Parkinson’s Law in bacterial regulation Sergei Maslov Brookhaven National Laboratory

Regulation inside bacteria Genomes of bacteria contain between several 100s to 10,000s genes Only a small subset of proteins encoded by these genes is needed under any given environmental condition Protein production from genes is turned on and off by special regulatory genes – transcription factors often in response to environmental signals

How E. coli utilizes lactose LacZ LacY LacA Lactose LacI

How many regulators does a bacterium need? Transcription factors“Workhorse” genes

+ N R =N G 2 /80,000  N R /N G = N G /80,000 5 Stover et al., Nature (2000), van Nimwegen, TIG (2003) figure from Maslov et al. PNAS (2007)

The total of those employed inside a bureaucracy grew by 5-7% per year "irrespective of any variation in the amount of work (if any) to be done." Parkinson explains the growth of bureaucracy by two forces: "An official wants to multiply subordinates, not rivals" "Officials make work for each other." Is this what happens in bacterial genomes? Probably not!

Economies of scale in bacterial evolution N R =N G 2 /80,000  N G /N R =80,000/N G Economies of scale: as genome gets larger it gets easier to add new pathways as they get shorter

nutrient Horizontal gene transfer: entire pathways could be added in one step Pathways could be also removed nutrient Redundant enzymes are removed Central metabolic core  anabolic pathways  biomass production

“Home Depot” or toolbox model Disclaimer: authors of this study (unfortunately) received no financial support from Home Depot, Inc. Homebase, LTD or Obi, GMBH

Bottom-down modeling metabolic networks Food Waste Milk Spherical cow approximation

New pathways come from the “universal metabolic network” of size N univ : the union of all reactions in all organisms (bacterial answer to “Home depot”) Metabolic network in a given bacterium (# of enzymes ~ # of metabolites): N G Probability of a new pathway to merge with existing pathways: p merge = N G /N univ Length before merger: L added pathway =1/p merge =N univ /N G Assume one regulator per function/pathway: ΔN G /ΔN R =L added pathway +1 ~ N univ /N G Quadratic law: N R =N G 2 /2N univ

Toolbox modelE. coli metabolic network (spanning tree)

Inspired by “scope-expansion” algorithm by Reinhart Heinrich and collaborators TY Pang, S. Maslov, PNAS 2011

Model with multi-substrate & multi-products reactions from KEGG and minimal pathways TY Pang, S. Maslov, PNAS 2011

P(U)~U -γ =U -1.5 Does not work for P(U)=const What about non-metabolic genes?

N selected packages ~ N installed packages 1.7 Software packages for Linux

What it all means for regulatory networks? Trends in complexity of regulation vs. genome size N R =N G =number of edges in a regulatory network N R /N G = / increases with N G Either decreases with N G : functions become more specialized Or grows with N G : regulation gets more coordinated & interconnected Most likely both trends at once E. van Nimwegen, TIG (2003)

nutrient TF1 nutrient TF2 Regulatory templates: one worker – one boss :  =1=const

nutrient TF1 nutrient Regulatory templates: long top-to-bottom regulation =const :  TF2 :  : 

nutrient TF1 TF2 Hierarchy & middle management: too slow! TF3

One hub to rule them all (CRP) nutrient TF1 nutrient TF2 TF3

Predictions of the toolbox model Powerlaw distribution of pathways sizes: (# of pathways of size S) ~ (S, # of genes in a pathway) -3 Same as powerlaw distribution of regulon sizes = out-degrees of TFs in the regulatory network?

Green – regulons in E. coli from RegulonDB Red – KEGG toolbox model Distribution of regulon sizes

Regulon size distribution nutrient TF1 nutrient TF2

 Pavel Novichkov and collaborators, LBL

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Take home messages Contrary to human organizations Parkinson’s law does not apply to bacterial genomes: Thanks, natural selection! Economies of scale make it easier to add pathways to large genomes Open questions: What sets the upper bound of 10,000 genes in bacterial genomes? Model of overlap between regulons and pathways? How to describe non-metabolic TFs and genes? Apply toolbox to other systems: see Linux on Thursday

US Department Of Energy, Office of Biological and Environmental Research Systems Biology Knowledgebase (KBase)Visit kbase.us Toolbox model: Tin Yau Pang (Stony Brook) Kim Sneppen (CMOL, NBI Copenhagen) Sandeep Krishna (NCBS, India) Marco C. Lagomarsino (U. of Pierre and Marie Curie, Paris) Jacopo Grilli (U. of Milano) Bruno Bassetti (U. of Milano) Collaborators and Funding Kbase: Adam Arkin (Berkeley) Rick Stevens (Argonne) Bob Cottingham (Oak Ridge) Pavel Novichkov (LBL) Mark Gerstein (Yale) Doreen Ware (Cold Spring Harbor) David Weston (Oak Ridge) 60+ other collaborators

Thank you!