UC Davis, May 18th 2006

Introduction to

Biological Networks

Eivind AlmaasMicrobial Systems Division

Biological network examples

• Gene-regulation • Protein interaction • Metabolism• Cell signaling• Cytoskeleton

• …

• Neural network• Lymphatic node system• Circulatory system

protein-gene interactions

protein-protein interactions

PROTEOME

GENOME

METABOLISM

Bio-chemical reactions

Citrate Cycle

Cellular networks:

Protein InteractionNetworks (PIN)

Protein interactions: Yeast two-hybrid method

P. Uetz et. al. Nature 403, 601 (2000)H. Jeong et. al. Nature 411, 41 (2001)

C. Elegans Drosophila M.

Giot et al, Science 302, 1727 (2003)Li et al, Science 303, 540 (2003)

PINs are scale-free…

Protein interaction networks are scale-free.

• is this because of preferential attachment?

• another mechanism?

• how can we determine the cause?

Comparison of proteins through evolution

Eisenberg E, Levanon EY, Phys. Rev. Lett. 2003.

Use Protein-Protein BLAST (Basic Local Alignment Search Tool)-check each yeast protein against whole organism dataset-identify significant matches (if any)

Preferential Attachment!

k vs. k : linear increase in the # of links

Eisenberg E, Levanon EY, Phys. Rev. Lett. 2003.

S. Cerevisiae PIN: proteins classified into 4 age groups

t

kk

t

k ii

i

~)( For given t: k (k)

SF topology from: duplication & diversification

Wagner (2001); Vazquez et al. 2003; Sole et al. 2001; Rzhetsky & Gomez (2001); Qian et al. (2001); Bhan et al. (2002).

Proteins with more interactions are more likely to get a new link:Π(k)~k

preferential attachment

Copying DNA: when mistake (gene duplication) happens

Effect on network:

How can we dissect the PIN?

Network motifs

Definition: A motif is a recurrent network module

Examples:

• Can think of networks as constructed by combining these “basic” building blocks

• Do these motifs have special properties?

PIN motifs and evolution

S. Wuchty, Z.N. Oltvai,A.-L.Barabasi, 2003.

Protein BLAST against: A. thaliana C. elegans D. melanogaster M. musculus H. sapiens

Network peeling

Core decomposition method: • the k-core consists of all nodes with degree >= k.• recursively remove nodes with degree < k.

S. Wuchty and E. Almaas, Proteomics 5, 444 (2005).

S. Wuchty and E. Almaas, Proteomics 5, 444 (2005).

Local vs. global centrality

Properties of globally central proteins

S. Wuchty and E. Almaas, Proteomics 5, 444 (2005).

Metabolic Networks

Metabolic Networks:

H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature 407, 651 (2000).

100+ organisms, all domains of life are scale-free

networks.

Archaea Bacteria Eukaryotes

Nodes: chemicals (substrates)

Links: chem. reaction

The metabolism forms a hierarchical network! (why?)

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

Scaling of clustering coefficient C(k)

Hierarchical Networks

C(k)=# links between k neighbors

k(k-1)/2

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

Remember definition of clustering:

In hierarchical networks, hubs act as connectors between modules!

Why could this be beneficial?

How does metabolic network structure

influence function?

Constraints & Optimization for growth

R1

R2

R3

R4

R5

R6

T1

T2

T3

M1

M2 M3

M4 M5

M1ext

M5ext

M3ext

J.S. Edwards & B.O. Palsson, Proc. Natl. Acad. Sci. USA 97, 5528 (2000)R.U. Ibarra, J.S. Edwards & B.O. Palsson, Nature 420, 186 (2002)D. Segre, D. Vitkup & G.M. Church, Proc. Natl. Acad. Sci. USA 99, 15112 (2002)

M1M2…

M5

R1 R2 … T3S11S21

S12S22

…..

V1V2

...

= 0

Stoichiometricmatrix Flux vector

How can we simulate metabolic function?

We need: • List of metabolic reactions• Reaction stoichiometry• Assume mass balance• Assume steady state

Edwards, J. S. & Palsson, B. O, PNAS 97, 5528 (2000).Edwards, J. S., Ibarra, R. U. & Palsson, B. O. Nat Biotechnol 19, 125 (2001). Ibarra, R. U., Edwards, J. S. & Palsson, B. O. Nature 420, 186 (2002).

Simple example:

1 2 6

3 4 5 7

Reaction network:

Optimal fluxes in E. coli

SUCC: Succinate uptakeGLU : Glutamate uptake

Central Metabolism,Emmerling et. al, J Bacteriol 184, 152 (2002)

E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai and A.-L. Barabási, Nature 427, 839 (2004).

How are metabolic fluxes

correlated with network topology?

Weights and network structure

Weights are correlated with local topology

A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, PNAS 101, 3747 (2004)P.J. Macdonald, E. Almaas and A.-L. Barabasi, Europhys Lett 72, 308 (2005)

Single metabolite use patterns

Mass predominantly flows along un-branched pathways!

E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai and A.-L. Barabási, Nature 427, 839 (2004).

2Evaluate single metabolite usepattern by calculating:

Two possible scenarios:(a) All fluxes approx equal (b) One flux dominates

Functional plasticity of metabolism

• Sample 30,000 different optimal conditions randomly and uniformly

• Metabolic network adapts to environmental changes using:(a) Flux plasticity (changes in flux rates)(b) Structural plasticity (reaction [de-] activation)

Functional plasticity of metabolism

• Sample 30,000 different optimal conditions randomly and uniformly

• Metabolic network adapts to environmental changes using:(a) Flux plasticity (changes in flux rates)(b) Structural plasticity (reaction [de-] activation)

• There exists a group of reactions NOT subject to structural plasticity: the metabolic core

• These reactions must play a key role in maintaining the metabolism’s overall functional integrity

• The core is highly essential: 75% lethal (only 20% in non-core) for E. coli. 84% lethal (16% non-core) for S. cerevisiae.

• The core is highly evolutionary conserved: 72% of core enzymes (48% of non-core) for E. coli.

Essential metabolic core

E. Almaas, Z. N. Oltvai, A.-L. Barabási, PLoS Comput. Biol. 1(7):e68 (2005)

Metabolic core flux variations synchronized

• Flux correlations as metric for hierarchical average-linkage clustering

• One cluster of highly correlated reactions with significant overlap with core (green)

E. Almaas, Z. N. Oltvai, A.-L. Barabási, PLoS Comput. Biol. 1(7):e68 (2005)

• Experimental mRNA data (Blattner group) for 41 conditions

• Correlations are significantly higher for core reactions (red) with <Cij> = 0.23

• Non-core correlations: <Cij> = 0.07

Summary

• Cellular networks are predominantly scale-free

• Network structure constrains dynamics

• Protein interaction network from preferential attachment

• Networks motifs and k-core decomposition

• Metabolic fluxes are scale-free

• Metabolic fluxes correlate with the network topology

• Fluxes predominantly flow along metabolic super-highways

• Synchronized & essential metabolic core