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Why bacteria run Linux
while eukaryotes run Windows?
Sergei Maslov
Brookhaven National Laboratory
New York
Physical vs. Biological Laws
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Physical Laws are often discovered by
finding simple common explanation for
very different phenomena
Newton’s Law:
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Apples fall to the ground
Planets revolve around the Sun
Discovery of Biological Laws is slowed down
by us having cookie-cutter explanation in
terms of natural selection:
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Drawing from Facebook group: Trust me, I'm a "Biologist"'
~
Genes encoded
in bacterial genomes
Packages installed on
Linux computers
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Complex systems have many components
 Genes (Bacteria)
 Software packages (Linux OS)
Components do not work alone:
they need to be assembled to work
In individual systems only a subset of
components is installed
 Genome (Bacteria) – collection of genes
 Computer (Linux OS) – collection of
software packages
Components have vastly
different frequencies of installation
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IKEA kits have many components
Justin Pollard,
http://www.designboom.com
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They need to be assembled to work
Justin Pollard,
http://www.designboom.com
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Different frequencies of use
vs
Common
Rare
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What determines the frequency
of installation/use of a gene/package?
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Popularity: AKA preferential attachment
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Frequency ~ self-amplifying popularity
Relevant for social systems: WWW links,
facebook friendships, scientific citations
Functional role:
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Frequency ~ breadth or importance
of the functional role
Relevant for biological and technological systems
where selection adjusts undeserved popularity
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Empirical data on component frequencies
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Bacterial genomes (eggnog.embl.de):
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Linux packages (popcon.ubuntu.com):
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500 sequenced prokaryotic genomes
44,000 Orthologous Gene families
200,000 Linux packages installed on
2,000,000 individual computers
Binary tables: component is either
present or not in a given system
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Frequency distributions
Cloud
Shell
Core
ORFans
P(f)~ f-1.5 except the top √N “universal” components with f~1
TY Pang, S. Maslov, PNAS (2013)
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How to quantify functional importance?
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We want to check Frequency ~ Importance
Usefulness=Importance ~ Component is
needed for proper functioning of other
components
Dependency network
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A  B means A depends on B for its function
Formalized for Linux software packages
For metabolic enzymes given by upstreamdownstream positions in pathways
Frequency ~ dependency degree, Kdep
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Kdep = the total number of components that
directly or indirectly depend on the selected one
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TY Pang, S. Maslov, PNAS (2013)
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Frequency is positively correlated
with functional importance
Correlation coefficient ~0.4 for both Linux and genes
Could be improved by using weighted dependency degree
TY Pang, S. Maslov, PNAS (2013)
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Warm-up: tree-like metabolic network
TCA cycle
Kdep=15
Kdep=5
TY Pang, S. Maslov, PNAS (2013)
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Dependency degree distribution
on a critical branching tree
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P(K)~K-1.5 for a critical branching tree
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Paradox: Kmax-0.5 ~ 1/N  Kmax=N2>N
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Answer: parent tree size imposes a cutoff:
there will be √N “core” nodes with Kmax=N
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present in almost all systems (ribosomal genes or core
metabolic enzymes)
Need a new model: in a tree D=1, while in real
systems D~2>1
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Bottom-down model of
dependency network evolution
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Components added gradually over
evolutionary time
New component directly depends on
D previously existing components selected
randomly
Versions:
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D is drawn from some distribution
same as above
Recent components are preferentially selected
citations
There is a fixed probability to connect to any
previously existing components
food webs
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•
p(t,T) –probability that component added at time T
directly or indirectly depends on one added at time t
T
DD
1- p(t,T
(1- p(tp(
,Tt ),T× ) ×) )dt
log(1p(t,T) =)) =Õ
ò log(1-
t t
t =t+1:T
t
dp(t,T )
D
dt
= log(1- p(t,T ) )
1- p(t,T )
t
p(t,T ) =
1
Tætö
1+ ç ÷
DèTø
D
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N
K dep (t) = 1+ ò p(t,T )dT
t
K dep
N
t ~T
*
( D-1)/ D
æ t ö
K dep (t) = ç ÷
è Nø
-D
t
K out (t) = 1+ ò p(t ,t)dt
1
K out (t) = Ct
D-1
D
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Kdep and Kout degree distributions
P(Kdep (t) ³ K dep ) = P((t / N )- D ³ K dep ) = P(t / N £ Kdep -1/ D ) = K dep -1/ D
P(Kdep ) ~ K
-(1+1/ D)
dep
P(Kout (t) £ Kout ) = P(t ( D-1)/ D £ Kout ) = P(t £ Kout D/( D-1) ) = K D/( D-1) / N
P(Kout ) ~ K
1/( D-1)
out
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Kdep decreases layer number
Linux
Model with D=2
TY Pang, S. Maslov, PNAS (2013)
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Zipf plot for Kdep distributions
Metabolic enzymes
vs
Model
Linux
vs
Model
TY Pang, S. Maslov, PNAS (2013)
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Frequency distributions
Core
Shell
Cloud
ORFans
P(f)~ f-1.5 except the top √N “universal” components with f~1
TY Pang, S. Maslov, PNAS (2013)
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What experiments does
P(f) help to interpret?
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Pan-genome of E. coli strains
M Touchon et al. PLoS Genetics (2009)
Metagenomes
The Human Microbiome Project Consortium, Nature (2012)
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Pan-genome scaling
DP
-g
-(2-g )
= ò f × f ×exp(- Nf )df = N
DN
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Pan-genome of all bacteria
(# of genes in pan-genome)
(# of new genes added to pan-genome)

~ (# of sequenced genomes)0.5
~ (# of sequenced genomes)-0.5
P. Lapierre
JP Gogarten
TIG 2009
Slope=-0.4
predictions of
the toolbox
model (-0.5)
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Bacterial genome evolution
happens in cooperation with phages
+
=
Comparative genomics of E. coli
implicates phages for BitTorrent
1kb:
gene length
K-12 to B comparison
Phage capacity: 20kb
Other strains up to 40kb
WWW from AT&T website circa 1996
visualized by Mark Newman
Phage-Bacteria Infection Network
Data from Flores et al 2011
experiments by Moebus,Nattkemper,1981
Why eukaryotes run windows?
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Dependency network = reuse of components
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Bacteria do not keep redundant genes after HGT
Linux developers rely on previous efforts
Pros: smaller genomes, open source,
economies of scale
Cons: less specialized, potentially unstable,
“dependency hell”
Eukaryotes are like Windows or Mac OS X
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Keep redundant components
Proprietary software
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# of pathways (or their regulators)
Figure adapted from S. Maslov, TY Pang, K. Sneppen, S. Krishna, PNAS (2009)
# of genes
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5
10
Software packages for Linux
Nselected packages ~ Ninstalled packages1.7
1.8
# of selected packages
4
10
1.7
3
10
1.6 0
10
2
10
4
10
2
10
Linux data
1
10
slope 1.7
0
10 1
10
2
3
4
10
10
10
# of installed packages
5
10
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Collaborators: Tin Yau Pang, Stony Brook University
Support:
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Office of Biological and Environmental Research
Thank you!