1 network motifs in prebiotic metabolic networks omer markovitch and doron lancet, department of...
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Network Motifs in Prebiotic Metabolic Networks
Omer Markovitch and Doron Lancet,Department of Molecular Genetics,Weizmann Institute of Science
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“Prebiotic Soup”
4,000,000,000 years ago
The emergence of the first cell-like entity, the Protocell.
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Life is a self-sustaining system capable of undergoing Darwinian evolution.
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The Lipid World Scenario for the Origin of Life
Spontaneous formation of lipid assemblies may seed
life
Lipid(Hydrophilic head; Hydrophobic tail)
Micelle / Assembly
Membrane
Segre, Ben-Eli, Deamer and Lancet, Orig. Life Evol. Biosph. 31 (2001)
Spontaneous aggregation
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RNAMicelles
&Vesicles
DNA / RNA / Polymers Sequence
Assemblies / Clusters / Vesicles / Membranes Composition
Segre and Lancet, EMBO Reports 1 (2000)
<<Bridging Metabolism and Replicator>>
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RNA world: Increasing node count
Two scenarios for increasing network complexity
Lipid World: Increasing node fidelity
How the network structure & properties affect evolution ?
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GARD model (Graded Autocatalysis Replication Domain)
Homeostatic growth
Fission / Split
Com
posi
tion
Segre, Ben-Eli and Lancet, Proc. Natl. Acad. Sci. 97 (2000)
Solving a set of coupled differential equations, using Gillespie’s algorithm.
Symbolic lipids
Environmental Chemistry
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Example of GARD Similarity ‘Carpet’
Following a single lineage.
Generation
Gen
erat
ion
ng=30; split=1.5; seed=361
200 400 600 800 1000
200
400
600
800
1000
0
0.2
0.4
0.6
0.8
1
Com
posi
tiona
l Sim
ilari
tyComposome, quasi-stationary
state
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Populations in GARD
Fixed population size.
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j iijij
; Catalytic Network of Rate-Enhancments
More mutualistic More selfish
*Self-catalysis is the chemical manifestation of self-replication [Orgel, Nature 358 (1992)]
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110 1 2 3 4 5
x 104
0
200
400
600
800
1000POP select; seed=70; NG=split=100; Lpop=1000;
Time [splits]
Fra
ctio
n *
1,00
0
C1 beforeC1 afterC2 beforeC2 after
Negative response
0 1 2 3 4 5
x 104
0
200
400
600
800
1000POP select; seed=157; NG=split=100; Lpop=1000;
Time [splits]
Fra
ctio
n *
1,00
0
C1 beforeC1 afterC2 beforeC2 after
Positive response
Target before selectionTarget after selection
Examples for selection in GARD
Slightly biasing the growth rate of assemblies, depending on similarity / dis-similarity to a target composome.
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0 0.5 1 1.5 2 2.5 30
100
200
300
400
500
600pop; ng=split=100; Spop=1000;
Selection excess
Hit
s
Selection in GARD
beforefrequency Target
afterfrequency Target ExcessSelection
Based of 1,000 simulations.
PositiveNegative
Markovitch and Lancet, Artificial Life (2012)
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How the network effects selection ?
Based of 1,000 simulations, each based on a different network.
Log10
[mutual catalysis power]
Sel
ectio
n ex
cess
POPULATION; selection; NG=100; split=1; Seed=1-1000; Spop=1000
-2 -1 0 1 2 30
0.5
1
1.5
2
-4
-3.5
-3
-2.5
-2
-1.5
-1
Pro
babi
lity
(lo
g 10 s
cale
)
Self | Mutual
Markovitch and Lancet, Artificial Life (2012)
2
1
1 1
G
GN
qqq
N
i
N
jij
mc N
Np
G
G G
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High mutual-catalysis is required for effective evolvability.
Too much self-catalysis hampers evolution (dead-end).
Metabolic networks tend to be mutualistic.
Micro Macro
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So we need more mutual-catalysis But of what type / shape?
Network motifs – design patterns of nature. (sub-graphs that appear more then random)
Uri Alon, Nature Review Genetics (2007)
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Network motifs in GARD
Graded to binary
Find motifs
( Feed forward
loop {5} )
Graded (weights)
Binary (1, 0)
Catalytic score ijScore ln
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(omitted from web presentation)
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Milo et al, Science (2004)
Families of networks
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Principle Component analysis (PCA)
Project the 13th dimensional space of network motifs into another
13th dimensional space, that maximizes the variance in the original
data.
For each , a 13-long vector describes its network motifs profile, but this time with linear combination that maximizes the variance.
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(omitted from web presentation)
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21Omer Markovitch
Acknowledgments:Uri Alon.Avi Mayo.Lancet group.
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Compotype diversity of 10,000 GARD lineages
Each based on a different network.
Self | MutualLog
10 [ mutual catalysis power ]
Com
poty
pe c
ount
(N
C)
NG=100; split=1; Seed=1-10000; Gen=5000
-2 -1 0 1 2 3
1
2
3
4
5
6
-4
-3.5
-3
-2.5
-2
-1.5
-1
Pro
babi
lity
(lo
g 10 s
cale
)
Markovitch and Lancet, Artificial Life (2012)
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Real GARD (Rafi Zidovezki from U. California Riverside)Real lipids: phosphate-idyl-(serine / amine / choline), sphingo-myelin
and cholesterol.Actual physical properties (charge, length, unsaturation).
Variability of lipid lengths in vesicle is highly correlated to vesicle replication time
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
0.5 0.6 0.7 0.8 0.9
St. dev of lipid length in vesicle
Ves
icle
gro
wth
tim
eR = -0.85
Armstrong, Markovitch, Zidovetzki and Lancet, Phys. Biol. 8 (2011).
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Selection towards a specific target composition
C and 1.1
Cor '
urrentjiH
urrentji
ij
ijij
Selection of GARD assemblies towards a target compotype.1) Identify most frequent compotype (= target).2) Rerun the same simulation while modifying the ij values at each
generation, biasing the growth rate towards the target.
beforefrequency Target
afterfrequency Target ExcessSelection
H: compositional similarity between current and target.
Markovitch and Lancet, Artificial Life (2012)
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Assembly growth
Fission (split)
back
war
d (le
ave)
forw
ard
(join
)
GARD model (graded autocatalytic replication domain)
G
G
N
ii
N
nN
nnnn
1
21 ,,,
Gj
N
jijibif
i NiN
nnkNk
dt
dn G
...11 1
nn
nnH
),(
Rate enhancementMolecular repertoire
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Selection response of 1,000 GARD populations
Each based on a different network.
No selection
Und
er s
elec
tion
POPULATION; selection; NG=100; split=1; Seed=1-1000; Spop=1000
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
-4
-3.5
-3
-2.5
-2
-1.5
-1
Pro
babi
lity
(lo
g 10 s
cale
)
Target frequency, before selection
Tar
get f
requ
ency
, aft
er s
elec
tion
Markovitch and Lancet, Artificial Life (2012)