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The predictability of evolution is expected to depend on the relative contribution of deterministic and stochastic processes. This ratio is modulated by effective population size. Smaller effective populations harbor less genetic diversity and stochastic processes are generally expected to play a larger role, leading to less repeatable evolutionary trajectories. Empirical insight into the relationship between effective population size and repeatability is limited and focused mostly on asexual organisms. Here, we tested whether fitness evolution was less repeatable after a population bottleneck in obligately outcrossing populations of Caenorhabditis elegans. Replicated populations founded by 500, 50, or five individuals (no/moderate/strong bottleneck) were exposed to a novel environment with a different bacterial prey. As a proxy for fitness, population size was measured after one week of growth before and after 15 weeks of evolution. Surprisingly, we found no significant differences among treatments in their fitness evolution. Even though the strong bottleneck reduced the relative contribution of selection to fitness variation, this did not translate to a significant reduction in the repeatability of fitness evolution. Thus, although a bottleneck reduced the contribution of deterministic processes, we conclude that the predictability of evolution may not universally depend on effective population size, especially in sexual organisms. ispartof: EVOLUTION vol:76 issue:8 pages:1896-1904 ispartof: location:United States status: published

Evolution is a key process by which populations can adapt to novel conditions, but it is not well understood how predictable this process is. Predictability is expected to depend on the ratio of deterministic and stochastic processes that contribute to evolutionary change and this ratio is modulated by the effective population size. Smaller effective populations harbor less genetic diversity and stochastic processes are generally expected to play a larger role, leading to less repeatable evolutionary trajectories. Empirical insight into the relationship between effective population size and repeatability is limited and biased towards asexual unicellular organisms. Here, we used populations of obligately outcrossing Caenorhabditis elegans to test whether fitness increase and selection response were more heterogeneous after a moderate or strong population bottleneck compared to a scenario without bottleneck. Nematodes were exposed to a novel bacterial prey and lower temperature. Population sizes after one week of growth (as a proxy of fitness) were measured before and after 15 generations of evolution. We found that replicates across all (no/moderate/strong bottleneck) treatments evolved higher fitness and no significant difference in average or maximum fitness was found among treatments. Partitioning fitness variance among effects from selection and effects from chance showed that a strong (but not a moderate) bottleneck reduced the relative contribution of selection effects to fitness variation. However, the reduced contribution from selection did not translate to a significant reduction in the repeatability of fitness evolution. Thus, although a strong bottleneck reduced the contribution of deterministic evolutionary change, we found only marginal effects on quantitative measurements of repeatability in evolution. We conclude that the extent to which evolution is predictable may not universally depend on effective population size. IMPACT SUMMARYEvolution is a key process by which populations can adapt to novel conditions. The predictability of evolution is elusive, but the extent to which evolution is predictable is central to our understanding of evolutionary processes and to emergent applications in medicine, agriculture, and conservation. Predictability is expected to be high when evolutionary change is mainly driven by selection, because this leads to repeatable evolutionary trajectories. However, chance effects, e.g. from genetic drift, reduce repeatability. In populations with smaller effective sizes (and thus reduced genetic diversity), chance effects are generally thought to be more prevalent than in large effective populations, suggesting that effective population size influences evolutionary repeatability. Recent theoretical insights cast doubt on the universality of this relationship between evolutionary repeatability and effective population size. Thus far, empirical work testing these theoretical insights is limited to asexual species, leaving a gap in our knowledge. Therefore, we performed an evolutionary experiment using sexually reproducing populations of the nematode Caenorhabditis elegans. Populations either went through a strong or moderate bottleneck or through no bottleneck at all to create populations with different degrees of genetic variation. These populations with different histories (but similar census size) were then exposed to novel conditions. Our results showed that neither average fitness in the novel environment or the repeatability of fitness evolution were significantly lower following a bottleneck. This was despite a reduced contribution from selection and increased contribution from chance to fitness variation in populations that experienced a strong bottleneck. We therefore show that in sexually reproducing species, increased contributions from chance in populations with lower effective sizes do not necessarily affect evolutionary repeatability. This is an important novel insight that is relevant both for our fundamental understanding as well as for evolutionary forecasting applications in agriculture and conservation, which are primarily targeted at sexual species.

Microbial communities in fluctuating environments can contain many species and diversity within species, both in natural environments such as the human gut, and in laboratory settings when communities are propagated for a long time. Whether this diversity is at the species level, within the species level, or a combination of both, the question remains: what processes lead to the origination and maintenance of this diversity? When nutrient levels fluctuate over time, one possibly relevant process is that different types specialize on low and high nutrient levels. The relevance of this process is supported by observations of types co-existing through this mechanism when put together in the laboratory, and by simple models, that show that negative frequency dependence of two types, specialized on low and high resource level, can stabilize coexistence. However, when microbial populations are in an environment for a long time, they evolve. In this article we determine what happens when species can evolve; whether branching can occur to create diversity and whether evolution will destabilize coexistence. We find that for the trade-off data between growth at low and high substrate concentrations, available for the bacterium Escherichia coli and the yeast Saccharomyces cerevisiae on glucose, there is only a small portion of the trait-space that allows for coexistence. Moreover, this coexistence is destabilized by evolution, and the only evolutionary stable outcome is a single type. When we combine two species that are well-adapted on their own, we do find that they can form an evolutionary singular coalition, i.e. a coexistence that is evolutionarily stable. We conclude that although specialization on resource level can support diversity within a species, it is likely not a cause by itself. In contrast, for species consortia this specialization can lead to evolutionarily stable coexistence.

Continual evolution describes the unceasing evolution of at least one trait involving at least one organism. The Red Queen Hypothesis is a specific case in which continual evolution results from coevolution of at least two species. While microevolutionary studies have described examples in which evolution does not cease, understanding which general conditions lead to continual evolution or to stasis remains a major challenge. In many cases, it is unclear which experimental features or model assumptions are necessary for the observed continual evolution to emerge, and whether the described behavior is robust to variations in the given setup. Here, we aim to find the minimal set of conditions under which continual evolution occurs. To this end, we present a theoretical framework that does not assume any specific functional form and, therefore, can be applied to a wide variety of systems. Our framework is also general enough to make predictions about both monomorphic and polymorphic populations. We show that the combination of a fast positive and a slow negative feedback between environment, population, and evolving traits causes continual evolution to emerge even from the evolution of a single evolving trait, provided that the ecological timescale is sufficiently faster than the timescales of mutation and the negative feedback. Our approach and results thus contribute to a deeper understanding of the evolutionary dynamics resulting from biotic interactions.

The Red Queen Hypothesis proposes that perpetual co-evolution among organisms can result from purely biotic drivers. After more than four decades, there is no satisfactory understanding as to which mechanisms trigger Red Queen dynamics or their implications for ecosystem features such as biodiversity. One reason for such a knowledge gap is that typical models are complicated theories where limit cycles represent an idealized Red Queen, and therefore cannot be used to devise experimental setups. Here, we bridge this gap by introducing a simple model for microbial systems able to show Red Queen dynamics. We explore diverse biotic sources that can drive the emergence of the Red Queen and that have the potential to be found in nature or to be replicated in the laboratory. Our model enables an analytical understanding of how Red Queen dynamics emerge in our setup, and the translation of model terms and phenomenology into general underlying mechanisms. We observe, for example, that in our system the Red Queen offers opportunities for the increase of biodiversity by facilitating challenging conditions for intraspecific dominance, whereas stasis tends to homogenize the system. Our results can be used to design and engineer experimental microbial systems showing Red Queen dynamics.

Microbes may maximize the number of daughter cells per time or per amount of nutrients consumed. These two strategies correspond, respectively, to the use of enzyme-efficient or substrate-efficient metabolic pathways. In reality, fast growth is often associated with wasteful, yield-inefficient metabolism, and a general thermodynamic trade-off between growth rate and biomass yield has been proposed to explain this. We studied growth rate/yield trade-offs by using a novel modeling framework, Enzyme-Flux Cost Minimization (EFCM) and by assuming that the growth rate depends directly on the enzyme investment per rate of biomass production. In a comprehensive mathematical model of core metabolism in E. coli, we screened all elementary flux modes leading to cell synthesis, characterized them by the growth rates and yields they provide, and studied the shape of the resulting rate/yield Pareto front. By varying the model parameters, we found that the rate/yield trade-off is not universal, but depends on metabolic kinetics and environmental conditions. A prominent trade-off emerges under oxygen-limited growth, where yield-inefficient pathways support a 2-to-3 times higher growth rate than yield-efficient pathways. EFCM can be widely used to predict optimal metabolic states and growth rates under varying nutrient levels, perturbations of enzyme parameters, and single or multiple gene knockouts., Author summary When cells compete for nutrients, those that grow faster and produce more offspring per time are favored by natural selection. In contrast, when cells need to maximize the cell number at a limited nutrient supply, fast growth does not matter and an efficient use of nutrients (i.e. high biomass yield) is essential. This raises a basic question about metabolism: can cells achieve high growth rates and yields simultaneously, or is there a conflict between the two goals? Using a new modeling method called Enzymatic Flux Cost Minimization (EFCM), we predict cellular growth rates and find that growth rate/yield trade-offs and the ensuing preference for enzyme-efficient or substrate-efficient metabolic pathways are not universal, but depend on growth conditions such as external glucose and oxygen concentrations.

Many organisms have several similar transporters with different affinities for the same substrate. Typically, high-affinity transporters are expressed when substrate is scarce and low-affinity ones when it is abundant. The benefit of using low instead of high-affinity transporters remains unclear, especially when additional nutrient sensors are present. Here, we investigate two hypotheses. It was previously hypothesized that there is a trade-off between the affinity and the catalytic efficiency of transporters, and we find some but no definitive support for it. Additionally, we propose that for uptake by facilitated diffusion, at saturating substrate concentrations, lowering the affinity enhances the net uptake rate by reducing substrate efflux. As a consequence, there exists an optimal, external-substrate-concentration dependent transporter affinity. A computational model of Saccharomyces cerevisiae glycolysis shows that using the low affinity HXT3 transporter instead of the high affinity HXT6 enhances the steady-state flux by 36%. We tried to test this hypothesis with yeast strains expressing a single glucose transporter modified to have either a high or a low affinity. However, due to the intimate link between glucose perception and metabolism, direct experimental proof for this hypothesis remained inconclusive. Still, our theoretical results provide a novel reason for the presence of low-affinity transport systems.

Cells require membrane-located transporter proteins to import nutrients from the environment. Many organisms have several similar transporters for the same nutrient, which differ in their affinity. Typically, high affinity transporters are expressed when substrate is scarce and low affinity ones when substrate is more abundant. The benefit of using low affinity transporters when high affinity ones are available has so far remained unclear. Here, we investigate two hypotheses. First, it was previously hypothesized that a trade-off between the affinity and the maximal catalytic rate explains this phenomenon. We find some theoretical and experimental support for this hypothesis, but no conclusive evidence. Secondly, we propose a new hypothesis: for uptake by facilitated diffusion, at saturating extracellular substrate concentrations, lowering the affinity enhances the net uptake rate by reducing the substrate efflux rate. As a consequence, there exists an optimal, external substrate concentration dependent transporter affinity. Anin silicoanalysis of glycolysis inSaccharomyces cerevisiaeshows that using the low affinity HXT3 transporter instead of the high affinity HXT6 enhances the steady-state flux by 36%. We tried to test this hypothesis using yeast strains expressing a single glucose transporter that was modified to have either a high or a low affinity. Due to the intimate and reciprocal link between glucose perception and metabolism, direct experimental proof for this hypothesis remained inconclusive in our hands. Still, our theoretical results provide a novel reason for the presence of low affinity transport systems which might have more general implications for enzyme catalyzed conversions.

Protein expression is shaped by evolutionary processes that tune microbial fitness. The limited biosynthetic capacity of a cell constrains protein expression and forces the cell to carefully manage its protein economy. In a chemostat, the physiology of the cell feeds back on the growth conditions, hindering intuitive understanding of how changes in protein concentration affect fitness. Here, we aim to provide a theoretical framework that addresses the selective pressures and optimal evolutionary-strategies in the chemostat. We show that the optimal enzyme levels are the result of a trade-off between the cost of their production and the benefit of their catalytic function. We also show that deviations from optimal enzyme levels are directly related to selection coefficients. The maximal fitness strategy for an organism in the chemostat is to express a well-defined metabolic subsystem known as an elementary flux mode. Using a coarse-grained, kinetic model of Saccharomyces cerevisiae’s metabolism and growth, we illustrate that the dynamics and outcome of evolution in a chemostat can be very counter-intuitive: Strictly-respiring and strictly-fermenting strains can evolve from a common ancestor. This work provides a theoretical framework that relates a kinetic, mechanistic view on metabolism with cellular physiology and evolutionary dynamics in the chemostat.

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism., Author Summary Organisms depend on huge networks of molecular reactions for environmental sensing, information integration, gene expression, and metabolism. The discovery of general principles of network behavior is a major ambition of systems biology and of great interest to biotechnology and medicine. We present a computational tool that calculates all optimal states of metabolism in terms of pathways, which is arguably the most intuitive and preferred approach to characterize whole-cell metabolism. We show how the space of all feasible flux distributions can be compactly described in terms of a unique set of minimal and feasible pathways, given realistic stoichiometric, thermodynamic, and optimization-objective constraints. This description clarifies the interplay between flux constraints and optimization objectives. We explain why some fluxes are variable and cross-correlate within the solution space while others do not and how multi-objective optimization shrinks the solution space. We illustrate our findings with a toy metabolic model to explain the main insights and apply it to a genome-scale stoichiometric model of Escherichia coli metabolism.

Introduction Cells use multilayered regulatory systems to respond adequately to changing environments or perturbations. Failure in regulation underlies cellular malfunctioning, loss of fitness, or disease. How molecular components dynamically interact to give rise to robust and adaptive responses is not well understood. Here, we studied how the model eukaryote Saccharomyces cerevisiae can cope with transition to high glucose levels, a failure of which results in metabolic malfunctioning and growth arrest. Methods We combined experimental and modeling approaches to unravel the mechanisms used by yeast to cope with sudden glucose availability. We studied growth characteristics and metabolic state at population and single-cell levels (through flow cytometry and colony plating) of the wild type and of mutants unable to transit properly to excess glucose; such mutants are defective in trehalose synthesis, a disaccharide associated with stress resistance. Dynamic 13 C tracer enrichment was used to estimate dynamic intracellular fluxes immediately after glucose addition. Mathematical modeling was used to interpret and generalize results and to suggest subsequent experiments. Results The failure to cope with glucose is caused by imbalanced reactions in glycolysis, the essential pathway in energy metabolism in most organisms. In the failure mode, the first steps of glycolysis carry more flux than the downstream steps, resulting in accumulating intermediates at constant low levels of adenosine triphosphate (ATP) and inorganic phosphate. We found that cells with such an unbalanced glycolysis coexist with vital cells with normal glycolytic function. Spontaneous, nongenetic metabolic variability among individual cells determines which state is reached and consequently which cells survive. In mutants of trehalose metabolism, only 0.01% of the cells started to grow on glucose; in the wild type, the success rate was still only 93% (i.e., 7% of wild-type yeast did not properly start up glycolysis). Mathematical models predicted that the dynamics of inorganic phosphate is a key determinant in successful transition to glucose, and that phosphate release through ATP hydrolysis reduces the probability of reaching an imbalanced state. 13 C-labeling experiments confirmed the hypothesis that trehalose metabolism constitutes a futile cycle that would provide proper phosphate balance: Upon a glucose pulse, almost 30% of the glucose is transiently shuttled into trehalose metabolism. Discussion Our work reveals how cell fate can be determined by glycolytic dynamics combined with cell heterogeneity purely at the metabolic level. Specific regulatory mechanisms are required to initiate the glycolytic pathway; in yeast, trehalose cycling pushes glycolysis transiently into the right direction, after which cycling stops. The coexistence of two modes of glycolysis—an imbalanced state and the normal functional state—arises from the fundamental design of glycolysis. This makes the imbalanced state a generic risk for humans as well, extending our fundamental knowledge of this central pathway that is dysfunctional in diseases such as diabetes and cancer.

In the model eukaryote Saccharomyces cerevisiae, it has long been known that a functional trehalose pathway is indispensable for transitions to high glucose conditions. Upon addition of glucose, cells with a defect in trehalose 6-phosphate synthase (Tps1), the first committed step in the trehalose pathway, display what we have termed an imbalanced glycolytic state; in this state the flux through the upper part of glycolysis outpaces that through the lower part of glycolysis. As a consequence, the intermediate fructose 1,6-bisphosphate (FBP) accumulates at low concentrations of ATP and inorganic phosphate (Pi). Despite significant research efforts, a satisfactory understanding of the regulatory role that trehalose metabolism plays during such transitions has remained infamously unresolved. In a recent study, we demonstrate that the startup of glycolysis exhibits two dynamic fates: a proper, functional, steady state or the imbalanced state described above. Both states are stable, attracting states, and the probability distribution of initial states determines the fate of a yeast cell exposed to glucose. Trehalose metabolism steers the dynamics of glycolysis towards the proper functional state through its ATP hydrolysis activity; a mechanism that ensures that the demand and supply of ATP is balanced with Pi availability under dynamic conditions. [van Heerden et al. Science (2014), DOI: 10.1126/science.1245114.]

Performance of industrial microorganisms as cell factories is limited by the capacity to channel nutrients to desired products, of which optimal production usually requires careful manipulation of process conditions, or strain improvement. The focus in process improvement is often on understanding and manipulating the regulation of metabolism. Nonetheless, one encounters situations where organisms are remarkably resilient to further optimization or their properties become unstable. Therefore it is important to understand the origin of these apparent limitations to find whether and how they can be improved. We argue that by considering fitness effects of regulation, a more generic explanation for certain behaviour can be obtained. In this view, apparent process limitations arise from trade-offs that cells faced as they evolved to improve fitness. A deeper understanding of such trade-offs using a systems biology approach can ultimately enhance performance of cell factories. © 2012 The Author(s).

Although phenotypic plasticity can be advantageous in fluctuating environments, it may come too late if the environment changes fast. Complementary chromatic adaptation is a colorful form of phenotypic plasticity, where cyanobacteria tune their pigmentation to the prevailing light spectrum. Here, we study the timescale of chromatic adaptation and its impact on competition among phytoplankton species exposed to fluctuating light colors. We parameterized a resource competition model using monoculture experiments with green and red picocyanobacteria and the cyanobacterium Pseudanabaena, which can change its color within approximately 7 days by chromatic adaptation. The model predictions were tested in competition experiments, where the incident light color switched between red and green at different frequencies (slow, intermediate, and fast). Pseudanabaena (the flexible phenotype) competitively excluded the green and red picocyanobacteria in all competition experiments. Strikingly, the rate of competitive exclusion was much faster when the flexible phenotype had sufficient time to fully adjust its pigmentation. Thus, the flexible phenotype benefited from its phenotypic plasticity if fluctuations in light color were relatively slow, corresponding to slow mixing processes or infrequent storms in their natural habitat. This shows that the timescale of phenotypic plasticity plays a key role during species interactions in fluctuating environments.