transcript Protein-Protein Interaction Network

Protein-Protein Interaction
Network
Gautam Chaurasia
08.07.04
Overview
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Introduction.
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Three Different Models:
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Structure of the protein-protein interaction network.
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Evolutoin of the network.
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Non-power law.
Power Law Random Graphs.
Detection of functional modules from protein interaction
networks.
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Clustering algorithm
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Introduction
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The network is viewed as a graph whose nodes correspond to
proteins. Two proteins are connected by an edge if they interact.
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The collection of all interactions between the proteins of an
organism is called interactome.
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The Y2H system (yeast-two-hybrid) is used to yield a
comprehensive map of protein-protein interaction network.
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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.
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Structure of PPI Network
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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.
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Structure of PPI Network
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Degree:
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Described by the connectivity k of the node, which tells us how
many links the node has to other nodes.
Degree distribution:
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The degree distribution p(k), gives the probability that a selected
node has exactly k links.
P(k) is obtained by:
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ER Random Graph
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ER Random Graphs:
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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.
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Start with a given number of nodes and add links randomly.
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which creates a graph with approximately pN(N–1)/2 randomly
placed links.
The node degrees follow a Poisson distribution.
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Scale-Free Network
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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 γ > 0, so that a plot of log(degree) by log(frequency)
shows a decreasing linear trend.
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Model-I: Non-Power Law-I
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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.
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Model-I: Non-Power Law-II
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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:
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All the Xi are independent and identically distributed.
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Thus, the average number of sites per protein l = 2mp.
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Model-I: Non-Power Law-III
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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
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Model-I: Non-Power Law-IV
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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.
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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.
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Log-log plot of the distribution
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f(y) is plotted for n=6000 proteins, m=1000 domains and
λ = 1,2.
The resulting graph shows clear non-linearity.
Fig: Log–log 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
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Degree distribution of sampled subgraphs
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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.
Fig:The 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.
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Degree distribution of sampled subgraphs
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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.
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Conclusions
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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
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Example
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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 oRaf1, 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.
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Model-II
The Yeast Protein Interaction Network
Evolves Rapidly and Contains Few
Redundant Duplicate Genes.
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Evolution of Function
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Examples:
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Partially redundant duplicates
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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
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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.
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Objective
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Two main questions are addressed in this model are:
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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?
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Data for Analysis
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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).
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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 .
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Ks is the measure of the similarity between two genes.
Only those genes pairs were considered for further analysis whose
Ks < 5 cutoff.
There were such 9,059 pairs among ~6,000 genes with Ks < 5.
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Power Law Random Graphs-I
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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 > 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 > 0 , is a constant.
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Power Law Random Graphs-II
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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.
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Power Law Random Graphs-III
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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 node‘s
degree.
Nodes were connected as per the number of edges and this was
done untill the number of edges is S/2 = k.
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Interaction Network vs. Random Graph
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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.
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Duplications and Interactions
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This figure illustrate the effect of gene duplication on gene
products involved in protein interactions.
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Divergence of Interactions
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20% of duplicate gene pairs share an interaction partner with
0.5 < Ks < 1.0, whereas 80% of genes have no common
interaction partner with their duplicates approximately 100 Myr
after duplication.
Ks > 2 approaches the value expected for randomly chosen
gene pairs.
200-300 myr
The histogram of the
fraction of duplicates genes
whose products have at
least one interacting protein
in common as a function of
Ks.
Intercation turn over
every 200-300 Myr
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Divergence of Interactions
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Only 57% of the most closely related duplicate gene pairs
(0<Ks<.5) for which both genes interact with other proteins
share any protein interaction partner in the same subnet.
For 380 gene pairs with Ks > 0.5 the fraction of duplicate
partners with shared interaction is < 20%.
Ks > 1.5 is close to the random expected value.
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The Rate of Interaction Loss
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The divergence in protein interaction after gene
duplication is largely due to interaction loss.
127 pairs with KS < 2, where both duplicates engage
in protein-protein interaction network.
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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?
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interaction data noise leads to overestimates.
young pairs and double-losses lead to underestimates.
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Divergence of Self-interactions
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Loss or gain of interactions between a pair of paralogs
due to self-interaction.
Self-Interactions and
interactions between
products of duplicate
genes.
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Divergence of Self-interactions
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Total of 25 paralogs.
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Only few conserved self-interactions
was found.
New interactions
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13/25 new interactions at the rate of
2.88 x 10-6 /Myr per pair Ks = 1
corresponds to 100 Myr.
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Conclusions
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Protein-protein interaction network shows a power-law degree
distribution.
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Total 6280 ORF in yeast genome with 1.97 x 107 possible pairwise interactions.
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New interactions forming at slow rates/pair, and evolved at a rate
of 2.88x10-6 per protein pair per million year.
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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.
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Model-III- Cluster Analysis
Detection of Functional Modules from
Protein Interaction Networks of
S.cerevisiae.
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Cluster Analysis
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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.
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Clustering Algorithm
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The protein interaction data were obtained from DIP database.
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The network of proteins is first transformed into a weighted graph.
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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.
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Clustering Algorithm
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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.
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Clustering Algorithm
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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.
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Results
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Total of 1046 clusters were obtained.
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In this analysis, each protein was on average present in 2.1 clusters.
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Only 76 interactions and 146 proteins (represent only < 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.
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KEGG: regulatory and metabolic classifications (20%).
GQFC: Genequiz automatic functional classification (45%).
MIPS: Cellular localization (48%).
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Validation of the Clustering Method-I
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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).
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Validation of the Clustering Method-II
Fig.: Module validation using biological classification
schemes
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Validation of the Clustering Method-III
Fig.: Module validation using biological classification schemes
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Validation of the Clustering Method-IV
Fig.: Module validation using biological classification schemes
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Example-I Cluster 55
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Here, cluster 55 recovers
a set of protein interactions
(inset) that are involved in
vaculor transport and
fusion from ER via prevacuolar compartment.
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Examples-II clusters 32 and 86
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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.
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Network of functional modules
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This graph shows the connection between 40 functional
modules connected by shared proteins.
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Conclusions
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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.
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References
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On the structure of protein–protein 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):1283–1292. 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 54:49–57 (2004).
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