Download Prebiotic evolution: Circumventing Information threshold

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Prebiotic evolution:
Circumventing Information threshold(?)
emergence of higher levels of selection
Course Computational Biology 2016/2017; Paulien Hogeweg;
Theoretical Biology and Bioinformatics Grp Utrecht University
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How to ’solve’ or ’circumvent’ information threshold?
Did we ask the wrong question?
Did we use the wrong model?
Only little information needed for higher quality replication?
2(3) main directions to try to circumvent problem
“more replicators”
“more RNA in replicators”
BOTH
FIRST
more replicators: ecosystem based solution
Hypercycles (Eigen’s original solution)
Emergence of higher levels of selection
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First attempt to circumvent information threshold:
Hypercycles, Eigen and Schuster
If one replicator has too little information - use many
However beyond the many of the quasispecies: evolved and
coordinately optimized.
Specific catalysis of reactions
dXi/dt = aiXi + biXiXj − Ωi
• (no mutations): look at ’ecosystem’
• ONLY stable topology: cycle
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Hypercycle properties
• Selection LOCAL on amount of catalysis received
• growth and contraction of cycles
HOWEVER
• Once only selection/survival of the first
• NO selection for GIVING catalysis: Parasites
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Nothing in biology makes sense except ....
• ......in the light of Evolution (Dobzhansky 1973)
• ......in the light of CA (s.l.)
.............................local interactions
............................micro-macro transitions
............................non-linear dynamics etc.
...........................”simple rules − > complex behavior”
nothing in biology makes sense except in the light of Both
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Hypercycle model (Eigen and Schuster ’79): cycle only
possible topology
dXi/dt = aiXi + biXiXj − Ωi
CA model:
1992
Boerlijst and Hogeweg
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Spiral waves: generic patterns in oscillating systems
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Hypercycle model prototype of multilevel selection
chaotic waves (N=4)
stable spiral waves (N> 5 (9))
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PARASITE INVASIONS AND EXTINCTION
spiral dynamics
regrowth from core
diffusion(low,none,high)
’inclusive fitness’
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Properties of Spirals
• Faster Rotating Spirals: Take over the domain of slower
rotating ones
• Core of Spiral: produces all offsprings in long run
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positive selection for early death
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Selection for higher decay
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Spirals and the Edge of Chaos
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Conclusion
Hypercycle properties: in spatial model
everything differs from well mixed system
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Limitcycle –> spiral wave patters (>> 5 stabiel)
CAN be resistent to strong parasites
Local interactions − > Selection non Local
Not “once only selection”
Spiral waves enslave molecules
Positive selection for: early death, giving catalysis
evolution towards ’edge of chaos’ (’border of order’)
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Multilevel evolution
• CA Universe: (cf.Crutchfield, Wolfram)
Micro − > Macro (....− >....− >..... etc )
STATIC (simple) ’rockbottom’
?one more soul?
• BUT: In evolving systems also Macro − > Micro:
lowest level
does not make sense except in the light of
higher level processes
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Did we solve the Information threshold problem?
NO.......
because in PDE hypercycles not resistant to parasites?...NO
because spirals do not exist?.... NO
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Shortcut mutants
5 − > 4 => 5
7 − > 6 => 6
6 − > 5 => ||
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!!STUDIED SO FAR ONLY AS ECOSYSTEM WITH INVASIONS!!
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Limited stability of Spatial Hypercycle
with mutations!
a minimal eco-evolutioary model of emerging higher level of
“Darwinian entities”
(Takeuchi & H. PLOS Comp Biol 2009)
Minimal replicator system
with parasitic L’s
replicated when unfolded
’functional’ when folded
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Classical problem
ODE model of RP system
evolutionary extinction (increase of kL and decrease of l)
kR = .6
intrinsic advantage of parasite (L)
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particle model of RP system
evolutionary stable (long transient)
Asynchronous CA choose random patch and random NB
perform reaction or diffusion
with prob. according to
individual (evolving) parameters
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long term evolution: towards smaller waves
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Long term evolution (parameters)
emergent ’trade-off’ kL and l
Maximizing l : potential ’new’ function
Average in population
WHY?
evolution of higher level entities
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The waves of replicase and parasites
are higher level “Darwinian” entities
Birth
Maturation
Death
Mutation
Selection
Competing
Maximizing birth rate
KL = 1
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LargerKL and l increase birthrate of waves
analysis of transient in ODE (for evolved parameters)
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evolutionary attractor
at “edge of chaos” (“border of order”)
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2 levels of Darwinian selection
Wave level evolution
• Waves: long lived ( death not by parasites but by collision)
• Maximize Birthrate + growth rate of newborns
• Birthrate higher for high l (’escape’)
• However higher birthrate − > more (smaller) waves
• − > increase collision! (= deathrate of waves))
Individual level evolution
• Within waves: parasites evolve towards ’nastiness’ (low l)
• However viability maintained −− >
“prudent” parasites
• because of higher level selection; which also
• ’frees’ parasites to do other things (be folded)
through parasites
evolution of novel functionality
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Evolution of replicases in RP system
Strong parasites lead to strong replicases
The model
Study for evol of k different values of β
Study for evolution of k and β
Study for replication duration
Colizzi and Hogeweg Plos Comp Biol 2016
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Phase transition and bistability
maximizing birth rate of waves OR
maximizing invasion rate of empty space
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coevolution of replication (ki) and parasite strength β
for different time in complex
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coevolution of replication (ki) and parasite strength β
for different time in complex : timeplots
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“Ghost” attractors (bistabity)
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conclusion
Because of wave-level selection
Parasites enhance replication potential
Bistability:
maximizing birth rate of waves vs maximizing wave stability
minimizing ’altruism’ of replicators vs maximizing invasion
rate
’Ghosts’ of bistability
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