The structure of cellular networks The structure of cellular - - PowerPoint PPT Presentation

The structure of cellular networks The structure of cellular networks

To be able to construct and analyze a cellular network, we need to clearly define what we identify as a node and what we represent with an edge. The nodes and edges have to be at least similar to each other, e.g. represent the same type of cellular component (protein, chemical) or the same type of interaction (mass transfer, regulation). We can, and often need to, define different types of nodes and edges.

Life at the cellular level

• Gene mRNA protein
• Proteins

– provide structure to cells and tissues – work as molecular motors – sense chemicals in the environment – drive chemical reactions – regulate gene expression

• Cellular functions rely on the

coordinated action of gene products.

• Interconnections between

components are the essence of a living process.

David Goodsell/ Science Photo Library

Cellular processes form networks on many levels

Reaction networks

• nodes: substrates, enzymes
• edges: chemical reactions
• nodes: genes, proteins
• edges: translation
• r regulation ,
• activating or inhibiting

Regulatory networks

Examples of cellular networks Examples of cellular networks

• 1. Protein interaction networks

nodes: proteins edges: protein-protein interactions (binding)

• 2. Biochemical reaction networks

several types of nodes reactants (substrates) or products of the reactions enzymes – catalyze the reactions reactant-enzyme complex (“reaction node”) edges need to reflect reactions and also catalysis (regulation)

• ne possibility: directed edges from reactants/enzymes to

complex, from complex to products/enzyme

Examples of cellular networks (cont.) Examples of cellular networks (cont.)

• 3. Gene regulatory networks

at least two types of nodes: mRNA, protein transcription factor protein – DNA interaction represented as protein- mRNA directed edge translation represented as mRNA – protein directed edge protein-protein interactions that regulate transcription factors – can be directed or symmetrical

• 4. Signal transduction networks

nodes: proteins, molecules edges: reactions and processes (e.g. ligand/receptor binding protein conformational changes); common to all is that they reflect information transfer Signal transduction networks have defined inputs and

• utputs.

Protein-protein interactions are identified on the genomic level by using the yeast two- hybrid method

Transcription factors bind to the promoter regions of genes. They have a DNA binding domain and an activation domain. In the two-hybrid method the two domains are separated, and fused to two proteins. If the two proteins interact by binding, the transcription factor activates the expression of a reporter gene. Systematic experiments with all proteins in a given organism lead to genome-wide protein interaction maps.

Each “bait” protein can interact with a large number of “prey” proteins

• Although usually tested in a given

bait/prey setting, protein interactions are considered symmetrical

• Many untested interactions – problem
• All networks have giant connected

components.

• The topological properties of diverse

protein interaction networks are similar.

Protein interaction maps now contain thousands of nodes and edges

Ito (yeast): 8868 interactions between 3280 proteins Uetz (yeast): 4480 interactions, 2115 proteins Giot (Drosophila): 4780 interactions among 4679 proteins Li (C. elegans): 5534 interactions, 3024 proteins Rual (human): 2800 interactions, 8300 proteins

• H. Jeong et al.Nature 411, 41-42 (2001)

S.-H Yook, Z.N. Oltvai, A.-L. Barabasi, Proteomics 4, 928 (2004)

Degree distribution of the yeast protein network is a power law with exponential cutoff

) exp( ) ( ~ ) (

τ γ

k k k k k k P + − +

−

• H. Jeong, S.P. Mason, A.-L. Barabasi, Z.N. Oltvai, Nature 411, 41-42 (2001)

Degree distribution of C. elegans and D. melanogaster protein networks

The degree distribution gets closer to a power-law as more interactions are mapped.

• C. elegans

Drosophila m.

) k exp( Ak ) k ( P β

γ

− =

−

Comparison of yeast interaction networks

Degree distribution Clustering coefficient Connected components

5 . 2

k ~ ) k ( P

−

2

k ~ ) k ( C

−

Yook, Oltvai and Barabási, Proteomics 4, 928 (2004)

Average path length larger, short cycles more abundant than in randomized networks

Randomization: swap the endpoints of two edges, node degrees stay the same.

The bad news: protein interaction maps are far from perfect

• Protein interaction networks are incomplete

– false negatives

• Little overlap (~7%) between maps

constructed by different labs

• Est. coverage of Drosophila map is 21%,

for C. elegans it is 10%

• A significant percentage (~20%) of interactions observed by the two-

hybrid method are not biologically relevant - false positives

• Independent verification of interactions needs be done by alternative

methods such as co-immunoprecipitation or co-affinity purification pull- down assays.

• These methods are small scale and slow, thus there is a need for

prediction methods able to give a short list of candidates.

Not all interactions are simultaneously active

Calculate the correlation between the expression time-course of genes encoding the first neighbors of hub proteins. Two peaks – two different types of hubs. Party hubs are inside connected modules that interact simultaneously. Date hubs connect different modules. Han et al, Nature 443, 88 (2004)

Networks of chemical reactions

Metabolism: Sum of chemical processes by which energy is stored or released.

Metabolic network visualization

Enzymes shown in blue, co-enzymes (small molecules necessary for enzyme activity) in red. Double arrows mean reversible reactions. Reactants, products in black, box indicates that node appears in several locations.

• Node types:

– Metabolites (substrates or products), open rectangles – No distinction between metabolites and coenzymes – Metabolite-enzyme complexes, black rectangles – Enzymes, open ovals

• Edges:

– Substrate to complex or complex to product – Symmetrical edges between enzyme and complex

Tri-partite representation of metabolic network

Reaction Stoichiometry

A + B → C + D (1) A + D → E (2) B + C → F (3) Stoichiometric Matrix (S) Reaction Pathway Reactants (Substrates/Metabolites) Reactions

A B C D E F 1 2 3

• 1
• 1

1 1

• 1
• 1

1

• 1
• 1

1

Sij = Number of molecules of substrate i participating in reaction j Sij < 0 if substrate i is a reactant in reaction j Sij > 0 if substrate i is a product in reaction j i = 1,2,…,N = # of substrates = # rows j = 1,2,…,M = # of reactions = # columns

Network Representation – Bi-partite Graph

A + B → C + D (1) A + D → E (2) B + C → F (3) Reaction Pathway

A B C D E F 1 2 3

Bi-partite Graph (“S-Graph”) Substrate Node Reaction Node Two types of nodes: Directed edges No direct arcs between nodes of the same type

Network Representation – Substrate Graph

A + B → C + D (1) A + D → E (2) B + C → F (3) Reaction Pathway Substrate Graph

A B D C E F A D E B C F A D B C Rxn-2 Rxn-1 Rxn-3

Substrate Node One type of node: Un-directed edges Each reaction represented as a clique

• A. Wagner & D. Fell, Proc. Roy. Soc. 268 (2001)

Network Representation – Reaction Graph

A + B → C + D (1) A + D → E (2) B + C → F (3) Reaction Pathway Reaction Graph

1 2 3

Reaction Node One type of node: Un-directed edges An edge between two reactions if they share at least one substrate in common Three alternate network representations for the same reaction pathway !

Bi-partite Graph

A B C D E F 1 2 3

Directed Substrate Graph

A B D C E F

Directed Reaction Graph

1 2 3 Derived

Connect two substrates if there exists a “2-hop” path in the bi-partite graph between them Connect two reactions if there exists at least one “2-hop” path in the bi-partite graph between them

Key Properties of Metabolic Networks

Metabolic networks are scale-free P(k) = Probability that a given substrate participates in k reactions ≈ k-γ In- and out- degree of substrate nodes in the bi-partite representation Existence of “hub” substrates such as ATP, ADP, NADP, NADPH (Carrier Metabolites)

a: A. fulgidus b: E. coli d: C. elegans e: Average (43 organisms)

• H. Jeong et al., Nature 407, 651 (2000)

2 2 2 2 . .

) ( ) (

− −

≈ ≈ k k P k k P

• ut

in

Distances in Metabolic Networks

Distance distribution Relatively small and constant network diameter across organisms

• H. Jeong et al., Nature 407, 651 (2000)

In-degree Out-degree

Average degree

• E. coli

Paths defined to connect educts to products, the average is calculated on the reachable pairs only

Clustering-degree relation in metabolic networks

Average clustering coefficient of nodes with degree k

Ravasz et al., Science 297, 1551 (2002)

Open symbols: a model with the same degree distribution Straight line:

1

k ~ ) k ( C

−

• E. Ravasz et al., Science 297, 1551 -1555 (2002)

No modularity Modularity Model of hierarchical modularity

Degree distributions in metabolite and reaction networks

Construct non-directed projections to metabolite and reaction networks Rank vs. degree plot, similar to P(k>K). The degree exponent γ=|slope|+1 Undirected substrate network Undirected reaction network Tanaka, Phys. Rev Lett. 94, 168101 (2005)

Gene regulatory networks

• nodes: genes (circle) mRNAs (ovals), proteins (boxes)
• edges: mass flow (continuous) or regulation (dashed)
• regulatory edges acting on edges – similar to catalysis
• edges can be activating or inhibiting

Simplified representation for gene regulatory networks

• Direct modulation towards

product, i.e. TF – mRNA edge or protein- modified protein edge

• General meaning of

edges: (positive or negative) information propagation

• Need rules for combining

several regulatory effects

indegree

• utdegree

Out-degree distribution long - tailed, in-degree distribution more limited

• S. cerevisiae

Guelzim et al, Nature Genetics 31, 60 (2002) Lee et al, Science 298, 799 (2002)

Regulatory motifs

• Regulators (TFs), blue

circles

• Genes, red rectangles
• Dashed edges mean

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

Regulatory themes

R: transc. reg P: prot. Interaction H: seq. homology Zhang et al, J. Biol 4, 6 (2005) Feed-forward Co-regulation Co-pointing Protein complex

Condition-dependent transcription sub-networks

Luscombe et al, Nature 431, 308 (2004)

Representation of chemical reactions+ regulation

convergence two reactant reactions coenzyme positive modulation negative modulation autoinhibition irreversible reaction reversible reaction divergence

• E. O. Voit, Computational Analysis of Biochemical Systems

ABA signal transduction network

Red: enzymes Blue: transport Orange: small molecules Green: sign. transd. proteins Black points: unknown intermediary nodes

Song Li, PSU

Signal transduction pathways

• Protein-protein interaction network – Static picture
• Mapping signaling pathways – Spatial information
• Mapping motifs and patterns during signal propagation

– Pseudo-dynamics

• Analyzing signal processing through networks

– Dynamic modeling

Mapping signaling pathways

Yalçın Arga, et al. Biotech. and Bioeng. (2006)

Signal transduction network of the hippocampal CA1 neuron

Data (binary interactions) collected form the experimental literature System of interacting cellular components involved in phenotypic behavior Edges can be directed or undirected (neutral) Directed edges are activating

• r inhibitory

Ma’ayan et al, Science 309, 1078 (2005)

Build subnetworks that start at a specific ligand Signal propagation can be traced by looking at links per step

LIGAND

RECEPTOR OR MEMBRANE PROTEIN RECEPTOR OR MEMBRANE PROTEIN

CENTRAL SIGNALLING ION CHANNEL ION CHANNEL ION CHANNEL CHEMICAL REACTIONS

STEP 1

STEP 2 Fast change Permanent change

Motif abundance, homeostasis, and plasticity

Looked at three key regulators of plasticity 1. Motif counts increase linearly with steps for all regulators – preferential paths to key effectors; 2. Positive and negative motifs are balanced for glutamate and BDNF - homeostasis; 3. More positive than negative FBL and FFL in NE – long- term info storage

POSITIVE AND NEGATIVE FEEDBACK LOOPS POSITIVE AND NEGATIVE FEED-FORWARD LOOPS

Rapid Rapid-

• change ligands engage more motifs in fewer steps;

change ligands engage more motifs in fewer steps; At early steps, more FFL than expected; at later steps, more +FB At early steps, more FFL than expected; at later steps, more +FBL L than expected than expected

BIFANS SCAFFOLDS