Proteolytic stability and aggregation in a key metabolic enzyme of bacteria.

Proteins that are kinetically stable are thought to be less prone to both aggregation and proteolysis. We demonstrate that the classical lac system of Escherichia coli can be leveraged as a model system to study this relation. ß-galactosidase (LacZ) plays a critical role in lactose metabolism and is an extremely stable protein that can persist in growing cells for multiple generations after expression has stopped. By attaching degradation tags to the LacZ protein, we find that LacZ can be transiently degraded during lac operon expression but once expression has stopped functional LacZ is protected from degradation. We reversibly destabilize its tetrameric assembly using α-complementation, and show that unassembled LacZ monomers and dimers can either be degraded or lead to formation of aggregates within cells, while the tetrameric state protects against proteolysis and aggregation. We show that the presence of aggregates is associated with cell death, and that these proteotoxic stress phenotypes can be alleviated by attaching an ssrA tag to LacZ monomers which leads to their degradation. We unify our findings using a biophysical model that enables the interplay of protein assembly, degradation, and aggregation to be studied quantitatively in vivo. This work may yield approaches to reversing and preventing protein-misfolding disease states, while elucidating the functions of proteolytic stability in constant and fluctuating environments.

Evolutionary advantage of cell size control.

We analyze the advantage of cell size control strategies in growing populations under mortality constraints. We demonstrate a general advantage of the adder control strategy in the presence of growth-dependent mortality, and for different size-dependent mortality landscapes. Its advantage stems from epigenetic heritability of cell size, which enables selection to act on the distribution of cell sizes in a population to avoid mortality thresholds and adapt to a mortality landscape.

Correlated substitutions reveal SARS-like coronaviruses recombine frequently with a diverse set of structured gene pools.

Quantifying SARS-like coronavirus (SL-CoV) evolution is critical to understanding the origins of SARS-CoV-2 and the molecular processes that could underlie future epidemic viruses. While genomic analyses suggest recombination was a factor in the emergence of SARS-CoV-2, few studies have quantified recombination rates among SL-CoVs. Here, we infer recombination rates of SL-CoVs from correlated substitutions in sequencing data using a coalescent model with recombination. Our computationally-efficient, non-phylogenetic method infers recombination parameters of both sampled sequences and the unsampled gene pools with which they recombine. We apply this approach to infer recombination parameters for a range of positive-sense RNA viruses. We then analyze a set of 191 SL-CoV sequences (including SARS-CoV-2) and find that ORF1ab and S genes frequently undergo recombination. We identify which SL-CoV sequence clusters have recombined with shared gene pools, and show that these pools have distinct structures and high recombination rates, with multiple recombination events occurring per synonymous substitution. We find that individual genes have recombined with different viral reservoirs. By decoupling contributions from mutation and recombination, we recover the phylogeny of non-recombined portions for many of these SL-CoVs, including the position of SARS-CoV-2 in this clonal phylogeny. Lastly, by analyzing >400,000 SARS-CoV-2 whole genome sequences, we show current diversity levels are insufficient to infer the within-population recombination rate of the virus since the pandemic began. Our work offers new methods for inferring recombination rates in RNA viruses with implications for understanding recombination in SARS-CoV-2 evolution and the structure of clonal relationships and gene pools shaping its origins.

A unified framework for measuring selection on cellular lineages and traits.

Intracellular states probed by gene expression profiles and metabolic activities are intrinsically noisy, causing phenotypic variations among cellular lineages. Understanding the adaptive and evolutionary roles of such variations requires clarifying their linkage to population growth rates. Extending a cell lineage statistics framework, here we show that a population's growth rate can be expanded by the cumulants of a fitness landscape that characterize how fitness distributes in a population. The expansion enables quantifying the contribution of each cumulant, such as variance and skewness, to population growth. We introduce a function that contains all the essential information of cell lineage statistics, including mean lineage fitness and selection strength. We reveal a relation between fitness heterogeneity and population growth rate response to perturbation. We apply the framework to experimental cell lineage data from bacteria to mammalian cells, revealing distinct levels of growth rate gain from fitness heterogeneity across environments and organisms. Furthermore, third or higher order cumulants' contributions are negligible under constant growth conditions but could be significant in regrowing processes from growth-arrested conditions. We identify cellular populations in which selection leads to an increase of fitness variance among lineages in retrospective statistics compared to chronological statistics. The framework assumes no particular growth models or environmental conditions, and is thus applicable to various biological phenomena for which phenotypic heterogeneity and cellular proliferation are important.

Core genes can have higher recombination rates than accessory genes within global microbial populations.

Recombination is essential to microbial evolution, and is involved in the spread of antibiotic resistance, antigenic variation, and adaptation to the host niche. However, assessing the impact of homologous recombination on accessory genes which are only present in a subset of strains of a given species remains challenging due to their complex phylogenetic relationships. Quantifying homologous recombination for accessory genes (which are important for niche-specific adaptations) in comparison to core genes (which are present in all strains and have essential functions) is critical to understanding how selection acts on variation to shape species diversity and genome structures of bacteria. Here, we apply a computationally efficient, non-phylogenetic approach to measure homologous recombination rates in the core and accessory genome using >100,000 whole genome sequences from Streptococcus pneumoniae and several additional species. By analyzing diverse sets of sequence clusters, we show that core genes often have higher recombination rates than accessory genes, and for some bacterial species the associated effect sizes for these differences are pronounced. In a subset of species, we find that gene frequency and homologous recombination rate are positively correlated. For S. pneumoniae and several additional species, we find that while the recombination rate is higher for the core genome, the mutational divergence is lower, indicating that divergence-based homologous recombination barriers could contribute to differences in recombination rates between the core and accessory genome. Homologous recombination may therefore play a key role in increasing the efficiency of selection in the most conserved parts of the genome.

Ecological memory preserves phage resistance mechanisms in bacteria.

Bacterial defenses against phage, which include CRISPR-mediated immunity and other mechanisms, can carry substantial growth rate costs and can be rapidly lost when pathogens are eliminated. How bacteria preserve their molecular defenses despite their costs, in the face of variable pathogen levels and inter-strain competition, remains a major unsolved problem in evolutionary biology. Here, we present a multilevel model that incorporates biophysics of molecular binding, host-pathogen population dynamics, and ecological dynamics across a large number of independent territories. Using techniques of game theory and non-linear dynamical systems, we show that by maintaining a non-zero failure rate of defenses, hosts sustain sufficient levels of pathogen within an ecology to select against loss of the defense. This resistance switching strategy is evolutionarily stable, and provides a powerful evolutionary mechanism that maintains host-pathogen interactions, selects against cheater strains that avoid the costs of immunity, and enables co-evolutionary dynamics in a wide range of systems.

Roadmap on biology in time varying environments.

Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.

Origin of exponential growth in nonlinear reaction networks.

Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of long-term growth: scalability of flux functions and ergodicity of the rescaled systems. Our theory shows that nonlinear fluxes can generate not only balanced growth but also oscillatory or chaotic growth modalities, explaining nonequilibrium dynamics observed in cell cycles and ecosystems. Our mathematical framework is broadly useful in predicting long-term growth rates from natural and synthetic networks, analyzing the effects of system noise and perturbations, validating empirical and phenomenological laws on growth rate, and studying autocatalysis and network evolution.

Cell Cycle Heritability and Localization Phase Transition in Growing Populations.

The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate the existence of a phase transition, which can be continuous or first order, by which a nonzero fraction of the population becomes localized at a minimal division time. Just below the transition, we demonstrate the coexistence of localized and delocalized age-structure phases and the power law decay of correlation functions. Above it, we observe the self-synchronization of cell cycles, collective divisions, and the slow "aging" of population growth rates.

Inferring bacterial recombination rates from large-scale sequencing datasets.

We present a robust, computationally efficient method ( https://github.com/kussell-lab/mcorr ) for inferring the parameters of homologous recombination in bacteria, which can be applied in diverse datasets, from whole-genome sequencing to metagenomic shotgun sequencing data. Using correlation profiles of synonymous substitutions, we determine recombination rates and diversity levels of the shared gene pool that has contributed to a given sample. We validated the recombination parameters using data from laboratory experiments. We determined the recombination parameters for a wide range of bacterial species, and inferred the distribution of shared gene pools for global Helicobacter pylori isolates. Using metagenomics data of the infant gut microbiome, we measured the recombination parameters of multidrug-resistant Escherichia coli ST131. Lastly, we analyzed ancient samples of bacterial DNA from the Copper Age 'Iceman' mummy and from 14th century victims of the Black Death, obtaining measurements of bacterial recombination rates and gene pool diversity of earlier eras.

The impact of bottlenecks on microbial survival, adaptation, and phenotypic switching in host-pathogen interactions.

Microbial pathogens and viruses can often maintain sufficient population diversity to evade a wide range of host immune responses. However, when populations experience bottlenecks, as occurs frequently during initiation of new infections, pathogens require specialized mechanisms to regenerate diversity. We address the evolution of such mechanisms, known as stochastic phenotype switches, which are prevalent in pathogenic bacteria. We analyze a model of pathogen diversification in a changing host environment that accounts for selective bottlenecks, wherein different phenotypes have distinct transmission probabilities between hosts. We show that under stringent bottlenecks, such that only one phenotype can initiate new infections, there exists a threshold stochastic switching rate below which all pathogen lineages go extinct, and above which survival is a near certainty. We determine how quickly stochastic switching rates can evolve by computing a fitness landscape for the evolutionary dynamics of switching rates, and analyzing its dependence on both the stringency of bottlenecks and the duration of within-host growth periods. We show that increasing the stringency of bottlenecks or decreasing the period of growth results in faster adaptation of switching rates. Our model provides strong theoretical evidence that bottlenecks play a critical role in accelerating the evolutionary dynamics of pathogens.

Inferring fitness landscapes and selection on phenotypic states from single-cell genealogical data.

Recent advances in single-cell time-lapse microscopy have revealed non-genetic heterogeneity and temporal fluctuations of cellular phenotypes. While different phenotypic traits such as abundance of growth-related proteins in single cells may have differential effects on the reproductive success of cells, rigorous experimental quantification of this process has remained elusive due to the complexity of single cell physiology within the context of a proliferating population. We introduce and apply a practical empirical method to quantify the fitness landscapes of arbitrary phenotypic traits, using genealogical data in the form of population lineage trees which can include phenotypic data of various kinds. Our inference methodology for fitness landscapes determines how reproductivity is correlated to cellular phenotypes, and provides a natural generalization of bulk growth rate measures for single-cell histories. Using this technique, we quantify the strength of selection acting on different cellular phenotypic traits within populations, which allows us to determine whether a change in population growth is caused by individual cells' response, selection within a population, or by a mixture of these two processes. By applying these methods to single-cell time-lapse data of growing bacterial populations that express a resistance-conferring protein under antibiotic stress, we show how the distributions, fitness landscapes, and selection strength of single-cell phenotypes are affected by the drug. Our work provides a unified and practical framework for quantitative measurements of fitness landscapes and selection strength for any statistical quantities definable on lineages, and thus elucidates the adaptive significance of phenotypic states in time series data. The method is applicable in diverse fields, from single cell biology to stem cell differentiation and viral evolution.

Correlated Mutations and Homologous Recombination Within Bacterial Populations.

Inferring the rate of homologous recombination within a bacterial population remains a key challenge in quantifying the basic parameters of bacterial evolution. Due to the high sequence similarity within a clonal population, and unique aspects of bacterial DNA transfer processes, detecting recombination events based on phylogenetic reconstruction is often difficult, and estimating recombination rates using coalescent model-based methods is computationally expensive, and often infeasible for large sequencing data sets. Here, we present an efficient solution by introducing a set of mutational correlation functions computed using pairwise sequence comparison, which characterize various facets of bacterial recombination. We provide analytical expressions for these functions, which precisely recapitulate simulation results of neutral and adapting populations under different coalescent models. We used these to fit correlation functions measured at synonymous substitutions using whole-genome data on Escherichia coli and Streptococcus pneumoniae populations. We calculated and corrected for the effect of sample selection bias, i.e., the uneven sampling of individuals from natural microbial populations that exists in most datasets. Our method is fast and efficient, and does not employ phylogenetic inference or other computationally intensive numerics. By simply fitting analytical forms to measurements from sequence data, we show that recombination rates can be inferred, and the relative ages of different samples can be estimated. Our approach, which is based on population genetic modeling, is broadly applicable to a wide variety of data, and its computational efficiency makes it particularly attractive for use in the analysis of large sequencing datasets.

Evolutionary Phase Transitions in Random Environments.

We present analytical results for long-term growth rates of structured populations in randomly fluctuating environments, which we apply to predict how cellular response networks evolve. We show that networks which respond rapidly to a stimulus will evolve phenotypic memory exclusively under random (i.e., nonperiodic) environments. We identify the evolutionary phase diagram for simple response networks, which we show can exhibit both continuous and discontinuous transitions. Our approach enables exact analysis of diverse evolutionary systems, from viral epidemics to emergence of drug resistance.

Complex Interplay of Physiology and Selection in the Emergence of Antibiotic Resistance.

Emergence of antibiotic resistance, an evolutionary process of major importance for human health [1], often occurs under changing levels of antibiotics. Selective sweeps, in which resistant cells become dominant in the population, are a critical step in this process [2]. While resistance emergence has been studied in laboratory experiments [3-8], the full progression of selective sweeps under fluctuating stress, from stochastic events in single cells to fixation in populations, has not been characterized. Here, we study fluctuating selection using Escherichia coli populations engineered with a stochastic switch controlling tetracycline resistance. Using microfluidics and live-cell imaging, we treat multiple E. coli populations with the same total amount of tetracycline but administered in different temporal patterns. We find that populations exposed to either short or long antibiotic pulses are likely to develop resistance through selective sweeps, whereas intermediate pulses allow higher growth rates but suppress selective sweeps. On the basis of single-cell measurements and a dynamic growth model, we identify the major determinants of population growth and show that both physiological memory and environmental durations can strongly modulate the emergence of resistance. Our detailed quantification in a model synthetic system provides key lessons on the interaction between single-cell physiology and selection that should inform the design of treatment regimens [9-12] and the analysis of phenotypically diverse populations adapting under fluctuating selection [13-17].

Noise-driven growth rate gain in clonal cellular populations.

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a "speed limit" for proliferation.

Bacterial Autoimmunity Due to a Restriction-Modification System.

Restriction-modification (RM) systems represent a minimal and ubiquitous biological system of self/non-self discrimination in prokaryotes [1], which protects hosts from exogenous DNA [2]. The mechanism is based on the balance between methyltransferase (M) and cognate restriction endonuclease (R). M tags endogenous DNA as self by methylating short specific DNA sequences called restriction sites, whereas R recognizes unmethylated restriction sites as non-self and introduces a double-stranded DNA break [3]. Restriction sites are significantly underrepresented in prokaryotic genomes [4-7], suggesting that the discrimination mechanism is imperfect and occasionally leads to autoimmunity due to self-DNA cleavage (self-restriction) [8]. Furthermore, RM systems can promote DNA recombination [9] and contribute to genetic variation in microbial populations, thus facilitating adaptive evolution [10]. However, cleavage of self-DNA by RM systems as elements shaping prokaryotic genomes has not been directly detected, and its cause, frequency, and outcome are unknown. We quantify self-restriction caused by two RM systems of Escherichia coli and find that, in agreement with levels of restriction site avoidance, EcoRI, but not EcoRV, cleaves self-DNA at a measurable rate. Self-restriction is a stochastic process, which temporarily induces the SOS response, and is followed by DNA repair, maintaining cell viability. We find that RM systems with higher restriction efficiency against bacteriophage infections exhibit a higher rate of self-restriction, and that this rate can be further increased by stochastic imbalance between R and M. Our results identify molecular noise in RM systems as a factor shaping prokaryotic genomes.

Quantifying selective pressures driving bacterial evolution using lineage analysis.

Organisms use a variety of strategies to adapt to their environments and maximize long-term growth potential, but quantitative characterization of the benefits conferred by the use of such strategies, as well as their impact on the whole population's rate of growth, remains challenging. Here, we use a path-integral framework that describes how selection acts on lineages -i.e. the life-histories of individuals and their ancestors- to demonstrate that lineage-based measurements can be used to quantify the selective pressures acting on a population. We apply this analysis to E. coli bacteria exposed to cyclical treatments of carbenicillin, an antibiotic that interferes with cell-wall synthesis and affects cells in an age-dependent manner. While the extensive characterization of the life-history of thousands of cells is necessary to accurately extract the age-dependent selective pressures caused by carbenicillin, the same measurement can be recapitulated using lineage-based statistics of a single surviving cell. Population-wide evolutionary pressures can be extracted from the properties of the surviving lineages within a population, providing an alternative and efficient procedure to quantify the evolutionary forces acting on a population. Importantly, this approach is not limited to age-dependent selection, and the framework can be generalized to detect signatures of other trait-specific selection using lineage-based measurements. Our results establish a powerful way to study the evolutionary dynamics of life under selection, and may be broadly useful in elucidating selective pressures driving the emergence of antibiotic resistance and the evolution of survival strategies in biological systems.

Populations adapt to fluctuating selection using derived and ancestral allelic diversity.

Populations can adapt to changing environments by using allelic diversity, yet whether diversity is recently derived or ancestral is often debated. Although evolution could productively use both types of diversity in a changing environment, their relative frequency has not been quantified. We address this question experimentally using budding yeast strains that harbor a tandem repeat containing URA3 gene, which we expose to cyclical selection and counterselection. We characterize and quantify the dynamics of frameshift events in the URA3 gene in eight populations over 12 cycles of selection and find that ancestral alleles account for 10-20% of all adaptive events. Using a general model of fluctuating selection, we determine how these results depend on mutation rates, population sizes, and fluctuation timescales. We quantify the contribution of derived alleles to the adaptation process using the de novo mutation rate along the population's ancestral lineage, a novel measure that is applicable in a wide range of settings. We find that the adaptive dynamics undergoes a sharp transition from selection on ancestral alleles to selection on derived alleles as fluctuation timescales increase. Our results demonstrate that fluctuations can select between different modes of adaptation over evolutionary timescales.

Memory and fitness optimization of bacteria under fluctuating environments.

Bacteria prudently regulate their metabolic phenotypes by sensing the availability of specific nutrients, expressing the required genes for their metabolism, and repressing them after specific metabolites are depleted. It is unclear, however, how genetic networks maintain and transmit phenotypic states between generations under rapidly fluctuating environments. By subjecting bacteria to fluctuating carbon sources (glucose and lactose) using microfluidics, we discover two types of non-genetic memory in Escherichia coli and analyze their benefits. First, phenotypic memory conferred by transmission of stable intracellular lac proteins dramatically reduces lag phases under cyclical fluctuations with intermediate timescales (1-10 generations). Second, response memory, a hysteretic behavior in which gene expression persists after removal of its external inducer, enhances adaptation when environments fluctuate over short timescales (< 1 generation). Using a mathematical model we analyze the benefits of memory across environmental fluctuation timescales. We show that memory mechanisms provide an important class of survival strategies in biology that improve long-term fitness under fluctuating environments. These results can be used to understand how organisms adapt to fluctuating levels of nutrients, antibiotics, and other environmental stresses.