Evolution of RNA Viruses: Reasons for the Existence of Separate Plus, Minus, and Double-Strand Replication Strategies.

Plus, minus, and double-strand RNA viruses are all found in nature. We use computational models to study the relative success of these strategies. We consider translation, replication, and virion assembly inside one cell, and transmission of virions between cells. For viruses which do not incorporate a polymerase in the capsid, transmission of only plus strands is the default strategy because virions containing minus strands are not infectious. Packaging only plus strands has a significant advantage if the number of RNA strands produced per cell is larger than the number of capsids. In this case, by not packaging minus strands, the virus produces more plus-strand virions. Therefore, plus-strand viruses are selected at low multiplicity of infection. However, at high multiplicity of infection, it is preferable to package both strands because the additional minus virions produced are helpful when there are multiple infections per cell. The fact that plus-strand viruses are widespread while viruses that package both strands are not seen in nature suggests that RNA strands are indeed produced in excess over capsids, and that the multiplicity of infection is not sufficiently high to favor the production of both kinds of virions. For double-strand viruses, we show that it is advantageous to produce only plus strands from the double strand within the cell, as is observed in real viruses. The reason for the success of minus-strand viruses is more puzzling initially. For viruses that incorporate a polymerase in the virion, minus virions are infectious. However, this is not sufficient to explain the success of minus-strand viruses, because in this case, viruses that package both strands outcompete those that package only minus or only plus. Real minus-strand viruses make use of replicable strands that are coated by a nucleoprotein, and separate translatable plus strands that are uncoated. Here we show that when there are distinct replicable and translatable strands, minus-strand viruses are selected.

Evolution of Bipartite and Segmented Viruses from Monopartite Viruses.

RNA viruses may be monopartite (all genes on one strand), multipartite (two or more strands packaged separately) or segmented (two or more strands packaged together). In this article, we consider competition between a complete monopartite virus, A, and two defective viruses, D and E, that have complementary genes. We use stochastic models that follow gene translation, RNA replication, virus assembly, and transmission between cells. D and E multiply faster than A when stored in the same host as A or when together in the same host, but they cannot multiply alone. D and E strands are packaged as separate particles unless a mechanism evolves that allows assembly of D + E segmented particles. We show that if defective viruses assemble rapidly into separate particles, the formation of segmented particles is selected against. In this case, D and E spread as parasites of A, and the bipartite D + E combination eliminates A if the transmissibility is high. Alternatively, if defective strands do not assemble rapidly into separate particles, then a mechanism for assembly of segmented particles is selected for. In this case, the segmented virus can eliminate A if transmissibility is high. Conditions of excess protein resources favor bipartite viruses, while conditions of excess RNA resources favor segmented viruses. We study the error threshold behavior that arises when deleterious mutations are introduced. Relative to bipartite and segmented viruses, deleterious mutations favor monopartite viruses. A monopartite virus can give rise to either a bipartite or a segmented virus, but it is unlikely that both will originate from the same virus.

Rolling Circles as a Means of Encoding Genes in the RNA World.

The rolling circle mechanism found in viroids and some RNA viruses is a likely way that replication could have begun in the RNA World. Here, we consider simulations of populations of protocells, each containing multiple copies of rolling circle RNAs that can replicate non-enzymatically. The mechanism requires the presence of short self-cleaving ribozymes such as hammerheads, which can cleave and re-circularize RNA strands. A rolling circle must encode a hammerhead and the complement of a hammerhead, so that both plus and minus strands can cleave. Thus, the minimal functional length is twice the length of the hammerhead sequence. Selection for speed of replication will tend to reduce circles to this minimum length. However, if sequence errors occur when copying the hammerhead sequence, this prevents cleavage at one point, but still allows cleavage on the next passage around the rolling circle. Thus, there is a natural doubling mechanism that creates strands that are multiple times the length of the minimal sequence. This can provide space for the origin of new genes with beneficial functions. We show that if a beneficial gene appears in this new space, the longer sequence with the beneficial function can be selected, even though it replicates more slowly. This provides a route for the evolution of longer circles encoding multiple genes.

Computer simulations of Template-Directed RNA Synthesis driven by temperature cycling in diverse sequence mixtures.

We present simulations of non-enzymatic template-directed RNA synthesis that incorporate primer extension, ligation, melting, and reannealing. Strand growth occurs over multiple heating/cooling cycles, producing strands of several hundred nucleotides in length, starting with random oligomers of 4 to 10 nucleotides. A strand typically grows by only 1 or 2 nucleotides in each cycle. Therefore, a strand is copied from many different templates, not from one specific complementary strand. A diverse sequence mixture is produced, and there is no exact copying of sequences, even if single base additions are fully accurate (no mutational errors). It has been proposed that RNA systems may contain a virtual circular genome, in which sequences partially overlap in a way that is mutually catalytic. We show that virtual circles do not emerge naturally in our simulations, and that a system initiated with a virtual circle can only maintain itself if there are no mutational errors and there is no input of new sequences formed by random polymerization. Furthermore, if a virtual sequence and its complement contain repeated short words, new sequences can be produced that were not on the original virtual circle. Therefore the virtual circle sequence cannot maintain itself. Functional sequences with secondary structures contain complementary words on opposite sides of stem regions. Both these words are repeated in the complementary sequence; hence, functional sequences cannot be encoded on a virtual circle. Additionally, we consider sequence replication in populations of protocells. We suppose that functional ribozymes benefit the cell which contains them. Nevertheless, scrambling of sequences occurs, and the functional sequence is not maintained, even when under positive selection.

When Is a Reaction Network a Metabolism? Criteria for Simple Metabolisms That Support Growth and Division of Protocells.

With the aim of better understanding the nature of metabolism in the first cells and the relationship between the origin of life and the origin of metabolism, we propose three criteria that a chemical reaction system must satisfy in order to constitute a metabolism that would be capable of sustaining growth and division of a protocell. (1) Biomolecules produced by the reaction system must be maintained at high concentration inside the cell while they remain at low or zero concentration outside. (2) The total solute concentration inside the cell must be higher than outside, so there is a positive osmotic pressure that drives cell growth. (3) The metabolic rate (i.e., the rate of mass throughput) must be higher inside the cell than outside. We give examples of small-molecule reaction systems that satisfy these criteria, and others which do not, firstly considering fixed-volume compartments, and secondly, lipid vesicles that can grow and divide. If the criteria are satisfied, and if a supply of lipid is available outside the cell, then continued growth of membrane surface area occurs alongside the increase in volume of the cell. If the metabolism synthesizes more lipid inside the cell, then the membrane surface area can increase proportionately faster than the cell volume, in which case cell division is possible. The three criteria can be satisfied if the reaction system is bistable, because different concentrations can exist inside and out while the rate constants of all the reactions are the same. If the reaction system is monostable, the criteria can only be satisfied if there is a reason why the rate constants are different inside and out (for example, the decay rates of biomolecules are faster outside, or the formation rates of biomolecules are slower outside). If this difference between inside and outside does not exist, a monostable reaction system cannot sustain cell growth and division. We show that a reaction system for template-directed RNA polymerization can satisfy the requirements for a metabolism, even if the small-molecule reactions that make the single nucleotides do not.

Rolling-circle and strand-displacement mechanisms for non-enzymatic RNA replication at the time of the origin of life.

It is likely that RNA replication began non-enzymatically, and that polymerases were later selected to speed up the process. We consider replication mechanisms in modern viruses and ask which of these is possible non-enzymatically, using mathematical models and experimental data found in the literature to estimate rates of RNA synthesis and replication. Replication via alternating plus and minus strands is found in some single-stranded RNA viruses. However, if this occurred non-enzymatically it would lead to double-stranded RNA that would not separate. With some form of environmental cycling, such as temperature, salinity, or pH cycling, double-stranded RNA can be melted to form single-stranded RNA, although re-annealing of existing strands would then occur much faster than synthesis of new strands. We show that re-annealing blocks this form of replication at a very low concentration of strands. Other kinds of viruses synthesize linear double strands from single strands and then make new single strands from double strands via strand-displacement. This does not require environmental cycling and is not blocked by re-annealing. However, under non-enzymatic conditions, if strand-displacement occurs from a linear template, we expect the incomplete new strand to be almost always displaced by the tail end of the old strand through toehold-mediated displacement. A third kind of replication in viruses and viroids is rolling-circle replication which occurs via strand-displacement on a circular template. Rolling-circle replication does not require environmental cycling and is not prevented by toehold-mediated displacement. Rolling-circle replication is therefore expected to occur non-enzymatically and is a likely starting point for the evolution of polymerase-catalysed replication.

Can the RNA World Still Function without Cytidine?

Most scenarios for the origin of life assume that RNA played a key role in both catalysis and information storage. The A, U, G, and C nucleobases in modern RNA all participate in secondary structure formation and replication. However, the rapid deamination of C to U and the absence of C in meteorite samples suggest that prebiotic RNA may have been deficient in cytosine. Here, we assess the ability of RNA sequences formed from a three-letter AUG alphabet to perform both structural and genetic roles in comparison to sequences formed from the AUGC alphabet. Despite forming less thermodynamically stable helices, the AUG alphabet can find a broad range of structures and thus appears sufficient for catalysis in the RNA World. However, in the AUG case, longer sequences are required to form structures with an equivalent complexity. Replication in the AUG alphabet requires GU pairing. Sequence fidelity in the AUG alphabet is low whenever G's are present in the sequence. We find that AUG sequences evolve to AU sequences if GU pairing is rare, and to RU sequences if GU pairing is common (R denotes A or G). It is not possible to conserve a G at a specific site in either case. These problems do not rule out the possibility of an RNA World based on AUG, but they show that it wouldbe significantly more difficult than with a four-base alphabet.

Survival of RNA Replicators is much Easier in Protocells than in Surface-Based, Spatial Systems.

In RNA-World scenarios for the origin of life, replication is catalyzed by polymerase ribozymes. Replicating RNA systems are subject to invasion by non-functional parasitic strands. It is well-known that there are two ways to avoid the destruction of the system by parasites: spatial clustering in models with limited diffusion, or group selection in protocells. Here, we compare computational models of replication in spatial models and protocells as closely as possible in order to determine the relative importance of these mechanisms in the RNA World. For the survival of the polymerases, the replication rate must be greater than a minimum threshold value, kmin, and the mutation rate in replication must be less than a maximum value, Mmax, which is known as the error threshold. For the protocell models, we find that kmin is substantially lower and Mmax is substantially higher than for the equivalent spatial models; thus, the survival of polymerases is much easier in protocells than on surfaces. The results depend on the maximum number of strands permitted in one protocell or one lattice site in the spatial model, and on whether replication is limited by the supply of monomers or the population size of protocells. The substantial advantages that are seen in the protocell models relative to the spatial models are robust to changing these details. Thus, cooperative polymerases with limited accuracy would have found it much easier to operate inside lipid compartments, and this suggests that protocells may have been a very early step in the development of life. We consider cases where parasites have an equal replication rate to polymerases, and cases where parasites multiply twice as fast as polymerases. The advantage of protocell models over spatial models is increased when the parasites multiply faster.

Evolution of protein interfaces in multimers and fibrils.

A majority of cellular proteins function as part of multimeric complexes of two or more subunits. Multimer formation requires interactions between protein surfaces that lead to closed structures, such as dimers and tetramers. If proteins interact in an open-ended way, uncontrolled growth of fibrils can occur, which is likely to be detrimental in most cases. We present a statistical physics model that allows aggregation of proteins as either closed dimers or open fibrils of all lengths. We use pairwise amino-acid contact energies to calculate the energies of interacting protein surfaces. The probabilities of all possible aggregate configurations can be calculated for any given sequence of surface amino acids. We link the statistical physics model to a population genetics model that describes the evolution of the surface residues. When proteins evolve neutrally, without selection for or against multimer formation, we find that a majority of proteins remain as monomers at moderate concentrations, but strong dimer-forming or fibril-forming sequences are also possible. If selection is applied in favor of dimers or in favor of fibrils, then it is easy to select either dimer-forming or fibril-forming sequences. It is also possible to select for oriented fibrils with protein subunits all aligned in the same direction. We measure the propensities of amino acids to occur at interfaces relative to noninteracting surfaces and show that the propensities in our model are strongly correlated with those that have been measured in real protein structures. We also show that there are significant differences between amino acid frequencies at isologous and heterologous interfaces in our model, and we observe that similar effects occur in real protein structures.

The evolution of antibiotic production rate in a spatial model of bacterial competition.

We consider competition between antibiotic producing bacteria, non-producers (or cheaters), and sensitive cells in a two-dimensional lattice model. Previous work has shown that these three cell types can survive in spatial models due to the presence of spatial patterns, whereas coexistence is not possible in a well-mixed system. We extend this to consider the evolution of the antibiotic production rate, assuming that the cost of antibiotic production leads to a reduction in growth rate of the producers. We find that coexistence occurs for an intermediate range of antibiotic production rate. If production rate is too high or too low, only sensitive cells survive. When evolution of production rate is allowed, a mixture of cell types arises in which there is a dominant producer strain that produces sufficient to limit the growth of sensitive cells and which is able to withstand the presence of cheaters in its own species. The mixture includes a range of low-rate producers and non-producers, none of which could survive without the presence of the dominant producer strain. We also consider the case of evolution of antibiotic resistance within the sensitive species. In order for the resistant cells to survive, they must grow faster than both the non-producers and the producers. However, if the resistant cells grow too rapidly, the producing species is eliminated, after which the resistance mutation is no longer useful, and sensitive cells take over the system. We show that there is a range of growth rates of the resistant cells where the two species coexist, and where the production mechanism is maintained as a polymorphism in the producing species and the resistance mechanism is maintained as a polymorphism in the sensitive species.

Constraining the Time Interval for the Origin of Life on Earth.

Estimates of the time at which life arose on Earth make use of two types of evidence. First, astrophysical and geophysical studies provide a timescale for the formation of Earth and the Moon, for large impact events on early Earth, and for the cooling of the early magma ocean. From this evidence, we can deduce a habitability boundary, which is the earliest point at which Earth became habitable. Second, biosignatures in geological samples, including microfossils, stromatolites, and chemical isotope ratios, provide evidence for when life was actually present. From these observations we can deduce a biosignature boundary, which is the earliest point at which there is clear evidence that life existed. Studies with molecular phylogenetics and records of the changing level of oxygen in the atmosphere give additional information that helps to determine the biosignature boundary. Here, we review the data from a wide range of disciplines to summarize current information on the timings of these two boundaries. The habitability boundary could be as early as 4.5 Ga, the earliest possible estimate of the time at which Earth had a stable crust and hydrosphere, or as late as 3.9 Ga, the end of the period of heavy meteorite bombardment. The lack of consensus on whether there was a late heavy meteorite bombardment that was significant enough to prevent life is the largest uncertainty in estimating the time of the habitability boundary. The biosignature boundary is more closely constrained. Evidence from carbon isotope ratios and stromatolite fossils both point to a time close to 3.7 Ga. Life must have emerged in the interval between these two boundaries. The time taken for life to appear could, therefore, be within 200 Myr or as long as 800 Myr. Key Words: Origin of life-Astrobiology-Habitability-Biosignatures-Geochemistry-Early Earth. Astrobiology 18, 343-364.

The Role of Templating in the Emergence of RNA from the Prebiotic Chemical Mixture.

Biological RNA is a uniform polymer in three senses: it uses nucleotides of a single chirality; it uses only ribose sugars and four nucleobases rather than a mixture of other sugars and bases; and it uses only 3'-5' bonds rather than a mixture of different bond types. We suppose that prebiotic chemistry would generate a diverse mixture of potential monomers, and that random polymerization would generate non-uniform strands of mixed chirality, monomer composition, and bond type. We ask what factors lead to the emergence of RNA from this mixture. We show that template-directed replication can lead to the emergence of all the uniform properties of RNA by the same mechanism. We study a computational model in which nucleotides react via polymerization, hydrolysis, and template-directed ligation. Uniform strands act as templates for ligation of shorter oligomers of the same type, whereas mixed strands do not act as templates. The three uniform properties emerge naturally when the ligation rate is high. If there is an exact symmetry, as with the chase of chirality, the uniform property arises via a symmetry-breaking phase transition. If there is no exact symmetry, as with monomer selection and backbone regioselectivity, the uniform property emerges gradually as the rate of template-directed ligation is increased.

Chemical Evolution and the Evolutionary Definition of Life.

Darwinian evolution requires a mechanism for generation of diversity in a population, and selective differences between individuals that influence reproduction. In biology, diversity is generated by mutations and selective differences arise because of the encoded functions of the sequences (e.g., ribozymes or proteins). Here, I draw attention to a process that I will call chemical evolution, in which the diversity is generated by random chemical synthesis instead of (or in addition to) mutation, and selection acts on physicochemical properties, such as hydrolysis, photolysis, solubility, or surface binding. Chemical evolution applies to short oligonucleotides that can be generated by random polymerization, as well as by template-directed replication, and which may be too short to encode a specific function. Chemical evolution is an important stage on the pathway to life, between the stage of "just chemistry" and the stage of full biological evolution. A mathematical model is presented here that illustrates the differences between these three stages. Chemical evolution leads to much larger differences in molecular concentrations than can be achieved by selection without replication. However, chemical evolution is not open-ended, unlike biological evolution. The ability to undergo Darwinian evolution is often considered to be a defining feature of life. Here, I argue that chemical evolution, although Darwinian, does not quite constitute life, and that a good place to put the conceptual boundary between non-life and life is between chemical and biological evolution.

Error thresholds for RNA replication in the presence of both point mutations and premature termination errors.

We consider a spatial model of replication in the RNA World in which polymerase ribozymes use neighbouring strands as templates. Point mutation errors create parasites that have the same replication rate as the polymerase. We have shown previously that spatial clustering allows survival of the polymerases as long as the error rate is below a critical error threshold. Here, we additionally consider errors where a polymerase prematurely terminates replication before reaching the end of the template, creating shorter parasites that are replicated faster than the functional polymerase. In well-known experiments where Qß RNA is replicated by an RNA polymerase protein, the virus RNA is rapidly replaced by very short non-functional sequences. If the same thing were to occur when the polymerase is a ribozyme, this would mean that termination errors could potentially destroy the RNA World. In this paper, we show that this is not the case in the RNA replication model studied here. When there is continued generation of parasites of all lengths by termination errors, the system can survive up to a finite error threshold, due to the formation of travelling wave patterns; hence termination errors are important, but they do not lead to the inevitable destruction of the RNA World by short parasites. The simplest assumption is that parasite replication rate is inversely proportional to the strand length. In this worst-case scenario, the error threshold for termination errors is much lower than for point mutations. We also consider a more realistic model in which the time for replication of a strand is the sum of a time for binding of the polymerase, and a time for polymerization. When the binding step is considered, termination errors are less serious than in the worst case. In the limit where the binding time is dominant, replication rates are equal for all lengths, and the error threshold for termination is the same as for point mutations.

Co-operation between Polymerases and Nucleotide Synthetases in the RNA World.

It is believed that life passed through an RNA World stage in which replication was sustained by catalytic RNAs (ribozymes). The two most obvious types of ribozymes are a polymerase, which uses a neighbouring strand as a template to make a complementary sequence to the template, and a nucleotide synthetase, which synthesizes monomers for use by the polymerase. When a chemical source of monomers is available, the polymerase can survive on its own. When the chemical supply of monomers is too low, nucleotide production by the synthetase is essential and the two ribozymes can only survive when they are together. Here we consider a computational model to investigate conditions under which coexistence and cooperation of these two types of ribozymes is possible. The model considers six types of strands: the two functional sequences, the complementary strands to these sequences (which are required as templates), and non-functional mutants of the two sequences (which act as parasites). Strands are distributed on a two-dimensional lattice. Polymerases replicate strands on neighbouring sites and synthetases produce monomers that diffuse in the local neighbourhood. We show that coexistence of unlinked polymerases and synthetases is possible in this spatial model under conditions in which neither sequence could survive alone; hence, there is a selective force for increasing complexity. Coexistence is dependent on the relative lengths of the two functional strands, the strand diffusion rate, the monomer diffusion rate, and the rate of deleterious mutations. The sensitivity of this two-ribozyme system suggests that evolution of a system of many types of ribozymes would be difficult in a purely spatial model with unlinked genes. We therefore speculate that linkage of genes onto mini-chromosomes and encapsulation of strands in protocells would have been important fairly early in the history of life as a means of enabling more complex systems to evolve.

The Effect of Limited Diffusion and Wet-Dry Cycling on Reversible Polymerization Reactions: Implications for Prebiotic Synthesis of Nucleic Acids.

A long-standing problem for the origins of life is that polymerization of many biopolymers, including nucleic acids and peptides, is thermodynamically unfavourable in aqueous solution. If bond making and breaking is reversible, monomers and very short oligomers predominate. Recent experiments have shown that wetting and drying cycles can overcome this problem and drive the formation of longer polymers. In the dry phase, bond formation is favourable, but diffusion is restricted, and bonds only form between monomers that are initially close together. In the wet phase, some of the bonds are hydrolyzed. However, repositioning of the molecules allows new bonds to form in the next dry phase, leading to an increase in mean polymer length. Here, we consider a simple theoretical model that explains the effect of cycling. There is an equilibrium length distribution with a high mean length that could be achieved if diffusion occurred freely in the dry phase. This equilibrium is inaccessible without diffusion. A single dry cycle without diffusion leads to mean lengths much shorter than this. Repeated cycling leads to a significant increase in polymerization relative to a single cycle. In the most favourable case, cycling leads to the same equilibrium length distribution as would be achieved if free diffusion were possible in the dry phase. These results support the RNA World scenario by explaining a potential route to synthesis of long RNAs; however, they also imply that cycling would be beneficial to the synthesis of other kinds of polymers, including peptides, where bond formation involves a condensation reaction.

Estimating the Frequency of Horizontal Gene Transfer Using Phylogenetic Models of Gene Gain and Loss.

We analyze patterns of gene presence and absence in a maximum likelihood framework with rate parameters for gene gain and loss. Standard methods allow independent gains and losses in different parts of a tree. While losses of the same gene are likely to be frequent, multiple gains need to be considered carefully. A gene gain could occur by horizontal transfer or by origin of a gene within the lineage being studied. If a gene is gained more than once, then at least one of these gains must be a horizontal transfer. A key parameter is the ratio of gain to loss rates, a/v We consider the limiting case known as the infinitely many genes model, where a/v tends to zero and a gene cannot be gained more than once. The infinitely many genes model is used as a null model in comparison to models that allow multiple gains. Using genome data from cyanobacteria and archaea, it is found that the likelihood is significantly improved by allowing for multiple gains, but the average a/v is very small. The fraction of genes whose presence/absence pattern is best explained by multiple gains is only 15% in the cyanobacteria and 20% and 39% in two data sets of archaea. The distribution of rates of gene loss is very broad, which explains why many genes follow a treelike pattern of vertical inheritance, despite the presence of a significant minority of genes that undergo horizontal transfer.

Pathways of Genetic Code Evolution in Ancient and Modern Organisms.

There have been two distinct phases of evolution of the genetic code: an ancient phase--prior to the divergence of the three domains of life, during which the standard genetic code was established--and a modern phase, in which many alternative codes have arisen in specific groups of genomes that differ only slightly from the standard code. Here we discuss the factors that are most important in these two phases, and we argue that these are substantially different. In the modern phase, changes are driven by chance events such as tRNA gene deletions and codon disappearance events. Selection acts as a barrier to prevent changes in the code. In contrast, in the ancient phase, selection for increased diversity of amino acids in the code can be a driving force for addition of new amino acids. The pathway of code evolution is constrained by avoiding disruption of genes that are already encoded by earlier versions of the code. The current arrangement of the standard code suggests that it evolved from a four-column code in which Gly, Ala, Asp, and Val were the earliest encoded amino acids.

The RNA World: molecular cooperation at the origins of life.

The RNA World concept posits that there was a period of time in primitive Earth's history - about 4 billion years ago - when the primary living substance was RNA or something chemically similar. In the past 50 years, this idea has gone from speculation to a prevailing idea. In this Review, we summarize the key logic behind the RNA World and describe some of the most important recent advances that have been made to support and expand this logic. We also discuss the ways in which molecular cooperation involving RNAs would facilitate the emergence and early evolution of life. The immediate future of RNA World research should be a very dynamic one.

The origin and spread of a cooperative replicase in a prebiotic chemical system.

The origin of life requires the emergence of a system of autocatalytic polymers such as RNA. We consider a trans-acting replicase that catalyses replication of a template (either a copy of itself or another sequence). Our model includes alternating plus/minus strand replication where only the plus strand is a catalyst. Prebiotic chemistry generates random sequences and allows for non-catalysed, template-directed synthesis of new strands. These chemical reactions are insufficient to sustain replication, but they provide a background in which the first replicase can arise. In the well-mixed case, the minimum value of the catalytic rate parameter k for which a stable replicating state survives scales as 1/f, where f is the fraction of random sequences that are catalysts. When catalysts are rare (f→0), the replicating state is not stable in for any finite k because the replicases are overrun by parasitic templates already present in the prebiotic system, and by additional parasites created by mutation of the catalyst. In contrast, in 2d spatial simulations, the replicating state is stable for moderate k with appropriate values of the local diffusion constant. We calculate the probability of spread of the replicating state from a single isolated catalyst. This occurs in a parameter range that is narrower than that in which existing replicators are stable. The 2d model uses 'Two׳s Company' rules, where two molecules on a site may replicate, but crowding occurs when three molecules are on one site. A mean-field theory is presented which predicts the most important results of the spatial model. Our results emphasize that the origin of replication is a spatially-localized stochastic transition between a 'dead' state controlled by prebiotic chemistry and a 'living' state controlled by autocatalytic replication.