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6 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 1 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 2 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 3 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 4 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 5 Hypercycle model (Eigen and Schuster ’79): cycle only possible topology dXi/dt = aiXi + biXiXj − Ωi CA model: 1992 Boerlijst and Hogeweg 6 Spiral waves: generic patterns in oscillating systems 7 Hypercycle model prototype of multilevel selection chaotic waves (N=4) stable spiral waves (N> 5 (9)) 8 PARASITE INVASIONS AND EXTINCTION spiral dynamics regrowth from core diffusion(low,none,high) ’inclusive fitness’ 9 Properties of Spirals • Faster Rotating Spirals: Take over the domain of slower rotating ones • Core of Spiral: produces all offsprings in long run 10 positive selection for early death 11 Selection for higher decay 12 Spirals and the Edge of Chaos 13 Conclusion Hypercycle properties: in spatial model everything differs from well mixed system • • • • • • • 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’) 14 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 15 Did we solve the Information threshold problem? NO....... because in PDE hypercycles not resistant to parasites?...NO because spirals do not exist?.... NO 16 Shortcut mutants 5 − > 4 => 5 7 − > 6 => 6 6 − > 5 => || . !!STUDIED SO FAR ONLY AS ECOSYSTEM WITH INVASIONS!! : 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 17 Classical problem ODE model of RP system evolutionary extinction (increase of kL and decrease of l) kR = .6 intrinsic advantage of parasite (L) 18 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 19 long term evolution: towards smaller waves 20 Long term evolution (parameters) emergent ’trade-off’ kL and l Maximizing l : potential ’new’ function Average in population WHY? evolution of higher level entities 21 The waves of replicase and parasites are higher level “Darwinian” entities Birth Maturation Death Mutation Selection Competing Maximizing birth rate KL = 1 22 LargerKL and l increase birthrate of waves analysis of transient in ODE (for evolved parameters) 23 evolutionary attractor at “edge of chaos” (“border of order”) 24 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 25 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 26 Phase transition and bistability maximizing birth rate of waves OR maximizing invasion rate of empty space 27 coevolution of replication (ki) and parasite strength β for different time in complex 28 coevolution of replication (ki) and parasite strength β for different time in complex : timeplots 29 “Ghost” attractors (bistabity) 30 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 31