Introduction to Bioinformatics

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Introduction to Bioinformatics
Lecture 20 Global network behaviour
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Networks
"The thousands of components of a living cell are
dynamically interconnected, so that the cells
functional properties are ultimately encoded into
a complex intracellular web network of
molecular interactions." "This is perhaps most
evident with cellular metabolism, a fully
connected biochemical network in which hundreds
of metabolic substrates are densely integrated
through biochemical reactions." (Ravasz E, et
al.)
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TF
Ribosomal proteins
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(4-
1/(4 (4-1)/2) 1/6
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Small-world networks
A seminal paper, Collective dynamics of
"small-world" networks, by Duncan J. Watts and
Steven H. Strogatz, which appeared in Nature
volume 393, pp. 440-442 (4 June 1998), has
attracted considerable attention. One can
consider two extremes of networks The first are
regular networks, where "nearby" nodes have large
numbers of interconnections, but "distant" nodes
have few. The second are random networks, where
the nodes are connected at random. Regular
networks are highly clustered, i.e., there is a
high density of connections between nearby nodes,
but have long path lengths, i.e., to go from one
distant node to another one must pass through
many intermediate nodes. Random networks are
highly un-clustered but have short path lengths.
This is because the randomness makes it less
likely that nearby nodes will have lots of
connections, but introduces more links that
connect one part of the network to another.
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Regular and random networks
random
regular
regular complete
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Regular, small-world and random
networksRewiring experiments (Watts and
Strogatz, 1998)
p is the probability that a randomly chosen
connection will be randomly redirected elsewhere
(i.e., p0 means nothing is changed, leaving the
network regular p1 means every connection is
changed and randomly reconnected, yielding
complete randomness). For example, for p  .01,
(so that only 1 of the edges in the graph have
been randomly changed), the "clustering
coefficient" is over 95 of what it would be for
a regular graph, but the "characteristic path
length" is less than 20 of what it would be for
a regular graph.
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Small-world and networks
A small-world network can be generated from a
regular one by randomly disconnecting a few
points and randomly reconnecting them elsewhere.
Another way to think of a small world network
is that some so-called 'shortcut' links are added
to a regular network as shown here
The added links are shortcuts because they allow
travel from node (a) to node (b), to occur in
only 3 steps, instead of 5 without the shortcuts.
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Small-world networks

• Network characterisation
• L characteristic path length
• C clustering coefficient
• A small-world network is much more highly
  clustered than an equally sparse random graph (C
  gtgt Crandom), and its characteristic path length L
  is close to the theoretical minimum shown by a
  random graph (L Lrandom).
• The reason a graph can have small L despite being
  highly clustered is that a few nodes connecting
  distant clusters are sufficient to lower L.
• Because C changes little as small-worldliness
  develops, it follows that small-worldliness is a
  global graph property that cannot be found by
  studying local graph properties.

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Small-world networks

A network or order (0ltplt1 as in earlier slides)
can be characterized by the average shortest
length L(p) between any two points, and a
clustering coefficient C(p) that measures the
cliquishness of a typical neighbourhood (a local
property).

These can be calculated from mathematical
simulations and yield the following behavior
(Watts and Strogatz)


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Small-world networks
Part of the reason for the interest in the
results of Watts and Strogatz is that small-world
networks seem to be good models for a wide
variety of physical situations. They showed that
the power grid for the western U.S. (nodes are
power stations, and there is an edge joining two
nodes if the power stations are joined by
high-voltage transmission lines), the neural
network of a nematode worm (nodes are neurons and
there is an edge joining two nodes if the neurons
are joined by a synapse or gap junction), and the
Internet Movie Database (nodes are actors and
there is an edge joining two nodes if the actors
have appeared in the same movie) all have the
characteristics (high clustering coefficient but
low characteristic path length) of small-world
networks. Intuitively, one can see why
small-world networks might provide a good model
for a number of situations. For example, people
tend to form tight clusters of friends and
colleagues (a regular network), but then one
person might move from New York to Los Angeles,
say, introducing a random edge. The results of
Watts and Strogatz then provide an explanation
for the empirically observed phenomenon that
there often seem to be surprisingly short
connections between unrelated people (e.g., you
meet a complete stranger on an airplane and soon
discover that your sister's best friend went to
college with his boss's wife).  
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Small world example metabolism.

• Wagner and Fell (2001) modeled the known
  reactions of 287 substrates that represent the
  central routes of energy metabolism and
  small-molecule building block synthesis in E.
  coli. This included metabolic sub-pathways such
  as
• glycolysis
• pentose phosphate and Entner-Doudoro pathways
• glycogen metabolism
• acetate production
• glyoxalate and anaplerotic reactions
• tricarboxylic acid cycle
• oxidative phosphorylation
• amino acid and polyamine biosynthesis
• nucleotide and nucleoside biosynthesis
• folate synthesis and 1-carbon metabolism
• glycerol 3-phosphate and membrane lipids
• riboflavin
• coenzyme A
• NAD(P)
• porphyrins, haem and sirohaem
• lipopolysaccharides and murein
• pyrophosphate metabolism

• These sub-pathways form a network because some
  compounds are part of more than one pathway and
  because most of them include common components
  such as ATP and NADP.
• The graphs on the left show that considering
  either reactants or substrates, the clustering
  coefficient CgtgtCrandom, and the length
  coefficient L is near that of Lrandom,
  characteristics of a small world system.

random
Wagner A, Fell D (2001) The small world inside
large metabolic networks. Proc. R. Soc. London
Ser. B 268, 1803-1810.
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Scale-free Networks
Using a Web crawler, physicist Albert-Laszlo
Barabasi and his colleagues at the University of
Notre Dame in Indiana in 1998 mapped the
connectedness of the Web. They were surprised to
find that the structure of the Web didn't conform
to the then-accepted model of random
connectivity. Instead, their experiment yielded a
connectivity map that they christened
"scale-free."

• Often small-world networks are also scale-free.
• In a scale-free network the characteristic
  clustering is maintained even as the networks
  themselves grow arbitrarily large.

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Scale-free Networks

• In any real network some nodes are more highly
  connected than others.
• P(k) is the proportion of nodes that have
  k-links.
• For large, random graphs only a few nodes have a
  very small k and only very few have a very large
  k, leading to a bell-shaped Poisson distribution
  

Scale-free networks fall off more slowly and are
more highly skewed than random ones due to the
combination of small-world local highly connected
neighborhoods and more 'shortcuts' than would be
expected by chance.
Scale-free networks are governed by a power law
of the form P(k) k-?
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Scale-free Networks
Because of the P(k) k-? power law relationship,
a log-log plot of P(k) versus k gives a straight
line of slope -?         
Some networks, especially small-world networks of
modest size do not follow a power law, but are
exponential. This point can be significant when
trying to understand the rules that underlie the
network.
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Comparing Random and Scale-Free DistributionIn
the random network (right), the five nodes with
the most links (in red) are connected to only 27
of all nodes (green). In the scale-free network
(left), the five most connected nodes (red),
often called hubs, are connected to 60 of all
nodes (green).
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Scale-free Networks
Before discovering scale-free networks, Barabasi
and his team had been doing work that modeled
surfaces in terms of fractals, which are also
scale-free. Their discoveries about networks
have been found to have implications well beyond
the Internet the notion of scale-free networks
has turned the study of a number of fields upside
down. Scale-free networks have been used to
explain behaviors as diverse as those of power
grids, the stock market and cancerous cells, as
well as the dispersal of sexually transmitted
diseases.
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Scale-free Networks
Put simply, the nodes of a scale-free network
aren't randomly or evenly connected. Scale-free
networks include many "very connected" nodes,
hubs of connectivity that shape the way the
network operates. The ratio of very connected
nodes to the number of nodes in the rest of the
network remains constant as the network changes
in size. In contrast, random connectivity
distributionsthe kinds of models used to study
networks like the Internet before Barabasi and
his team made their observationpredicted that
there would be no well-connected nodes, or that
there would be so few that they would be
statistically insignificant. Although not all
nodes in that kind of network would be connected
to the same degree, most would have a number of
connections hovering around a small, average
value. Also, as a randomly distributed network
grows, the relative number of very connected
nodes decreases.
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Scale-free Networks
The ramifications of this difference between the
two types of networks are significant, but it's
worth pointing out that both scale-free and
randomly distributed networks can be what are
called "small world" networks. That means it
doesn't take many hops to get from one node to
anotherthe science behind the notion that there
are only six degrees of separation between any
two people in the world. So, in both scale-free
and randomly distributed networks, with or
without very connected nodes, it may not take
many hops for a node to make a connection with
another node. There's a good chance, though, that
in a scale-free network, many transactions would
be funneled through one of the well-connected hub
nodes - one like Yahoos or Googles Web portal.
Because of these differences, the two types of
networks behave differently as they break down.
The connectedness of a randomly distributed
network decays steadily as nodes fail, slowly
breaking into smaller, separate domains that are
unable to communicate.
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Scale-free Networks
Resists Random Failure Scale-free networks, on
the other hand, may show almost no degradation as
random nodes fail. With their very connected
nodes, which are statistically unlikely to fail
under random conditions, connectivity in the
network is maintained. It takes quite a lot of
random failure before the hubs are wiped out, and
only then does the network stop working. (Of
course, there's always the possibility that the
very connected nodes would be the first to go.)
In a targeted attack, in which failures aren't
random but are the result of mischief, or worse,
directed at hubs, the scale-free network fails
catastrophically. Take out the very connected
nodes, and the whole network stops functioning.
In these days of concern about cyber attacks on
the critical infrastructure, whether the nodes on
the network in question are randomly distributed
or are scale-free makes a big difference. With
scale-free networks, targeted attacks can be
resisted by implementing extra protective
measures for the hubs.
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Scale-free Networks
Epidemiologists are also pondering the
significance of scale-free connectivity. Until
now, it has been accepted that stopping sexually
transmitted diseases requires reaching or
immunizing a large proportion of the population
most contacts will be safe, and the disease will
no longer spread. But if societies of people
include the very connected individuals of
scale-free networksindividuals who have sex
lives that are quantitatively different from
those of their peersthen health offensives will
fail unless they target these individuals. These
individuals will propagate the disease no matter
how many of their more subdued neighbors are
immunized. Now consider the following
Geographic connectivity of Internet nodes is
scale-free, the number of links on Web pages is
scale-free, Web users belong to interest groups
that are connected in a scale-free way, and
e-mails propagate in a scale-free way. Barabasi's
model of the Internet tells us that stopping a
computer virus from spreading requires that we
focus on protecting the hubs.
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Scale Free Network Hubs, highly connected
nodes, bring together different parts of the
network Rubustness Removing random nodes have
little effect Low attack resistance Removing a
hub is lethal. Random Network No hubs Low
robustness Low attack resistance
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connect preferentially to a hub
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Robustness of the biodegradation network against
perturbations is tested here by removing 200
edges randomly (simulating each time that the
enzyme catalysing the reaction step has
mutated) (A) For each connection lost (red line),
1.6 compounds lose their pathway to the Central
Metabolism (CM). (B) However, the increase in
the average pathway length to the CM for the
remaining compounds is small
The biodegradation network appears to be less
tolerant to perturbations than metabolic networks
(Jeong et al., 2000)
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Preferential attachment in biodegradation networks
New degradable compounds are observed to attach
prefentially to hubs close to (or in) the Central
Metabolism
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Protein Function Prediction

• How can we get the edges (connections) of the
  cellular networks?
• We can predict functions of genes or proteins so
  we know where they would fit in a metabolic
  network
• There are also techniques to predict whether two
  proteins interact, either functionally (e.g. they
  are involved in a two-step metabolic process) or
  directly physically (e.g. are together in a
  protein complex)

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Protein Function Prediction
The state of the art its not complete Many
genes are not annotated, and many more are
partially or erroneously annotated. Given a
genome which is partially annotated at best, how
do we fill in the blanks? Of each sequenced
genome, 20-50 of the functions of proteins
encoded by the genomes remains unknown! How then
do we build a reasonably complete networks when
the parts list is so incomplete?
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Protein Function Prediction
For all these reasons, improving automated
protein function prediction is now a cornerstone
of bioinformatics and computational biology New
methods will need to integrate signals coming
from sequence, expression, interaction and
structural data, etc.
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Classes of function prediction methods (Recap)

• Sequence based approaches
• protein A has function X, and protein B is a
  homolog (ortholog) of protein A Hence B has
  function X
• Structure-based approaches
• protein A has structure X, and X has so-so
  structural features Hence As function sites are
  .
• Motif-based approaches
• a group of genes have function X and they all
  have motif Y protein A has motif Y Hence
  protein As function might be related to X
• Function prediction based on guilt-by-association
  
• gene A has function X and gene B is often
  associated with gene A, B might have function
  related to X

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Phylogenetic profile analysis (recap)

• Function prediction of genes based on
  guilt-by-association a non-homologous
  approach
• The phylogenetic profile of a protein is a string
  that encodes the presence or absence of the
  protein in every sequenced genome
• Because proteins that participate in a common
  structural complex or metabolic pathway are
  likely to co-evolve, the phylogenetic profiles of
  such proteins are often similar'
• This means that such proteins have a good chance
  of being physically or metabolically connected

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Phylogenetic profile analysis (Recap)

• Phylogenetic profile (against N genomes)
• For each gene X in a target genome (e.g., E
  coli), build a phylogenetic profile as follows
• If gene X has a homolog in genome i, the ith bit
  of Xs phylogenetic profile is 1 otherwise it
  is 0

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Phylogenetic profile analysis (recap)

• Example phylogenetic profiles based on 60
  genomes

genome
gene
orf1034111011011001011111010001010000000011110001
1111110110111010101 orf10361011110001000001010000
010010000000010111101110011011010000101 orf103711
01100110000001110010000111111001101111101011101111
000010100 orf103811101001100100101100100111000001
01110101101111111111110000101 orf1039111111111111
1111111111111111111111111111101111111111111111101
orf104 10001010000000000000001010000000001100000
00000000100101000100 orf1040111011111111110111110
1111100000111111100111111110110111111101 orf10411
11111111111111111011111111111110111111110111111111
1111111101 orf10421110100101010010010110000100001
001111110111110101101100010101 orf104311101001100
10000010100111100100001111110101111011101000010101
orf104411111001111100100101110101111110011111111
11111101101100010101 orf1045111111011011001111111
1111111111101111111101111111111110010101 orf10460
10110000001000101100000011111000001010000000101001
0100000000 orf10470000000000000001000010000001000
100000000000000010000000000000 orf105
01101101101000101111011010101110011011001011111000
10000010001 orf1054010010011000000110000100010000
0000100100100001000100100000000
By correlating the rows (open reading frames
(ORF) or genes) you find out about joint presence
or absence of genes this is a signal for a
functional connection
Genes with similar phylogenetic profiles have
related functions or functionally linked D
Eisenberg and colleagues (1999)
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Phylogenetic profile analysis (recap)

• Phylogenetic profiles contain great amount of
  functional information
• Phlylogenetic profile analysis can be used to
  distinguish orthologous genes from paralogous
  genes
• Subcellular localization 361 yeast
  nucleus-encoded mitochondrial proteins are
  identified at 50 accuracy with 58 coverage
  through phylogenetic profile analysis
• Functional complementarity By examining inverse
  phylogenetic profiles, one can find functionally
  complementary genes that have evolved through one
  of several mechanisms of convergent evolution.

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Prediction of protein-protein interactions
(recap)Rosetta stone method

• Gene fusion is the an effective method for
  prediction of protein-protein interactions
• If proteins A and B are homologous to two domains
  of a protein C, A and B are predicted to have
  interaction

A
B
C
Though gene-fusion has low prediction coverage,
it false-positive rate is low (high specificity)
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Protein interaction database (recap)

• There are numerous databases of protein-protein
  interactions
• DIP is a popular protein-protein interaction
  database

The DIP database catalogs experimentally
determined interactions between proteins. It
combines information from a variety of sources to
create a single, consistent set of
protein-protein interactions.
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Protein interaction databases (Recap)

• BIND - Biomolecular Interaction Network Database
• DIP - Database of Interacting Proteins
• PIM Hybrigenics
• PathCalling Yeast Interaction Database
• MINT - a Molecular Interactions Database
• GRID - The General Repository for Interaction
  Datasets
• InterPreTS - protein interaction prediction
  through tertiary structure
• STRING - predicted functional associations among
  genes/proteins
• Mammalian protein-protein interaction database
  (PPI)
• InterDom - database of putative interacting
  protein domains
• FusionDB - database of bacterial and archaeal
  gene fusion events
• IntAct Project
• The Human Protein Interaction Database (HPID)
• ADVICE - Automated Detection and Validation of
  Interaction by Co-evolution
• InterWeaver - protein interaction reports with
  online evidence
• PathBLAST - alignment of protein interaction
  networks
• ClusPro - a fully automated algorithm for
  protein-protein docking
• HPRD - Human Protein Reference Database

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Protein interaction database (recap)
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Recap
Network of protein interactions and predicted
functional links involving silencing information
regulator (SIR) proteins. Filled circles
represent proteins of known function open
circles represent proteins of unknown function,
represented only by their Saccharomyces genome
sequence numbers ( http//genome-www.stanford.edu/
Saccharomyces). Solid lines show experimentally
determined interactions, as summarized in the
Database of Interacting Proteins19
(http//dip.doe-mbi.ucla.edu). Dashed lines show
functional links predicted by the Rosetta Stone
method12. Dotted lines show functional links
predicted by phylogenetic profiles16. Some
predicted links are omitted for clarity.
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Recap
Network of predicted functional linkages
involving the yeast prion protein20 Sup35. The
dashed line shows the only experimentally
determined interaction. The other functional
links were calculated from genome and expression
data11 by a combination of methods, including
phylogenetic profiles, Rosetta stone linkages and
mRNA expression. Linkages predicted by more than
one method, and hence particularly reliable, are
shown by heavy lines. Adapted from ref. 11.  
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STRING - predicted functional associations among
genes/proteins
Recap

• STRING is a database of predicted functional
  associations among genes/proteins.
• Genes of similar function tend to be maintained
  in close neighborhood, tend to be present or
  absent together, i.e. to have the same
  phylogenetic occurrence, and can sometimes be
  found fused into a single gene encoding a
  combined polypeptide.
• STRING integrates this information from as many
  genomes as possible to predict functional links
  between proteins.

Berend Snel en Martijn Huynen (RUN) and the group
of Peer Bork (EMBL, Heidelberg)
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STRING - predicted functional associations among
genes/proteins
Recap

• STRING is a database of known and predicted
  protein-protein interactions.The interactions
  include direct (physical) and indirect
  (functional) associations they are derived from
  four sources
• Genomic Context (Synteny)
• High-throughput Experiments 
• (Conserved) Co-expression 
• Previous Knowledge
• STRING quantitatively integrates interaction
  data from these sources for a large number of
  organisms, and transfers information between
  these organisms where applicable. The database
  currently contains 736429 proteins in 179 species

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STRING - predicted functional associations among
genes/proteins
Recap
Conserved Neighborhood This view shows
runs of genes that occur repeatedly in close
neighborhood in (prokaryotic) genomes. Genes
located together in a run are linked with a black
line (maximum allowed intergenic distance is 300
bp). Note that if there are multiple runs for a
given species, these are separated by white
space. If there are other genes in the run that
are below the current score threshold, they are
drawn as small white triangles. Gene fusion
occurences are also drawn, but only if they are
present in a run.
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Wrapping up this and last lecture

• Know the graph definitions
• Understand graph-based clustering e.g. know
  Prims algorithm for MST and derived clustering
  protocol
• Know the Stable Marriage algorithm for mapping
  two different networks (graphs)
• Understand regular, random, small-world and
  scale-free networks
• Read the paper on biodegradation networks by
  Pazos et al. (2003) follow link on course
  website
• Comparing and overlaying various networks (e.g.
  regulation, signalling, metabolic, PPI) and
  studying conservation at these network levels is
  one of the current grand challenges, and will be
  crucially important for a systemsbased approach
  to (intra)cellular behaviour.