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Biological ComputationArtificial Chemistries

Life through Artificial Chemistries?part one

Dave Dembeck

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Questions

n How did we get from simple molecules toself-replicating systems?

n Is the emergence of self-replicatingsystems a probablistically miraculousevent?

n Is it possible to model some meaningfulmesoscopic phenomenon essential tobiological life?

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Previous work

n Hüning : Interested in determining thenumber of autocatalytic sets possiblegiven some artificial chemistry [2000].n Farmer, Kauffman and Packard (1986)

Bagley, Farmer and Fontana (1992)n large set cardinality, element size

n Dittrich and Banzhaff (1998)

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Size matters.

n Previous work suggested to Hüning thatautocatalytic sets are only a small part ofthe reaction network.n at this point, large simulations of large

networks had been done.

n Hüning wanted more information about thesesets, perhaps they could be consideredadaptive systems?

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Hüning’s Approach

n Hüning wanted to investigate exhaustively,which required smaller set sizes(tractability).n wanted to get away from the dependency on

initial populations. Ergo : Search the reactiongraph.

n Used boolean networks to define theartificial chemistry; different than themethod of Dittrich and Banzhaf.

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Dittrich and Banzhaf

n Molecules : S={0,1}32 (Bit strings)n Reactions : A + B Ë C A,B,C Œ S

n Dynamics : Select two objects T and Sfrom reactor (without replacement). If therule { T + S Ë G } exists, and is satisfiedby the filter function f(T,S,G) then replacea random object R with G.

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Dittrich and Banzhaf

n Results : there is an initial explorationphase with high diversity, then a smallnumber of strings dominates thepopulation.

n An example of 8 autocatalytic strings :n a reaction between any two produce one of

the original 8 strings.

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Back to Hüning…

n Hüning’s search for autocatalytic sets:n the properties of a reaction graph that indicate

the existence of an autocatalytic set :n all elements are produced from reactions within

the set

n all reactions between elements produce elementsof the set.

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and Searching…

n Take advantage of the reaction graph!Search it instead of simulation ‡ reducethe dependency on the initial population.n saying nothing about the stability or size.

n subsets may compete with supersets.

n So combine information from searchingwith information from simulations.

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Results

n Simulations show a high sensitivity to filterrate, causing emergence of differentstable sets.

n The number of sets which are robust issmall.n too little freedom to be considered adaptive

systems

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Results

n The search may not show all sets thatcould be found through simulation as:n large sets may have subsets (competition)

n Parasites are not detected by the search –and they may dramatically affect stability.

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Summary

n Behavior of simulated results was quitesimilar to Dittrich and Banzhafn emergence of autocatalytic sets seems to be

reliable independent of the implementation

n we gain some confidence about howautocatalytic sets could be “the right stuff”.

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Questions Arise:

n what about point mutation?

n how much “concentration” of the molecules isrequired to have the behavior come about?n what about this primordial soup?

n Do populations reliably discover these sets?n are we just some probablistic fluke?

n Do they persist?n more than a snowball’s chance in… the oven.

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Enter : Fraser and Reidys

n The evolution of random catalyticnetworksn interested in the relation between size of

population and the emergence of autocatalyticsets.

n dynamics of the population in attainingautocatalytic cycles.

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Catalytic reactions

n Used a random chemistry – a directed graphof catalytic activity.

origin terminus

• The molecule at the origin catalyzes the moleculeat the terminus

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A side note…

n Not all random chemistries exhibit catalyticcycles.n in random chemistries where the number of

catalyzing molecules for any one molecule islimited to 2, cycles are rare.

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Some things to consider…

n Interested in cycles with no outgoingedgesn the notion of parasites destabilizing

autocatalytic cycles.

n Each molecule should, on average,catalyze, on average, one other tomaximize the probability of finding cycleswith no outgoing edges.

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Molecules / Structures

n Qna is the generalized hypercube with

vertex set of all sequences of length nover an alphabet D with a members.

n Here the alphabet D={A,U,G,C}n nucleotides of an RNA sequence

n e.g.: [A,A,U,C,G,A] Œ Q64

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Contact Graphs

n creating random structures

secondary bonds (gray)

tertiary bonds (thin black)

Fraser and Reidys

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Structures

n A mapping f : Qna ‡ {sn}

n Compatability : Sequence V, V Œ Qna is

compatible to a structure sn iff for each edge inthe contact graph, the nucleotides at theextremities of the edge fulfill:n Watson-Crick base-pairing rules observed for

secondary structures

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Sequences and theircompatibility with structures.

Fraser and Reidys

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Algorithm

n finite multiset population V of size kn pick Va with P{ fit(Va)/E[fit(V)] }n pick Vb with P{ 1/(k-1) }n Va=(x1…xn) ‡ V*=(x’1…x’n)

n where x’i = xi if rand(1) > p x’i otherwise

n …error prone translation

n delete Vb , map V* into all compatible structureswith Probability c

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Time and Fitness

n Time : Choose (Va ,Vb) at equidistant timesteps. For population of size k, ageneration is k such time steps.

n Va is assigned a fitness F in time step i. ati+1 Va’s fitness returns to 1 (one) unless itis catalyzed again.

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Population Dynamic

n A replication-deletion approach whichmaintains the relatedness amongindividuals in population.n Moves are local, caused by point mutations

Replicating coreNearby exploration

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Result parameters

n Length : n=30

n Population : k=2000-8000

n F=100

n n*p = 1n On average, we get 1 point mutation per translation

n 1000 (random) predefined structures.

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Population Analysis (2000)

Generations ‡

Fraser and Reidys

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Population analysis (5000)

Fraser and Reidys

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reliable catalization ‡Mean fitness high (cycles)

high entropy = populationwell spread out among compatible structures

Reliably finding cyclesand then destabilizing…

Fraser and Reidys

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darker grey ‡ greater proportionof the population realizing structure.

Fraser and Reidys

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A note about transitions…

n Transitions are not restricted to takingplace between structures joined by acatalytic edge.n the presence of the edge increases the

likelihood that the terminus will be thedestination for a transition, because of fitnesslevels.

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More Questions!

n If artificial chemistries are the "right stuff",shouldn't we be able to come up with amodel for perhaps a cell?

n Can we describe a cell's self-maintenanceand self-reproduction with a simpleartificial chemistry?

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Enter : Ono and Ikegami (1999)

n For any interesting behavior to happen in a realchemical system, enclosure is neededn In a cell, this is the cell membrane – this is

maintained by the cell (self-maintenance).

n Wanted to show how primitive cells can emergeand evolve from a simple chemical network.(Based on Varela’s work)n address the issues of self-maintenance and self-

replication.

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…and Others

n Recent work by Fenizio, Dittrich andBanzhaf (2001) is in the same theme.

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Ono and Ikegami

n Molecules : abstract chemicalsn {A,M,W,X,Y}, catalyzing each other’s reactions

n Topology : A triangular lattice. Each blockhas a population

Ono & Ikegami (1999)[edited]

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Molecules

n There is a repulsive force between somemolecules

n Rotation ‡ chemical transitionn probabilistically based on potential energies of self

and neighbors and presence of catalysts

n Hopping around ‡ mobile transitionn probabilistically based on potential energies of self

and neighbors.

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Repulsion?

n M can have isotropic or anisotropic repulsion

from http://www.neilblevins.com/cg_education/tut18/tut18.htm

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Rotation?

Ono & Ikegami (1999)

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Some molecular details

n W – like water; cannot change into any otherchemical

n A – autocatalytic

n X – high chemical potential, not autocatalyticn Y – product of decay – lowest chemical potentialn M – a product of reactions, with variable

repulsion

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Molecular structure

n The cell model can maintain it’s structureas long as the membrane is intact.n A within the cell keep reproducing

themselves, while providing enough M tomaintain the membrane. The membrane thenprevents the A from diffusing outward.

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Cell… death?

n Insufficient supply of A causes themembrane to decay and disappear


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Self-Maintenance

n Cells ingest nutrients and excrete wastethrough the membrane.n In our model : allow X and Y to permeate

through membrane at a rate proportional togradient of their density

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Self-Replication

n when cell reaches a certain size, becomesunstable and generates a new membraneinside (independently). Eventually divides thecell. (Growth through ingesting X)

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Self-Replication

n Cell grows, becomes unstable and starts toproduce membrane inward…


black – Membrane gray – Water white - X

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Self-Replication cont…

n membrane grows inward, creating newcompartments


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Cell Membrane Types

n By varying repulsion rules of M, canchange the properties of membranes.

flexiblestiff


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Future work for Ono and Ikegami

n Looking to extend the model to 3dimensions

n want to include the evolution of selectivepermeability of the membrane

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Summary

n Found interesting behavior in autocatalyticchemistriesn with a search, we found cycles are common,

though stability is rather rare – withstandingthe initial population.

n with diverse starting conditions, they reliablyfind cycles on which to replicate – as long asthe population (concentration) is high enough!

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Summary

n We have a cell model thatn has an internal autocatalytic cycle of

chemicalsn maintains the membrane itselfn membrane prevents the cell from collapsing

and/or cell prevents the membrane fromdeteriorating…

n cell self-replicates : molecular reproduction ‡cellular reproduction

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Many Thanks!

n Resourcesn 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 ofthe Fifth European Conference on Artificial Life (ECAL99), Berlin, pp. 399--406. Springer.

n Huning, H. (2000). A search for multiple autocatalytic sets in artificial chemistries based onboolean networks. Artificial Life VII, 1-6 August 2000, Portland, OR, USA.

n Fraser, S., & Reidys, C. (1997). Evolution of random catalytic networks. In ECAL97.

n Peter Dittrich, Jens Ziegler, and Wolfgang Banzhaf (2001). Artificial Chemistries - A Review.Artificial Life, 7(3):225-275

n Pietro Speroni di Fenizio, Peter Dittrich, and Wolfgang Banzhaf (2001). SpontaneousFormation 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 onArtificial Life), LNCS 2159, pp. 206-215,Prague, September 10-14, 2001. Springer, Berlin.

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