Network Motifs in Prebiotic Metabolic Networks

1

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 ?

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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

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.

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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


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)

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

)


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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.


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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


Documents

Network Motifs in Prebiotic Metabolic Networks