Eivind Almaas
Microbial Systems Division
Introduction to
Biological Networks
UC Davis, May 18th 2006
Biological network examples
• Gene-regulation
• Protein interaction
• Metabolism
• Cell signaling
• Cytoskeleton
•…
• Neural network
• Lymphatic node system
• Circulatory system
Cellular networks:
GENOME
protein-gene
interactions
PROTEOME
protein-protein
interactions
METABOLISM
Bio-chemical
reactions
Citrate Cycle
Protein Interaction
Networks (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
Li et al, Science 303, 540 (2003)
Drosophila M.
Giot et al, Science 302, 1727 (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
Use Protein-Protein BLAST (Basic Local Alignment Search Tool)
-check each yeast protein against whole organism dataset
-identify significant matches (if any)
Eisenberg E, Levanon EY, Phys. Rev. Lett. 2003.
Preferential Attachment!
ki
k i
  ( ki ) ~
t
t
For given t: k  (k)
k vs. k : linear increase in the # of links
S. Cerevisiae PIN: proteins classified into 4 age groups
Eisenberg E, Levanon EY, Phys. Rev. Lett. 2003.
SF topology from: duplication & diversification
Copying DNA: when mistake (gene duplication) happens
Effect on network:
Proteins with more interactions are more likely to get a new link:
Π(k)~k
preferential attachment
Wagner (2001); Vazquez et al. 2003; Sole et al. 2001; Rzhetsky & Gomez (2001);
Qian et al. (2001); Bhan et al. (2002).
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
Protein BLAST against:
A. thaliana
C. elegans
D. melanogaster
M. musculus
H. sapiens
S. Wuchty, Z.N. Oltvai,
A.-L.Barabasi, 2003.
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).
Local vs. global centrality
S. Wuchty and E. Almaas, Proteomics 5, 444 (2005).
Properties of globally central proteins
S. Wuchty and E. Almaas, Proteomics 5, 444 (2005).
Metabolic Networks
Metabolic Networks:
Nodes: chemicals (substrates)
Links: chem. reaction
Archaea
Bacteria
Eukaryotes
100+
organisms, all
domains of life
are scale-free
networks.
H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, and A.L. Barabasi, Nature 407, 651 (2000).
Scaling of clustering coefficient C(k)
The metabolism forms a hierarchical network!
Ravasz, et al, Science 297, 1551 (2002).
(why?)
Hierarchical Networks
Remember definition of clustering:
# links between k neighbors
C(k)=
k(k-1)/2
In hierarchical networks, hubs act as
connectors between modules!
Why could this be beneficial?
Ravasz, et al, Science 297, 1551 (2002).
How does metabolic network
structure
influence function?
How can we simulate metabolic function?
T3
M2
M1ext T1
M1
M3ext
M3
R3
R1
R4
M4 R5
M5
R2
M5ext
R6
T2
Stoichiometric
matrix
…
T3
V1
V2
…
...
R1 R2
M1 S11 S12
M2 S21 S22
Flux vector
=0
Constraints &
Optimization for growth
M5
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)
Simple example:
Reaction network:
1
2
3
6
4
5
7
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).
Optimal fluxes in E. coli
SUCC: Succinate uptake
GLU : 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
2
Evaluate single metabolite use
pattern by calculating:
Two possible scenarios:
(a) All fluxes approx equal
(b) One flux dominates
Mass predominantly flows
along un-branched pathways!
E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai and A.-L. Barabási, Nature 427, 839 (2004).
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
Essential metabolic core
• 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.
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)
• 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
E. Almaas, Z. N. Oltvai, A.-L. Barabási, PLoS Comput. Biol. 1(7):e68 (2005)
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