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.     

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.     

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.     

Replicator Equations and the Principle of Minimal Production of Information

Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize the KL-divergence of the initial and current distributions under time-dependent constraints, which in their turn, can be computed explicitly at every instant due to the system dynamics. Therefore, the Kullback principle of minimum discrimination information, as well as the maximum entropy principle, for systems governed by the replicator equations can be derived from the system dynamics rather than postulated. Applications to the Malthusian inhomogeneous models, global demography, and the Eigen quasispecies equation are given.     

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 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.     

The replicon revisited: an old model learns new tricks in metazoan chromosomes

The origins of DNA replication were proposed in the replicon model to be specified genetically by replicator elements that coordinate the initiation of DNA synthesis with gene expression and cell growth. Recent studies have identified DNA sequences in mammalian cells that fulfil the genetic criteria for replicators and are beginning to uncover the sequence requirements for the initiation of DNA replication. Mammalian replicators are com- posed of non-redundant modules that cooperate to direct initiation to specific chromosomal sites. Conversely, replicators do not show strong sequence similarity, and their ability to initiate replication depends on the chromosomal context and epigenetic factors, as well as their primary sequence. Here, we review the properties of metazoan replicators, and discuss the genetic and epigenetic factors that determine where and when DNA replication is initiated.     

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.     

Yeast DNA replication in vitro: initiation and elongation events mimic in vivo processes

An enzyme system prepared from Saccharomyces cerevisiae carries out the replication of exogenous yeast plasmid DNA. Replication in vitro mimics that in vivo in that DNA synthesis in extracts of strain cdc8, a temperature-sensitive DNA replication mutant, is thermolabile relative to the wild-type, and in that aphidicolin inhibits replication in vitro. Furthermore, only plasmids containing a functional yeast replicator, ARS, initiate replication at a specific site in vitro. Analysis of replicative intermediates shows that plasmid YRp7, which contains the chromosomal replicator ARS1, initiates bidirectional replication in a 100 bp region within the sequence required for autonomous replication in vivo. Plasmids containing ARS2, another chromosomal replicator, and the ARS region of the endogenous yeast plasmid 2 microns circle give similar results, suggesting that ARS sequences are specific origins of chromosomal replication. Used in conjunction with deletion mapping, the in vitro system allows definition of the minimal sequences required for the initiation of replication.     

Originator dynamics

We study the origin of evolution. Evolution is based on replication, mutation, and selection. But how does evolution begin? When do chemical kinetics turn into evolutionary dynamics? We propose "prelife" and "prevolution" as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting "prevolutionary dynamics" have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this "originator equation" gives the classical selection equation. In the other limit, we obtain "prelife." There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to "reversals" in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence.     

Replication methods and tools in high-throughput cultivation processes - recognizing potential variations of growth and product formation by on-line monitoring

Background  

High-throughput cultivations in microtiter plates are the method of choice to express proteins from recombinant clone libraries. Such processes typically include several steps, whereby some of them are linked by replication steps: transformation, plating, colony picking, preculture, main culture and induction. In this study, the effects of conventional replication methods and replication tools (8-channel pipette, 96-pin replicators: steel replicator with fixed or spring-loaded pins, plastic replicator with fixed pins) on growth kinetics of Escherichia coli SCS1 pQE-30 pSE111 were observed. Growth was monitored with the BioLector, an on-line monitoring technique for microtiter plates. Furthermore, the influence of these effects on product formation of Escherichia coli pRhotHi-2-EcFbFP was investigated. Finally, a high-throughput cultivation process was simulated with Corynebacterium glutamicum pEKEx2-phoD-GFP, beginning at the colony picking step.     

Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

Alpha functions are commonly used to describe different receptor channel kinetics (non-NMDA, GABA_A and GABA_B). In this paper we show that they may be represented as solutions to simple ordinary differential equations. This alternative method is compared with the commonly used direct summation of the alpha function conductances in a high-level neuronal circuit model. A parametric study shows that the differential equation method greatly speeds up the previous summation method. The forward Euler method used to solve this differential equation is shown to be accurate for this type of simulation. The modelling of NMDA receptor channel kinetics is also discussed. Received: 18 December 1992/Accepted in revised form: 28 June 1993     

Lotka-Volterra equation and replicator dynamics: A two-dimensional classification

The replicator equation arises if one equips a certain game theoretical model for the evolution of behaviour in animal conflicts with dynamics. It serves to model many biological processes not only in sociobiology but also in population genetics, mathematical ecology and even in prebiotic evolution. After a short survey of these applications, a complete classification of the two-dimensional phase flows is presented. The methods are also used to obtain a classification of phase portraits of the well-known generalized Lotka-Volterra equation in the plane.     

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.