Diapositiva 1 - unibo.itStart with affinity purification of a single epitope-tagged protein This...

......OMICS

..OMICS..

Today, people talk about:

Genomics

Variomics

Transcriptomics

Proteomics

Interactomics

Regulomics

Metabolomics

Many more at:

http://www.genomicglossaries.com/content/omes.asp

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OMICS AND

HIGH-THROUGHPUT METHODS

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WHICH EXPERIMENTAL METHODS ARE

SUITABLE FOR: Genomics?

NGS sequencing, DNA Microarrays

Variomics?

Transcriptomics?

Proteomics?

2D gels, Protein arrays, Mass Spectrometry, Isotope tag

Protein-protein Interactomics?

Yeast 2-hybrid, affìnity purification + Mass Spec

Protein-DNA Interactomics?

Chromatine immunoprecipitation on chip, ChIP-Seq

Metabolomics?

Mass Spec, NMR

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WHICH ARE THE PROS AND CONS OF THE

ALTERNATIVE METHODS?

TO WHICH LEVEL DO THE DIFFERENT

METHODS AGREE?

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INTERACTOMICS: FINDING THE

INTERACTING PROTEINS

Yeast two hybrids

CHARACTERIZATION OF PHYSICAL

INTERACTIONS

Obligation

obligate (protomers only found/function together)

non-obligate (protomers can exist/function alone)

Time of interaction

permanent (complexes, often obligate)

strong transient (require trigger, e.g. G proteins)

weak transient (dynamic equilibrium)

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EXAMPLES: GPCR

obligate, permanent

non-obligate,

strong transient

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APPROACHES BY INTERACTION TYPE

Physical Interactions

Yeast two hybrid screens

Affinity purification (mass spec)

Other measures of ‘association’

Genetic interactions (double deletion mutants)

Genomic context (STRING)

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YEAST TWO-HYBRID METHOD

Y2H assays interactions in vivo.

Uses property that transcription

factors generally have separable

transcriptional activation (AD) and

DNA binding (DBD) domains.

A functional transcription factor can

be created if a separately expressed

AD can be made to interact with a

A protein ‘bait’ B is fused to a DBD

and screened against a library of

protein “preys”, each fused to a AD.

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YEAST TWO-HYBRID METHOD

Ito et al., Trends Biotechnol. 19, S23 (2001)

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The Protein Interaction Network of Yeast

Uetz et al, Nature 2000

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The Protein Interaction Network of Drosophila

Giot et al, Science 2003

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ISSUES WITH Y2H

Strengths High sensitivity (transient & permanent PPIs)

Takes place in vivo

Independent of endogenous expression

Weaknesses: False positive interactions Auto-activation

‘sticky’ prey

Detects “possible interactions” that may not take place under real physiological conditions

May identify indirect interactions (A-C-B)

Weaknesses: False negatives interactions Similar studies often reveal very different sets of interacting proteins (i.e.

False negatives)

May miss PPIs that require other factors to be present (e.g. ligands, proteins, PTMs)

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DIFFERENT Y2H EXPERIMENTS GIVE

DIFFERENT RESULTS….

Deane et al, Mol Cell Proteomics 1:349 (2002)

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DIFFERENT Y2H EXPERIMENTS GIVE

DIFFERENT RESULTS….

Deane et al, Mol Cell Proteomics 1:349 (2002)

A Venn diagram illustrates the overlap between the datasets in YEAST-DIP.

Each oval represents a high throughput Y2H study, and the overlaps

between the Y2H studies are given at the intersections. The number in

parentheses represents those interactions that have been determined by

small scale methods (see "Experimental Procedures" for more details).

Thus, the numbers within parentheses represent the INT set. Notice the

small overlap among the datasets.

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Y2H FOR MEMBRANE PROTEINS

Fields, FEBS Journal 272, 5391 (2005)

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EXERCISE: Y2H

Draw the correspondent graph

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Mass spectrometry

PROTEIN INTERACTIONS BY IMMUNO-PRECIPITATION

FOLLOWED BY MASS SPECTROMETRY

Start with affinity purification of a single epitope-tagged

protein

This enriched sample typically has a low enough

complexity to be fractionated on a standard

polyacrylamide gel.

Individual bands can be excised from the gel and

identified with mass spectrometry.

logy -

PROTEIN INTERACTIONS BY IMMUNO-PRECIPITATION

FOLLOWED BY MASS SPECTROMETRY

Kumar & Snyder, Nature 415, 123 (2002)

TANDEM AFFINITY PURIFICATION

LA Huber Nature Reviews Molecular Cell Biology 4, 74-80 (2003)

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AFFINITY PURIFICATION

Strengths

• High specificity

• Well suited for detecting permanent or

strong transient interactions (complexes)

• Detects real, physiologically relevant

Weaknesses

• Less suited for detecting weaker

transient interactions (low sensitivity)

• May miss complexes not present under

the given experimental conditions (low

sensitivity)

• May identify indirect interactions (A-C-B)

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Franzot & Carugo, J Struct Funct Biol 4, 245 (2004)

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Titz et al, Exp Review Proteomics, 2004

Caveat: different experiments give different results P

rtelli-

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DIFFERENT INFORMATION HAVE TO BE

CROSSED TO LOWER THE ERROR RATE

The fraction of interactions in

which both partners have the

same protein

localization. Here, only proteins

clearly assigned to a single

category are considered

Von Mering, Nature,2002

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Genomic methods

Rost et al.Cellular Molecular Life Sciences, 2003, 60:2637-2650

http://cubic.bioc.columbia.edu/papers/2003_rev_func/paper.html

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REGULOMICS: FINDING THE

TRANSCRIPTION NETWORK

ChIP-chip: Chromatine ImmunoPrecipitation on chip

ChIPSeq: Chromatine ImmunoPrecipitation coupled to

CHIP-CHIP MEASUREMENT OF PROTEIN-

DNA INTERACTIONS

Simon et al., Cell 2001

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CHIP-CHIP MEASUREMENT OF PROTEIN-

DNA INTERACTIONS

Lee et al., Science 2002

CHIP-SEQ MEASUREMENT OF PROTEIN-

DNA INTERACTIONS

Szalkowski, A.M, and Schmid, C.D.(2010).

Rapid innovation in ChIP-seq peak-calling algorithms is

outdistancing banchmarking efforts.

Briefings in Bioinfomatics.

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MAPPING TRANSCRIPTION FACTOR BINDING

Harbison C., Gordon B., et al. Nature 2004

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PROMOTER ARCHITECTURES

Harbison C., Gordon B., et al. Nature 2004

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TRANCRIPTION NETWORKS

Babu et al., Curr. Opin. Struct. Biol. 14, 283 (2004)

REGULATION OF TRANSCRIPTION FACTORS

Lee et al., Science 298, 799 (2002)

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METABOLOMICS: FINDING

THE CORRELATIONS

AMONG METABOLITESChromatography-Mass spectroscopy, NMR

Separation methodsGas chromatography, especially when interfaced with mass spectrometry

(GC-MS), is one of the most widely used and powerful methods It offers very

high chromatographic resolution, but requires chemical derivatization for many

biomolecules: only volatile chemicals can be analysed without derivatization.

(Some modern instruments allow '2D' chromatography, using a short polar

column after the main analytical column, which increases the resolution still

further.) Some large and polar metabolites cannot be analysed by GC.

High performance liquid chromatography (HPLC). Compared to GC, HPLC

has lower chromatographic resolution, but it does have the advantage that a

much wider range of analytes can potentially be measured.

Capillary electrophoresis (CE). CE has a higher theoretical separation

efficiency than HPLC, and is suitable for use with a wider range of metabolite

classes than is GC. As for all electrophoretic techniques, it is most appropriate

for charged analytes.

Wikipedia: Metabolomics

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Detection methodsMass spectrometry (MS) is used to identify and to quantify metabolites after

separation by GC, HPLC (LC-MS), or CE. GC-MS is the most 'natural' combination of

the three, and was the first to be developed. In addition, mass spectral fingerprint

libraries exist or can be developed that allow identification of a metabolite according

to its fragmentation pattern. MS is both sensitive (although, particularly for HPLC-MS,

sensitivity is more of an issue as it is affected by the charge on the metabolite, and

can be subject to ion suppression artifacts) and can be very specific. There are also a

number of studies which use MS as a stand-alone technology: the sample is infused

directly into the mass spectrometer with no prior separation, and the MS serves to

both separate and to detect metabolites.

Nuclear magnetic resonance (NMR) spectroscopy. NMR is the only detection

technique which does not rely on separation of the analytes, and the sample can thus

be recovered for further analyses. All kinds of small molecule metabolites can be

measured simultaneously - in this sense, NMR is close to being a universal detector.

The main advantages of NMR are high analytical reproducibility and simplicity of

sample preparation. Practically, however, it is relatively insensitive compared to mass

spectrometry-based techniques.

Wikipedia: Metabolomics

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Weckwerth, Annu. Rev. Plant Biol. 54, 669 (2003)

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FINDING CORRELATION BETWEEN THE

METABOLITE CONTENT

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METABOLITE NETWORK

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IS THE CORRELATION

EVALUATION SUFFICIENT?

COLLECT THE MEASURES FOR VARIABLES

X AND Y

… …

Covariance:

1),cov(

Linear regression

If correlation is significant enough: X Y

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COLLECT THE MEASURES FOR VARIABLES

Y AND Z

… …

Covariance:

1),cov(

Linear regression

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If correlation is significant enough:

WHAT ABOUT THE X AND Z?

In general: 'cXaYaZ XZYZ

IF we suppose that Z depends on X ONLY indirectly,

via Y, aXZ=0 :

dXadXaacbXaacYaZ XZXYYZXYYZYZ ~''

So, Z and X have a regression with coefficient aXYaYZ

,cov,cov,cov~

ZYYXZXa

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WHAT ABOUT THE X AND Z?Y ZX

ZYYXZYYX

ZYYXZX

,,,cov,cov

,cov,cov,cov

X and Z have a correlation index equal to the

product of correlation indexes, even if there is not

direct relation between them.

Correlation is not sufficient to establish the direct

relation between the variables

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EXAMPLE

σ2X=4 , σ2

Y=3 , cov(X,Y) =2

σ2Y=3 , σ2

Z=6 , cov(Z,Y) =1.5

If X and Z are not directly dependent:

So the overall covariance matrix is:

5.12,cov,cov,cov

ZYYXZX

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EXAMPLE

Gaussian model:

COVxT 1

The inverse of the correlation matrix (called

precision matrix, K) is involved

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EXAMPLE

190.0095.00

095.0548.0250.0

0250.0375.01COVK

The element of the precision matrix corresponding

to the non directly related variable vanishes!

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“DIRECT LINKS” ARE RECOVERED FROM THE

PRECISION MATRIX

Given a set of sample describe by variables

X1 X2 X3 X4 … XN

Compute the Covariance Matrix

Compute the Precision Matrix (K) as the inverse of

the covariance matrix

The partial correlation indexes between pairs of

variables Xi Xj, with i≠j is

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PARTIAL CORRELATION COEFFICIENT

Formally, the partial correlation between X and Y

given a set of n controlling variables Z = {Z1, Z2, ...,

Zn}, written ρXY|Z, is the correlation between the

residuals RX and RY resulting from the linear

regression of X with Z and of Y with Z, respectively.

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APPLICATION IN METABOLOMICS ANALYSIS

In our new approach we propose the application of a Gaussian graphical model

(GGM), an undirected probabilistic graphical model estimating the conditional

dependence between variables. GGMs are based on partial correlation

coefficients, that is pairwise Pearson correlation coefficients conditioned against

the correlation with all other metabolites. We first demonstrate the general validity

of the method and its advantages over regular correlation networks with computer-

simulated reaction systems. Then we estimate a GGM on data from a large

human population cohort, covering 1020 fasting blood serum samples with

151 quantified metabolites. The GGM is much sparser than the correlation

network, shows a modular structure with respect to metabolite classes, and is

stable to the choice of samples in the data set. On the example of human fatty acid

metabolism, we demonstrate for the first time that high partial correlation

coefficients generally correspond to known metabolic reactions. This feature

is evaluated both manually by investigating specific pairs of high-scoring

metabolites, and then systematically on a literature-curated model of fatty acid

synthesis and degradation. Our method detects many known reactions along with

possibly novel pathway interactions, representing candidates for further

experimental examination.

Krumsiek et al. BMC Systems Biology 2011, 5:21

http://www.biomedcentral.com/1752-0509/5/21

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APPLICATION IN PROTEIN STRUCTURE

PREDICTION

Marks DS, Colwell LJ, Sheridan R, Hopf TA, Pagnani A, et al. (2011). PLoS

ONE 6(12): e28766. doi:10.1371/journal.pone.0028766

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PREDICTION

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PREDICTION

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PREDICTION

See also PSICOV:

Jones D, Buchan DWA, Cozzetto D, Pontil M, Bioinformatics 28:184-190 (2012)

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How to Describe a System As a Whole?

Networks - The Language of Complex Systems

Air Transportation Network Pie

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The World Wide Web Pie

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Fragment of a Social Network(Melburn, 2004)

Friendship among 450 people in Canberra

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Biological NetworksA. Intra-Cellular Networks

Protein interaction networks

Metabolic Networks

Signaling Networks

Gene Regulatory Networks

Composite networksNetworks of Modules, Functional Networks Disease networks

B. Inter-Cellular NetworksNeural Networks

C. Organ and Tissue Networks

D. Ecological Networks

E. Evolution Network

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The Protein Interaction Network of Yeast

Yeast two hybrid

Uetz et al., Nature 2000

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Source: ExPASy

Metabolic Networks Pie

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Gene Regulation Networks

Abdollahi A et al., PNAS 2007

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Networks derived from networks

Goh,..,Barabasi (2007) PNAS 104:8685

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Networks derived from networks

Goh,..,Barabasi (2007) PNAS 104:8685

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protein-gene

interactions

protein-protein

interactions

PROTEOME

GENOME

Citrate Cycle

METABOLISM

Bio-chemical

reactions

L-A Barabasi

regulation?-

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

What is a Network?

Network is a mathematical structure composed of points connected by lines

Network Theory <-> Graph Theory

Network Graph

Nodes Vertices (points)

Links Edges (Lines)

A network can be build for any functional system

System vs. Parts = Networks vs. Nodes

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The 7 bridges of Königsberg

The question is whether it is possible to walk with a route that crosses each bridge exactly once.

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The representation of Euler

The shape of a graph may be distorted inany way without changing the graph itself,so long as the links between nodes areunchanged. It does not matter whetherthe links are straight or curved, orwhether one node is to the left or right ofanother.

In 1736 Leonhard Euler formulated the problem in terms of abstracted the case of Königsberg:

1) by eliminating all features except the landmasses and the bridges connecting them;

2) by replacing each landmass with a dot (vertex) and each bridge with a line (edge).

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The solution depends on the node degree

In a continuous path crossing the edges exactly once, each visited node requires an edge for entering and a different edge for exiting (except for the start and the end nodes).

A path crossing once each edge is called Eulerian path.It possible IF AND ONLY IF there are exactly two or zero nodes of odd degree. Since the graph corresponding to Königsberg has four nodes of odd degree, it cannot have an Eulerian path.

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The solution depends on the node degree

If there are two nodes of odd degree, those must be the starting and ending points of an Eulerian path.

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Hamiltonian paths

Find a path visiting each node exactly one

Conditions of existence for Hamiltonian paths are not simple

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Hamiltonian pathsP

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Graph nomenclature

Graphs can be simple or multigraphs, depending on whetherthe interaction between two neighboring nodes is unique or can be multiple, respectively.

A node can have or not self loops

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Graph nomenclature

Networks can be undirected or directed, depending on whetherthe interaction between two neighboring nodes proceeds in bothdirections or in only one of them, respectively.

The specificity of network nodes and links can be quantitativelycharacterized by weights

7.3 3.3 12.7

Vertex-Weighted Edge-Weighted

1 2 3 4 5 6

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Networks having no cycles are termed trees. The more

cycles the network has, the more complex it is.

A network can be connected (presented by a single

component) or disconnected (presented by several disjoint

components).

connected disconnected

cyclic graphs

Graph nomenclatureP

rtelli-

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Cycles

Complete Graphs

Graph nomenclatureP

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Large graphs = NetworksP

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• Vertex degree distribution (the degree of a vertex is the number of vertices connected with it via an edge)

Statistical features of networksP

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• Clustering coefficient: the average proportion of neighbours of a vertex that are themselves neighbours

Statistical features of networks

Node4 Neighbours (N)

2 Connections among the Neighbours

6 possible connections among the Neighbours(Nx(N-1)/2)

Clustering for the node = 2/6

Clustering coefficient: Average over all the nodes

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• Clustering coefficient: the average proportion of neighbours of a vertex that are themselves neighbours

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Given a pair of nodes, compute the shortest path between them

• Average shortest distance between two vertices

• Diameter: maximal shortest distance

How many degrees of separation are they between two random people in the world, when friendship networks are considered?

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Wutchy, Ravasz, Barabasi. In: Complex Systems in Biomedicine, Kluwer 2003

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How to compute the shortest path between home and work?

Edge-weighted Graph

The exaustive search can be too much time-consuming

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The Dijkstra’s algorithm

Initialization:Fix the distance between “Casa” and “Casa”

equal to 0Compute the distance between “Casa” and its

neighboursSet the distance between “Casa” and its NON-

neighbours equal to ∞

Fixed nodesNON –fixed nodes

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Iteration (1):Search the node with the minimum distance

among the NON-fixed nodes and Fix its distance, memorizing the incoming direction

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Iteration (2):

Update the distance of NON-fixed nodes, starting from the fixed distances

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The updated distance is different from the previous one

Iteration:

Fix the NON-fixed nodes with minimum distance

Update the distance of NON-fixed nodes, starting from the fixed distances.

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Iteration:

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Iteration:

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Iteration:

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Iteration:

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Conclusion:

The label of each node represents the minimal distance from the starting node

The minimal path can be reconstructed with a back-tracing procedure

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• Average shortest distance between two vertices (L)

• Diameter: maximal shortest distance

• Vertex degree (k) distribution

• Clustering coefficient (C)

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Two reference models for networks

Regular network (lattice) Random network (Erdös+Renyi, 1959)

Each edge is randomly set with probability p

Regular connections

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Two reference models for networksComparing networks with the same total number of nodes (N) and edges (E)

Degree (k) distribution

Poisson distribution

Exp decay

Average shortest path

Average clustering

≈ N High ≈ log (N) Low

≈1.5 (s-1)/(2s-1) High

with s=E/N

≈2s/N Low

Some examples for real networks

Network size vertex degree

shortest path

Shortest path in fitted random graph

Clustering Clustering in random graph

Film actors 225,226 61 3.65 2.99 0.79 0.00027

MEDLINE coauthorship

1,520,251 18.1 4.6 4.91 0.43 1.8 x 10-4

E.Coli substrate graph

282 7.35 2.9 3.04 0.32 0.026

C.Elegans neuron network

282 14 2.65 2.25 0.28 0.05

Real networks are not regular (low shortest path)Real networks are not random (high clustering)

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Adding randomness in a regular network

Random changes in edges

Addition of random links

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Adding randomness in a regular network(rewiring)

Networks with high clustering (like regular ones) and low path length (like random ones) can be obtained:SMALL WORLD NETWORKS (Strogatz and Watts, 1999)

Small World Networks

A small amount of random shortcuts can decrease the path length, still maintaining a high clustering: this model “explains” the 6-degrees of separations in human friendship network

What about the degree distribution in real networks?

Both random and small world models predict an approximate Poisson distribution: most of the values are near the mean;Exponential decay when k gets higher: P(k) ≈ e-k, for large k.

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What about the degree distribution in real networks?

In 1999, modelling the WWW (pages: nodes; link: edges), Barabasi and Albert discover a slower than exponential decay:

P(k) ≈ k-a with 2 < a < 3, for large k

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Scale-free networks

Networks that are characterized by a power-law degree distribution are highly non-uniform: most of the nodes have only a few links. A few nodes with a very large number of links, which are often called hubs, hold these nodes together. Networks with a power degree distribution are called scale-free

It is the same distribution of wealth following Pareto’s 20-80 law:Few people (20%) possess most of the wealth (80%), most of the people (80%) possess the rest (20%)

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Attacks to hubs can rapidly destroy the network

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Three non biological scale-free networks

Albert and Barabasi, Science, 1999

Note the log-log scaleLINEAR PLOT

kAkPkAkP loglog)(log)(

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AttackTolerance

Complex systems maintain their basic functions

even under errors and failures

(cell mutations; Internet router breakdowns)

node failure

Albert and Barabasi, Rev Mod Phys, 2002

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Attack Tolerance

• Robust. For <3, removing

nodes does not break

network into islands.

• Very resistant to random

attacks, but attacks targeting

key nodes are more

dangerous. P

Length

Albert and Barabasi, Rev Mod Phys, 2002

Targeted

attackRandom

attack

Targeted

attackRandom

attack

Targeted

attackRandom

attack

Targeted

attackRandom

attack

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How can a scale-free network emerge?

Network growth models: start with one vertex.

Network growth models: new vertex attaches to existing vertices by preferential attachment: vertex tends choose vertex according to vertex degree

In economy this is called Matthew’s effect: The rich get richerThis explain the Pareto’s distribution of wealth

Network growth models: hubs emerge(in the WWW: new pages tend to link to existing, well linked pages)

Metabolic pathways are scale-free

Hubs are pyruvate, coenzyme A….

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Protein interaction networks are scale-free

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Albert R, J Cell Sci, 2005

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Degree is in some measure related to phenotypic effect upon gene knock-out

Red : lethalGreen: non lethalYellow: Unknown

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Proteins with ≤ 6 neighbours 21% are essential (lethality upon knock-out)

Proteins with ≥ 15 neighbours 62% are essential (lethality upon knock-out)

Are central proteins essential? Pie

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Titz et al, Exp Review Proteomics, 2004

Caveat: different experiments give different results P

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How can a scale-free interaction network emerge?

Gene duplication (and differentiation): duplicated genes give origin to a protein that interacts with the same proteins as the original protein (and then specializes its functions)

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Trancription networks

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The incoming connectivity is the number of transcription factors regulating a target gene, which quantifies the combinatorial effect of gene regulation.

The fraction of target genes with a given incoming connectivity decreases exponentially.

Most target genes are regulated by similar numbers of factors (93% of genes are regulated by 1–4 factors in yeast).

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The outgoing connectivity is the number of target genes regulated by each transcription factor.

It is distributed according to a power law.This is indicative of a hub-containing network structure, in which a select few transcription factors participate in the regulation of a disproportionately large number of target genes. These hubs can be viewed as ‘global regulators’, as opposed to the remaining transcription factors that can be considered ‘fine tuners’.

In the transcriptional network in yeast, regulatoryhubs have a propensity to be lethal if removed.

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These mechanisms alone cannot explain the evolution of network motifs and the scale-free topology.

Caveat on the use of the scale-free theory

The same noisy data can be fitted in different ways

Keller, BioEssays 2006

dzzfxF )()( has to be used: more discriminative

)1()( Cxxf

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Caveat on the use of the scale-free theory

Finding a scale-free behaviour do NOT imply the growth with preferential attachment mechanism

A sub-net of a non-free-scale network can have a scale-free behaviour

Keller, BioEssays 2006

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Hierarchical networks

Standard free scale models have low clustering: a modular hierarchical model accounts for high clustering, low average path and scale-freeness

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Hierarchical Modularity

Metabolic Networks Protein Networks

E. Ravasz et al., Science, 2002

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Hierarchical structures in directed networks

master regulators (nodes with zero in-degree),

workhorses (nodes with zero out-degree),

middle managers (nodes with nonzero in- and out-degree).

Yan & Gerstein, PNAS 2010

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Yan & Gerstein, PNAS 2010

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Bhardvaj, Yan, Gerstein PNAS 2010

Sc: Yeast

Hs: Homo

Rr: Rat

Mm: Mouse

Ec: E.coli

Mt: Mycobacteriun tubercolosis

Ph: Phosphorilation

Mo: Modification

Tr: Trancriptional regulation

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Bhardvaj, Yan, Gerstein, PNAS, 2010

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Sub-graphs more represented than expected

Motifs

209 bi-fan motifs found in the E.coli regulatory network

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Measures of centrality

Degree centrality is defined as the number of links incident upon a node

Betweenness is the ratio between the number of shortest paths passing through a given vertex over the number of shortest pairs.

Closeness is defined as the mean shortest path between a vertex v and all other vertices reachable from it.

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Measures of centrality

Which is the node with the highest degree centrality?Which is the node with the highest closeness?Which is the node with the highest betweenness?

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Del Rio et al.,

BMC Systems Biology 2009, 3:102

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Community structure

subsets of vertices within which vertex–vertex connections are dense,

but between which connections are less dense.

Girvan and Newman, PNAS, 2002

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Detecting communities

Betweenness can be computed also fo edges: ratio between the number of shortest paths passing through a given edge over the number of shortest pairs. bottleneck of the communication though the network

GIRVAN NEWMAN ALGORITHM

1. Calculate the betweenness for all edges in the network.2. Remove the edge with the highest betweenness.3. Recalculate betweennesses for all edges affected by theremoval.4. Repeat from step 2 until no edges remain.

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Girvan and Newman, PNAS, 2002

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Community clustering of protein-protein interaction networks

Dunn et al, BMC Bioinformatics, 2005

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Science 298, 2002

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Geometric structure for networks

Geometric random networks

Higham, et al , Bioinformatics, 2008

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Algorithm for embedding the

graph in a metric space

IS = ?

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YHC: Yeast

ER: Random

ER-DD: Random with the

same degree distribution

as YHC

GEO-3D: Geometric in

GEO-3D-10%: GEO-3D

with 10% noise

SF: Scale free

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Barabasi and Oltvai (2004) Network Biology: understanding the cell’s functional

organization. Nature Reviews Genetics 5:101-113

Stogatz (2001) Exploring complex networks. Nature 410:268-276

Hayes (2000) Graph theory in practice. American Scientist 88:9-13/104-109

Mason and Verwoerd (2006) Graph theory and networks in Biology

Keller (2005) Revisiting scale-free networks. BioEssays 27.10: 1060-1068

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