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.

Interlocked feedforward loops control cell-type-specific Rhodopsin expression in the Drosophila eye.

How complex networks of activators and repressors lead to exquisitely specific cell-type determination during development is poorly understood. In the Drosophila eye, expression patterns of Rhodopsins define at least eight functionally distinct though related subtypes of photoreceptors. Here, we describe a role for the transcription factor gene defective proventriculus (dve) as a critical node in the network regulating Rhodopsin expression. dve is a shared component of two opposing, interlocked feedforward loops (FFLs). Orthodenticle and Dve interact in an incoherent FFL to repress Rhodopsin expression throughout the eye. In R7 and R8 photoreceptors, a coherent FFL relieves repression by Dve while activating Rhodopsin expression. Therefore, this network uses repression to restrict and combinatorial activation to induce cell-type-specific expression. Furthermore, Dve levels are finely tuned to yield cell-type- and region-specific repression or activation outcomes. This interlocked FFL motif may be a general mechanism to control terminal cell-fate specification.

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.

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.

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.

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.

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 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.

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.

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.

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.

Evolutionary pressures on simple sequence repeats in prokaryotic coding regions.

Simple sequence repeats (SSRs) are indel mutational hotspots in genomes. In prokaryotes, SSR loci can cause phase variation, a microbial survival strategy that relies on stochastic, reversible on-off switching of gene activity. By analyzing multiple strains of 42 fully sequenced prokaryotic species, we measure the relative variability and density distribution of SSRs in coding regions. We demonstrate that repeat type strongly influences indel mutation rates, and that the most mutable types are most strongly avoided across genomes. We thoroughly characterize SSR density and variability as a function of N→C position along protein sequences. Using codon-shuffling algorithms that preserve amino acid sequence, we assess evolutionary pressures on SSRs. We find that coding sequences suppress repeats in the middle of proteins, and enrich repeats near termini, yielding U-shaped SSR density curves. We show that for many species this characteristic shape can be attributed to purely biophysical constraints of protein structure. In multiple cases, however, particularly in certain pathogenic bacteria, we observe over enrichment of SSRs near protein N-termini significantly beyond expectation based on structural constraints. This increases the probability that frameshifts result in non-functional proteins, revealing that these species may evolutionarily tune SSR positions in coding regions to facilitate phase variation.

Stochastic de-repression of Rhodopsins in single photoreceptors of the fly retina.

The photoreceptors of the Drosophila compound eye are a classical model for studying cell fate specification. Photoreceptors (PRs) are organized in bundles of eight cells with two major types - inner PRs involved in color vision and outer PRs involved in motion detection. In wild type flies, most PRs express a single type of Rhodopsin (Rh): inner PRs express either Rh3, Rh4, Rh5 or Rh6 and outer PRs express Rh1. In outer PRs, the K(50) homeodomain protein Dve is a key repressor that acts to ensure exclusive Rh expression. Loss of Dve results in de-repression of Rhodopsins in outer PRs, and leads to a wide distribution of expression levels. To quantify these effects, we introduce an automated image analysis method to measure Rhodopsin levels at the single cell level in 3D confocal stacks. Our sensitive methodology reveals cell-specific differences in Rhodopsin distributions among the outer PRs, observed over a developmental time course. We show that Rhodopsin distributions are consistent with a two-state model of gene expression, in which cells can be in either high or basal states of Rhodopsin production. Our model identifies a significant role of post-transcriptional regulation in establishing the two distinct states. The timescale for interconversion between basal and high states is shown to be on the order of days. Our results indicate that even in the absence of Dve, the Rhodopsin regulatory network can maintain highly stable states. We propose that the role of Dve in outer PRs is to buffer against rare fluctuations in this network.

Measuring cell identity in noisy biological systems.

Global gene expression measurements are increasingly obtained as a function of cell type, spatial position within a tissue and other biologically meaningful coordinates. Such data should enable quantitative analysis of the cell-type specificity of gene expression, but such analyses can often be confounded by the presence of noise. We introduce a specificity measure Spec that quantifies the information in a gene's complete expression profile regarding any given cell type, and an uncertainty measure dSpec, which measures the effect of noise on specificity. Using global gene expression data from the mouse brain, plant root and human white blood cells, we show that Spec identifies genes with variable expression levels that are nonetheless highly specific of particular cell types. When samples from different individuals are used, dSpec measures genes' transcriptional plasticity in each cell type. Our approach is broadly applicable to mapped gene expression measurements in stem cell biology, developmental biology, cancer biology and biomarker identification. As an example of such applications, we show that Spec identifies a new class of biomarkers, which exhibit variable expression without compromising specificity. The approach provides a unifying theoretical framework for quantifying specificity in the presence of noise, which is widely applicable across diverse biological systems.

Individual histories and selection in heterogeneous populations.

The strength of selection in populations has traditionally been inferred by measuring changes in bulk population parameters, such as mean reproductive rates. Untangling the effect of selection from other factors, such as specific responses to environmental fluctuations, poses a significant problem both in microbiology and in other fields, including cancer biology and immunology, where selection occurs within phenotypically heterogeneous populations of cells. Using "individual histories"--temporal sequences of all reproduction events and phenotypic changes of individuals and their ancestors--we present an alternative approach to quantifying selection in diverse experimental settings. Selection is viewed as a process that acts on histories, and a measure of selection that employs the distribution of histories is introduced. We apply this measure to phenotypically structured populations in fluctuating environments across different evolutionary regimes. Additionally, we show that reproduction events alone, recorded in the population's tree of cell divisions, may be sufficient to accurately measure selection. The measure is thus applicable in a wide range of biological systems, from microorganisms--including species for which genetic tools do not yet exist--to cellular populations, such as tumors and stem cells, where detailed temporal data are becoming available.

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.

Evolutionary dynamics of restriction site avoidance.

Molecular noise in bacterial restriction-modification systems can cause rare events of host DNA cleavage at restriction sites. Such noise-induced selective pressure may result in evolved sequences exhibiting restriction site avoidance. We identify a two-state regime of evolutionary dynamics, in which populations either develop avoidance or go extinct. Using perturbation theory, we show that equilibrium sequence statistics exhibit power-law scaling in the ratio of restriction strength to mutation rate. Noise levels comparable to mutation rates can be sufficient to evolve detectable avoidance.

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.

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.

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.