Evolutionary dynamics of RNA-like replicator systems: A bioinformatic approach to the origin of life

We review computational studies on prebiotic evolution, focusing on informatic processes in RNA-like replicator systems. In particular, we consider the following processes: the maintenance of information by replicators with and without interactions, the acquisition of information by replicators having a complex genotype–phenotype map, the generation of information by replicators having a complex genotype–phenotype–interaction map, and the storage of information by replicators serving as dedicated templates. Focusing on these informatic aspects, we review studies on quasi-species, error threshold, RNA-folding genotype–phenotype map, hypercycle, multilevel selection (including spatial self-organization, classical group selection, and compartmentalization), and the origin of DNA-like replicators. In conclusion, we pose a future question for theoretical studies on the origin of life.     

Nonequilibrium phase transitions associated with DNA replication

Thermodynamics governing the synthesis of DNA and RNA strands under a template is considered analytically and applied to the population dynamics of competing replicators. We find a nonequilibrium phase transition for high values of polymerase fidelity in a single replicator, where the two phases correspond to stationary states with higher elongation velocity and lower error rate than the other. At the critical point, the susceptibility linking velocity to thermodynamic force diverges. The overall behavior closely resembles the liquid-vapor phase transition in equilibrium. For a population of self-replicating macromolecules, Eigen's error catastrophe transition precedes this thermodynamic phase transition during starvation. For a given thermodynamic force, the fitness of replicators increases with increasing polymerase fidelity above a threshold.     

Fitness distributions in exponentially growing asexual populations

We explore a mean-field model for the evolution of exponentially growing populations of mutating replicators. Motivated by recent in vitro experiments devised to analyze phenotypic properties of bacterial and viral populations subjected to serial population transfers, we allow our in silico individuals to undergo unrestricted growth before applying bottleneck events. Different dynamical regimes of our model can be mapped to different experimental situations. Numerical and analytical results for fitness distributions calculated at the statistically stationary states of the dynamics compare favorably with available experimental data. Our model and results provide a common framework to better understand populations evolving under different selection pressures.     

Dynamical role of the degree of intraspecific cooperation: A simple model for prebiotic replicators and ecosystems

We present a simple mean field model to analyze the dynamics of competition between two populations of replicators in terms of the degree of intraspecific cooperation (i.e., autocatalysis) in one of these populations. The first population can only replicate with Malthusian kinetics while the second one can reproduce with Malthusian or autocatalytic replication or with a combination of both reproducing strategies. The model consists of two coupled, nonlinear, autonomous ordinary differential equations. We investigate analytically and numerically the phase plane dynamics and the bifurcation scenarios of this ecologically coupled system, focusing on the outcome of competition for several degrees of intraspecific cooperation, σ, in the second population of replicators. We demonstrate that the dynamics of both populations can not be governed by a limit cycle, and also that once cooperation is considered, the topology of phase space does not allow for coexistence. Even for low values of the degree of intraspecific cooperation, for large enough autocatalytic replication rates, the second population of replicators is able to outcompete the first one, having a wide basin of attraction in state space. We characterize the same power law dependence between the outcompetition extinction times, τ, and the degree of intraspecific cooperation for both populations, given by τ∼c_iσ⁻¹. Our results suggest that, under some kinetic conditions, the appearance of autocatalysis might be favorable in a population of replicators growing with Malthusian kinetics competing with another population also reproducing exponentially.     

Spatio-temporal dynamics in simple asymmetric hypercycles under weak parasitic coupling

Hypercycles represent an example of cooperation at the molecular level suggested to be involved in the evolution of the first autonomous, self-reproducing molecular living-like systems. However, they are vulnerable to parasites: an established hypercycle may decay if a selfish replicator appears i.e. one that receives catalytic help but does not reciprocate catalysis. In this work we study the dynamics of a two-member hypercycle with an attached, weak parasite. We are using a mean field model and a stochastic cellular automaton (CA) focusing on the role of the kinetic properties of both hypercycle replicators, exploited by the parasite. Both approaches show three possible, parameter-dependent outcomes: (i) hypercycle stability and parasite extinction; (ii) extinction of the entire system; and (iii) coexistence between the hypercycle and the parasite. Scenario (iii) is shown to be structurally unstable in the mean field model but the addition of space allows a wider coexistence phase. Moreover the CA model also indicates that the degree of hypercycle’s asymmetry may be relevant in the survival of the catalytic replicators, being also responsible for qualitatively different dynamics e.g. if the parasite is attached to the fittest hypercycle unit, low-dimensional chaos arises. The coexistence phase is characterized by the emergence of hypercyclic aggregates with a broad distribution of cluster sizes and mixed patterns of replicators able to provide the hypercycle with resistance against the parasites. Nevertheless the resistance to the parasite is shown to reduce with increase of diffusion. The role of the kinetic properties of the hypercycle and of diffusion in the survival of the hypercycle is discussed in the context of prebiotic evolution.     

The minimal and the optimal size for two different types of encapsulated replicator systems

During this work, the viability of encapsulated replicators systems as a function of the vesicle size is revisited. Now, instead of considering in detail the diffusion process, the existence of a well-mixed solution inside the vesicle was assumed. Our results corroborated previous numerical estimations about the existence of a minimal size for vesicles immersed in an extremely hostile environment. In this particular case, we found analytical expressions for the critical radius as a function of the kinetics parameters for the two different families of replicators considered during the study. Furthermore, we also reported the existence of an optimal radius of the vesicle where the replicator population reaches a maximum, a value that may change slightly according to the replicator type. On the other hand, we also found that there is not a critical radius if the conditions of the external environment are not so extreme. However, even in this case, there is an optimal radius where the replicator population within the vesicle is noticeably larger than its value in the external medium. According to our results, the size of the vesicle may determine how efficiently the process of encapsulation took place on early Earth, probably one of the key steps during the process of abiogenesis.     

An introduction to physical theory of molecular evolution

This work is a tutorial in Molecular Evolution from the point of view of Physics. We discuss Eigen's model, a link between evolutionary theory and physics. We will begin by assuming the existence of (marco) molecules or replicators with the template property, that is, the capacity to self-replicate. According to this assumption, information will be randomly generated and destroyed by mutations in the code (i.e., errors in the copying process) and new bits of information will be fixed (made stable) by the existence of an external pressure on the system (i.e., selection), and the ability of the molecules to replicate themselves. Our aim is to build a model in order to describe molecular evolution from as general a standpoint as possible. As we will see, even very simple models from the theoretical point of view will have surprisingly deep consequences.     

Metabolic network dynamics in open chaotic flow

We have analyzed the dynamics of metabolically coupled replicators in open chaotic flows. Replicators contribute to a common metabolism producing energy-rich monomers necessary for replication. The flow and the biological processes take place on a rectangular grid. There can be at most one molecule on each grid cell, and replication can occur only at localities where all the necessary replicators (metabolic enzymes) are present within a certain neighborhood distance. Due to this finite metabolic neighborhood size and imperfect mixing along the fractal filaments produced by the flow, replicators can coexist in this fluid system, even though coexistence is impossible in the mean-field approximation of the model. We have shown numerically that coexistence mainly depends on the metabolic neighborhood size, the kinetic parameters, and the number of replicators coupled through metabolism. Selfish parasite replicators cannot destroy the system of coexisting metabolic replicators, but they frequently remain persistent in the system. (c) 2002 American Institute of Physics.     

Evolutionary dynamics on degree-heterogeneous graphs

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for voter model dynamics and to 1/k for invasion process dynamics.     

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.     

Interplay of viral miRNAs and host mRNAs and proteins

Recent experiments indicate that several viruses may encode microRNAs (miRNAs) in cells. Such RNAs may interfere with the host mRNAs and proteins. We present a kinetic analysis of this interplay. In our treatment, the viral miRNA is considered to be able to associate with the host mRNA with subsequent degradation. This process may result in a decline of the mRNA population and also in a decline of the population of the protein encoded by this mRNA. With these ingredients, we first show the types of the corresponding steady-state kinetics in the cases of positive and negative regulation of the miRNA synthesis by the protein. In addition, we scrutinize the situation when the protein regulates the virion replication or, in other words, provides a feedback for the replication. For the negative feedback, the replication rate is found to increase with increasing the intracellular virion population. For the positive feedback, the replication rate first increases and then drops. These features may determine the stability of steady states.     

Strongly screening electron capture for nuclides ~(52,53,59,60)Fe by the Shell-Model Monte Carlo method in pre-supernovae

The death of massive stars due to supernova explosions is a key ingredient in stellar evolution and stellar population synthesis.Electron capture(EC) plays a vital role in supernova explosions.Using the Shell-Model Monte Carlo method,based on the nuclear random phase approximation and linear response theory model for electrons,we study the strong screening EC rates of ~(52,53,59,60)Fe in pre-supernovae.The results show that the screening rates can decrease by about 18.66%.Our results may become a good foundation for future investigation of the evolution of late-type stars,supernova explosion mechanisms and numerical simulations.     

The ambivalent effect of lattice structure on a spatial game

The evolution of cooperation is studied in lattice-structured populations, in which each individual who adopts one of the following strategies ‘always defect’ (ALLD), ‘tit-for-tat’ (TFT), and ‘always cooperate’ (ALLC) plays the repeated Prisoner’s Dilemma game with its neighbors according to an asynchronous update rule. Computer simulations are applied to analyse the dynamics depending on major parameters. Mathematical analyses based on invasion probability analysis, mean-field approximation, as well as pair approximation are also used. We find that the lattice structure promotes the evolution of cooperation compared with a non-spatial population, this is also confirmed by invasion probability analysis in one dimension. Meanwhile, it also inhibits the evolution of cooperation due to the advantage of being spiteful, which indicates the key role of specific life-history assumptions. Mean-field approximation fails to predict the outcome of computer simulations. Pair approximation is accurate in two dimensions but fails in one dimension.     

Birthrates and delay times of Type Ia supernovae

Type Ia supernovae (SNe Ia) play an important role in diverse areas of astrophysics, from the chemical evolution of galaxies to observational cosmology. However, the nature of the progenitors of SNe Ia is still unclear. In this paper, according to a detailed binary population synthesis study, we obtained SN Ia birthrates and delay times from different progenitor models, and compared them with observations. We find that the Galactic SN Ia birthrate from the double-degenerate (DD) model is close to those infe...     

The Effect of the Protein Synthesis Entropy Reduction on the Cell Size Regulation and Division Size of Unicellular Organisms

The underlying mechanism determining the size of a particular cell is one of the fundamental unknowns in cell biology. Here, using a new approach that could be used for most of unicellular species, we show that the protein synthesis and cell size are interconnected biophysically and that protein synthesis may be the chief mechanism in establishing size limitations of unicellular organisms. This result is obtained based on the free energy balance equation of protein synthesis and the second law of thermodynamics. Our calculations show that protein synthesis involves a considerable amount of entropy reduction due to polymerization of amino acids depending on the cytoplasmic volume of the cell. The amount of entropy reduction will increase with cell growth and eventually makes the free energy variations of the protein synthesis positive (that is, forbidden thermodynamically). Within the limits of the second law of thermodynamics we propose a framework to estimate the optimal cell size at division.     

Error thresholds for quasispecies on dynamic fitness landscapes

In this paper we investigate error thresholds on dynamic fitness landscapes. We show that there exists both a lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error threshold present on a static landscape. The upper error threshold is a new limit that only exists on dynamic fitness landscapes. We also show that for long genomes and/or highly dynamic fitness landscapes there exists a lower bound on the selection pressure required for the effective selection of genomes with superior fitness independent of mutation rates, i.e. there are distinct nontrivial limits to evolutionary parameters in dynamic environments.     

Multiple and Strong Luminosity Evolution in the Population of Elliptical Galaxies

The traditional single burst and passive evolution model for elliptical galaxies should not be accepted. In this paper we demonstrate further by comparison of the model predictions with the observed B-K color distribution of galaxies, that the internal extinction by dust cannot save the traditional scenario for ellipticals either. Hence we do not agree with Zepf's (S.E. Zepf, Nature 390 (1997) 377) argument that such a scenario could still survive if ellipticals might have formed in dusty starburst environments. Furthermore, we have also found that the luminosity evolution within the population of ellipticals should be strong, complicated or multiple, which is not favored by our previous study of number counts for ellipticals. The conflicting results simply suggest that the pure luminosity evolution model should not be accepted, and hence the number evolution for ellipticals is a straightforward inference. Our conclusions hold in any one of the three cosmological models, i.e., flat, open, or Λ-dominated, under consideration.     

Immunolocalization of an osteopontin-like protein in dense granules of Toxoplasma gondii tachyzoites and its association with the parasitophorous vacuole

Toxoplasma gondii is an apicomplexan parasite infecting a broad host range, including humans. The parasite invades host cell by active penetration with the participation of its secretory organelles proteins during this process. Until now, only a limited number of secretory proteins have been discovered, and the effectors molecules involved in parasite invasion and survival are not well understood. Osteopontin (OPN) is a multifunctional glycophosphoprotein, secreted by different cell types, which is involved in various physiological and pathological events including cell signaling and survival. For the first time we demonstrated in this work by immunofluorescence and immunoelectron microscopy approaches the localization of an OPN-like protein in dense granules of extracellular T. gondii tachyzoites. Western blotting and RT-PCR confirmed this protein expression by the parasites. Our results also showed, after macrophage invasion, an intense positive labeling for OPN-like protein at the sub-apical portion of tachyzoites, the site of dense granules secretion, and the localization of this protein at the parasitophorous vacuole membrane. These data suggest that dense granules secrete an OPN-like protein, and we speculate that this protein participates during the parasite interaction process with host cells and parasitophorous vacuole formation.     

Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population is governed by correlation functions that although being formally down by powers ofN (the population size), nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean-field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.