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 and Tin 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 Quotient EQ~M(brain) 1/  /M(body) From Carl Sagan's book: “Dragons of Eden: Speculations on the Evolution of Human Intelligence”

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

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 N R =N G 2 /80,000 -->  N R =  N G 2N G /80,000  N G /  N R =40,000/N G ~40 new genes per regulator for N G =1000 ~4 new genes (1 regulator + 3 non-regulatory genes) for the largest bacterial genomes with N G ~10,000 Important observation:  N G /  N R decreases with genome size

10. Now to our model Disclaimer: authors of this study (unfortunately) received no 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 tools are 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! N univ – the total number of tools in “Home Depot” N G – the number of tools in my toolbox L pathway – the number of tools needed for each new functional task If overlap is random then L pathway  N G / N univ are redundant (already in the toolbox) dN G /dN R = L pathway - L pathway  N G / N univ Superlinear only due to logarithmic corrections: N G = L pathway  N R / N univ log N R max /(N R max -N R ) Networks are needed for non-random overlap between functional pathways

13. Spherical cow model of metabolic networks Food Waste Milk

14. nutrient Horizontal gene transfer: entire pathways could be added in one step Pathways could be also removed Central metabolism  anabolic pathways  biomass 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 N univ The current size of the toolbox (# of genes ~ # of enzymes ~ # of metabolites): N G Probability to join the existing pathway: p join = N G /N univ L pathway =1/p join =N univ /N G If one regulator per pathway:  N G /  N R =L pathway =N univ /N G Quadratic law: N R =N G 2 /2N univ + =

16. We tried several versions of the toolbox model On a random network: analytically solved to give N R ~N met 2 On a union of all KEGG reactions: numerically solved to give N R ~N met 1.8 ~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 prokaryotes Red – toolbox model on KEGG universal network with N univ =1800 From SM, S. Krishna, T.Y. Pang, K. Sneppen, PNAS (2009)

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

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? N R =N G =number of regulatory interactions N R /N G = / increases with N G Either decreases with N G : pathways become shorter as in our model Or grows with N G : regulation gets more coordinated Most likely both trends at once E. van Nimwegen, TIG (2003)

21. nutrient TF1 TF2 Regulating pathways: basic version :  =1=const

22. nutrient TF1 Regulating pathways: long regulons TF2 =const : 

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

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

31. Toolbox modelE. coli metabolic network (spanning tree)

33. nutrient TF1 TF2 TF1 Deleting pathways

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

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

37. KEGG pathways vs reactions In ~500 fully sequenced prokaryotes # of reactions ~ N G # of pathways ~ N R 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 TF1 TF2

46. Table from Erik van Nimwegen, TIG 2003

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

48. Basic version Coordinated activity of pathways 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

52. Trivia facts Zebrafish – the largest # of TFs (~2700) or 10% of ~27,000 genes. (humans ~1900 TFs or 8% of 24,000 genes) In bacteria it is Burkholderia sp. 383 : ~800 TFs out of 8000 genes (also 10% of the total) Linear fit to log(N R ) with log(N genes ) explains 87% of the variance (cc~0.93) Linear fit to N R /N genes with N genes explains 50%- 60% of the variance (cc~0.7-0.75).

53. Gut/sewer bacterium: E. coli K12: 4467 genes 271 TFs 6% http://www.g-language.org/g3/

54. Aphid parasite: Buchnera aphidicola APS: 618 genes 6 TFs 1% http://www.g-language.org/g3/

55. Soil bacterium: Rhodococcus sp. RHA1: 9221 genes 641 TFs 7% http://www.g-language.org/g3/

56. Gut/free bacterium: E. coli K12: 4467 genes 271 TFs 6% http://www.g-language.org/g3/