Blank for whiteboard 1

Transcription

1 Blank for whiteboard 1

2 Biological Computation Artificial Chemistries Life through Artificial Chemistries? part one Dave Dembeck 2

3 Questions How did we get from simple molecules to self-replicating systems? Is the emergence of self-replicating systems a probablistically miraculous event? Is it possible to model some meaningful mesoscopic phenomenon essential to biological life? 3

4 Previous work Hüning : Interested in determining the number of autocatalytic sets possible given some artificial chemistry [2000]. Farmer, Kauffman and Packard (1986) Bagley, Farmer and Fontana (1992) large set cardinality, element size Dittrich and Banzhaff (1998) 4

5 Size matters. Previous work suggested to Hüning that autocatalytic sets are only a small part of the reaction network. at this point, large simulations of large networks had been done. Hüning wanted more information about these sets, perhaps they could be considered adaptive systems? 5

6 Hüning s Approach 6 Hüning wanted to investigate exhaustively, which required smaller set sizes (tractability). wanted to get away from the dependency on initial populations. Ergo : Search the reaction graph. Used boolean networks to define the artificial chemistry; different than the method of Dittrich and Banzhaf.

7 Dittrich and Banzhaf Molecules : S={0,1} 32 (Bit strings) Reactions : A + B Ë C A,B,C Œ S Dynamics : Select two objects T and S from reactor (without replacement). If the rule { T + S Ë G } exists, and is satisfied by the filter function f(t,s,g) then replace a random object R with G. 7

8 Dittrich and Banzhaf Results : there is an initial exploration phase with high diversity, then a small number of strings dominates the population. An example of 8 autocatalytic strings : a reaction between any two produce one of the original 8 strings. 8

9 Back to Hüning Hüning s search for autocatalytic sets: the properties of a reaction graph that indicate the existence of an autocatalytic set : all elements are produced from reactions within the set all reactions between elements produce elements of the set. 9

10 and Searching Take advantage of the reaction graph! Search it instead of simulation reduce the dependency on the initial population. saying nothing about the stability or size. subsets may compete with supersets. So combine information from searching with information from simulations. 10

11 Results Simulations show a high sensitivity to filter rate, causing emergence of different stable sets. The number of sets which are robust is small. too little freedom to be considered adaptive systems 11

12 Results The search may not show all sets that could be found through simulation as: large sets may have subsets (competition) Parasites are not detected by the search and they may dramatically affect stability. 12

13 Summary Behavior of simulated results was quite similar to Dittrich and Banzhaf emergence of autocatalytic sets seems to be reliable independent of the implementation we gain some confidence about how autocatalytic sets could be the right stuff. 13

14 Questions Arise: what about point mutation? how much concentration of the molecules is required to have the behavior come about? what about this primordial soup? Do populations reliably discover these sets? are we just some probablistic fluke? Do they persist? more than a snowball s chance in the oven. 14

15 Enter : Fraser and Reidys The evolution of random catalytic networks interested in the relation between size of population and the emergence of autocatalytic sets. dynamics of the population in attaining autocatalytic cycles. 15

16 Catalytic reactions Used a random chemistry a directed graph of catalytic activity. origin terminus The molecule at the origin catalyzes the molecule at the terminus 16

17 A side note Not all random chemistries exhibit catalytic cycles. in random chemistries where the number of catalyzing molecules for any one molecule is limited to 2, cycles are rare. 17

18 Some things to consider Interested in cycles with no outgoing edges the notion of parasites destabilizing autocatalytic cycles. Each molecule should, on average, catalyze, on average, one other to maximize the probability of finding cycles with no outgoing edges. 18

19 Molecules / Structures Q n a is the generalized hypercube with vertex set of all sequences of length n over an alphabet D with a members. Here the alphabet D={A,U,G,C} nucleotides of an RNA sequence e.g.: [A,A,U,C,G,A] ΠQ

20 Contact Graphs creating random structures secondary bonds (gray) tertiary bonds (thin black) 20 Fraser and Reidys

21 Structures A mapping f : Q n a {s n } Compatability : Sequence V, V ΠQ n a is compatible to a structure s n iff for each edge in the contact graph, the nucleotides at the extremities of the edge fulfill: Watson-Crick base-pairing rules observed for secondary structures 21

22 Sequences and their compatibility with structures. 22 Fraser and Reidys

23 Algorithm finite multiset population V of size k pick V a with P{ fit(v a )/E[fit(V)] } pick V b with P{ 1/(k-1) } V a =(x 1 x n ) V*=(x 1 x n ) where x i = x i if rand(1) > p x i otherwise error prone translation delete V b, map V* into all compatible structures with Probability c 23

24 Time and Fitness Time : Choose (V a,v b ) at equidistant time steps. For population of size k, a generation is k such time steps. V a is assigned a fitness F in time step i. at i+1 V a s fitness returns to 1 (one) unless it is catalyzed again. 24

25 Population Dynamic A replication-deletion approach which maintains the relatedness among individuals in population. Moves are local, caused by point mutations Replicating core Nearby exploration 25

26 Result parameters Length : n=30 Population : k= F=100 n*p = 1 On average, we get 1 point mutation per translation 1000 (random) predefined structures. 26

27 Population Analysis (2000) Generations 27 Fraser and Reidys

28 Population analysis (5000) 28 Fraser and Reidys

29 reliable catalization Mean fitness high (cycles) high entropy = population well spread out among compatible structures Reliably finding cycles and then destabilizing 29 Fraser and Reidys

30 darker grey greater proportion of the population realizing structure. 30 Fraser and Reidys

31 A note about transitions Transitions are not restricted to taking place between structures joined by a catalytic edge. the presence of the edge increases the likelihood that the terminus will be the destination for a transition, because of fitness levels. 31

32 More Questions! If artificial chemistries are the "right stuff", shouldn't we be able to come up with a model for perhaps a cell? Can we describe a cell's self-maintenance and self-reproduction with a simple artificial chemistry? 32

33 Enter : Ono and Ikegami (1999) For any interesting behavior to happen in a real chemical system, enclosure is needed In a cell, this is the cell membrane this is maintained by the cell (self-maintenance). Wanted to show how primitive cells can emerge and evolve from a simple chemical network. (Based on Varela s work) address the issues of self-maintenance and selfreplication. 33

34 and Others Recent work by Fenizio, Dittrich and Banzhaf (2001) is in the same theme. 34

35 Ono and Ikegami Molecules : abstract chemicals {A,M,W,X,Y}, catalyzing each other s reactions Topology : A triangular lattice. Each block has a population 35 Ono & Ikegami (1999) [edited]

36 Molecules There is a repulsive force between some molecules Rotation chemical transition probabilistically based on potential energies of self and neighbors and presence of catalysts Hopping around mobile transition probabilistically based on potential energies of self and neighbors. 36

37 Repulsion? M can have isotropic or anisotropic repulsion 37 from

38 Rotation? 38 Ono & Ikegami (1999)

39 Some molecular details W like water; cannot change into any other chemical A autocatalytic X high chemical potential, not autocatalytic Y product of decay lowest chemical potential M a product of reactions, with variable repulsion 39

40 Molecular structure The cell model can maintain it s structure as long as the membrane is intact. A within the cell keep reproducing themselves, while providing enough M to maintain the membrane. The membrane then prevents the A from diffusing outward. 40

41 Cell death? Insufficient supply of A causes the membrane to decay and disappear 41 Ono & Ikegami (1999)

42 Self-Maintenance Cells ingest nutrients and excrete waste through the membrane. In our model : allow X and Y to permeate through membrane at a rate proportional to gradient of their density 42

43 Self-Replication when cell reaches a certain size, becomes unstable and generates a new membrane inside (independently). Eventually divides the cell. (Growth through ingesting X) 43

44 Self-Replication Cell grows, becomes unstable and starts to produce membrane inward black Membrane gray Water white - X 44 Ono & Ikegami (1999)

45 Self-Replication cont membrane grows inward, creating new compartments 45 Ono & Ikegami (1999)

46 Cell Membrane Types By varying repulsion rules of M, can change the properties of membranes. stiff flexible 46 Ono & Ikegami (1999)

47 Future work for Ono and Ikegami Looking to extend the model to 3 dimensions want to include the evolution of selective permeability of the membrane 47

48 Summary Found interesting behavior in autocatalytic chemistries with a search, we found cycles are common, though stability is rather rare withstanding the initial population. with diverse starting conditions, they reliably find cycles on which to replicate as long as the population (concentration) is high enough! 48

49 Summary We have a cell model that has an internal autocatalytic cycle of chemicals maintains the membrane itself membrane prevents the cell from collapsing and/or cell prevents the membrane from deteriorating cell self-replicates : molecular reproduction cellular reproduction 49

50 Many Thanks! Resources Ono, N. and T. Ikegami (1999). Model of self-replicating cell capable of self-maintenance. In D. Floreano, J.-D. Nicoud, and F. Mondana (Eds.), Advances in Artificial Life. Proceedings of the Fifth European Conference on Artificial Life (ECAL99), Berlin, pp Springer. Huning, H. (2000). A search for multiple autocatalytic sets in artificial chemistries based on boolean networks. Artificial Life VII, 1-6 August 2000, Portland, OR, USA. Fraser, S., & Reidys, C. (1997). Evolution of random catalytic networks. In ECAL97. Peter Dittrich, Jens Ziegler, and Wolfgang Banzhaf (2001). Artificial Chemistries - A Review. Artificial Life, 7(3): Pietro Speroni di Fenizio, Peter Dittrich, and Wolfgang Banzhaf (2001). Spontaneous Formation of Proto-Cells in an Universal Artificial Chemistry on a Planar Graph. in: J. Kelemen and P. Sosik (Eds.), Advances in Artificial Life (Proc. 6th European Conference on Artificial Life), LNCS 2159, pp ,Prague, September 10-14, Springer, Berlin. 50