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1. Lecture WS 2005/06
Bioinformatics III 1
Bioinformatics III “Systems biology”
“Integrative cell biology”“Cellular networks”
“Computational cell biology”
Course will teach mathematical methods that are applied
from protein complexes to interaction networks
1. Lecture WS 2005/06
Bioinformatics III 2
Content
Week1 networks in biology: effects of different topologies
Week2 intro of protein complexes: exp. data
Week3 protein networks: computational analysis
Week4 protein networks: graphical layout (force minimization)
Week5 protein networks: quality check (Bayesian analysis)
Week6 protein networks: modularity
Week7 FFT protein-protein docking, fitting into EM maps, tomography
Week8 transcription, regulatory networks, motifs
Week9 integration of interactome and regulome (Lichtenberg)
Week10+11 metabolic networks: metabolic flux analysis, extreme pathways,
elementary modes, C13 method
Week12 mathematical modelling of signal transduction networks
Week13 integration of protein networks with metabolic pathways
Week14 exam
1. Lecture WS 2005/06
Bioinformatics III 3
Appetizer 1
Cell cycle proteins that are part
of complexes or other physical
interactions are shown within
the circle.
For the dynamic proteins, the
time of peak expression is
shown by the node color;
static proteins are represented
as white nodes.
Outside the circle, the dynamic
proteins without interactions
are positioned and colored
according to their peak time.
Lichtenberg et al. Science 307, 724 (2005)
1. Lecture WS 2005/06
Bioinformatics III 4
Appetizer 2
c, Standard statistics (global topological measures and local network motifs) describing network structures. These vary between endogenous and exogenous conditions; those that are high compared with other conditions are shaded. (Note, the graph for the static state displays only sections that are active in at least one condition, but the table provides statistics for the entire network including inactive regions.)
Luscombe, Babu, … Teichmann, Gerstein, Nature 431, 308 (2004)
a, Schematics and summary of properties for the endogenous and exogenous sub-networks.
b, Graphs of the static and condition-specific networks. Transcription factors and target genes are shown as nodes in the upper and lower sections of each graph respectively, and regulatory interactions are drawn as edges; they are coloured by the number of conditions in which they are active. Different conditions use distinct sections of the network.
1. Lecture WS 2005/06
Bioinformatics III 5
Appetizer 3
Klamt & Stelling Trends Biotech 21, 64 (2003)
A C P
B
D
A(ext) B(ext) C(ext)R1 R2 R3
R5
R4 R8
R9
R6
R7bR7f
3 EFMs are not systemically independent:EFM1 = EP4 + EP5EFM2 = EP3 + EP5EFM4 = EP2 + EP3
1. Lecture WS 2005/06
Bioinformatics III 6
Mathematical techniques covered
Mathematical graphs – classification of protein-protein interaction networks,
– algorithms on graphs
– regulatory networks
Fourier transformation – protein/protein-docking, pattern matching
Linear and convex algebra
– metabolic networks
Ordinary and stochastic differential equations
– kinetic modelling of signal transduction pathways
1. Lecture WS 2005/06
Bioinformatics III 7
Literature
lecture slides will be available prior to lectures
suggested reading: links will be put up on course website
http://gepard.bioinformatik.uni-saarland.de/teaching...
1. Lecture WS 2005/06
Bioinformatics III 8
assignments
10 - 12 weekly assignments planned
Homework assignments are handed out in the Thursday lectures and are
available on the course website on the same day.
Homework will include many programming assignments. You can program in
any popular programming language. We recommend powerful script languages
such as Phython or Perl that allow to solve problems efficiently.
Solutions need to be returned until Thursday of the following week 14.00
to Tihamer Geyer in room 1.09 Geb. 17.1, first floor, or handed in prior (!) to the
lecture starting at 14.15. 2 students may submit one joint solution.
Also possible: submit solution by e-mail as 1 printable PDF-file to
Tutorial: participation is recommended but not mandatory. Date: Tue 11-13 ?
Homeworks submitted on Thursdays will be discussed on the following Tuesday.
Each student needs to present his solution to one of the assignments on the
blackboard once in the tutorial session.
1. Lecture WS 2005/06
Bioinformatics III 9
Schein = successful written exam
The successful participation in the lecture course („Schein“) will be certified upon
successful completion of the written exam in February 2006.
Participation at the exam is open to those students who have received 50% of
credit points for the assignments and presented once during the tutorials.
Unless published otherwise on the course website until 3 weeks prior to exam,
the exam will be based on all material covered in the lectures and in the
assignments.
In case of illness please send E-mail to:
[email protected] and provide a medical certificate.
A „second and final chance“ exam will be offered in April 2006.
1. Lecture WS 2005/06
Bioinformatics III 10
tutor
Dr. Tihamer Geyer – assignments
Geb. 17.1, room 1.09
1. Lecture WS 2005/06
Bioinformatics III 11
Systems biology
Biological research in the 1900s followed a reductionist approach:
detect unusual phenotype isolate/purify 1 protein/gene, determine its
function
However, it is increasingly clear that discrete biological function can only rarely
be attributed to an individual molecule.
new task of understanding the structure and dynamics of the complex
intercellular web of interactions that contribute to the structure and function of
a living cell.
1. Lecture WS 2005/06
Bioinformatics III 12
Systems biology
Development of high-throughput data-collection techniques,
e.g. microarrays, protein chips, yeast two-hybrid screens
allow to simultaneously interrogate all cell components at any given time.
there exists various types of interaction webs/networks
- protein-protein interaction network
- metabolic network
- signalling network
- transcription/regulatory network ...
These networks are not independent but form „network of networks“.
1. Lecture WS 2005/06
Bioinformatics III 13
DOE initiative: Genomes to Lifea coordinated effort
slides borrowedfrom talk of
Marvin FrazierLife Sciences DivisionU.S. Dept of Energy
1. Lecture WS 2005/06
Bioinformatics III 14
Facility IProduction and Characterization of Proteins
Estimating Microbial Genome Capability
• Computational Analysis– Genome analysis of genes, proteins, and operons– Metabolic pathways analysis from reference data– Protein machines estimate from PM reference data
• Knowledge Captured– Initial annotation of genome– Initial perceptions of pathways and processes– Recognized machines, function, and homology– Novel proteins/machines (including
prioritization)– Production conditions and experience
1. Lecture WS 2005/06
Bioinformatics III 15
• Analysis and Modeling
– Mass spectrometry expression analysis
– Metabolic and regulatory pathway/ network analysis and modeling
• Knowledge Captured– Expression data and conditions– Novel pathways and processes– Functional inferences about novel
proteins/machines– Genome super annotation: regulation, function,
and processes (deep knowledge about cellular subsystems)
Facility II Whole Proteome Analysis
Modeling Proteome Expression, Regulation, and Pathways
1. Lecture WS 2005/06
Bioinformatics III 16
Facility III Characterization and Imaging of Molecular Machines
Exploring Molecular Machine Geometry and Dynamics
• Computational Analysis, Modeling and Simulation
– Image analysis/cryoelectron microscopy
– Protein interaction analysis/mass spec
– Machine geometry and docking modeling
– Machine biophysical dynamic simulation
• Knowledge Captured
– Machine composition, organization, geometry,
assembly and disassembly
– Component docking and dynamic simulations
of machines
1. Lecture WS 2005/06
Bioinformatics III 17
Facility IVAnalysis and Modeling of Cellular Systems
Simulating Cell and Community Dynamics
• Analysis, Modeling and Simulation
– Couple knowledge of pathways, networks, and
machines to generate an understanding of
cellular and multi-cellular systems
– Metabolism, regulation, and machine simulation
– Cell and multicell modeling and flux visualization
• Knowledge Captured
– Cell and community measurement data sets
– Protein machine assembly time-course data sets
– Dynamic models and simulations of cell processes
1. Lecture WS 2005/06
Bioinformatics III 18
“Genomes To Life” Computing Roadmap
Biological Complexity
ComparativeGenomics
Constraint-BasedFlexible Docking
Co
mp
uti
ng
an
d I
nfo
rmat
ion
In
fras
tru
ctu
re C
apab
ilit
ies
Constrained rigid
docking
Genome-scale protein threading
Community metabolic regulatory, signaling simulations
Molecular machine classical simulation
Protein machineInteractions
Cell, pathway, and network
simulation
Molecule-basedcell simulation
Current U.S. Computing
1. Lecture WS 2005/06
Bioinformatics III 19
Are biological networks special?
Albert-Laszlo Barabasi
Statistical physics:
Tries to finding universal scaling laws of systems,
e.g. how does the dynamics of a glass change
when you lower the temperature?
Phase-transition „critical slowing down“.
„Relaxtion times in spin-glasses or glasses are observed to
grow to such an extent at low temperatures that these systems
do not reach thermal equilibrium on experimentally accessible
time-scales. Properties of such systems are then often found to
depend on their history of preparation; such systems are said to
age.
Similar observations are made in coarsening dynamics at first
order phase transitions. Some properties of spin-glasses and
glasses must therefore be studied via dynamical approaches
which allow taking possible history dependence explicitly into
account.“
1. Lecture WS 2005/06
Bioinformatics III 20
A power law relationship between two scalar quantities x and y is any such that the
relationship can be written as
where a (the constant of proportionality) and k (the exponent of the power law) are
constants.
Power laws can be seen as a straight line on a log-log graph since, taking logs of
both sides, the above equation is equal to
which has the same form as the equation for a line
Power laws are observed in many fields, including physics, biology, geography,
sociology, economics, and war and terrorism. They are among the most frequent
scaling laws that describe the scaling invariance found in many natural phenomena.
www.wikipedia.org
Power laws
kaxy
axk
axy k
loglog
)log(log
cmxy
1. Lecture WS 2005/06
Bioinformatics III 21
First breakthrough: scale-free metabolic networks
(d) The degree distribution, P(k), of the metabolic network illustrates its scale-free topology.
(e) The scaling of the clustering coefficient C(k) with the degree k illustrates the hierarchical
architecture of metabolism.
(f) The flux distribution in the central metabolism of Escherichia coli follows a power law.
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
1. Lecture WS 2005/06
Bioinformatics III 22
Second breakthrough: Yeast protein interaction network:first example of a scale-free network
A map of protein–protein interactions in
Saccharomyces cerevisiae, which is
based on early yeast two-hybrid
measurements, illustrates that a few
highly connected nodes (which are also
known as hubs) hold the network
together.
The largest cluster, which contains
78% of all proteins, is shown.
The colour of a node indicates the
phenotypic effect of removing the
corresponding protein (red = lethal,
green = non-lethal, orange = slow
growth, yellow = unknown). Barabasi & Oltvai, Nature Rev Gen 5, 101 (2004)
1. Lecture WS 2005/06
Bioinformatics III 23
Degree
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
The most elementary characteristic of a node is its
degree (or connectivity), k, which tells us how
many links the node has to other nodes.
a In the undirected network, node A has k = 5.
b In networks in which each link has a selected
direction there is an incoming degree, kin, which
denotes the number of links that point to a node,
and an outgoing degree, kout, which denotes the
number of links that start from it.
E.g., node A in b has kin = 4 and kout = 1.
An undirected network with N nodes and L links is
characterized by an average degree <k> = 2L/N
(where <> denotes the average).
Why?
1. Lecture WS 2005/06
Bioinformatics III 24
Degree distribution
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
The degree distribution, P(k), gives the
probability that a selected node has exactly k
links.
P(k) is obtained by counting the number of nodes
N(k) with k = 1,2... links and dividing by the total
number of nodes N.
The degree distribution allows us to distinguish
between different classes of networks.
1. Lecture WS 2005/06
Bioinformatics III 25
Clustering coefficient
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
In many networks, if node A is connected to B, and B is
connected to C, then it is highly probable that A also has
a direct link to C. This phenomenon can be quantified
using the clustering coefficient
where nI is the number of links connecting the kI
neighbours of node I to each other.
In other words, CI gives the number of 'triangles' that go
through node I, whereas kI (kI -1)/2 is the total number of
triangles that could pass through node I, should all of
node I's neighbours be connected to each other.
12
kk
nC ll
1. Lecture WS 2005/06
Bioinformatics III 26
Clustering coefficient
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
For example, only one pair of node A's five neighbours in a are
linked together (B and C), which gives nA = 1 and CA = 2/20. By
contrast, none of node F's neighbours link to each other, giving
CF = 0. The average clustering coefficient, <C >, characterizes
the overall tendency of nodes to form clusters or groups.
An important measure of the network's structure is the function
C(k), which is defined as the average clustering coefficient of all
nodes with k links. For many real networks C(k) k-1, which is
an indication of a network's hierarchical character.
The average degree <k>, average path length <ℓ> and average
clustering coefficient <C> depend on the number of nodes and
links (N and L) in the network. By contrast, the P(k) and C(k )
functions are independent of the network's size and they
therefore capture a network's generic features, which allows
them to be used to classify various networks.
1. Lecture WS 2005/06
Bioinformatics III 27
Barabasi & Oltvai, Nature Rev Gen 5, 101 (2004)
Aa
The Erdös–Rényi (ER) model of a random network starts with N
nodes and connects each pair of nodes with probability p, which
creates a graph with approximately pN (N-1)/2 randomly placed
links.
Ab
The node degrees follow a Poisson distribution, where most
nodes have approximately the same number of links (close to
the average degree <k>). The tail (high k region) of the degree
distribution P(k ) decreases exponentially, which indicates that
nodes that significantly deviate from the average are extremely
rare.
Ac
The clustering coefficient is independent of a node's degree, so
C(k) appears as a horizontal line if plotted as a function of k.
The mean path length is proportional to the logarithm of the
network size, l log N, which indicates that it is characterized by
the small-world property.
Random networks
Why?
1. Lecture WS 2005/06
Bioinformatics III 28
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
Scale-free networks Scale-free networks are characterized by a power-law degree
distribution; the probability that a node has k links follows
P(k) ~ k- -, where is the degree exponent.
The probability that a node is highly connected is statistically
more significant than in a random graph, the network's properties
often being determined by a relatively small number of highly
connected nodes („hubs“, see blue nodes in Ba).
In the Barabási–Albert model of a scale-free network, at each
time point a node with M links is added to the network, it
connects to an already existing node I with probability I = kI/JkJ,
where kI is the degree of node I and J is the index denoting the
sum over network nodes. The network that is generated by this
growth process has a power-law degree distribution with = 3.
1. Lecture WS 2005/06
Bioinformatics III 29
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
Scale-free networks
(Bb) Power-law distributions are seen as a straight
line on a log–log plot.
(Bc) The network that is created by the Barabási–
Albert model does not have an inherent modularity,
so C(k) is independent of k.
Scale-free networks with degree exponents 2<
<3, a range that is observed in most biological and
non-biological networks, are ultra-small, with the
average path length following ℓ ~ log log N, which
is significantly shorter than log N that characterizes
random small-world networks.
1. Lecture WS 2005/06
Bioinformatics III 30
Importance of the degree exponent
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
The value of in P(k) k - determines many properties of the
system. The smaller the value of , the more important the role
of the hubs is in the network.
In general, the unusual properties of scale-free networks are
valid only for < 3.
For 2> >3 there is a hierarchy of hubs, with the most
connected hub being in contact with a small fraction of all
nodes.
For = 2 a hub-and-spoke network emerges, with the largest
hub being in contact with a large fraction of all nodes.
Here, the dispersion of the P(k) distribution, defined as 2 = <k2>
- <k>2, increases with the number of nodes (that is, diverges),
resulting in a series of unexpected features, such as a high
degree of robustness against accidental node failures.
For >3, the hubs are not relevant, most unusual features are
absent, and in many respects the scale-free network behaves
like a random one.
1. Lecture WS 2005/06
Bioinformatics III 31
Shortest path and mean path length
Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
The distance in networks is measured by the path length,
which tells us how many links we need to pass through to
travel between two nodes.
As there are many alternative paths between two nodes,
the shortest path — the path with the smallest number of
links between the selected nodes — has a special role.
In directed networks, the distance ℓAB from node A to node
B is often different from the distance ℓBA from B to A. E.g. in
b , ℓBA = 1, whereas ℓAB = 3.
Often there is no direct path between two nodes. As shown
in b, although there is a path from C to A, there is no path
from A to C. The mean path length, <ℓ>, represents the
average over the shortest paths between all pairs of nodes
and offers a measure of a network's overall navigability.
1. Lecture WS 2005/06
Bioinformatics III 32
First breakthrough: scale-free metabolic networks
(d) The degree distribution, P(k), of the metabolic network illustrates its scale-free topology.
(e) The scaling of the clustering coefficient C(k) with the degree k illustrates the hierarchical
architecture of metabolism (The data shown in d and e represent an average over 43
organisms).
(f) The flux distribution in the central metabolism of Escherichia coli follows a power law,
which indicates that most reactions have small metabolic flux, whereas a few reactions, with
high fluxes, carry most of the metabolic activity. It should be noted that on all three plots the
axis is logarithmic and a straight line on such log–log plots indicates a power-law scaling.
CTP, cytidine triphosphate; GLC, aldo-hexose glucose; UDP, uridine diphosphate; UMP,
uridine monophosphate; UTP, uridine triphosphate.Barabasi & Oltvai, Nature Reviews Genetics 5, 101 (2004)
1. Lecture WS 2005/06
Bioinformatics III 33
Second breakthrough: Yeast protein interaction network:first example of a scale-free network
A map of protein–protein interactions in
Saccharomyces cerevisiae, which is
based on early yeast two-hybrid
measurements, illustrates that a few
highly connected nodes (which are also
known as hubs) hold the network
together.
The largest cluster, which contains
78% of all proteins, is shown. The colour
of a node indicates the phenotypic effect
of removing the corresponding protein
(red = lethal, green = non-lethal, orange
= slow growth, yellow = unknown).
Barabasi & Oltvai, Nature Rev Gen 5, 101 (2004)
1. Lecture WS 2005/06
Bioinformatics III 34
Summary Many cellular networks show properties of scale-free networks
- protein-protein interaction networks
- metabolic networks
- genetic regulatory networks (where nodes are individual genes and links are
derived from expression correlation e.g. by microarray data)
- protein domain networks
However, not all cellular networks are scale-free.
E.g. the transcription regulatory networks of S. cerevisae and E.coli are examples
of mixed scale-free and exponential characteristics.
It is a topic of ongoing debate whether the analysis of subnetworks (available data
is sparse) allows conclusions on the underlying topology of the entire network.
Next lecture:
- mathematical properties of networks
- origin of scale-free topology
- topological robustnessBarabasi & Oltvai, Nature Rev Gen 5, 101 (2004)