Evolution Before Genes

04/05/2012, Barcelona Vera Vasas PhD Viva

EVOLUTION BEFORE GENES

Theoretical analysis of autocatalytic molecular networks and its implications to metabolism-first theories of the origin of life

Vera Vasas

Supervisors: Dr. Mauro Santos Departament de Genètica i de Microbiologia, Grup de Biologia Evolutiva (GBE), Universitat Autònoma de Barcelona, Spain

Dr. Eörs Szathmáry Institute of Biology, Eötvös University, Budapest, Hungary Introduction

Outline

1. Introduction 1. Origin of life 2. Motivation

2. Collectively autocatalytic chemical networks 1. GARD model and its evolvability 2. The autocatalytic set model and its evolvability 3. Cooptive evolution

3. Conclusions 1. Network motifs that enable selectability 2. Summary

04/05/2012, Barcelona Vera VasasPhD viva 2 Introduction

Origin of life theories

Genetics-first theory Metabolism-first theory

Self-replicating ? Self-reproducing oligonucleotids First living cell? catalytic networks (RNA world)

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Origin of the unit of evolution

Random chemistry

Start of evolution - Chemical system - Information storage and transmission First protocell What could it be..? - Template replication - Metabolism - Lipid membrane

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Units of evolution (JMS)

1. Multiplication hereditary traits affecting 2. Heredity survival and/or 3. Variation reproduction

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Template replicators

• Unlimited variation and heredity • Experimental evidence for the RNA world • BUT! Origin of template replicators?

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Autocatalytic cycles

• Direct autocatalysis (in multiple steps) • Non-enzymatic cycles, e.g. formose reaction • BUT! Variations are not heritable

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Ensemble replication of molecular networks

• Indirect autocatalysis (many more topologies) • Compositional inheritance • Models, e.g. GARD, Autocatalytis Sets • BUT! Evolvable?

04/05/2012, Barcelona Vera VasasPhD viva 8 The GARD model

GARD model: micelle-like molecular assemblies Molecules spontaneously aggregate and grow

βij define the incorporation of molecular species ‘i’ in the growing assembly catalyzed by species ‘j’ Randomly drawn from lognormal distribution Segré et al. 2000. PNAS 97:4112-4117.

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GARD model: ‘ensemble replicators’

Growth and splitting:

Hereditary trait: composition Segré et al. 2000. PNAS 97:4112-4117.

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Quasi-stationary states Time-dependent progression of one assembly

Time correlation matrix of assemblies

QSSs: quasi-stationary states

A,B,C: compotypes generations

generations Segré et al. 2000. PNAS 97:4112-4117.

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Natural selection introduced Mutation, variability, heredity… BUT!

Selection included 1. Analytical scenario 2. Stochastic simulations Fitness (growth rate): similarity to target Frequency distributions of composomes does not change

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But why isn’t it evolvable?

1 2 3 4 5 6 7 8 9 10 11 … 100 1 0,00 0,00 0,23 0,00 0,01 0,00 1,76 0,00 0,38 0,11 0,32 … 351,29 2 0,00 0,00 0,00 0,03 0,06 0,21 9,10 0,00 0,00 0,18 10,96 … 0,00 3 0,03 0,95 0,17 0,01 4,45 0,00 4,64 0,06 0,28 0,00 0,00 … 0,89 4 0,06 0,00 0,00 0,00 0,04 0,00 0,00 0,00 0,00 0,51 0,00 … 16,92 5 0,00 0,07 0,03 2,09 0,00 0,01 0,11 0,00 0,67 0,00 0,04 … 0,74 6 2,15 0,05 0,00 0,02 12,64 0,05 0,70 58,13 0,00 1,48 0,15 … 0,00 7 2,13 0,02 0,00 0,16 0,50 0,01 0,00 0,01 0,06 0,02 0,00 … 1,03 8 0,02 0,00 0,12 0,00 0,05 19,16 0,04 675,62 0,00 0,00 0,06 … 0,00 9 0,07 0,00 0,01 0,00 0,27 12,04 0,39 0,01 0,00 0,00 0,00 … 0,16 10 0,04 0,00 2,58 0,06 0,00 0,22 0,00 0,04 0,03 0,04 0,01 … 0,00 11 0,01 0,00 0,00 0,03 0,56 0,03 0,00 0,74 0,00 0,04 0,01 … 0,00 … … … … … … … … … … … … … … 100 0,01 0,00 2,94 0,00 0,01 0,33 0,04 0,07 4,86 0,07 0,04 … 0,00

Matrix of catalytic parameters (ß values)

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Hidden compartmentalization Compotypes form where large β values fall = strongly catalytic and strongly catalyzed molecules

Vasas et al. 2010. PNAS 107:1470-1475.

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Analytical scenario

Molecular repertoire: NG = 10

Assembly size: N = 3-6

Catalytic interactions: NG x NG matrix lognormal distribution

Number of possible assemblies: Ω = 220 e.g.: 0 1 0 0 0 0 2 0 0 0

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Analytical scenario: Eigen equation

 X'  (r  E)X   X k k k l1 kl l

k = 1,2,…, Ω – all possible assemblies … ' X k - density of one assembly …

r k - self-replication factor …  kl - mutation rate … E - overall excess productivity lk

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Analytical scenario: fitness matrix

' X  (W  E)X w kl  kl

W – fitness matrix w kk  rk

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Composition of a composome

• 0.1 % of the catalytic interactions govern the dynamics, while the rest is noise

40 composome size 35

30 strongly catalyzed

25 number of 20 molecules 15

10 strongly catalytic

0 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 generations

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Lack of strongly autocatalytic loops

• Autocatalytic One giant component loops are unlikely

NG  NG  L   P(loop)  1 1 P  L    Full connectedness L1

• Inherent kinetic instability of autocatalytic loops

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Explanation for the lack of evolvability

• Strongly catalytic molecules give rise to ‘phenotypes’ • Strongly catalytic molecules are halved in each division The phenotype is eventually lost ∑ Informational molecules are not autocatalytic

04/05/2012, Barcelona Vera VasasPhD viva 20 The autocatalytic set model

Kauffman’s model: polymer chemistry

• Catalysed ligation/cleavage reactions of peptides

• P: probability that a given molecule catalyses a given reaction

• Food set

Kauffman 1986. JTB 119:1-24.

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Autocatalytic sets

‘set of species in which the production of each species in the set is catalysed by at least one other species in the set’ = collection of heterocatalytic molecules

Propositions of the model: • Self-organization without natural selection • Natural selection acts on the autocatalytic set

Chemistry behind: peptides, or any other polymers

But what about hereditary variation…?

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Reimplementation of Kauffman’s model

Mathematical model: supracritical growth

Chemical implementation in a flow reactor: logistic growth

Farmer et al. 1986. Phisica D 22:50-67.

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Earlier criticisms

Lifson: P is a composite probability P’= probability of being a catalyst P’’= probability of catalysing a particular reaction with high P’ and P’’ there is supracritical growth

P = 0.0003, K = 0.001 Szathmáry: ‘paradox of specifity’ K: probability that a given molecule inhibits a given reaction

∑: only quantitative issues

24 The autocatalytic set model

Framework for testing selectability

Compartmentalization Flow reactor

Multiple attractors Shuffling concentrations Growth - splitting in one lineage

Selectability in a population Artificial selection (N = 10) Natural selection (Moran process, N = 100)

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Results: Kauffman’s original model

Only one attractor Only one type Selection is meaningless

Equilibrium mass after shuffling initial concentrations

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Results: the inhibition model

Multiple attractors, but: Transitions between them are rare and random, no response to selection Existence of multiple attractors does not garantee ! selectability

Two examples of artificial selection for increased non-food mass

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Growth by novel autocatalytic loops

Extra: rare uncatalysed reactions result in novel species Rarely: non-food generated autocatalytic loops

tendency to increase in mass and complexity

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Mutation - selection balance Propagule size = 2000 Only the large network ~ higher growth rate

Propagule size = 800 Both networks: selection not strong enough Propagule size = 500 Only the small network ~ meltdown

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Network motifs of heritable adaptation

Shared periphery of Cores 1 & 2 Periphery of Core 2

Core 1 Core 2

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Results and conclusions

• Rare novel species generate reaction avalanches • Novel extensions to the network (autocatalytic loops) bits of heritable information

• Properties: • Attractor-based evolution • Weakly correlated variation • Limited heredity

• Small catalytic networks are selectable in a population • Any chemistry Vasas et al. 2012. Biol. Dir. 7: 1.

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Evolvability analyses Selection is only possible in the cooptive evolution model

Aut Sets: Aut Sets: Cooptive GARD model Standard Inhibition evolution model model model

Compartments

Multiple attractors

Selectability

04/05/2012, Barcelona Vera VasasPhD viva 32 Summary

Open questions • Ecology of compartments • Waste products • Fusion -> Infection dynamics of cores

• Chemical basis for cooptive evolution? • Peptides – pattern matching, realistic reaction rates • RNA – catalytic properties of small RNA • Small metabolites – realistic simulations of organic chemistry

• Origin of compartments? • Autocatalytic lipophils (as in GARD) • Micropores in alkaline hydrotermal vents

• Transition to RNA world?

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The GARD model

Autocatalytic loops in GARD

Catalyzed inclusion/exclusion chemistry

Reaction graph Catalytic graph

04/05/2012, Barcelona Vera VasasPhD viva 35 Evolvability of the GARD model

Structural reasons for QSSs

Matrix of catalytic parameters (ß values)

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Structural reasons for QSSs Compartmentalization analysis of the beta matrix

Interaction occuring

No Yes

Different A B Compartment membership Same C D

Criterion = A + D – B – C

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Structural reasons for QSSs Compotypes = quasi-compartments

93 4 82 98 64 50 76 85 A 6 47 95 61 87 1 71 18 99 37 23 91 35 74 30 29 5 72 9 36 17 69 67 44 25 46 12 15 21 83 16 92 40 7 48 A 45 34 49 88 2 55 81 62 43 84 33 38 80 77 24 53 28 94 20 B 78 11 27 42 59 86 C 19 56 13 58 41 10 68 70 54 96 26 60 75 73 14 8 22 31 66 39 65 100 89 51 32 79 A 63 57 3 97 52 90 Quasi-compartmentalization of the beta matrix

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Analytical scenario with natural selection Mutation, variability, heredity… BUT!

Selection included: growth rate x fH Equilibrium frequencies are the same

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Simulations

Molecular repertoire: NG = 100

Assembly size: N = 40-80

Catalytic interactions: NG x NG matrix lognormal distribution

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Simulations with natural selection

Mutation, variability, heredity… BUT!

Selection included: stochastic simulations: Moran population of 1500 assemblies fitness: similarity to target stationary distribution?

Frequency distributions of composomes does not change Can NOT deviate from the background dynamics

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Lack of strongly autocatalytic loops

• Autocatalytic One giant component loops are unlikely

NG  NG  L   P(loop)  1 1 P  L    Full connectedness L1

• Inherent kinetic instability of autocatalytic loops

04/05/2012, Barcelona Vera VasasPhD viva 42 Evolvability of the GARD model

Disjoint autocatalytic loops are unlikely

1 0,9 0,8 0,7 0,6 any cycles weak connectedness freq 0,5 0,4 disjoint cycles 0,3 0,2 0,1 0 0,000 0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040 P

1 0,9 0,8 0,7 0,6 any cycles freq 0,5 0,4 0,3 disjoint cycles 0,2 0,1 weak connectedness 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 cut-off Empirical frequency of autocatalytic loops

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Kinetic instability of autocatalytic loops

• Equilibrium concentrations x  ky  dxx  y  v  z g = 100, k = 1 and d = 0.1 y  gx  dyx  y  v  z v x y z v  kx  dvx  y  v  z x, y,v,z  0.9 9 0.09 90 z  gy  dzx  y  v  z • General linear model

Type I Sum of Source df Mean Square F Sig. Squares Corrected Model 21.885(a) 3 7.295 15.958 .000 Intercept 16.000 1 16.000 35.001 .000 Catalyzed 21.334 1 21.334 46.670 .000 cycle_p0.010 .257 1 .257 .563 .455 catalyzed * cycle_p0.010 .293 1 .293 .641 .425 Error 43.885 96 .457 Total 81.769 100 Corrected Total 65.769 99

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Anatomy of autocatalytic sets

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Main achievements

• Previous state-of-the-art • Lipid world (GARD) – one lineage, multiple attractors • Autocatalytic polymer networks – self-organization

• Population dynamics for existing models and suggestions • GARD • Autocatalytic sets • Autocatalytic sets with inhibition

• Theory of selectable chemical network organizations • Proof of concept for their selectability

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