Noisy clues to the origin of life

The origin of stable self-replicating molecules represents a fundamental obstacle to the origin of life. The low fidelity of primordial replicators places restrictions on the quantity of information encoded in a primitive nucleic acid alphabet. Further difficulties for the origin of life are the role of drift in small primordial populations, reducing the rate of fixation of superior replicators, and the hostile conditions increasing developmental noise. Thus, mutation, noise and drift are three different stochastic effects that are assumed to make the evolution of life improbable. Here we show, to the contrary, how noise present in hostile early environments can increase the probability of faithful replication, by amplifying selection in finite populations. Noise has negative consequences in infinite populations, whereas in finite populations, we observe a synergistic interaction among noise sources. Hence, two factors formerly considered inimical to the origin of life-developmental noise and drift in small populations-can in combination give rise to conditions favourable to robust replication.     

Diffusion approximations for one-locus multi-allele kin selection,mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size. In memory of Sam Karlin.     

The information capacity of hypercycles

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates n_m that can coexist in a hypercycle and show that it is a decreasing function of the length L of the templates. In the case of high replication accuracy we find that the product n_mL tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits.     

Gas vesicle assembly in Microcyclus aquaticus.

When observed in the electron microscope intact gas vesicles appeared as transparent areas in whole cells of Microcylus aquaticus, whereas vesicles collapsed by centrifugation were not discernible. Within 5 min of suspending cells containing collapsed vesicles in growth medium, small transparent vesicles were detected. By 15 min the average number of vesicles per cell was 15. This number remained relatively constant while the size of the vesicles increased until they attained their maximum diamtere of 100 nm. At this time the vesicles, interpreted as biconical structures, began to elongate presumably due to the synthesis of the cylindrical midsection. Closely correlated with the time at which vesicles began to elongate was the initiation of smaller vesicles which resulted in a doubling of the number of vesicles per cell by 90 min. This evidence coupled with the isolation of a mutant which assembles only the conical portions of the vesicle suggests that assembly occurs in two distinct stages subject to genetic mutation. Protein and ribonucleic acid synthesis, and presumably adenosine triphosphate formation, were required for gas vesicle assembly. In addition, inhibition of protein or ribonucleic acid synthesis resulted in a loss of extant gas vesicles. Over the time course of our study, deoxyribonucleic acid synthesis was not required for gas vesicle assembly or stability.     

Genetic load in sexual and asexual diploids: segregation, dominance and genetic drift

In diploid organisms, sexual reproduction rearranges allelic combinations between loci (recombination) as well as within loci (segregation). Several studies have analyzed the effect of segregation on the genetic load due to recurrent deleterious mutations, but considered infinite populations, thus neglecting the effects of genetic drift. Here, we use single-locus models to explore the combined effects of segregation, selection, and drift. We find that, for partly recessive deleterious alleles, segregation affects both the deterministic component of the change in allele frequencies and the stochastic component due to drift. As a result, we find that the mutation load may be far greater in asexuals than in sexuals in finite and/or subdivided populations. In finite populations, this effect arises primarily because, in the absence of segregation, heterozygotes may reach high frequencies due to drift, while homozygotes are still efficiently selected against; this is not possible with segregation, as matings between heterozygotes constantly produce new homozygotes. If deleterious alleles are partly, but not fully recessive, this causes an excess load in asexuals at intermediate population sizes. In subdivided populations without extinction, drift mostly occurs locally, which reduces the efficiency of selection in both sexuals and asexuals, but does not lead to global fixation. Yet, local drift is stronger in asexuals than in sexuals, leading to a higher mutation load in asexuals. In metapopulations with turnover, global drift becomes again important, leading to similar results as in finite, unstructured populations. Overall, the mutation load that arises through the absence of segregation in asexuals may greatly exceed previous predictions that ignored genetic drift.     

Probability of Fixation and Mean Fixation Time of an Overdominant Mutation

The probability of fixation of an overdominant mutation in a finite population depends on the equilibrium gene frequency in an infinite population (m) and the product (A) of population size and selection intensity. If m < 0.5 (disadvantageous overdominant genes), the probability is generally much lower than that of neutral genes; but if m is close to 0.5 and A is relatively small, it becomes higher. If m > 0.5 (advantageous overdominant genes), the probability is largely determined by the fitness of heterozygotes rather than that of mutant homozygotes. Thus, overdominance enhances the probability of fixation of advantageous mutations. The average number of generations until fixation of an overdominant mutation also depends on m and A. This average time is long when m is close to 0.5 but short when m is close to 0 or 1. This dependence on m and A is similar to that of Robertson's retardation factor.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Extreme Selection Unifies Evolutionary Game Dynamics in Finite and Infinite Populations

We show that when selection is extreme—the fittest strategy always reproduces or is imitated—the unequivalence between the possible evolutionary game scenarios in finite and infinite populations resolves, in the sense that the three generic outcomes—dominance, coexistence, and mutual exclusion—emerge in well-mixed populations of any size. We consider the simplest setting of a 2-player-2-strategy symmetric game and the two most common microscopic definitions of strategy spreading—the frequency-dependent Moran process and the imitation process by pairwise comparison—both in the case allowing any intensity of selection. We show that of the seven different invasion and fixation scenarios that are generically possible in finite populations—fixation being more or less likely to occur and rapid compared to the neutral game—the three that are possible in large populations are the same three that occur for sufficiently strong selection: (1) invasion and fast fixation of one strategy; (2) mutual invasion and slow fixation of one strategy; (3) no invasion and no fixation. Moreover (and interestingly), in the limit of extreme selection 2 becomes mutual invasion and no fixation, a case not possible for finite intensity of selection that better corresponds to the deterministic case of coexistence. In the extreme selection limit, we also derive the large population deterministic limit of the two considered stochastic processes.     

Genetic evidence for an equilibrium between docked and undocked vesicles

By using the shibire mutation to block endocytosis in a temperature-dependent fashion, we have manipulated the number of synaptic vesicles in a nerve terminal and have observed a remarkable proportionality of the number of quanta released to the size of the total vesicle pool. In the experiments described below we determine that approximately 0.3% of the vesicle pool is released per stimulus. The data suggest that the pool of readily releasable docked vesicles does not represent the saturation of a limiting number of release sites, but instead represents a subset of vesicles that is in equilibrium with the larger pool of vesicles. Before presenting this data and the significance of the finding for the regulation of neurotransmission, we will briefly review the use of Drosophila genetics as a tool for dissecting synaptic transmission.     

Isoallele Frequencies in Very Large Populations

The frequencies of electrophoretically distinguishable allelic forms of enzymes may be very different from the corresponding frequencies of structurally distinct forms, because many sequence variants may have identical electrophoretic charge. In large populations such frequencies will be determined largely by the number of amino acid sites that are free to vary. The number of distinguishable electrophoretic variants will remain fairly small. Beyond some limiting size, no further effect of population size on allele frequencies is expected, so isolated large populations will have closely similar allele frequencies if polymorphism is due largely to mutation and drift. The most common electrophoretic alleles are expected to be flanked by the next most common, with the rarer alleles increasingly distal. Neither strong selection nor mutation/drift interpretations of enzyme polymorphism are yet disproven, nor is any point between these extremes.     

On the Distribution of the Mean and Variance of a Quantitative Trait under Mutation-Selection-Drift Balance

The distributions of the mean phenotype and of the genetic variance of a polygenic trait under a balance between mutation, stabilizing selection and genetic drift are investigated. This is done by stochastic simulations in which each individual and each gene are represented. The results are compared with theoretical predictions. Some aspects of the existing theories for the evolution of quantitative traits are discussed. The maintenance of genetic variance and the average dynamics of phenotypic evolution in finite populations (with N(e) < 1000) are generally simpler than those suggested by some recent deterministic theories for infinite populations.     

Group selection of early replicators and the origin of life

A major problem of the origin of life has been that of information integration. As Eigen (1971) has shown, a mutant distribution of RNAs replicating without the aid of a replicase cannot integrate sufficient information for the functioning of a higher-level unit utilizing several types of encoded enzymes. He proposed the hypercycle model to bridge this gap in prebiology. It can be shown by a nonlinear game model, incorporating mutation of a hypercycle, that the selection properties of hypercycles make them inefficient information integrators as they cannot compete favourably with all kinds of less efficient information carriers or mutationally coupled hypercycles. The stochastic corrector model is presented as an alternative resolution of Eigen's paradox. It assumes that replicative templates are competing within replicative compartments, whose selective values depend on the internal template composition via a catalytic acid in replication and "metabolism". The dynamics of template replication are analyzed by numerical simulation of master equations. Due to the stochasticity in replication and compartment fission the best compartment types recur. An Eigen equation at the compartment level is set up and calculated. Even selfish template mutants cannot destroy the system though they make it less efficient. The genetic information of templates is evaluated at both levels, and the higher (compartment) level successfully constrains the lower (template) one. Compartmentation together with stochastic effects is sufficient to integrate information dispersed in competitive replicators. Compartment selection is considered to be group selection of replicators. Implications for the origin of life are discussed.     

Evolutionary dynamics of collective action in N-person stag hunt dilemmas

In the animal world, collective action to shelter, protect and nourish requires the cooperation of group members. Among humans, many situations require the cooperation of more than two individuals simultaneously. Most of the relevant literature has focused on an extreme case, the N-person Prisoner's Dilemma. Here we introduce a model in which a threshold less than the total group is required to produce benefits, with increasing participation leading to increasing productivity. This model constitutes a generalization of the two-person stag hunt game to an N-person game. Both finite and infinite population models are studied. In infinite populations this leads to a rich dynamics that admits multiple equilibria. Scenarios of defector dominance, pure coordination or coexistence may arise simultaneously. On the other hand, whenever one takes into account that populations are finite and when their size is of the same order of magnitude as the group size, the evolutionary dynamics is profoundly affected: it may ultimately invert the direction of natural selection, compared with the infinite population limit.     

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null.     

Sex ratio evolution through group selection using diffusion approximation

We consider a haploid, hermaphrodite population subdivided into an infinite number of demes of finite size N. Assuming recurrent mutation, random union of gametes, partial dispersal, genetic drift, and incorporating group competition, a diffusion approximation is used to describe the evolution of sex ratio, corresponding to sex allocation to male versus female functions. The stationary distribution is deduced. In presence of group selection, a female-biased sex ratio in the whole population is found to be optimal in the sense that an allele coding for this sex ratio is always more frequent at equilibrium when segregating with another allele coding for a different sex ratio than for the same sex ratio. Numerical studies are presented to check the validity and accuracy of this prediction.Research supported in part by grants from NSERC of Canada and FCAR of Quebec. This work is part of the first authors Ph.D. thesis at the Université de Montréal under the supervision of the second author.Send offprint requests to: Sabin Lessard     

Control of neural information transmission by synaptic dynamics.

The computational processing of a neural system is strongly influenced by the dynamical characteristics of the information transmission between neurons. In this work, the control of neural information transmission by synaptic dynamics is investigated by means of a master-equation-based stochastic model of pre-synaptic release of neurotransmitter-containing vesicles. The model incorporates facilitation of vesicle fusion with the pre-synaptic membrane due to intracellular calcium ions and depletion of readily releasable vesicles. The message to be transmitted is coded by the pre-synaptic firing sequence, and the received signal corresponds to the post-synaptic membrane potential response. At the sending end, the stochastic character of the vesicle release contributes to the entropy of the probability distribution of the number of vesicles released and represents noise with respect to information transmission. At the receiving end, the generation of post-synaptic membrane potentials is influenced by the temporal behaviour of ionic currents and membrane charging and is determined by means of a low-dimensional model. The rate and temporal types of neural coding are compatible with limiting cases of the synaptic information transmission as a function of initial vesicle release probability and pre-synaptic firing rate. The effects of the nonlinear dependencies of the vesicle release probability on intracellular calcium concentration and number of available vesicles are analysed. The model is compared with phenomenological and reduced models, a principal advantage being the capability of also determining fluctuations of dynamic variables Copyright 2002 Academic Press.     

Synaptotagmin-7 controls the size of the reserve and resting pools of synaptic vesicles in hippocampal neurons

Continuous neurotransmitter release is subjected to synaptic vesicle availability, which in turn depends on vesicle recycling and the traffic of vesicles between pools. We studied the role of Synaptotagmin-7 (Syt-7) in synaptic vesicle accessibility for release in hippocampal neurons in culture. Synaptic boutons from Syt-7 knockout (KO) mice displayed normal basal secretion with no alteration in the RRP size or the probability of release. However, stronger stimuli revealed an increase in the size of the reserve and resting vesicle pools in Syt-7 KO boutons compared with WT. These data suggest that Syt-7 plays a significant role in the vesicle pool homeostasis and, consequently, in the availability of vesicles for synaptic transmission during strong stimulation, probably, by facilitating advancing synaptic vesicles to the readily releasable pool.     

The effects of genetic drift in experimental evolution

Experimental evolution is characterized by exponential or logistic growth and periodic population bottlenecks. The fate of a rare beneficial mutation in these systems is influenced both by the bottleneck effect and by genetic drift. This paper explores the effects of incorporating genetic drift into models of fixation probability in populations with periodic bottlenecks. To model the inherent stochasticity during the growth phase in these populations, we assume a Poisson distribution of offspring. An analytical solution is developed to calculate the fixation probability and a computer simulation is used to verify the results. We find that the fixation rate of a favourable mutant is significantly lower when genetic drift is considered; fixation probability is reduced by over 25% for realistic experimental protocols. Our method is valid for both weak and strong selection; since very large selection coefficients have been reported in the experimental literature, this is an important improvement over previous results.     

Lateral drift correction in time-laps images by the particle-tracking algorithm

In long-term time-laps imaging of living cells, a significant lateral drift of the fluorescently labeled structures is often observed due to many reasons including superfusion of solution, temperature gradients, bolus addition of pharmacological agents and cell motility. We have detected lateral drift in long-term time-laps confocal imaging by tracking fluorescent puncta, which represent single exocytotic vesicles expressing synaptopHluorin (spH), a pH sensitive green fluorescence protein. Following the initial increase in fluorescence intensity due to alkalinization of vesicle lumen, the spH fluorescent puncta dimmed, which may be attributed to the resealing of the fusion pore and subsequent slow reacidification of the vesicle, or alternatively the dimming may be due to a significant lateral drift of the vesicle out of the region of interest (ROI). We identified and compensated the lateral drift by tracking particles present in the confocal images, without any additional mechanical and/or optical hardware components. The peak of the Gaussian two-dimensional (2D) curve fitted to the fluorescent particle intensity profile was recorded as the X and Y coordinates of the vesicle in each frame. The resulting coordinates of vesicle positions were averaged and rounded to the nearest pixel value, which was used to correct the drift in the time-laps images. In drift corrected time-laps images, the vesicle remained enclosed by the ROI, and the time dependent changes of spH fluorescence intensity averaged from the ROI remained at a constant level, revealing that endocytosis with subsequent slow reacidification of vesicles was an unlikely event.     

Simulation of the effect of population size on the evolution of the recombination fraction

A study, by means of computer simulation, has been performed on the evolution of recombination rate modifier genes in a system with three diallelic loci (A, B and C). The locus C, selectively neutral, is responsible for the modification of the recombination fraction between the major loci (A and B) which are subjected to selection. Two models have been analysed, the modifier allele being recessive in one of them, and codominant in the other, with infinite and finite populations. Distinct initial genic frequencies of the major loci and different selection coefficients have been utilised. We have found that the frequency of the allele which favours recombination increases in finite populations, and decreases slightly in infinite populations. These results are consistent with previous theory; presumably, selection favours alleles reducing recombination between epistatically interacting loci in a infinite population, since this reduces the breakup of advantageous combinations of alleles. However, in finite populations, selection favours the breakup of the random linkage disequilibria which are produced by random drift.