Parkinson’s Law in bacterial regulation

Sergei MaslovBrookhaven 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

LacZLacY LacA

Lactose

LacI

How many regulatorsdoes a bacterium need?

Transcription factors

“Workhorse” genes

5

+

NR=NG2/80,000

NR/NG = NG/80,000

Stover et al., Nature (2000), van Nimwegen, TIG (2003)figure from Maslov et al. PNAS (2007)

Parkinson's Law

The report of the Royal Commission on the Civil Service was published on Thursday afternoon. Time has not permitted any comment in this week's issue of The Economist on the contents of the Report. But the startling discovery enunciated by a correspondent in the following article is certainly relevant to what should have been in it.

Nov 19th 1955 | From The Economist print edition

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

• NR=NG2/80,000 NG/NR=80,000/NG

• 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 WasteMilk

Spherical cow approximation

• New pathways come from the “universal metabolic network” of size Nuniv : the union of all reactions in all organisms (bacterial answer to “Home depot”)

• Metabolic network in a given bacterium(# of enzymes ~ # of metabolites): NG

• Probability of a new pathway to merge with existing pathways: pmerge= NG /Nuniv

• Length before merger: Ladded

pathway=1/pmerge=Nuniv/NG

• Assume one regulator per function/pathway: ΔNG/ΔNR=Ladded pathway+1 ~ Nuniv/NG

• Quadratic law: NR=NG2 /2Nuniv

Toolbox model E. 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?

101

102

103

104

105

100

101

102

103

104

105

# of installed packages

# o

f se

lect

ed p

acka

ges

100

102

104

1.6

1.7

1.8

Linux data

slope 1.7

Nselected packages ~ Ninstalled packages

1.7

Software packages for Linux

What it all means for regulatory networks?

Trends in complexity of regulation vs. genome size

NR<Kout>=NG<Kin>=number of edges in a regulatory network

NR/NG= <Kin>/<Kout> increases with NG Either <Kout> decreases with NG:

functions become more specialized Or <Kin> grows with NG:

regulation gets more coordinated & interconnected

Most likely both trends at onceE. van Nimwegen, TIG (2003)

nutrient

TF1

nutrient

TF2

Regulatory templates:one worker – one boss

<Kout>: <Kin>=1=const

nutrient

TF1

nutrient

Regulatory templates:long top-to-bottom regulation

<Kout>=const<Kin>:

TF2<Kout>:<Kin> :

nutrient

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?

100

101

102

10-4

10-3

10-2

10-1

100

branch length/regulon size

cum

ula

tive

dis

trib

uti

on

-1=1

-1=2

Green – regulons in E. coli from RegulonDBRed – KEGG toolbox model

Distribution of regulon sizes

Regulon size distribution

nutrient

TF1

nutrient

TF2

Pavel Novichkov and collaborators, LBL

Pavel Novichkov and collaborators, LBL

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 us @ 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!