Repression/depression of conjugative plasmids and their influence on the mutation-selection balance in static environments.

We study the effect that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance of a population in a static environment. We consider a model whereby a population of unicellular organisms, capable of conjugation, comes to mutation-selection balance in the presence of an antibiotic, which induces a first-order death rate constant [Formula: see text] for genomes that are not resistant. We explicitly take into consideration the repression/de-repression dynamics of the conjugative plasmid, and assume that a de-repressed plasmid remains temporarily de-repressed after copying itself into another cell. We assume that both repression and de-repression are characterized by first-order rate constants [Formula: see text]and [Formula: see text], respectively. We find that conjugation has a deleterious effect on the mean fitness of the population, suggesting that HGT does not provide a selective advantage in a static environment, but is rather only useful for adapting to new environments. This effect can be ameliorated by repression, suggesting that while HGT is not necessarily advantageous for a population in a static environment, its deleterious effect on the mean fitness can be negated via repression. Therefore, it is likely that HGT is much more advantageous in a dynamic landscape. Furthermore, in the limiting case of a vanishing spontaneous de-repression rate constant, we find that the fraction of conjugators in the population undergoes a phase transition as a function of population density. Below a critical population density, the fraction of conjugators is zero, while above this critical population density the fraction of conjugators rises continuously to one. Our model for conjugation-mediated HGT is related to models of infectious disease dynamics, where the conjugators play the role of the infected (I) class, and the non-conjugators play the role of the susceptible (S) class.

RNA-magnesium-protein interactions in large ribosomal subunit.

Some of the magnesium ions in the ribosome are coordinated by multiple rRNA phosphate groups. These magnesium ions link distal sequences of rRNA, primarily by incorporating phosphate groups into the first coordination shell. Less frequently, magnesium interacts with ribosomal proteins. Ribosomal protein L2 appears to be unique by forming specific magnesium-mediated interactions with rRNA. Using optimized models derived from X-ray structures, we subjected rRNA/magnesium/water/rProtein L2 assemblies to quantum mechanical analysis using the density functional theory and natural energy decomposition analysis. The combined results provide estimates of energies of formation of these assemblies, and allow us to decompose the energies of interaction. The results indicated that RNA immobilizes magnesium by multidentate chelation with phosphate, and that the magnesium ions in turn localize and polarize water molecules, increasing energies and specificities of interaction of these water molecules with L2 protein. Thus, magnesium plays subtle, yet important, roles in ribosomal assembly beyond neutralization of electrostatic repulsion and direct coordination of RNA functional groups.

Effect of chromosomal instability on the mutation-selection balance in unicellular populations.

This paper develops a mathematical model describing the evolutionary dynamics of a unicellular, asexually replicating population exhibiting chromosomal instability. Chromosomal instability is a form of genetic instability characterized by the gain or loss of entire chromosomes during cell division. We assume that the cellular genome is divided into several homologous groups of chromosomes, and that a single functional chromosome per homologous group is required for the cell to have the wild-type fitness. If the fitness is unaffected by the total number of chromosomes in the cell, our model is analytically solvable, and yields a mean fitness at mutation-selection balance that is identical to the mean fitness when there is no chromosomal instability. If this assumption is relaxed and the total number of chromosomes in the cell is not allowed to increase without bound, then chromosomal instability leads to a reduction in mean fitness. The results of this paper provide a useful baseline that can inform both future theoretial and experimental studies of chromosomal instability.

Effect of the SOS response on the mean fitness of unicellular populations: a quasispecies approach.

The goal of this paper is to develop a mathematical model that analyzes the selective advantage of the SOS response in unicellular organisms. To this end, this paper develops a quasispecies model that incorporates the SOS response. We consider a unicellular, asexually replicating population of organisms, whose genomes consist of a single, double-stranded DNA molecule, i.e. one chromosome. We assume that repair of post-replication mismatched base-pairs occurs with probability , and that the SOS response is triggered when the total number of mismatched base-pairs is at least . We further assume that the per-mismatch SOS elimination rate is characterized by a first-order rate constant . For a single fitness peak landscape where the master genome can sustain up to mismatches and remain viable, this model is analytically solvable in the limit of infinite sequence length. The results, which are confirmed by stochastic simulations, indicate that the SOS response does indeed confer a fitness advantage to a population, provided that it is only activated when DNA damage is so extensive that a cell will die if it does not attempt to repair its DNA.

Semiconservative quasispecies equations for polysomic genomes: the general case.

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analog of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for noncomplementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

Second order catalytic quasispecies yields discontinuous mean fitness at error threshold.

The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by catalytic replication of different reaction orders. Specifically, we find that second order mechanisms lead to a discontinuity in the mean fitness of the population at the error threshold. This is in contrast to the behavior of the first order, autocatalytic replication mechanism considered in the standard quasispecies model. This suggests that quasispecies models with higher order replication mechanisms produce discontinuities in the mean fitness, and hence the viable population fraction as well, at the error threshold, while lower order replication mechanisms yield a continuous mean fitness function. We discuss potential implications for understanding replication in the RNA world and in virology.

The influence of horizontal gene transfer on the mean fitness of unicellular populations in static environments.

Horizontal gene transfer (HGT) is believed to be a major source of genetic variation, particularly for prokaryotes. It is believed that horizontal gene transfer plays a major role in shaping bacterial genomes and is also believed to be responsible for the relatively rapid dissemination and acquisition of new, adaptive traits across bacterial strains. Despite the importance of horizontal gene transfer as a major source of genetic variation, the bulk of research on theoretical evolutionary dynamics and population genetics has focused on point mutations (sometimes coupled with gene duplication events) as the main engine of genomic change. Here, we seek to specifically model HGT processes in bacterial cells, by developing a mathematical model describing the influence that conjugation-mediated HGT has on the mutation-selection balance in an asexually reproducing population of unicellular, prokaryotic organisms. It is assumed that mutation-selection balance is reached in the presence of a fixed background concentration of antibiotic, to which the population must become resistant to survive. We find that HGT has a nontrivial effect on the mean fitness of the population. However, one of the central results that emerge from our analysis is that, at mutation-selection balance, conjugation-mediated HGT has a slightly deleterious effect on the mean fitness of a population. Therefore, we conclude that HGT does not confer a selection advantage in static environments. Rather, its advantage must lie in its ability to promote faster adaptation in dynamic environments, an interpretation that is consistent with the observation that HGT can be promoted by environmental stresses on a population.

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.

Diploidy and the selective advantage for sexual reproduction in unicellular organisms.

This article develops mathematical models describing the evolutionary dynamics of both asexually and sexually reproducing populations of diploid unicellular organisms. The asexual and sexual life cycles are based on the asexual and sexual life cycles in Saccharomyces cerevisiae, Baker's yeast, which normally reproduces by asexual budding, but switches to sexual reproduction when stressed. The mathematical models consider three reproduction pathways: (1) Asexual reproduction, (2) self-fertilization, and (3) sexual reproduction. We also consider two forms of genome organization. In the first case, we assume that the genome consists of two multi-gene chromosomes, whereas in the second case, we consider the opposite extreme and assume that each gene defines a separate chromosome, which we call the multi-chromosome genome. These two cases are considered to explore the role that recombination has on the mutation-selection balance and the selective advantage of the various reproduction strategies. We assume that the purpose of diploidy is to provide redundancy, so that damage to a gene may be repaired using the other, presumably undamaged copy (a process known as homologous recombination repair). As a result, we assume that the fitness of the organism only depends on the number of homologous gene pairs that contain at least one functional copy of a given gene. If the organism has at least one functional copy of every gene in the genome, we assume a fitness of 1. In general, if the organism has l homologous pairs that lack a functional copy of the given gene, then the fitness of the organism is kappa(l). The kappa(l) are assumed to be monotonically decreasing, so that kappa(0) = 1 > kappa(1) > kappa(2) > cdots, three dots, centered > kappa(infinity) = 0. For nearly all of the reproduction strategies we consider, we find, in the limit of large N, that the mean fitness at mutation-selection balance is max{2e(-mu) - 1,0} where N is the number of genes in the haploid set of the genome, epsilon is the probability that a given DNA template strand of a given gene produces a mutated daughter during replication, and mu = Nepsilon. The only exception is the sexual reproduction pathway for the multi-chromosomed genome. Assuming a multiplicative fitness landscape where kappa(l) = alpha(l) for alpha in (0, 1), this strategy is found to have a mean fitness that exceeds the mean fitness of all the other strategies. Furthermore, while other reproduction strategies experience a total loss of viability due to the steady accumulation of deleterious mutations once mu exceeds [Formula: see text] no such transition occurs in the sexual pathway. Indeed, in the limit as alpha --> 1 for the multiplicative landscape, we can show that the mean fitness for the sexual pathway with the multi-chromosomed genome converges to e(-2mu), which is always positive. We explicitly allow for mitotic recombination in this study, which, in contrast to previous studies using different models, does not have any advantage over other asexual reproduction strategies. The results of this article provide a basis for understanding the selective advantage of the specific meiotic pathway that is employed by sexually reproducing organisms. The results of this article also suggest an explanation for why unicellular organisms such as Saccharomyces cerevisiae (Baker's yeast) switch to a sexual mode of reproduction when stressed. While the results of this article are based on modeling mutation-propagation in unicellular organisms, they nevertheless suggest that, in more complex organisms with significantly larger genomes, sex is necessary to prevent the loss of viability of a population due to genetic drift. Finally, and perhaps most importantly, the results of this article demonstrate a selective advantage for sexual reproduction with fewer and much less restrictive assumptions than those of previous studies.

Speculations on the emergence of self-awareness in big-brained organisms: the roles of associative memory and learning, existential and religious questions, and the emergence of tautologies.

This paper argues that self-awareness emerges in organisms whose brains have a sufficiently integrated, complex ability for associative learning and memory. Continual sensory input of information related to the organism leads to the formation of a set of associations that may be termed an organismal "self-image". After providing the basic mechanistic basis for the emergence of an organismal self-image, this paper proceeds to go through a representative list of behaviors associated with self-awareness, and shows how associative memory and learning, combined with an organismal self-image, leads to the emergence of these various behaviors. This paper also discusses various tautologies that invariably emerge when discussing self-awareness. We continue with various speculations on manipulating self-awareness, and discuss how concepts from set and logic theory may provide a useful set of tools for understanding the emergence of higher cognitive functions in complex organisms.

Selective advantage for sexual reproduction with random haploid fusion.

This article develops a simplified set of models describing asexual and sexual replication in unicellular diploid organisms. The models assume organisms whose genomes consist of two chromosomes, where each chromosome is assumed to be functional if it is equal to some master sequence sigma(0), and non-functional otherwise. We review the previously studied case of selective mating, where it is assumed that only haploids with functional chromosomes can fuse, and also consider the case of random haploid fusion. When the cost for sex is small, as measured by the ratio of the characteristic haploid fusion time to the characteristic growth time, we find that sexual replication with random haploid fusion leads to a greater mean fitness for the population than a purely asexual strategy. However, independently of the cost for sex, we find that sexual replication with a selective mating strategy leads to a higher mean fitness than the random mating strategy. The results of this article are consistent with previous studies suggesting that sex is favored at intermediate mutation rates, for slowly replicating organisms, and at high population densities. Furthermore, the results of this article provide a basis for understanding sex as a stress response in unicellular organisms such as Saccharomyces cerevisiae (Baker's yeast).

A comparison of sexual and asexual replication strategies in a simplified model based on the yeast life cycle.

This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in Saccharomyces cerevisiae, or Baker's yeast. The simplified models are based on the single-fitness-peak approximation in quasispecies theory. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. For the sake of generality, our model allows for mitotic recombination and asymmetric chromosome segregation. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. In the sexual pathway, we consider two mating strategies: (1) a selective strategy, where only haploids with functional chromosomes can fuse with one another; (2) a random strategy, where haploids randomly fuse with one another. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. When the cost for sex is low, sexual replication with random mating also has a higher mean fitness than asexual replication without mitotic recombination or asymmetric chromosome segregation. We also show that, at low replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. If the fitness penalty for having a defective chromosome is sufficiently high and the cost for sex sufficiently low, then at low replication fidelities the random mating strategy has a mean fitness that is a factor of square root 2 larger than the asexual mean fitness. We argue that for yeast, the selective mating strategy is the one that is closer to reality, which if true suggests that sex may provide a selective advantage under considerably more relaxed conditions than previous research has indicated. The results of this paper also suggest that S. cerevisiae switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes. That being said, our model does not contradict theories for the evolution of sex that argue that sex evolved because it allows a population to more easily adapt to changing conditions.

Effect of mutators on adaptability in time-varying fitness landscapes.

This Brief Report studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating genomes, whose only source of genetic variation is due to copying errors during replication. We consider a time-dependent, single-fitness-peak landscape where the master sequence changes by a single point mutation at every time tau. We are able to analytically solve for the evolutionary dynamics of the population in the point-mutation limit. In particular, our model provides an analytical expression for the fraction of mutators in the dynamic fitness landscape that agrees well with results from stochastic simulations.

Comparison of three replication strategies in complex multicellular organisms: asexual replication, sexual replication with identical gametes, and sexual replication with distinct sperm and egg gametes.

This paper studies the mutation-selection balance in three simplified replication models. The first model considers a population of organisms replicating via the production of asexual spores. The second model considers a sexually replicating population that produces identical gametes. The third model considers a sexually replicating population that produces distinct sperm and egg gametes. All models assume diploid organisms whose genomes consist of two chromosomes, each of which is taken to be functional if equal to some master sequence, and defective otherwise. In the asexual population, the asexual diploid spores develop directly into adult organisms. In the sexual populations, the haploid gametes enter a haploid pool, where they may fuse with other haploids. The resulting immature diploid organisms then proceed to develop into mature organisms. Based on an analysis of all three models, we find that, as organism size increases, a sexually replicating population can only outcompete an asexually replicating population if the adult organisms produce distinct sperm and egg gametes. A sexual replication strategy that is based on the production of large numbers of sperm cells to fertilize a small number of eggs is found to be necessary in order to maintain a sufficiently low cost for sex for the strategy to be selected for over a purely asexual strategy. We discuss the usefulness of this model in understanding the evolution and maintenance of sexual replication as the preferred replication strategy in complex, multicellular organisms.

Temporal differentiation and the optimization of system output.

We develop two simplified dynamical models with which to explore the conditions under which temporal differentiation leads to increased system output. By temporal differentiation, we mean a division of labor whereby different subtasks associated with performing a given task are done at different times. The idea is that, by focusing on one particular set of subtasks at a time, it is possible to increase the efficiency with which each subtask is performed, thereby allowing for faster completion of the overall task. In the first model, we consider the filling and emptying of a tank in the presence of a time-varying resource profile. If a given resource is available, the tank may be filled at some rate rf. As long as the tank contains a resource, it may be emptied at a rate re, corresponding to processing into some product, which is either the final product of a process or an intermediate that is transported for further processing. Given a resource-availability profile over some time interval T, we develop an algorithm for determining the fill-empty profile that produces the maximum quantity of processed resource at the end of the time interval. We rigorously prove that the basic algorithm is one where the tank is filled when a resource is available and emptied when a resource is not available. In the second model, we consider a process whereby some resource is converted into some final product in a series of three agent-mediated steps. Temporal differentiation is incorporated by allowing the agents to oscillate between performing the first two steps and performing the last step. We find that temporal differentiation is favored when the number of agents is at intermediate values and when there are process intermediates that have long lifetimes compared to other characteristic time scales in the system. Based on these results, we speculate that temporal differentiation may provide an evolutionary basis for the emergence of phenomena such as sleep, distinct REM and non-REM sleep states, and circadian rhythms in general. The essential argument is that in sufficiently complex biological systems, a maximal amount of information and tasks can be processed and completed if the system follows a temporally differentiated "work plan," whereby the system focuses on one or a few tasks at a time.

A quasispecies approach to the evolution of sexual replication in unicellular organisms.

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.

Asexual and sexual replication in sporulating organisms.

Replication via sporulation is the replication strategy for all multicellular life, and may even be observed in unicellular life (such as with budding yeast). We consider diploid populations replicating via one of two possible sporulation mechanisms. (1) Asexual sporulation, whereby adult organisms produce single-celled diploid spores that grow into adults themselves. (2) Sexual sporulation, whereby adult organisms produce single-celled diploid spores that divide into haploid gametes. The haploid gametes enter a haploid "pool," where they may recombine with other haploids to form a diploid spore that then grows into an adult. We consider a haploid fusion rate given by second-order reaction kinetics. We work with a simplified model where the diploid genome consists of only two chromosomes, each of which may be rendered defective with a single point mutation of the wild-type. We find that the asexual strategy is favored when the rate of spore production is high compared to the characteristic growth rate from a spore to a reproducing adult. Conversely, the sexual strategy is favored when the rate of spore production is low compared to the characteristic growth rate from a spore to a reproducing adult. As the characteristic growth time increases, or as the population density increases, the critical ratio of spore production rate to organism growth rate at which the asexual strategy overtakes the sexual one is pushed to higher values. Therefore, the results of this model suggest that, for complex multicellular organisms, sexual replication is favored at high population densities and low growth and sporulation rates.

Associative learning in biochemical networks.

It has been recently suggested that there are likely generic features characterizing the emergence of systems constructed from the self-organization of self-replicating agents acting under one or more selection pressures. Therefore, structures and behaviors at one length scale may be used to infer analogous structures and behaviors at other length scales. Motivated by this suggestion, we seek to characterize various "animate" behaviors in biochemical networks, and the influence that these behaviors have on genomic evolution. Specifically, in this paper, we develop a simple, chemostat-based model illustrating how a process analogous to associative learning can occur in a biochemical network. Associative learning is a form of learning whereby a system "learns" to associate two stimuli with one another. Associative learning, also known as conditioning, is believed to be a powerful learning process at work in the brain (associative learning is essentially "learning by analogy"). In our model, two types of replicating molecules, denoted as A and B, are present in some initial concentration in the chemostat. Molecules A and B are stimulated to replicate by some growth factors, denoted as G(A) and G(B), respectively. It is also assumed that A and B can covalently link, and that the conjugated molecule can be stimulated by either the G(A) or G(B) growth factors (and can be degraded). We show that, if the chemostat is stimulated by both growth factors for a certain time, followed by a time gap during which the chemostat is not stimulated at all, and if the chemostat is then stimulated again by only one of the growth factors, then there will be a transient increase in the number of molecules activated by the other growth factor. Therefore, the chemostat bears the imprint of earlier, simultaneous stimulation with both growth factors, which is indicative of associative learning. It is interesting to note that the dynamics of our model is consistent with certain aspects of Pavlov's original series of conditioning experiments in dogs. We discuss how associative learning can potentially be performed in vitro within RNA, DNA, or peptide networks. We also describe how such a mechanism could be involved in genomic evolution, and suggest relevant bioinformatics studies that could potentially resolve these issues.

When does division of labor lead to increased system output?

This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models: in the first model, we consider the flow of some resource into a compartment, and the conversion of this resource into some product. In the second model, we consider the growth of autoreplicating systems. In this case, we divide the replication and metabolic tasks among different agents. The general features that emerge from our models is that division of labor is favored when the resource to agent ratio is at intermediate values, and when the time cost associated with transporting intermediate products is small compared to characteristic process times. The results of our model are consistent with the behavior of the cellular slime mold Dictyostelium discodeum, which switches from a single-celled to a multi-celled state when resources become limited. We also argue that division of labor in the context of our replication model suggests an evolutionary basis for the emergence of the stem-cell-based tissue architecture in complex organisms. Finally, the results of this paper may be useful for understanding how, in an economic context, firm productivity is maximized at intermediate firm sizes.

Extracting viability landscapes from mutagen-response experiments.

This paper outlines a novel approach for determining the importance of various genes to the viability of an organism. The basic idea is to treat a population of cells at various concentrations of mutagen, and determine which genes lose functionality due to genetic drift at the various mutagen concentrations. The more strongly a given collection of genes contributes to the fitness of an organism, the higher the mutation rate required to induce loss of functionality in those genes via genetic drift. We argue that mutagen-based methods, if reliably implementable, can elucidate correlations amongst genes, and determine which sets of genes correspond to redundant pathways in the cell. The data obtained from mutagen-based methods could also be used to organize the genes in a genome into hierarchies of increasing importance to the fitness of the cell. Thus, such methods could shed light on the evolutionary history of an organism.