Topology of the protein network H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, (2001)

Erdös-Rényi model (1960) - Democratic - Random Pál Erdös Pál Erdös ( ) Connect with probability p p=1/6 N=10  k  ~ 1.5

Degree distribution of a random graph P(k): the probability that a node has k links P(k)= C k N-1 p k (1-p) N-1-k For large N P(k) can be replaced by a Poisson distribution: P(k)~ e - k /k! Poisson distribution

World Wide Web Over 3 billion documents ROBOT: collects all URL’s found in a document and follows them recursively Nodes: WWW documents Links: URL links R. Albert, H. Jeong, A-L Barabasi, Nature, (1999). WWW Expected P(k) ~ k -  Found Scale-free Network Exponential Network

Scale-free model Barabási & Albert, Science 286, 509 (1999) P(k) ~k -3 (1) Networks continuously expand by the addition of new nodes WWW : addition of new documents Citation : publication of new papers GROWTH: add a new node with m links PREFERENTIAL ATTACHMENT: the probability that a node connects to a node with k links is proportional to k. (2) New nodes prefer to link to highly connected nodes. WWW : linking to well known sites Citation : citing again highly cited papers

Other Models

Internet

Metabolic network Organisms from all three domains of life are scale-free networks! H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature, (2000) ArchaeaBacteriaEukaryotes

Many real world networks have a similar architecture: Scale-free networks WWW, Internet (routers and domains), electronic circuits, computer software, movie actors, coauthorship networks, sexual web, instant messaging, web, citations, phone calls, metabolic, protein interaction, protein domains, brain function web, linguistic networks, comic book characters, international trade, bank system, encryption trust net, energy landscapes, earthquakes, astrophysical network…

Copyright ©2002 American Society for Biochemistry and Molecular Biology Deane, C. M. (2002) Mol. Cell. Proteomics 1: Interacting yeast proteins as detected in several studies

L.Salwinski & D.Eisenberg. Curr.Op.Struct.Biol. 13 (2003)

J.S. Bader et al.. Nature Biotechnology 22 (2004)

Filtered Yeast Interactome dataset (Han et al., Nature 430, 2004) (HT-Y2H) projects (5,249 potential interactions - union of the available data sets) Co-IP (6,630 potential interactions from two datasets) in silico computational predictions of interactions (7,446 potential interactions from the 'von Mering' data set obtained from the union of gene co-occurrence, gene neighbourhood and gene fusion predictions) 'MIPS protein complexes' published singly in the literature (9,597 pairwise interactions between components of complexes MIPS physical interactions (excluding genome-scale experiments: 1,285 interactions).

J-D. Han et al. Nature 430 (2004)

UNIPROT DATABASE filtered by SEG UNIPROT DATABASE filtered by SEG VirusesBacteriaArchaeaAscomycotaMetazoaSpermatophyta

BLASTP S. Cerevisiae sequence as a query BACTERIA METAZOA VIRUSES ARCHAEA Top scoring sequences from each group  parwise SW homology check with 100 randomisations and Z-score cutoff

A-L. Barabasi & Z.N. Oltvai. Nature Reviews Genetics 5 (2004)

Archaea, Eubacteria, Fungi, Plants, Animals (33/26)  protein synthesis machinery (40S and 60S ribosomal subunits, translational factors, t-RNA synthetases  basic metabolism (e.g. ATP synthesis, Krebs cycle)  protein folding and degradation (chaperones, proteases)  domains participating in protein-protein interactions (TPR, WD40)  +Viruses (16/5)  replication (RNA polymerases, helicases, replication factor C, ribonucleotide reductase)  protein degradation (19S proteasome)

40S ribosome Mitochondrial ribosomal 40S subunit

S. Wuchty, Z.N. Oltvai & A-L. Barabasi. Nature Genetics 22 (2003)

Mitochondrial alpha-ketoglutarate dehydrogenase and pyruvate degydrogenase complexes Succinate dehydrogenase

General repressor of transcription Coatomer Nuclear pore Nuclear pore Anaphase-promoting complex (ubiquitin-protein ligase) Cyclophilin, heat shock protein (HSP82) and STI1 inhibitor

Eubacteria, Eukaryota |Archaea (4/4) Eubacteria, Eukaryota |Archaea (4/4)  catalytic core delta subunit of mitochondrial ATP-ase  tubulin (BtubA/B - Prosthecobacter  tubulin (BtubA/B - Prosthecobacter )  mitochondrial subunits of 60S ribosome  RNA-binding proteins (cleavage factor I)

Mitochondrial ribosomal proteins of the 60S subunit Central stalk of mitochondrial F1F0 ATP synthase Subunits of cleavage factor I (HRP1, RNA15), poly-A binding protein (PAB1, SGN1), uncharacterized protein YGR250C Alpha- and beta-tubulin

Archaea, Eukaryota | Eubacteria (8/8)  RNA polymerase II (non-catalytic subunits)  60S ribosomal subunits (cytoplasmatic)  splicing (archeal-like LSM proteins)  exosome 3’  5’ exoribonuclease complex  20S proteasome

Protein components of large 60S ribosome subunit Subunits of RNA polymerase II

Eukaryota | Archaea, Eubacteria, Viruses (24/19)  vesicle transport and membrane fusion (multicompartmental cell)  mitochondrial transporters  regulation of actin cytoskeleton stability

Actin cytoskeleton regulating complex Actin capping heterodimer Cofilin like protein and adenylyl cyclase-asssociated protein

Mitochondrial inner membrane ATP/ADP translocator and mitochondrial inner membrane transporters (TIM22, TIM9, MRS1) Mitochondrial transport system

M.C. Rivera & J.A.Lake Nature 431 (2004)

M.C. Rivera & J.A.Lake Nature 431 (2004) M.C. Rivera & J.A.Lake Nature 431 (2004)

M.C. Rivera & J.A. Lake Nature 431 (2004)

L.Giot et al. Science. 2003, 302 (2003)

Subunits of 26 S proteasome comlex

Trehalose-6-phosphate complex

PL GPL+EC The number of S. cerevisiae proteins The node degree

Linear combination of exponential decays method: „S” „F”

DEL

The contribution of “F” and “S” component

PL GPL+EC DEL AICc = 94.6 AICc = AICc = 112.4

Akaike's Information Criterion (AICc) - the average squared residual for a given model, m - the number of the model parameters, z - the number of observations

Interacting proteins