P. Uetz et. al. Nature 403, 601 (2000) H. Jeong et. al. Nature 411, 41 (2001)
C. ElegansDrosophila 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 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:
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. ArchaeaBacteriaEukaryotes 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 M2M3 M4M5 M1 ext M5 ext M3 ext 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) M1 M2 … M5 R1R2 … T3 S11 S21 S12 S22 ….. V1 V2... = 0 Stoichiometric matrix 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 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 Mass predominantly flows along un-branched pathways! E. Almaas, B. Kovács, T. Vicsek, Z. N. Oltvai and A.-L. Barabási, Nature 427, 839 (2004). 2 Evaluate single metabolite use pattern 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 = 0.23 Non-core correlations: = 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