In search of the holy replicator

After 40 years of searching for the eukaryotic replicator sequence, it is time to abandon the concept of 'the' replicator as a single genetic entity. Here I propose a 'relaxed replicon model' in which a positive initiator-replicator interaction is facilitated by a combination of several complex features of chromatin. An important question for the future is whether the positions of replication origins are simply a passive result of local chromatin structure or are actively localized to coordinate replication with other chromosomal activities.     

Strict ESS for n-species systems

A system of n asexual populations is considered where both intra- and interspecific frequency-dependent game conflicts with lack of information take place. The concept of a strict n-species ESS is introduced which implies local asymptotic stability of the replicator dynamics of pure phenotypes. The dynamical concept of strict stability is also introduced which turns out to be equivalent to the strict n-species ESS concept. The above notions are also related to similar concepts considered in the literature for the same biological situation.     

The human beta-globin replication initiation region consists of two modular independent replicators

Previous studies have shown that mammalian cells contain replicator sequences, which can determine where DNA replication initiates. However, the specific sequences that confer replicator activity were not identified. Here we report a detailed analysis of replicator sequences that dictate initiation of DNA replication from the human beta-globin locus. This analysis suggests that the beta-globin replication initiation region contains two adjacent, redundant replicators. Each replicator was capable of initiating DNA replication independently at ectopic sites. Within each of these two replicators, we identified short, discrete, nonredundant sequences, which cooperatively determine replicator activity. Experiments with somatic cell hybrids further demonstrated that the requirements for initiation at ectopic sites were similar to the requirements for initiation within native human chromosomes. The replicator clustering and redundancy exemplified in the human beta-globin locus may account for the extreme difficulty in identifying replicator sequences in mammalian cells and suggest that mammalian replication initiation sites may be determined by cooperative sequence modules.     

The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems

In the RNA world hypothesis, RNA(-like) self-replicators are suggested as the central player of prebiotic evolution. However, there is a serious problem in the evolution of complexity in such replicators, i.e., the problem of parasites. Parasites, which are replicated by catalytic replicators (catalysts), but do not replicate the others, can destroy a whole replicator system by exploitation. Recently, a theoretical study underlined complex formation between replicators--an often neglected but realistic process--as a stabilizing factor in a replicator system by demonstrating that complex formation can shift the viable range of diffusion intensity to higher values. In the current study, we extend the previous study of complex formation. Firstly, by investigating a well-mixed replicator system, we establish that complex formation gives parasites an implicit advantage over catalysts, which makes the system significantly more vulnerable to parasites. Secondly, by investigating a spatially extended replicator system, we show that the formation of traveling wave patterns plays a crucial role in the stability of the system against parasites, and that because of this the effect of complex formation is not straightforward; i.e., whether complex formation stabilizes or destabilizes the spatial system is a complex function of other parameters. We give a detailed analysis of the spatial system by considering the pattern dynamics of waves. Furthermore, we investigate the effect of deleterious mutations. Surprisingly, high mutation rates can weaken the exploitation of the catalyst by the parasite.     

Selection advantage of metabolic over non-metabolic replicators: A kinetic analysis

A kinetic analysis and simulation of the replication reactions of two competing replicators—one non-metabolic (thermodynamic), the other metabolic, are presented. Our analysis indicates that in a rich resource environment the non-metabolic replicator is likely to be kinetically selected for over the metabolic replicator. However, in the more typical resource-poor environment it will be the metabolic replicator that is the kinetically more stable entity, and the one that will be kinetically selected for. Accordingly, a causal relationship between the emergence of a simple replicator and the emergence of a metabolic system is indicated. The results lend further support for the “replication first” school of thought in the origin of life problem by providing a mechanistic basis for the emergence of a metabolism, once a simple non-metabolic replicating system has itself been established. The study reaffirms our view that the roots of Darwinian theory may be found within standard chemical kinetic theory.     

The replicator of the Epstein-Barr virus latent cycle origin of DNA replication, oriP, is composed of multiple functional elements

Replication of the Epstein-Barr virus genome initiates at one of several sites in latently infected, dividing cells. One of these replication origins is close to the viral DNA maintenance element, and, together, this replication origin and the maintenance element are referred to as oriP. The replicator of oriP contains four binding sites for Epstein-Barr virus nuclear antigen 1 (EBNA-1), the sole viral protein required for the replication and maintenance of oriP plasmids. We showed previously that these EBNA-1 sites function in pairs and that mutational inactivation of one pair does not eliminate replicator function. In this study we characterized the contribution of each EBNA-1 site within the replicator and flanking sequences through the use of an internally controlled replication assay. We present evidence that shows that all four EBNA-1 sites are required for an oriP plasmid to be replicated in every cell cycle. Results from these experiments also show that the paired EBNA-1 binding sites are not functionally equivalent and that the low affinity of sites 2 and 3 compared to that of sites 1 and 4 is not essential for replicator function. Our results suggest that a host cell protein(s) binds sequences flanking the EBNA-1 sites and that interactions between EBNA-1 and this protein(s) are critical for replicator function. Finally, we present evidence that shows that the minimal replicator of oriP consists of EBNA-1 sites 3 and 4 and two copies of a 14-bp repeat that is present in inverse orientation flanking these EBNA-1 sites. EBNA-1 sites 1 and 2, together with an element(s) within nucleotides 9138 to 9516, are ancillary elements required for full replicator activity.     

Immune networks modeled by replicator equations

In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function f(h), where the field h summarizes the effect of the network on a single clone. We show that by transforming into relative concentrations, the B-cell network equations can be brought into a form that closely resembles the replicator equation. We then show that when the total number of clones in a network is conserved, the dynamics of the network can be represented by the dynamics of a replicator equation. The number of equilibria and their stability are then characterized using methods developed for the study of second-order replicator equations. Analogies with standard Lotka-Volterra equations are also indicated. A particularly interesting result of our analysis is the fact that even though the immune network equations are not second-order, the number and stability of their equilibria can be obtained by a superposition of second-order replicator systems. As a consequence, the problem of finding all of the equilibrium points of the nonlinear network equations can be reduced to solving linear equations.     

Initiation of DNA replication at the human beta-globin 3' enhancer

The origin of DNA replication in the human β-globin gene contains an initiation region (IR) and two flanking auxiliary elements. Two replicator modules are located within the upstream auxiliary sequence and the IR core, but the functional sequences in the downstream auxiliary element are unknown. Here, we use a combination of benzoylated-naphthoylated DEAE (BND) cellulose purification and nascent strand abundance assays to show that replication initiation occurs at the β-globin 3′ enhancer on human chromosome 11 in the Hu11 hybrid murine erythroleukemia (MEL) cell line. To examine replicator function, 3′ enhancer fragments were inserted into an ectopic site in MEL cells via an optimized FRT/EGFP-FLP integration system. These experiments demonstrate that the 1.6 kb downstream auxiliary element is a third replicator module called bGRep-E in erythroid cells. The minimal 260 bp 3′ enhancer is required but not sufficient to initiate efficient replication, suggesting cooperation with adjacent sequences. The minimal 3′ enhancer also cooperates with elements in an expressing HS3β/γ-globin construct to initiate replication. These data indicate that the β-globin replicator has multiple initiation sites in three closely spaced replicator modules. We conclude that a mammalian enhancer can cooperate with adjacent sequences to create an efficient replicator module.     

Autocatalytic networks with translation

We consider the kinetics of an autocatalytic reaction network in which replication and catalytic actions are separated by a translation step. We find that the behaviour of such a system is closely related to second-order replicator equations, which describe the kinetics of autocatalytic reaction networks in which the replicators act also as catalysts. In fact, the qualitative dynamics seems to be described almost entirely be the second-order reaction rates of the replication step. For two species we recover the qualitative dynamics of the replicator equations. Larger networks show some deviations, however. A hypercyclic system consisting of three interacting species can converge toward a stable limit cycle in contrast to the replicator equation case. A singular perturbation analysis shows that the replication-translation system reduces to a second-order replicator equation if translation is fast. The influence of mutations on replication-translation networks is also very similar to the behavior of selection-mutation equations.     

The evolution of enzyme specificity in the metabolic replicator model of prebiotic evolution

The chemical machinery of life must have been catalytic from the outset. Models of the chemical origins have attempted to explain the ecological mechanisms maintaining a minimum necessary diversity of prebiotic replicator enzymes, but little attention has been paid so far to the evolutionary initiation of that diversity. We propose a possible first step in this direction: based on our previous model of a surface-bound metabolic replicator system we try to explain how the adaptive specialization of enzymatic replicator populations might have led to more diverse and more efficient communities of cooperating replicators with two different enzyme activities. The key assumptions of the model are that mutations in the replicator population can lead towards a) both of the two different enzyme specificities in separate replicators: efficient "specialists" or b) a "generalist" replicator type with both enzyme specificities working at less efficiency, or c) a fast-replicating, non-enzymatic "parasite". We show that under realistic trade-off constraints on the phenotypic effects of these mutations the evolved replicator community will be usually composed of both types of specialists and of a limited abundance of parasites, provided that the replicators can slowly migrate on the mineral surface. It is only at very weak trade-offs that generalists take over in a phase-transition-like manner. The parasites do not seriously harm the system but can freely mutate, therefore they can be considered as pre-adaptations to later, useful functions that the metabolic system can adopt to increase its own fitness.     

Evolutionary stability and quasi-stationary strategy in stochastic evolutionary game dynamics

Stochastic evolutionary game dynamics for finite populations has recently been widely explored in the study of evolutionary game theory. It is known from the work of Traulsen et al. [2005. Phys. Rev. Lett. 95, 238701] that the stochastic evolutionary dynamics approaches the deterministic replicator dynamics in the limit of large population size. However, sometimes the limiting behavior predicted by the stochastic evolutionary dynamics is not quite in agreement with the steady-state behavior of the replicator dynamics. This paradox inspired us to give reasonable explanations of the traditional concept of evolutionarily stable strategy (ESS) in the context of finite populations. A quasi-stationary analysis of the stochastic evolutionary game dynamics is put forward in this study and we present a new concept of quasi-stationary strategy (QSS) for large but finite populations. It is shown that the consistency between the QSS and the ESS implies that the long-term behavior of the replicator dynamics can be predicted by the quasi-stationary behavior of the stochastic dynamics. We relate the paradox to the time scales and find that the contradiction occurs only when the fixation time scale is much longer than the quasi-stationary time scale. Our work may shed light on understanding the relationship between the deterministic and stochastic methods of modeling evolutionary game dynamics.     

Replicator dominance in a eukaryotic chromosome.

Replicators are genetic elements that control initiation at an origin of DNA replication (ori). They were first identified in the yeast Saccharomyces cerevisiae as autonomously replicating sequences (ARSs) that confer on a plasmid the ability to replicate in the S phase of the cell cycle. The DNA sequences required for ARS function on a plasmid have been defined, but because many sequences that participate in ARS activity are not components of chromosomal replicators, a mutational analysis of the ARS1 replicator located on chromosome IV of S. cerevisiae was performed. The results of this analysis indicate that four DNA elements (A, B1, B2 and B3) are either essential or important for ori activation in the chromosome. In a yeast strain containing two closely spaced and identical copies of the ARS1 replicator in the chromosome, only one is active. The mechanism of replicator repression requires the essential A element of the active replicator. This element is the binding site for the origin recognition complex (ORC), a putative initiator protein. The process that determines which replicator is used, however, depends entirely upon flanking DNA sequences.     

Dissection of the Beta-Globin Replication-Initiation Region Reveals Specific Requirements for Replicator Elements during Gene Amplification

Gene amplification plays a pivotal role in malignant transformation of human cells. A plasmid with both a mammalian replication-initiation region (IR)/origin/replicator and a nuclear matrix-attachment region (MAR) is spontaneously amplified in transfected cells by a mechanism that involves amplification at the extrachromosomal site, followed by amplification at the chromosomal arm, ultimately generating a long homogeneously staining region (HSR). Several observations suggest that replication initiation from IR sequences might mediate amplification. To test this idea, we previously dissected c-myc and DHFR IRs to identify the minimum sequence required to support amplification. In this study, we applied an improved analysis that discriminates between two amplification steps to the ß-globin RepP IR, which contains separate elements already known to be essential for initiation on the chromosome arm. The IR sequence was required at least for the extrachromosomal amplification step. In addition to the vector-encoded MAR, amplification also required an AT-rich region and a MAR-like element, consistent with the results regarding replicator activity on the chromosome. However, amplification did not require the AG-rich tract necessary for replicator activity, but instead required a novel sequence containing another AG-rich tract. The differential sequence requirement might be a consequence of extrachromosomal replication.     

Models of Replicator Proliferation Involving Differential Replicator Subunit Stability

Several models for the origin of life involve molecules that are capable of self-replication, such as self-replicating polymers composed of RNA or DNA or amino acids. Here we consider a hypothetical replicator (AB) composed of two subunits, A and B. Programs written in Python and C programming languages were used to model AB replicator abundance as a function of cycles of replication (iterations), under specified hypothetical conditions. Two non-exclusive models describe how a reduced stability for B relative to A can have an advantage for replicator activity and/or evolution by generating free A subunits. In model 1, free A subunits associate with AB replicators to create AAB replicators with greater activity. In simulations, reduced stability of B was beneficial when the replication activity of AAB was greater than two times the replication activity of AB. In model 2, the free A subunit is inactive for some number of iterations before it re-creates the B subunit. A re-creates the B subunit with an equal chance of creating B or B′, where B′ is a mutant that increases AB’ replicator activity relative to AB. In simulations, at moderate number of iterations (< 15), a shorter survival time for B is beneficial when the stability of B is greater than the inactive time of A. The results are consistent with the hypothesis that reduced stability for a replicator subunit can be advantageous under appropriate conditions.     

Evolutionary game dynamics in finite populations with strong selection and weak mutation

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expected motion in our model resembles the standard replicator dynamics when the population is large, but is qualitatively different when the population is small. Our analysis shows that even in large finite populations the behavior of a replicator-like system can be different from that of the standard replicator dynamics. As an application, we consider selective language dynamics. We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics.     

Unpredictability induced by unfocused games in evolutionary game dynamics

Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously.     

When does the variance of replicator fitness decrease?

For the general replicator dynamics with regular relative advantage functions (having non-singular Jacobian and symmetrized Jacobian), it will be shown that the variance of marginal fitness of the replicators strictly decreases along each trajectory of the replicator dynamics near an interior rest point if and only if this rest point is a regular evolutionarily stable state.     

Binding of AlF-C, an Orc1-binding transcriptional regulator, enhances replicator activity of the rat aldolase B origin

A region encompassing the rat aldolase B gene (aldB) promoter acts as a chromosomal origin of DNA replication (origin) in rat aldolase B-nonexpressing hepatoma cells. To examine replicator function of the aldB origin, we constructed recombinant mouse cell lines in which the rat aldB origin and the mutant derivatives were inserted into the same position at the mouse chromosome 8 by cre-mediated recombination. Nascent strand abundance assays revealed that the rat origin acts as a replicator at the ectopic mouse locus. Mutation of site C in the rat origin, which binds an Orc1-binding protein AlF-C in vitro, resulted in a significant reduction of the replicator activity in the mouse cells. Chromatin immunoprecipitation (ChIP) assays indicated that the reduction of replicator activity was paralleled with the reduced binding of AlF-C and Orc1, suggesting that sequence-specific binding of AlF-C to the ectopic rat origin leads to enhanced replicator activity in cooperation with Orc1. Involvement of AlF-C in replication in vivo was further examined for the aldB origin at its original rat locus and for a different rat origin identified in the present study, which contained an AlF-C-binding site. ChIP assays revealed that both replication origins bind AlF-C and Orc1. We think that the results presented here may represent one mode of origin recognition in mammalian cells.     

In vivo linearization and autonomous replication of plasmids containing human telomeric DNA in Aspergillus nidulans

Plasmids containing two inverted 0.6-kb stretches of human telomeric repeats transform Aspergillus nidulans at frequencies characteristic of autonomously replicating vectors. Transformation frequency is not affected when the plasmids are linearized in vitro prior to transformation by cutting between the inverted repeats. Southern analysis reveals the presence of a homogeneous pool of linear plasmid molecules in mycelium of transformants. Addition of the AMA1 plasmid replicator to the telomere-containing plasmids has only a minor effect on transformation. The phenotypic stability of the transformants is low. However, unlike conventional replicative transformants containing AMA1-bearing plasmids, these transformants are prone to spontaneous stabilization which occurs predominantly by conversion of the mutant chromosomal allele of the marker gene to the plasmid-borne allele. The data strongly suggest that telomeric DNA can act as a plasmid replicator. An alternative interpretation is that autonomous replication of linear DNA fragments, in contrast to covalently closed supercoiled molecules, does not require any special replicator sequences.