The error threshold or ribo-organisms

Eörs Szathmáry

Collegium Budapest AND Eötvös University

Crucial assumptions

• There was in fact an RNA-dominated worlds

• RNAs acted as genes and as ribozymes

• Replication as a problem was solved

• The accuracy problem?

• The internal cometition problem?

Inaccurate replication immediately raises further concerns (Eigen, 971)

• Early replication must have been error-prone

• Error threshold sets the limit of maximal genome size to <100 nucleotides

• Not enough for several genes• Unlinked genes will compete• Genome collapses• Resolution???

An example of “replication”RNARNARNARNARNARGARNARNARNARNXRNARNARNHDNMRNARNARNARQARNARNJRPA

WORLDWORLFWORLDWORLLIDRYDWORLDWORLDKORLDWORLDWORLDWORLDWORLDWORUDWORLDWORHDWORLDWORLDWORWDWORLDWORLDWRRLD

HYPOTHESISEYPKTHYSIIHYPEXHESISHYPOTHESISHYPOTHESISHYPETHESKSHYYOTHESISHYPOTHESISHYPOTHESISHYPOTHESISHYPOTHESISHYPOTHESISHYPOSHESISHYPOTMESISHTPOTHESISCYPOTGESISHYPOTHEGIAHYPOXHLSISHYPXTHESISHYPOTHESISHYPUTHESIS

Eigen’s Paradox and theError threshold

ln

1

sN

q

N length

s superiority of the master

q error rate per digit

Quasispecies made simple

• For didactics, there are only two genotypes

• Only forward mutations

• Fitness values and mutations rates

Simplified error threshold

x + y = 1

Error theshold and error catastrophe

Error threshold and extinction threshold

Population dynamics on surfaces

• Reaction-diffusion on the surface (following Hogeweg and Boerlijst, 1991)

• One tends to interact with one’s neighbours

• This is important, because lesson from theoretical ecology indicates that such conditions promote coexistence of competitors

• Important effect on the dynamics of the primordial genome (cf. Eigen’s paradox)

Nature 420, 360-363 (2002).

Replicase RNA

Other RNA

Elements of the model

• A cellular automaton model simulating replication and dispersal in 2D

• Replication needs a template next door

• Replication probability proportional to rate constant (allowing for replication)

• Diffusion

X

i - 2 i - 1 i i + 1 i + 2

j -2

j - 1

j

j + 1

j + 2

S

Maximum as a function of molecule length

• Target and replicase efficiency

• Copying fidelity• Trade-off among

all three traits: worst case

Evolving population

Error rate Replicase activity

SCM is better than HPC at high mutation rates (Zintzaras, Santos, Szathmáry, J. theor. Biol. 2002)

• Survival of the flattest• SCM is better only at

high mutations rates• Exactly relevant for

early systems

RNA structure and the error theshold: Kun, Santos, Szathmáry (2005) Nature

Genetics 37, 1008-1011.

• The 3D shape of the molecule

• Enzymatic activity depends on the structure

• Phenotype of a ribozyme is the structure

• There are fewer structures than sequences

• A few mutations in the sequence usually do not change the structure

• The 2D structure can be computed easily

RNA structure – an example

AUCGUCUGUCGGCGAU

GCAUGACUCAUUAUGC

Master copy:

Mutant:

Same structure

Same fitness

(different text can have the same meaning)(different text can have the same meaning)

Aim / question

• The phenotype is more easily maintained than the genotype.

• Phenotypic error threshold, which is higher than the genotypic error threshold.

• For estimating the error threshold a fitness landscape is needed

• The proposed fitness landscapes will be based on mutagenesis experimental data

• Enzymatic activity will be used as a proxy for fitness (protocell)

Neurospora Varkund Satellite Ribozyme

uaagagcguuCg-CcC

gcgguaguaaGc AgG|||||| |||

A

GAACACGA CAC GUUaUgAcug||| ||| ||||||||||

GAC

GCU GUG-A-CGGuAuUggc

CUC-GC-GA-UC-GU-AC-G

A

g

a

ua

UUA

GUGUaUUGUCA|||||||||CguAgCAGUU

u

GGA

AA

aCuUuaaC||||||||uGaAauuGc

g

au

-U-

3’

5’AA

640

650

680

730

740

690

660

670

700

710

720

750

760

770

780II

III

IV V

VI

uaagagcguuCg-CcC

gcgguaguaaGc AgG|||||| |||

A

GAACACGA CAC GUUaUgAcug||| ||| ||||||||||

GAC

GCU GUG-A-CGGuAuUggc

CUC-GC-GA-UC-GU-AC-G

A

g

a

ua

UUA

GUGUaUUGUCA|||||||||CguAgCAGUU

u

GGA

AA

aCuUuaaC||||||||uGaAauuGc

g

au

-U-

3’

5’AA

640

650

680

730

740

690

660

670

700

710

720

750

760

770

780II

III

IV V

VI

N = 144

83/144 (57%) of the positions were mutated, we used 183 mutants

Hairpin Ribozyme

aaacaGAGAAGUcaACCAg|||||

A G AA

AUGGUcCAUUAUAUG

A C A

GUG

CACG|||

uu

1

10

20 30

40

50

5’

3’

H1

loop A

H2 H3 H4

loop BaaacaGAGAAGUcaACCAg

|||||A G A

A

AUGGUcCAUUAUAUG

A C A

GUG

CACG|||

uu

1

10

20 30

40

50

5’

3’

H1

loop A

H2 H3 H4

loop B

N = 50

39/50 (78%) of the positions were mutated, we used 142 mutants

General observations on ribozymes

1. Structure is important, individual base pairs are

not

2. Structure can be slightly varied

3. There are critical sites

4. The landscape is multiplicative (there might be a slight

synergy)

RNA Population dynamics

• Replication rate is proportional to fitness

• Copying is error-prone, but length does not change

• Degradation is independent of fitness

,i

ij

p

Phenotypic error threshold

0.047 0.048 0.049 0.050 0.051 0.052 0.0530

1000

2000

3000

4000

5000

6000

7000 Population size = 10000Estimated Error Threshold =0.0536r = -0.993

Tim

e to e

xtin

ctio

n (genera

tions)

Per digit effective mutation rate (*)

Mean Min. Max.

0.12 0.13 0.14 0.15 0.16 0.17 0.18

0

200

400

600

800

1000

1200

1400

1600

Tim

e to

Ect

ionc

tion

(gen

erat

ions

)

Per digit mutation rate ()

Mean Min. Max.

Population Size = 10000r = -0.95Estimated Error Threshold =0.146

* = 0.053 * = 0.146

VS Ribozyme Hairpin

Comparison with other types of landscapes

VS Ribozyme

0

0.01

0.02

0.03

0.04

0.05

0.06

Structural Mnt. Fuji (0.2) Mnt. Fuji (0.8) Single Peak Eigen (lns=1)

Est

imat

ed E

rror

Thre

shold

Hairpin ribozyme

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Structural Mnt. Fuji (0.2) Mnt. Fuji (0.8) Single Peak Eigen (lns=1)

Est

imat

ed E

rror

Thre

shold

Mnt. Fuji type of landscape

• No structure

• Activities based on point mutations

Single peak fitness landscape

• Based on average activity of point mutants

Neutral mutions tame the error threshold

• Extrapolation from the available mutants as samples to the whole fitness landscape

• Accuracy of viral RNA polymerases would be sufficient to run the genome of a ribo-organism of about 70 genes

Error rates and the origin of replicators

Some open questions

• The maximum genome size of the stochastic corrector model (how many genes in the bag?)

• The evolution of genome size through duplication and divergence of metabolic enzyme functions

• The origin of chromosomes