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AUTOCATALYTIC REPLICATION of Ijolymers J. Doyne FARMER Physica 220 (1986) SO-61 North-Holland, Amsterdam AUTOCATALYTIC REPLICATION OF IjOLYMERS J. Doyne FARMER Center for Nonlinear Studies, MS B2.58, Los Alamos National Laboratory, L.os Alamos, NM 87545, USA Stuart A. KAUFFMAN Department of Biochemistry and Biophysics, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA and Norman H. PACKARD The Institute /or Advanced Study Princeton, NJ 08540, USA We construct a simplified model for the chemistry of molecules such as polypeptides or single stranded nucleic acids, whose reactions can be restricted to catalyzed cleavage and condensation. We use this model to study the spontaneous emergence of autocatalytic sets from an initial set of simple building blocks, for example short strands of ammo acids or nucleotides. When the initial set exceeds a critical diversity, autocatalytic reactions generate large molecular species in abundance. Our results suggest that the critical diversity is not very large. Autocatalytic sets formed in this way can be regarded as primitive connected metabolisms, in which particular species are selected if their chemical properties are advantageous for the metabolism. Such autocatalytic sets may have played a crucial role in the origin of life, providing a bridge from simple molecular species to complex proteins and nucleic acids. Many of our results are experimentally testable. 1. Introduction way from there to the complex proteins and nucleic acids needed for contemporary life. The possibil- The origin of life poses fundamental problems ity that we study here is that the origin of life concerning the prebiotic origins of molecular came about through the evolution of autocatalytic species. Present life forms contain a rich set of sets of polypeptides and/or single stranded RNA. chemical constituents which regenerate themselves By autocatalytic set we mean that each member is through processes of replication, transcription, and the product of at Yeast one reaction catalyzed by at translation, relying heavily on the collaboration of least one other member. Our central thesis here is proteins and nucleic acids. Although contem- that templating is not required to achieve an auto- porary life may have evolved from earlier, simpler catalytic set. Instead, simple polymers can cata- forms, there seems to be a minimum level of lyze the formation of each other, generating complexity below which life based on templating autocatalytic sets that evolve in time to create is not possible. How, then, were the conditions complex chemical species whose properties are needed to achieve life based on templating ever tuned for effective collaboration with each other. ieachtSd? The system thus bootstraps itself from a simple The experiments of Miller and Urey [l] and initial state to a sophisticated autocatalytic set, others indicate that it is possible to form amino which might be regarded as a precursor life form. acids and other small metabolites from simpler The sets provide the rich substrate of raw materi- constituents in a fairly direct way, but it is a long als and coupled catalytic relationships needed for 0167-2789/86/$03.50 Q Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) J.D. Farmer et at/A utocatalytic replication of polymers 51 the origin of contemporary life. The importance of then single strands of RNA would be capable of autocatalytic properties has also been discussed by catalyzing each other in precisely the fashion that Calvin [2], Eigen [3], Eigen and Schuster [4, 5], we model here. Our model is general, describing Kauffman [6, 7], Rossler [8, 9, 10], and Dyson [11, any family of polymers undergoing catalyzed 121. cleavage and condensation reactions. The molecular species comprising our autocata- What we do here can be viewed as a preliminary lyric sets may be any polymers that can undergo attempt to simulate and understand the qualitative catalyzed cleavage and condensation reactions. behavior of a model chemistry. Simple con- Given a sufficiently diverse supply of simple stituents forming a food set are pumped into a monomers and small polymers as raw materials, stirred tank which is allowed to overflow. Our catalyzed reactions between them can form more results demonstrate that what happens is critically complex molecular species. The new species in dependent on the properties of the food set. Below turn serve as substrates and catalysts for further a critical complexity very little happens. Above reactions, increasing the complexity of the system this critical complexity, however, a chain reaction until an autocatalytic set is created. Catalyzed is triggered that generates a rich autocatalytic set. pathways from the "food set" maintain the mem- The model chemistry we construct here also bers of the autocatalytic set. The result is a presents an interesting problem in dynamical sys- metabolism converting simple molecules into com- tems theory. For a fixed set of chemical species we plex ones. Different catalytic pathways within the model the dynamics in terms of ordinary differen- network compete with each other, enhancing the tial equations describing the change in concentra- concentration of some species at the expense of tion of each species. The set of chemical species others. The set thus evolves in time, creating a rich can change in time, however, so that the equations but focused collection of molecular species whose themselves are dynamic. cooperative chemical properties make them more Rossler first stressed the qualitative dynamics of fit than others. Such autocatalytic sets might serve autocatalytic networks that grow in complexity [8, as a bridge from simple building blocks such as 9, 10]. Even though the system is always finite at amino acids and nucleotides to contemporary life any given time, it potentially explores an infinite based on a genetic code. dimensional space. The system evolves by chang- Experiments have shown that ligation (end con- ing its equation of motion. These changes can take densation) and cleavage reactions among poly- place over a very long time scale. Such systems peptides may be catalyzed by other polypeptides provide a novel type of dynamical system which [13, 14, 15]. More complicated reactions may also has received very little attention. be catalyzed, e.g. transpeptidation reactions, where The work described here has practical motiva- pieces of two polypeptides switch places. These tions as well. Current molecular cloning tech- more complicated reactions may, however, be re- niques now make it possible to generate very large garded as compositions of ligation and cleavage. numbers of novel DNA molecules in expression Thus, there is good experimental evidence indicat- vectors, hence to clone very large numbers of ing that the type of catalyzed reactions we study novel genes, and study their RNA or protein here occur for polypeptides. products for catalytic or other activities. Such In addition, recent experiments have shown that experiments are now underway, and may ulti- certain single stranded RNA sequences can be mately lead to actual construction of autocatalytic reproduced autocatalytically. It has been conjec- polymer systems, possibly with useful commercial tured that this mechanism might be extended to properties. Our work may be viewed as a feasi- include arbitrary sequences [16]. If this were true, bility study for this process. Our results suggest 52 J.D. Farmer et al./ Autocatalytic replication of polymers that there is a minimum critical complexity of the For simplicity, at this stage we consider only food set and catalytic properties which must be catalyzed reactions. Uncatalyzed reactions may achieved if such efforts are to succeed. ultimately play an important role in allowing Basic aspects of the model discussed here have "tunnelling" to new species, but in view of the already been introduced elsewhere [6, 7]. enormous discrepancy in reaction rates, it seems plausible to ignore them for the moment. Thus in order for a reaction to occur at all, it must have at 2. Description of the model least one catalyst present in the system. Our reac- tions are of the form. Real chemical reactions among large sets of e peptides or oligonucliotides are too complicated to c+hma+b, (1) have any ho~e of simulating in detail because of where c is the concatenation of a and b, e is the limitations on both our current knowledge of bio- enzyme catalyzing the reaction, and h represents chemistry and of current computer technology. water, which plays an important role in setting the Any simulation must use a drastically simplified equilibrium concentrations. model of chemical reactions. The goal in con- As illustrated in fig. 1, the list of species to- structing such models is to preserve the qualitative gether with their reactions can be visualized as a features that are most important in generating robust reproduction of what is typically seen in graph, with arrows connecting the two cleavage experiments. products a and b and the condensate c to a nodal point, corresponding to the reaction. The network The polymers under study are assumed to be one dimensional chains, represented by one di- of catalysts can be thought of as a superimposed mensional strings over an n letter alphabet, of the graph connecting the catalysts to the reaction form s x, s 2, • • •. The letters s may represent differ- nodes. These graphs can change in time as new ent amino acids, or alternatively, different nucleo- species are created or old species are eliminated from the system. Assignment of chemical proper- tides. The strings are oriented from left to right. In proteins this corresponds to the orientation from ties amounts to giving a procedure for determin- the amino terminal on one end to the carboxy ing the reaction and catalysis graphs, together with associated kinetic properties such as reaction terminal on the other end, and for single stranded velocities, equilibrium constants, etc. In the fol- RNA it corresponds to the asymmetry between lowing section we address the problem of con- the 5' and 3' ends.
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