RESUMO
In disciplines from biology to climate science, a routine task is to compute a correlation between a pair of time series and determine whether the correlation is statistically significant (i.e., unlikely under the null hypothesis that the time series are independent). This problem is challenging because time series typically exhibit autocorrelation and thus cannot be properly analyzed with the standard iid-oriented statistical tests. Although there are well-known parametric tests for time series, these are designed for linear correlation statistics and thus not suitable for the increasingly popular nonlinear correlation statistics. There are also nonparametric tests that can be used with any correlation statistic, but for these, the conditions that guarantee correct false positive rates are either restrictive or unclear. Here, we describe the truncated time-shift (TTS) test, a nonparametric procedure to test for dependence between 2 time series. We prove that this test correctly controls the false positive rate as long as one of the time series is stationary, a minimally restrictive requirement among current tests. The TTS test is versatile because it can be used with any correlation statistic. Using synthetic data, we demonstrate that this test performs correctly even while other tests suffer high false positive rates. In simulation examples, simple guidelines for parameter choices allow high statistical power to be achieved with sufficient data. We apply the test to datasets from climatology, animal behavior, and microbiome science, verifying previously discovered dependence relationships and detecting additional relationships.
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Microbial communities are capable of performing diverse functions with important bioindustrial and medical applications. One approach to improving community function is to breed new communities by artificially selecting for those displaying high community function ('community selection'). Importantly, community selection can improve the function of interest without needing to understand how the function arises, just like in classical artificial selection of individuals. However, experimental studies of community selection have had varied and largely limited success. Here, we review a conceptual framework to help foster an understanding of community selection and its associated challenges, and provide broad insights for designing effective selection strategies.
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MicrobiotaRESUMO
Assimilation of sulfur is vital to all organisms. In S. cerevisiae, inorganic sulfate is first reduced to sulfide, which is then affixed to an organic carbon backbone by the Met17 enzyme. The resulting homocysteine can then be converted to all other essential organosulfurs such as methionine, cysteine, and glutathione. This pathway has been known for nearly half a century, and met17 mutants have long been classified as organosulfur auxotrophs, which are unable to grow on sulfate as their sole sulfur source. Surprisingly, we found that met17Δ could grow on sulfate, albeit only at sufficiently high cell densities. We show that the accumulation of hydrogen sulfide gas underpins this density-dependent growth of met17Δ on sulfate and that the locus YLL058W (HSU1) enables met17Δ cells to assimilate hydrogen sulfide. Hsu1 protein is induced during sulfur starvation and under exposure to high sulfide concentrations in wild-type cells, and the gene has a pleiotropic role in sulfur assimilation. In a mathematical model, the low efficiency of sulfide assimilation in met17Δ can explain the observed density-dependent growth of met17Δ on sulfate. Thus, having uncovered and explained the paradoxical growth of a commonly used "auxotroph," our findings may impact the design of future studies in yeast genetics, metabolism, and volatile-mediated microbial interactions.
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Cisteína Sintase , Sulfeto de Hidrogênio , Proteínas de Saccharomyces cerevisiae , Sulfeto de Hidrogênio/metabolismo , Saccharomyces cerevisiae/genética , Saccharomyces cerevisiae/crescimento & desenvolvimento , Saccharomyces cerevisiae/metabolismo , Cisteína Sintase/genética , Cisteína Sintase/metabolismo , Deleção de Genes , Proteínas de Saccharomyces cerevisiae/genética , Proteínas de Saccharomyces cerevisiae/metabolismo , Sulfatos/metabolismo , Modelos BiológicosRESUMO
Complex systems are challenging to understand, especially when they defy manipulative experiments for practical or ethical reasons. Several fields have developed parallel approaches to infer causal relations from observational time series. Yet, these methods are easy to misunderstand and often controversial. Here, we provide an accessible and critical review of three statistical causal discovery approaches (pairwise correlation, Granger causality, and state space reconstruction), using examples inspired by ecological processes. For each approach, we ask what it tests for, what causal statement it might imply, and when it could lead us astray. We devise new ways of visualizing key concepts, describe some novel pathologies of existing methods, and point out how so-called 'model-free' causality tests are not assumption-free. We hope that our synthesis will facilitate thoughtful application of methods, promote communication across different fields, and encourage explicit statements of assumptions. A video walkthrough is available (Video 1 or https://youtu.be/AIV0ttQrjK8).
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Fatores de Tempo , CausalidadeRESUMO
Microbial communities often perform important functions that depend on inter-species interactions. To improve community function via artificial selection, one can repeatedly grow many communities to allow mutations to arise, and "reproduce" the highest-functioning communities by partitioning each into multiple offspring communities for the next cycle. Since improvement is often unimpressive in experiments, we study how to design effective selection strategies in silico. Specifically, we simulate community selection to improve a function that requires two species. With a "community function landscape", we visualize how community function depends on species and genotype compositions. Due to ecological interactions that promote species coexistence, the evolutionary trajectory of communities is restricted to a path on the landscape. This restriction can generate counter-intuitive evolutionary dynamics, prevent the attainment of maximal function, and importantly, hinder selection by trapping communities in locations of low community function heritability. We devise experimentally-implementable manipulations to shift the path to higher heritability, which speeds up community function improvement even when landscapes are high dimensional or unknown. Video walkthroughs: https://go.nature.com/3GWwS6j ; https://online.kitp.ucsb.edu/online/ecoevo21/shou2/ .
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Evolução Molecular Direcionada/métodos , Microbiota/genética , Modelos BiológicosRESUMO
Cooperation, paying a cost to benefit others, is widespread. Cooperation can be promoted by pleiotropic 'win-win' mutations which directly benefit self (self-serving) and partner (partner-serving). Previously, we showed that partner-serving should be defined as increased benefit supply rate per intake benefit. Here, we report that win-win mutations can rapidly evolve even under conditions unfavorable for cooperation. Specifically, in a well-mixed environment we evolved engineered yeast cooperative communities where two strains exchanged costly metabolites, lysine and hypoxanthine. Among cells that consumed lysine and released hypoxanthine, ecm21 mutations repeatedly arose. ecm21 is self-serving, improving self's growth rate in limiting lysine. ecm21 is also partner-serving, increasing hypoxanthine release rate per lysine consumption and the steady state growth rate of partner and of community. ecm21 also arose in monocultures evolving in lysine-limited chemostats. Thus, even without any history of cooperation or pressure to maintain cooperation, pleiotropic win-win mutations may readily evolve to promote cooperation.
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Evolução Biológica , Pleiotropia Genética/fisiologia , Mutação , Saccharomyces cerevisiae/fisiologia , Saccharomyces cerevisiae/genéticaRESUMO
In eukaryotes, conserved mechanisms ensure that cell growth is coordinated with nutrient availability. Overactive growth during nutrient limitation ("nutrient-growth dysregulation") can lead to rapid cell death. Here, we demonstrate that cells can adapt to nutrient-growth dysregulation by evolving major metabolic defects. Specifically, when yeast lysine-auxotrophic mutant lys- encountered lysine limitation, an evolutionarily novel stress, cells suffered nutrient-growth dysregulation. A subpopulation repeatedly evolved to lose the ability to synthesize organosulfurs (lys-orgS-). Organosulfurs, mainly reduced glutathione (GSH) and GSH conjugates, were released by lys- cells during lysine limitation when growth was dysregulated, but not during glucose limitation when growth was regulated. Limiting organosulfurs conferred a frequency-dependent fitness advantage to lys-orgS- by eliciting a proper slow growth program, including autophagy. Thus, nutrient-growth dysregulation is associated with rapid organosulfur release, which enables the selection of organosulfur auxotrophy to better tune cell growth to the metabolic environment. We speculate that evolutionarily novel stresses can trigger atypical release of certain metabolites, setting the stage for the evolution of new ecological interactions.
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Adaptação Fisiológica/genética , Lisina/farmacologia , Redes e Vias Metabólicas/efeitos dos fármacos , Nutrientes/farmacologia , Saccharomyces cerevisiae/metabolismo , Autofagia/efeitos dos fármacos , Autofagia/genética , Evolução Biológica , Glucose/metabolismo , Glucose/farmacologia , Lisina/deficiência , Redes e Vias Metabólicas/genética , Nitrogênio/metabolismo , Nitrogênio/farmacologia , Nutrientes/metabolismo , Ribossomos/efeitos dos fármacos , Ribossomos/metabolismo , Saccharomyces cerevisiae/efeitos dos fármacos , Saccharomyces cerevisiae/genética , Saccharomyces cerevisiae/crescimento & desenvolvimento , Sirolimo/farmacologia , Estresse FisiológicoRESUMO
BACKGROUND: Microbes live in dynamic environments where nutrient concentrations fluctuate. Quantifying fitness in terms of birth rate and death rate in a wide range of environments is critical for understanding microbial evolution and ecology. METHODS: Here, using high-throughput time-lapse microscopy, we have quantified how Saccharomyces cerevisiae mutants incapable of synthesizing an essential metabolite (auxotrophs) grow or die in various concentrations of the required metabolite. We establish that cells normally expressing fluorescent proteins lose fluorescence upon death and that the total fluorescence in an imaging frame is proportional to the number of live cells even when cells form multiple layers. We validate our microscopy approach of measuring birth and death rates using flow cytometry, cell counting, and chemostat culturing. RESULTS: For lysine-requiring cells, very low concentrations of lysine are not detectably consumed and do not support cell birth, but delay the onset of death phase and reduce the death rate compared to no lysine. In contrast, in low hypoxanthine, hypoxanthine-requiring cells can produce new cells, yet also die faster than in the absence of hypoxanthine. For both strains, birth rates under various metabolite concentrations are better described by the sigmoidal-shaped Moser model than the well-known Monod model, while death rates can vary with metabolite concentration and time. CONCLUSIONS: Our work reveals how time-lapse microscopy can be used to discover non-intuitive microbial birth and death dynamics and to quantify growth rates in many environments.
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Mutualisms can be promoted by pleiotropic win-win mutations which directly benefit self (self-serving) and partner (partner-serving). Intuitively, partner-serving phenotype could be quantified as an individual's benefit supply rate to partners. Here, we demonstrate the inadequacy of this thinking, and propose an alternative. Specifically, we evolved well-mixed mutualistic communities where two engineered yeast strains exchanged essential metabolites lysine and hypoxanthine. Among cells that consumed lysine and released hypoxanthine, a chromosome duplication mutation seemed win-win: it improved cell's affinity for lysine (self-serving), and increased hypoxanthine release rate per cell (partner-serving). However, increased release rate was due to increased cell size accompanied by increased lysine utilization per birth. Consequently, total hypoxanthine release rate per lysine utilization (defined as 'exchange ratio') remained unchanged. Indeed, this mutation did not increase the steady state growth rate of partner, and is thus solely self-serving during long-term growth. By extension, reduced benefit production rate by an individual may not imply cheating.
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Interações Microbianas , Mutação , Simbiose , Leveduras/crescimento & desenvolvimento , Leveduras/genética , Hipoxantina/metabolismo , Lisina/metabolismo , Leveduras/metabolismoRESUMO
Multispecies microbial communities often display "community functions" arising from interactions of member species. Interactions are often difficult to decipher, making it challenging to design communities with desired functions. Alternatively, similar to artificial selection for individuals in agriculture and industry, one could repeatedly choose communities with the highest community functions to reproduce by randomly partitioning each into multiple "Newborn" communities for the next cycle. However, previous efforts in selecting complex communities have generated mixed outcomes that are difficult to interpret. To understand how to effectively enact community selection, we simulated community selection to improve a community function that requires 2 species and imposes a fitness cost on one or both species. Our simulations predict that improvement could be easily stalled unless various aspects of selection are carefully considered. These aspects include promoting species coexistence, suppressing noncontributors, choosing additional communities besides the highest functioning ones to reproduce, and reducing stochastic fluctuations in the biomass of each member species in Newborn communities. These considerations can be addressed experimentally. When executed effectively, community selection is predicted to improve costly community function, and may even force species to evolve slow growth to achieve species coexistence. Our conclusions hold under various alternative model assumptions and are therefore applicable to a variety of communities.
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Microbiota/fisiologia , Seleção Artificial/genética , Biodiversidade , Biomassa , Simulação por Computador , Ecossistema , Microbiota/genética , Dinâmica PopulacionalRESUMO
Many microbial functions happen within communities of interacting species. Explaining how species with disparate growth rates can coexist is important for applications such as manipulating host-associated microbiota or engineering industrial communities. Here, we ask how microbes interacting through their chemical environment can achieve coexistence in a continuous growth setup (similar to an industrial bioreactor or gut microbiota) where external resources are being supplied. We formulate and experimentally constrain a model in which mediators of interactions (e.g. metabolites or waste-products) are explicitly incorporated. Our model highlights facilitation and self-restraint as interactions that contribute to coexistence, consistent with our intuition. When interactions are strong, we observe that coexistence is determined primarily by the topology of facilitation and inhibition influences not their strengths. Importantly, we show that consumption or degradation of chemical mediators moderates interaction strengths and promotes coexistence. Our results offer insights into how to build or restructure microbial communities of interest.
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Interações Microbianas/fisiologia , Microbiota/fisiologia , Modelos Biológicos , Brevibacillus/fisiologia , Escherichia coli/fisiologia , Staphylococcus/fisiologiaRESUMO
Quantitative modeling is useful for predicting behaviors of a system and for rationally constructing or modifying the system. The predictive power of a model relies on accurate quantification of model parameters. Here, we illustrate challenges in parameter quantification and offer means to overcome these challenges, using a case example in which we quantitatively predict the growth rate of a cooperative community. Specifically, the community consists of two Saccharomyces cerevisiae strains, each engineered to release a metabolite required and consumed by its partner. The initial model, employing parameters measured in batch monocultures with zero or excess metabolite, failed to quantitatively predict experimental results. To resolve the model-experiment discrepancy, we chemically identified the correct exchanged metabolites, but this did not improve model performance. We then remeasured strain phenotypes in chemostats mimicking the metabolite-limited community environments, while mitigating or incorporating effects of rapid evolution. Almost all phenotypes we measured, including death rate, metabolite release rate, and the amount of metabolite consumed per cell birth, varied significantly with the metabolite environment. Once we used parameters measured in a range of community-like chemostat environments, prediction quantitatively agreed with experimental results. In summary, using a simplified community, we uncovered and devised means to resolve modeling challenges that are likely general to living systems.
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Interações Microbianas/genética , Modelos Biológicos , Saccharomyces cerevisiae/metabolismo , Técnicas de Cocultura , Simulação por Computador , Engenharia Metabólica/métodos , Saccharomyces cerevisiae/genética , Saccharomyces cerevisiae/crescimento & desenvolvimentoRESUMO
BACKGROUND: Multiplexed milliliter-scale chemostats are useful for measuring cell physiology under various degrees of nutrient limitation and for carrying out evolution experiments. In each chemostat, fresh medium containing a growth rate-limiting metabolite is pumped into the culturing chamber at a constant rate, while culture effluent exits at an equal rate. Although such devices have been developed by various labs, key parameters - the accuracy, precision, and operational range of flow rate - are not explicitly characterized. METHODS: Here we re-purpose a published multiplexed culturing device to develop a multiplexed milliliter-scale chemostat. Flow rates for eight chambers can be independently controlled to a wide range, corresponding to population doubling times of 3~13 h, without the use of expensive feedback systems. RESULTS: Flow rates are precise, with the maximal coefficient of variation among eight chambers being less than 3%. Flow rates are accurate, with average flow rates being only slightly below targets, i.e., 3%-6% for 13-h and 0.6%-1.0% for 3-h doubling times. This deficit is largely due to evaporation and should be correctable. We experimentally demonstrate that our device allows accurate and precise quantification of population phenotypes. CONCLUSIONS: We achieve precise control of cellular growth in a low-cost milliliter-scale chemostat array, and show that the achieved precision reduces the error when measuring biological processes.
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Pairwise models are commonly used to describe many-species communities. In these models, an individual receives additive fitness effects from pairwise interactions with each species in the community ('additivity assumption'). All pairwise interactions are typically represented by a single equation where parameters reflect signs and strengths of fitness effects ('universality assumption'). Here, we show that a single equation fails to qualitatively capture diverse pairwise microbial interactions. We build mechanistic reference models for two microbial species engaging in commonly-found chemical-mediated interactions, and attempt to derive pairwise models. Different equations are appropriate depending on whether a mediator is consumable or reusable, whether an interaction is mediated by one or more mediators, and sometimes even on quantitative details of the community (e.g. relative fitness of the two species, initial conditions). Our results, combined with potential violation of the additivity assumption in many-species communities, suggest that pairwise modeling will often fail to predict microbial dynamics.
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Bioestatística/métodos , Interações Microbianas , Modelos BiológicosRESUMO
The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth's soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model-experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved.
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Microbiologia do Ar , Água do Mar/microbiologia , Microbiologia do Solo , Animais , Ecossistema , Humanos , Modelos TeóricosRESUMO
Much research has been invested into engineering microorganisms to perform desired biotransformations; nonetheless, these efforts frequently fall short of expected results due to the unforeseen effects of biofeedback regulation and functional incompatibility. In nature, metabolic function is compartmentalized into diverse organisms assembled into robust consortia, in which the division of labor is thought to lead to increased community efficiency and productivity. Here we consider whether and how consortia can be designed to perform bioprocesses of interest beyond the metabolic flexibility limitations of a single organism. Advances in post-genomic analysis of microbial consortia and application of high-resolution global measurements now offer the promise of systems-level understanding of how microbial consortia adapt to changes in environmental variables and inputs of carbon and energy. We argue that, when combined with appropriate modeling frameworks, systems-level knowledge can markedly improve our ability to predict the fate and functioning of consortia. Here we articulate our collective perspective on the current and future state of microbial community engineering and control while placing specific emphasis on ecological principles that promote control over community function and emergent properties.
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Bioengenharia/métodos , Genômica , Consórcios MicrobianosRESUMO
Cooperation based on the production of costly common goods is observed throughout nature. This is puzzling, as cooperation is vulnerable to exploitation by defectors which enjoy a fitness advantage by consuming the common good without contributing fairly. Depletion of the common good can lead to population collapse and the destruction of cooperation. However, population collapse implies small population size, which, in a structured population, is known to favor cooperation. This happens because small population size increases variability in cooperator frequency across different locations. Since individuals in cooperator-dominated locations (which are most likely cooperators) will grow more than those in defector-dominated locations (which are most likely defectors), cooperators can outgrow defectors globally despite defectors outgrowing cooperators in each location. This raises the possibility that defectors can lead to conditions that sometimes rescue cooperation from defector-induced destruction. We demonstrate multiple mechanisms through which this can occur, using an individual-based approach to model stochastic birth, death, migration, and mutation events. First, during defector-induced population collapse, defectors occasionally go extinct before cooperators by chance, which allows cooperators to grow. Second, empty locations, either preexisting or created by defector-induced population extinction, can favor cooperation because they allow cooperator but not defector migrants to grow. These factors lead to the counterintuitive result that the initial presence of defectors sometimes allows better survival of cooperation compared to when defectors are initially absent. Finally, we find that resource limitation, inducible by defectors, can select for mutations adaptive to resource limitation. When these mutations are initially present at low levels or continuously generated at a moderate rate, they can favor cooperation by further reducing local population size. We predict that in a structured population, small population sizes precipitated by defectors provide a "built-in" mechanism for the persistence of cooperation.
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Evolução Biológica , Comportamento Cooperativo , Aptidão Genética/genética , Genética Populacional , Modelos Genéticos , Mutação/genética , Altruísmo , Ecossistema , Teoria dos Jogos , Modelos Estatísticos , Densidade DemográficaRESUMO
Cooperators who pay a cost to produce publically-available benefits can be exploited by cheaters who do not contribute fairly. How might cooperation persist against cheaters? Two classes of mechanisms are known to promote cooperation: 'partner choice', where a cooperator preferentially interacts with cooperative over cheating partners; and 'partner fidelity feedback', where repeated interactions between individuals ensure that cheaters suffer as their cooperative partners languish (see, for example, Momeni et al., 2013). However when both mechanisms can act, differentiating them has generated controversy. Here, I resolve this controversy by noting that selection can operate on organismal and sub-organismal 'entities' such that partner fidelity feedback at sub-organismal level can appear as partner choice at organismal level. I also show that cooperation between multicellular eukaryotes and mitochondria is promoted by partner fidelity feedback and partner choice between sub-organismal entities, in addition to being promoted by partner fidelity feedback between hosts and symbionts, as was previously known.
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Evolução Biológica , Simbiose , EucariotosRESUMO
Theoretical ideas have a rich history in many areas of biology, and new theories and mathematical models have much to offer in the future.