Optimality models in the age of experimental evolution and genomics

Exploring the expanse between theoretical questions and experimental approaches in the modern study of evolvability

Despite several decades of computational and experimental work across many systems, evolvability remains on the periphery with regards to its status as a widely accepted and regularly applied theoretical concept. Here we propose that its marginal status is partly a result of large gaps between the diverse but disconnected theoretical treatments of evolvability and the relatively narrower range of studies that have tested it empirically. To make this case, we draw on a range of examples-from experimental evolution in microbes, to molecular evolution in proteins-where attempts have been made to mend this disconnect. We highlight some examples of progress that has been made and point to areas where synthesis and translation of existing theory can lead to further progress in the still-new field of empirical measurements of evolvability.

An Optimal Lysis Time Maximizes Bacteriophage Fitness in Quasi-Continuous Culture

Optimality models have a checkered history in evolutionary biology. While optimality models have been successful in providing valuable insight into the evolution of a wide variety of biological traits, a common objection is that optimality models are overly simplistic and ignore organismal genetics. We revisit evolutionary optimization in the context of a major bacteriophage life history trait, lysis time. Lysis time refers to the period spanning phage infection of a host cell and its lysis, whereupon phage progenies are released. Lysis time, therefore, directly determines phage fecundity assuming progeny assembly does not exhaust host resources prior to lysis. Noting that previous tests of lysis time optimality rely on batch culture, we implemented a quasi-continuous culture system to observe productivity of a panel of isogenic phage λ genotypes differing in lysis time. We report that under our experimental conditions, λ phage productivity is maximized around optimal lysis times ranging from 60 to 100 min, and λ wildtype strain falls within this range. It would appear that natural selection on phage λ lysis time uncovered a set of genetic solutions that optimized progeny production in its ecological milieu relative to alternative genotypes. We discuss this finding in light of recent results that lysis time variation is also minimized in the strains with lysis times closer to the λ wild-type strain. IMPORTANCE Optimality theory presents the idea that natural selection acts on organismal traits to produce genotypes that maximize organismal survival and reproduction. As such, optimality theory is a valuable tool in guiding our understanding of the genetic constraints and tradeoffs organisms experience as their genotypes are selected to produce optimal solutions to biological problems. However, optimality theory is often critiqued as being overly simplistic and ignoring the roles of chance and history in the evolution of organismal traits. We show here that the wild-type genotype of a popular laboratory model organism, the bacteriophage λ, produces a phenotype for a major life history trait, lysis time, that maximizes the reproductive success of bearers of that genotype relative to other possible genotypes. This result demonstrates, as is rarely shown experimentally, that natural selection can achieve optimal solutions to ecological challenges.

The evolution of collective infectious units in viruses

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Many viruses disperse in groups, as part of collective infectious units (CIUs).

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We modelled different factors that could influence the evolution of CIUs.

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Group infectivity benefits favoured CIUs, especially if CIUs were more efficient.

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Defective genomes did not favour or disfavour CIUs.

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Defective interfering genomes disfavoured CIUs.

Viruses frequently spread among cells or hosts in groups, with multiple viral genomes inside the same infectious unit. These collective infectious units can consist of multiple viral genomes inside the same virion, or multiple virions inside a larger structure such as a vesicle. Collective infectious units deliver multiple viral genomes to the same cell simultaneously, which can have important implications for viral pathogenesis, antiviral resistance, and social evolution. However, little is known about why some viruses transmit in collective infectious units, whereas others do not. We used a simple evolutionary approach to model the potential costs and benefits of transmitting in a collective infectious unit. We found that collective infectious units could be favoured if cells infected by multiple viral genomes were significantly more productive than cells infected by just one viral genome, and especially if there were also efficiency benefits to packaging multiple viral genomes inside the same infectious unit. We also found that if some viral sequences are defective, then collective infectious units could evolve to become very large, but that if these defective sequences interfered with wild-type virus replication, then collective infectious units were disfavoured.

Modeling the probability distribution of the bacterial burst size via a game-theoretic approach

Based on previous studies, empirical distribution of the bacterial burst size varies even in a population of isogenic bacteria. Since bacteriophage progenies increase linearly with time, it is the lysis time variation that results in the bacterial burst size variations. Here, the burst size variation is computationally modeled by considering the lysis time decisions as a game. Each player in the game is a bacteriophage that has initially infected and lysed its host bacterium. Also, the payoff of each burst size strategy is the average number of bacteria that are solely infected by the bacteriophage progenies after lysis. For calculating the payoffs, a new version of ball and bin model with time dependent occupation probabilities (TDOP) is proposed. We show that Nash equilibrium occurs for a range of mixed burst size strategies that are chosen and played by bacteriophages, stochastically. Moreover, it is concluded that the burst size variations arise from choosing mixed lysis strategies by each player. By choosing the lysis time and also the burst size stochastically, the released bacteriophage progenies infect a portion of host bacteria in environment and avoid extinction. The probability distribution of the mixed burst size strategies is also identified.

Pleiotropy, constraint, and modularity in the evolution of life histories: insights from genomic analyses

Multicellular organisms display an enormous range of life history (LH) strategies and present an evolutionary conundrum; despite strong natural selection, LH traits are characterized by high levels of genetic variation. To understand the evolution of life histories and maintenance of this variation, the specific phenotypic effects of segregating alleles and the genetic networks in which they act need to be elucidated. In particular, the extent to which LH evolution is constrained by the pleiotropy of alleles contributing to LH variation is generally unknown. Here, we review recent empirical results that shed light on this question, with an emphasis on studies employing genomic analyses. While genome-scale analyses are increasingly practical and affordable, they face limitations of genetic resolution and statistical power. We describe new research approaches that we believe can produce new insights and evaluate their promise and applicability to different kinds of organisms. Two approaches seem particularly promising: experiments that manipulate selection in multiple dimensions and measure phenotypic and genomic response and analytical approaches that take into account genome-wide associations between markers and phenotypes, rather than applying a traditional marker-by-marker approach.

Evolutionary dynamics of viral escape under antibodies stress: A biophysical model

Viruses constantly face the selection pressure of antibodies, either from innate immune response of the host or from administered antibodies for treatment. We explore the interplay between the biophysical properties of viral proteins and the population and demographic variables in the viral escape. The demographic and population genetics aspect of the viral escape have been explored before; however one important assumption was the a priori distribution of fitness effects (DFE). Here, we relax this assumption by instead considering a realistic biophysics-based genotype-phenotype relationship for RNA viruses escaping antibodies stress. In this model the DFE is itself an evolvable property that depends on the genetic background (epistasis) and the distribution of biophysical effects of mutations, which is informed by biochemical experiments and theoretical calculations in protein engineering. We quantitatively explore in silico the viability of viral populations under antibodies pressure and derive the phase diagram that defines the fate of the virus population (extinction or escape from stress) in a range of viral mutation rates and antibodies concentrations. We find that viruses are most resistant to stress at an optimal mutation rate (OMR) determined by the competition between supply of beneficial mutation to facilitate escape from stressors and lethal mutagenesis caused by excess of destabilizing mutations. We then show the quantitative dependence of the OMR on genome length and viral burst size. We also recapitulate the experimental observation that viruses with longer genomes have smaller mutation rate per nucleotide.

The genetical theory of social behaviour

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton's (Hamilton 1964 J. Theoret. Biol. 7, 1-16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.

Do-or-die life cycles and diverse post-infection resistance mechanisms limit the evolution of parasite host ranges

In light of the dynamic nature of parasite host ranges and documented potential for rapid host shifts, the observed high host specificity of most parasites remains an ecological paradox. Different variants of host-use trade-offs have become a mainstay of theoretical explanations of the prevalence of host specialism, but empirical evidence for such trade-offs is rare. We propose an alternative theory based on basic features of the parasite life cycle: host selection and subsequent intrahost replication. We introduce a new concept of effective burst size that accounts for the fact that successful host selection does not guarantee intrahost replication. Our theory makes a general prediction that a parasite will expand its host range if its effective burst size is positive. An in silico model of bacteria-phage coevolution verifies our predictions and demonstrates that the tendency for relatively narrow host ranges in parasites can be explained even in the absence of trade-offs.

Temporal variation favors the evolution of generalists in experimental populations of Drosophila melanogaster

In variable environments, selection should favor generalists that maintain fitness across a range of conditions. However, costs of adaptation may generate fitness trade-offs and lead to some compromise between specialization and generalization that maximizes fitness. Here, we evaluate the evolution of specialization and generalization in 20 populations of Drosophila melanogaster experimentally evolved in constant and variable thermal environments for 3 years. We developed genotypes from each population at two temperatures after which we measured fecundity across eight temperatures. We predicted that constant environments would select for thermal specialists and that variable environments would select for thermal generalists. Contrary to our predictions, specialists and generalists did not evolve in constant and spatially variable environments, respectively. However, temporal variation produced a type of generalist that has rarely been considered by theoretical models of developmental plasticity. Specifically, genotypes from the temporally variable selective environment were more fecund across all temperatures than were genotypes from other environments. These patterns suggest certain allelic effects and should inspire new directions for modeling adaptation to fluctuating environments.

An objective function exploiting suboptimal solutions in metabolic networks

Background

Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results

We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion

Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

What Can Phages Tell Us about Host-Pathogen Coevolution?

The outcomes of host-parasite interactions depend on the coevolutionary forces acting upon them, but because every host-parasite relation is enmeshed in a web of biotic and abiotic interactions across a heterogeneous landscape, host-parasite coevolution has proven difficult to study. Simple laboratory phage-bacteria microcosms can ameliorate this difficulty by allowing controlled, well-replicated experiments with a limited number of interactors. Genetic, population, and life history data obtained from these studies permit a closer examination of the fundamental correlates of host-parasite coevolution. In this paper, I describe the results of phage-bacteria coevolutionary studies and their implications for the study of host-parasite coevolution. Recent experimental studies have confirmed phage-host coevolutionary dynamics in the laboratory and have shown that coevolution can increase parasite virulence, specialization, adaptation, and diversity. Genetically, coevolution frequently proceeds in a manner best described by the Gene for Gene model, typified by arms race dynamics, but certain contexts can result in Red Queen dynamics according to the Matching Alleles model. Although some features appear to apply only to phage-bacteria systems, other results are broadly generalizable and apply to all instances of antagonistic coevolution. With laboratory host-parasite coevolutionary studies, we can better understand the perplexing array of interactions that characterize organismal diversity in the wild.

Redox balance is key to explaining full vs. partial switching to low-yield metabolism

BACKGROUND

Low-yield metabolism is a puzzling phenomenon in many unicellular and multicellular organisms. In abundance of glucose, many cells use a highly wasteful fermentation pathway despite the availability of a high-yield pathway, producing many ATP molecules per glucose, e.g., oxidative phosphorylation. Some of these organisms, including the lactic acid bacterium Lactococcus lactis, downregulate their high-yield pathway in favor of the low-yield pathway. Other organisms, including Escherichia coli do not reduce the flux through the high-yield pathway, employing the low-yield pathway in parallel with a fully active high-yield pathway. For what reasons do some species use the high-yield and low-yield pathways concurrently and what makes others downregulate the high-yield pathway? A classic rationale for metabolic fermentation is overflow metabolism. Because the throughput of metabolic pathways is limited, influx of glucose exceeding the pathway's throughput capacity is thought to be redirected into an alternative, low-yield pathway. This overflow metabolism rationale suggests that cells would only use fermentation once the high-yield pathway runs at maximum rate, but it cannot explain why cells would decrease the flux through the high-yield pathway.

RESULTS

Using flux balance analysis with molecular crowding (FBAwMC), a recent extension to flux balance analysis (FBA) that assumes that the total flux through the metabolic network is limited, we investigate the differences between Saccharomyces cerevisiae and L. lactis that downregulate the high-yield pathway at increasing glucose concentrations, and E. coli, which keeps the high-yield pathway functioning at maximal rate. FBAwMC correctly predicts the metabolic switching mode in these three organisms, suggesting that metabolic network architecture is responsible for differences in metabolic switching mode. Based on our analysis, we expect gradual, "overflow-like" switching behavior in organisms that have an additional energy-yielding pathway that does not consume NADH (e.g., acetate production in E. coli). Flux decrease through the high-yield pathway is expected in organisms in which the high-yield and low-yield pathways compete for NADH. In support of this analysis, a simplified model of metabolic switching suggests that the extra energy generated during acetate production produces an additional optimal growth mode that smoothens the metabolic switch in E. coli.

CONCLUSIONS

Maintaining redox balance is key to explaining why some microbes decrease the flux through the high-yield pathway, while other microbes use "overflow-like" low-yield metabolism.