network motifs in prebiotic metabolic networks
DESCRIPTION
Network Motifs in Prebiotic Metabolic Networks. Omer Markovitch and Doron Lancet, Department of Molecular Genetics, Weizmann Institute of Science. “Prebiotic Soup” 4,000,000,000 years ago. The emergence of the first cell-like entity, the Protocell. - PowerPoint PPT PresentationTRANSCRIPT
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Network Motifs in Prebiotic Metabolic Networks
Omer Markovitch and Doron Lancet,Department of Molecular Genetics,Weizmann Institute of Science
2
“Prebiotic Soup”
4,000,000,000 years ago
The emergence of the first cell-like entity, the Protocell.
3
Life is a self-sustaining system capable of undergoing Darwinian evolution.
4
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
5
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 ?
7
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
8
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.
10
j iijij
; Catalytic Network of Rate-Enhancments
More mutualistic More selfish
*Self-catalysis is the chemical manifestation of self-replication [Orgel, Nature 358 (1992)]
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.
12
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.
20
(omitted from web presentation)
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)