"Home Depot" Model of Evolution of Prokaryotic Metabolic Networks and Their Regulation

1. "Home Depot" Model of Evolution of Prokaryotic Metabolic Networks and Their Regulation Sergei Maslov Brookhaven National Laboratory In collaboration with Kim Sneppen and Sandeep Krishna, Center for Models of Life, Copenhagen U andTin Yau Pang, Stony Brook U

2. Stover et al., Nature (2000) van Nimwegen, TIG (2003)

3. The rise of bureaucracy! • Fraction of bureaucrats grows with organization size • Trend (if unchecked) could lead to a “bureaucratic collapse”: 100% bureaucrats and no workers • As human bureaucrats, transcription factors are replaceable and disposable • many anecdotal stories of one regulator replacing another in closely related organisms • Not very essential (at least in yeast) . • One is tempted to view regulators nearly as “parasites” or superficial add-ons that marginally improve the efficiency of an organism

4. But if you are a bureaucrat you see your role somewhat differently…

5. Encephalization QuotientEQ~M(brain)1//M(body) From Carl Sagan's book: “Dragons of Eden: Speculations on the Evolution of Human Intelligence”

6. Bacterial IQ Bacterial IQ~(Nsignal trasnsducers)1/2/Ngenes Table from M.Y. Galperin, BMC Microbiology (2005)

7. Quadratic scaling applies to all types of regulation and signaling Table from Molina, van Nimwegen, Biology Direct 2008

8. How to explain the quadratic law?

9. Let’s play with this scaling law • NR=NG2/80,000 --> NR=NG 2NG/80,000 • NG /NR=40,000/NG • ~40 new genes per regulator for NG=1000 • ~4 new genes (1 regulator + 3 non-regulatory genes) for the largest bacterial genomes with NG~10,000 • Important observation: NG /NR decreases with genome size

10. Now to our model Disclaimer: authors of this study (unfortunately) receivedno financial support from Home Depot, Inc. or Obi, GMBH

11. “Home Depot” argument • Inspired by personal experience as a new homeowner buying tools • Tools are bought to accomplish functional tasks e.g. fix a leaking faucet • Redundant toolsare returned to “Home Depot” • As your toolbox grows you need to get fewer and fewer new tools to accomplish a new task • Tools are e.g. metabolic pathways acquired by Horizontal Gene Transfer • Regulators control these pathways (we assume one regulator per task/pathway) • Redundant genes are promptly deleted (in prokaryotes) • Genomes shrink by deleting entire pathways that are no longer required • All non-regulatory “workhorse” genes of an organism - its toolbox • As it gets larger you need fewer new workhorse genes per new regulated function – FASTER THAN LINEAR SCALING

12. Random overlap between functions  no quadratic scaling! • Nuniv – the total number of tools in “Home Depot” • NG – the number of tools in my toolbox • Lpathway – the number of tools needed for each new functional task • If overlap is random then Lpathway NG / Nuniv are redundant (already in the toolbox) • dNG/dNR= Lpathway- Lpathway NG / Nuniv • Superlinear only due to logarithmic corrections: NG= Lpathway NR / Nuniv log NRmax/(NRmax-NR) • Networks are needed for non-random overlap between functional pathways

13. Spherical cow modelof metabolic networks Milk Food Waste

14. Central metabolism  anabolic pathways  biomass Pathways could be also removed nutrient Horizontal gene transfer:entire pathways could be added in one step nutrient nutrient

15. New pathways are added from the universal network formed by the union of all reactions in all organisms (bacterial answer to “Home depot”) • The only parameter - the size of the universal network Nuniv • The current size of the toolbox (# of genes ~ # of enzymes ~ # of metabolites): NG • Probability to join the existing pathway: pjoin= NG /Nuniv • Lpathway=1/pjoin=Nuniv/NG • If one regulator per pathway: NG/NR=Lpathway=Nuniv/NG • Quadratic law:NR=NG2 /2Nuniv = +

16. We tried several versions of the toolbox model • On a random network: analytically solved to give NR~Nmet2 • On a union of all KEGG reactions: numerically solved to give NR~Nmet1.8 • ~1800 reactions and metabolites upstream of the central metabolism • Randomly select nutrients • Follow linear pathways until they overlap with existing network

17. Green – all fully sequenced prokaryotesRed – toolbox model on KEGG universal network with Nuniv=1800 From SM, S. Krishna, T.Y. Pang, K. Sneppen, PNAS (2009)

18. Length distribution of metabolic pathways/branches -1=2 Green – linear branches in E. coli metabolic network Red – toolbox model on KEGG SM, S. Krishna, T.Y. Pang, K. Sneppen, PNAS (2009)

19. Model with shortest & branched instead of meandering & linear pathways Slope=1.7 SM, T.Y. Pang, in preparation (2010)

20. What does it mean for regulatory networks? • NR<Kout>=NG<Kin>=number of regulatory interactions • NR/NG= <Kin>/<Kout> increases with NG • Either <Kout> decreases with NG: pathways become shorter as in our model • Or <Kin>grows with NG:regulation gets more coordinated • Most likely both trends at once E. van Nimwegen, TIG (2003)

21. nutrient nutrient Regulating pathways: basic version <Kout>:  <Kin>=1=const TF1 TF2

22. nutrient nutrient Regulating pathways: long regulons <Kout>=const <Kin>:  TF1 TF2

23. nutrient nutrient Regulating pathways: TFTF + upstream suppression TF1 TF2

24. nutrient nutrient Regulating pathways: new TFs TF1 TF2 TF1

25. Conclusions and future plans • Toolbox “Home Depot” model explains: • Quadratic scaling of the number of regulators • Broad distribution (hubs and stubs) of regulon sizes:most functions need few tools, some need many • Gene duplication models offer an alternative way to explain hubs in biological networks but the ultimate explanation has to be functional • Our model relies on Horizontal Gene Transfer instead of gene duplication • To do list: • Coordination of regulation of different pathways: which of our proposed scenarios (if any) is realized? • What Nature is trying to minimize when adding branched pathways? The number of added reactions? The number of byproducts? Cross-talk with existing pathways? • Extensions to organizations, technology innovations, etc?

26. Thank you!

27. Target product By-product “Surface” By-product NM

31. Toolbox model E. coli metabolic network (spanning tree)

33. nutrient nutrient nutrient Deleting pathways TF1 TF1 TF2

34. Distribution of regulon sizes Green – regulons in E. coli Red – toolbox model on full KEGG

35. Bacterial IQ IQ~(Nsignal trasnsducers)1/2/Ngenes Table from M.Y. Galperin, BMC Microbiology (2005)

37. KEGG pathways vs reactions In ~500 fully sequenced prokaryotes # of pathways ~ NR # of reactions ~ NG SM, S. Krishna, K. Sneppen (2008)

40. Adaptive evolution of bacterial metabolic networks by horizontal gene transfer Csaba Pal, Balazs Papp & Martin Lercher, Nat. Gnet. (2005)

41. Adaptive evolution of bacterial metabolic networks by horizontal gene transfer Csaba Pal, Balazs Papp & Martin Lercher, Nat. Gnet. (2005)

42. nutrient nutrient nutrient TF1 TF2

46. Table from Erik van Nimwegen, TIG 2003

47. Complexity is manifested in Kin distribution E. coli vs. S. cerevisiae vs. H. sapiens

48. Coordinated activity of pathways Basic version SM, S. Krishna, K. Sneppen (2008)

49. Jerison 1983

50. Jerison 1983 The evolution of the mammalian brain as an information-processing system. pp. 113-146 IN Eisenberg, J. F. & Kleiman, D. G. (Ed.), Advances in the Study of Mammalian Behavior (Spec. Publ. Amer. Soc. Mamm. 7). Pittsburgh: American Society of Mammalogists. Figure redrawn from Jerison 1973 Jerison 1983