Multiscale selection in spatially structured populations.

The spatial structure of populations is key to many (eco-)evolutionary processes. In such cases, the strength and sign of selection on a trait may depend on the spatial scale considered. An example is the evolution of altruism: selection in local environments often favours cheaters over altruists, but this can be outweighed by selection at larger scales, favouring clusters of altruists over clusters of cheaters. For populations subdivided into distinct groups, this effect is described formally by multilevel selection theory. However, many populations do not consist of non-overlapping groups but rather (self-)organize into other ecological patterns. We therefore present a mathematical framework for multiscale selection. This framework decomposes natural selection into two parts: local selection, acting within environments of a certain size, and interlocal selection, acting among them. Varying the size of the local environments subsequently allows one to measure the contribution to selection of each spatial scale. To illustrate the use of this framework, we apply it to models of the evolution of altruism and pathogen transmissibility. The analysis identifies how and to what extent ecological processes at different spatial scales contribute to selection and compete, thus providing a rigorous underpinning to eco-evolutionary intuitions.

The interplay between metabolic stochasticity and cAMP-CRP regulation in single E. coli cells.

The inherent stochasticity of metabolism raises a critical question for understanding homeostasis: are cellular processes regulated in response to internal fluctuations? Here, we show that, in E. coli cells under constant external conditions, catabolic enzyme expression continuously responds to metabolic fluctuations. The underlying regulatory feedback is enabled by the cyclic AMP (cAMP) and cAMP receptor protein (CRP) system, which controls catabolic enzyme expression based on metabolite concentrations. Using single-cell microscopy, genetic constructs in which this feedback is disabled, and mathematical modeling, we show how fluctuations circulate through the metabolic and genetic network at sub-cell-cycle timescales. Modeling identifies four noise propagation modes, including one specific to CRP regulation. Together, these modes correctly predict noise circulation at perturbed cAMP levels. The cAMP-CRP system may thus have evolved to control internal metabolic fluctuations in addition to external growth conditions. We conjecture that second messengers may more broadly function to achieve cellular homeostasis.

Emergent multilevel selection in a simple spatial model of the evolution of altruism.

Theories on the evolutionary origins of altruistic behavior have a long history and have become a canonical part of the theory of evolution. Nevertheless, the mechanisms that allow altruism to appear and persist are still incompletely understood. It is well known, however, that the spatial structure of populations is an important determinant. In both theoretical and experimental studies, much attention has been devoted to populations that are subdivided into discrete groups. Such studies typically imposed the structure and dynamics of the groups by hand. Here, we instead present a simple individual-based model in which altruistic organisms spontaneously self-organize into spatially separated colonies that themselves reproduce by binary fission and hence behave as Darwinian entities in their own right. Using software to automatically track the rise and fall of colonies, we are able to apply formal theory on multilevel selection and thus quantify the within- and among-group dynamics. This reveals that individual colonies inevitably succumb to defectors in a within-colony "tragedy of the commons". Even so, altruism persists in the population because more altruistic colonies reproduce more frequently and drive less altruistic ones to extinction. Evidently, the colonies promote the selection of altruism but in turn depend on altruism for their existence; the selection of altruism hence involves a kind of evolutionary bootstrapping. The emergence of the colonies also depends crucially on the length scales of motility, altruism, and competition. This reconfirms the general relevance of these scales for social evolution, but also stresses that their impact can only be understood fully in the light of the emergent eco-evolutionary spatial patterns. The results also suggest that emergent spatial population patterns can function as a starting point for transitions of individuality.

Hierarchical and simultaneous utilization of carbon substrates: mechanistic insights, physiological roles, and ecological consequences.

Bacteria grown on a mixture of carbon substrates exhibit two utilization patterns: hierarchical utilization (HU) and simultaneous utilization (SU). How and why cells adopt these different behaviors remains poorly understood despite decades of research. Recent studies address various open questions from multiple viewpoints. From a mechanistic perspective, it was found that flux sensors play a central role in the regulation of substrate utilization, accounting for the known dependences on single-substrate growth rates, substrate concentrations, and the point where the substrate enters central metabolism. From a physiological perspective, several recent studies suggested HU or SU as growth-optimizing strategies through efficient allocation of essential proteome resources. However, other studies demonstrate that a significant fraction of the proteome is dedicated to functions apparently unnecessary for growth, casting doubt on explanations based on slight efficiency gains. From an ecological perspective, recent theoretical studies suggest that HU can help increase species diversity in bacterial communities.

The effect of natural selection on the propagation of protein expression noise to bacterial growth.

In bacterial cells, protein expression is a highly stochastic process. Gene expression noise moreover propagates through the cell and adds to fluctuations in the cellular growth rate. A common intuition is that, due to their relatively high noise amplitudes, proteins with a low mean expression level are the most important drivers of fluctuations in physiological variables. In this work, we challenge this intuition by considering the effect of natural selection on noise propagation. Mathematically, the contribution of each protein species to the noise in the growth rate depends on two factors: the noise amplitude of the protein's expression level, and the sensitivity of the growth rate to fluctuations in that protein's concentration. We argue that natural selection, while shaping mean abundances to increase the mean growth rate, also affects cellular sensitivities. In the limit in which cells grow optimally fast, the growth rate becomes most sensitive to fluctuations in highly abundant proteins. This causes abundant proteins to overall contribute strongly to the noise in the growth rate, despite their low noise levels. We further explore this result in an experimental data set of protein abundances, and test key assumptions in an evolving, stochastic toy model of cellular growth.

Identical sequences found in distant genomes reveal frequent horizontal transfer across the bacterial domain.

Horizontal gene transfer (HGT) is an essential force in microbial evolution. Despite detailed studies on a variety of systems, a global picture of HGT in the microbial world is still missing. Here, we exploit that HGT creates long identical DNA sequences in the genomes of distant species, which can be found efficiently using alignment-free methods. Our pairwise analysis of 93,481 bacterial genomes identified 138,273 HGT events. We developed a model to explain their statistical properties as well as estimate the transfer rate between pairs of taxa. This reveals that long-distance HGT is frequent: our results indicate that HGT between species from different phyla has occurred in at least 8% of the species. Finally, our results confirm that the function of sequences strongly impacts their transfer rate, which varies by more than three orders of magnitude between different functional categories. Overall, we provide a comprehensive view of HGT, illuminating a fundamental process driving bacterial evolution.

Repeated outbreaks drive the evolution of bacteriophage communication.

Recently, a small-molecule communication mechanism was discovered in a range of Bacillus-infecting bacteriophages, which these temperate phages use to inform their lysis-lysogeny decision. We present a mathematical model of the ecological and evolutionary dynamics of such viral communication and show that a communication strategy in which phages use the lytic cycle early in an outbreak (when susceptible host cells are abundant) but switch to the lysogenic cycle later (when susceptible cells become scarce) is favoured over a bet-hedging strategy in which cells are lysogenised with constant probability. However, such phage communication can evolve only if phage-bacteria populations are regularly perturbed away from their equilibrium state, so that acute outbreaks of phage infections in pools of susceptible cells continue to occur. Our model then predicts the selection of phages that switch infection strategy when half of the available susceptible cells have been infected.

Bacteriophages, or phages for short, are viruses that need to infect bacteria to multiply. Once inside a cell, phages follow one of two strategies. They either start to replicate quickly, killing the host in the process; or they lay dormant, their genetic material slowly duplicating as the bacterium divides. These two strategies are respectively known as a 'lytic' or a 'lysogenic' infection. In 2017, scientists discovered that, during infection, some phages produce a signalling molecule that influences the strategy other phages will use. Generally, a high concentration of the signal triggers lysogenic infection, while a low level prompts the lytic type. However, it is still unclear what advantages this communication system brings to the viruses, and how it has evolved. Here, Doekes et al. used a mathematical model to explore how communication changes as phages infect a population of bacteria, rigorously testing earlier theories. The simulations showed that early in an outbreak, when only a few cells have yet been infected, the signalling molecule levels are low: lytic infections are therefore triggered and the phages quickly multiply, killing their hosts in the process. This is an advantageous strategy since many bacteria are available for the viruses to prey on. Later on, as more phages are being produced and available bacteria become few and far between, the levels of the signalling molecule increase. The viruses then switch to lysogenic infections, which allows them to survive dormant, inside their host. Doekes et al. also discovered that this communication system only evolves if phages regularly cause large outbreaks in new, uninfected bacterial populations. From there, the model was able to predict that phages switch from lytic to lysogenic infections when about half the available bacteria have been infected. As antibiotic resistance rises around the globe, phages are increasingly considered as a new way to fight off harmful bacteria. Deciphering the way these viruses communicate could help to understand how they could be harnessed to control the spread of bacteria.

The naive T-cell receptor repertoire has an extremely broad distribution of clone sizes.

The clone size distribution of the human naive T-cell receptor (TCR) repertoire is an important determinant of adaptive immunity. We estimated the abundance of TCR sequences in samples of naive T cells from blood using an accurate quantitative sequencing protocol. We observe most TCR sequences only once, consistent with the enormous diversity of the repertoire. However, a substantial number of sequences were observed multiple times. We detect abundant TCR sequences even after exclusion of methodological confounders such as sort contamination, and multiple mRNA sampling from the same cell. By combining experimental data with predictions from models we describe two mechanisms contributing to TCR sequence abundance. TCRα abundant sequences can be primarily attributed to many identical recombination events in different cells, while abundant TCRß sequences are primarily derived from large clones, which make up a small percentage of the naive repertoire, and could be established early in the development of the T-cell repertoire.

Regulation underlying hierarchical and simultaneous utilization of carbon substrates by flux sensors in Escherichia coli.

Many microorganisms exhibit nutrient preferences, exemplified by the 'hierarchical' consumption of certain carbon substrates. Here, we systematically investigate under which physiological conditions hierarchical substrate utilization occurs and its mechanisms of implementation. We show utilization hierarchy of Escherichia coli to be ordered by the carbon-uptake flux rather than the identity of the substrates. A detailed study of glycerol uptake finds that it is fully suppressed if the uptake flux of another glycolytic substrate exceeds a threshold, which is set to the influx obtained when grown on glycerol alone. Below this threshold, limited glycerol uptake is 'supplemented' such that the total carbon uptake is maintained at the threshold. This behaviour results from total-flux feedback mediated by cAMP-Crp signalling but also requires inhibition by the regulator fructose 1,6-bisphosphate, which senses the upper-glycolytic flux and ensures that glycerol uptake defers to other glycolytic substrates but not to gluconeogenic ones. A quantitative model reproduces all of the observed utilization patterns, including those of key mutants. The proposed mechanism relies on the differential regulation of uptake enzymes and requires a specific operon organization. This organization is found to be conserved across related species for several uptake systems, suggesting the deployment of similar mechanisms for hierarchical substrate utilization by a spectrum of microorganisms.

Toxin production spontaneously becomes regulated by local cell density in evolving bacterial populations.

The production of anticompetitor toxins is widespread among bacteria. Because production of such toxins is costly, it is typically regulated. In particular, many toxins are produced only when the local cell density is high. It is unclear which selection pressures shaped the evolution of density-dependent regulation of toxin production. Here, we study the evolution of toxin production, resistance and the response to a cell-density cue in a model of an evolving bacterial population with spatial structure. We present results for two growth regimes: (i) an undisturbed, fixed habitat in which only small fluctuations of cell density occur, and (ii) a serial-transfer regime with large fluctuations in cell density. We find that density-dependent toxin production can evolve under both regimes. However, the selection pressures driving the evolution of regulation differ. In the fixed habitat, regulation evolves because it allows cells to produce toxin only when opportunities for reproduction are highly limited (because of a high local cell density), and the effective fitness costs of toxin production are hence low. Under serial transfers, regulation evolves because it allows cells to switch from a fast-growing non-toxic phenotype when colonising a new habitat, to a slower-growing competitive toxic phenotype when the cell density increases. Colonies of such regulating cells rapidly expand into unoccupied space because their edges consist of fast-growing, non-toxin-producing cells, but are also combative because cells at the interfaces with competing colonies do produce toxin. Because under the two growth regimes different types of regulation evolve, our results underscore the importance of growth conditions in the evolution of social behaviour in bacteria.

Noise propagation in an integrated model of bacterial gene expression and growth.

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple proteins that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections between noise propagation and the field of metabolic control analysis. We then present a many-protein model containing >1000 proteins parameterized by previously measured abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.

A growth-rate composition formula for the growth of E.coli on co-utilized carbon substrates.

When bacteria are cultured in medium with multiple carbon substrates, they frequently consume these substrates simultaneously. Building on recent advances in the understanding of metabolic coordination exhibited by Escherichia coli cells through cAMP-Crp signaling, we show that this signaling system responds to the total carbon-uptake flux when substrates are co-utilized and derive a mathematical formula that accurately predicts the resulting growth rate, based only on the growth rates on individual substrates.

The innate growth bistability and fitness landscapes of antibiotic-resistant bacteria.

To predict the emergence of antibiotic resistance, quantitative relations must be established between the fitness of drug-resistant organisms and the molecular mechanisms conferring resistance. These relations are often unknown and may depend on the state of bacterial growth. To bridge this gap, we have investigated Escherichia coli strains expressing resistance to translation-inhibiting antibiotics. We show that resistance expression and drug inhibition are linked in a positive feedback loop arising from an innate, global effect of drug-inhibited growth on gene expression. A quantitative model of bacterial growth based on this innate feedback accurately predicts the rich phenomena observed: a plateau-shaped fitness landscape, with an abrupt drop in the growth rates of cultures at a threshold drug concentration, and the coexistence of growing and nongrowing populations, that is, growth bistability, below the threshold.

On the rapidity of antibiotic resistance evolution facilitated by a concentration gradient.

The rapid emergence of bacterial strains resistant to multiple antibiotics is posing a growing public health risk. The mechanisms underlying the rapid evolution of drug resistance are, however, poorly understood. The heterogeneity of the environments in which bacteria encounter antibiotic drugs could play an important role. E.g., in the highly compartmentalized human body, drug levels can vary substantially between different organs and tissues. It has been proposed that this could facilitate the selection of resistant mutants, and recent experiments support this. To study the role of spatial heterogeneity in the evolution of drug resistance, we present a quantitative model describing an environment subdivided into relatively isolated compartments with various antibiotic concentrations, in which bacteria evolve under the stochastic processes of proliferation, migration, mutation and death. Analytical and numerical results demonstrate that concentration gradients can foster a mode of adaptation that is impossible in uniform environments. It allows resistant mutants to evade competition and circumvent the slow process of fixation by invading compartments with higher drug concentrations, where less resistant strains cannot subsist. The speed of this process increases sharply with the sensitivity of the growth rate to the antibiotic concentration, which we argue to be generic. Comparable adaptation rates in uniform environments would require a high selection coefficient (s > 0.1) for each forward mutation. Similar processes can occur if the heterogeneity is more complex than just a linear gradient. The model may also be applicable to other adaptive processes involving environmental heterogeneity and range expansion.

Speed, sensitivity, and bistability in auto-activating signaling circuits.

Cells employ a myriad of signaling circuits to detect environmental signals and drive specific gene expression responses. A common motif in these circuits is inducible auto-activation: a transcription factor that activates its own transcription upon activation by a ligand or by post-transcriptional modification. Examples range from the two-component signaling systems in bacteria and plants to the genetic circuits of animal viruses such as HIV. We here present a theoretical study of such circuits, based on analytical calculations, numerical computations, and simulation. Our results reveal several surprising characteristics. They show that auto-activation can drastically enhance the sensitivity of the circuit's response to input signals: even without molecular cooperativity, an ultra-sensitive threshold response can be obtained. However, the increased sensitivity comes at a cost: auto-activation tends to severely slow down the speed of induction, a stochastic effect that was strongly underestimated by earlier deterministic models. This slow-induction effect again requires no molecular cooperativity and is intimately related to the bimodality recently observed in non-cooperative auto-activation circuits. These phenomena pose strong constraints on the use of auto-activation in signaling networks. To achieve both a high sensitivity and a rapid induction, an inducible auto-activation circuit is predicted to acquire low cooperativity and low fold-induction. Examples from Escherichia coli's two-component signaling systems support these predictions.

Combinatorial gene regulation using auto-regulation.

As many as 59% of the transcription factors in Escherichia coli regulate the transcription rate of their own genes. This suggests that auto-regulation has one or more important functions. Here, one possible function is studied. Often the transcription rate of an auto-regulator is also controlled by additional transcription factors. In these cases, the way the expression of the auto-regulator responds to changes in the concentrations of the "input" regulators (the response function) is obviously affected by the auto-regulation. We suggest that, conversely, auto-regulation may be used to optimize this response function. To test this hypothesis, we use an evolutionary algorithm and a chemical-physical model of transcription regulation to design model cis-regulatory constructs with predefined response functions. In these simulations, auto-regulation can evolve if this provides a functional benefit. When selecting for a series of elementary response functions-Boolean logic gates and linear responses-the cis-regulatory regions resulting from the simulations indeed often exploit auto-regulation. Surprisingly, the resulting constructs use auto-activation rather than auto-repression. Several design principles show up repeatedly in the simulation results. They demonstrate how auto-activation can be used to generate sharp, switch-like activation and repression circuits and how linearly decreasing response functions can be obtained. Auto-repression, on the other hand, resulted only when a high response speed or a suppression of intrinsic noise was also selected for. The results suggest that, while auto-repression may primarily be valuable to improve the dynamical properties of regulatory circuits, auto-activation is likely to evolve even when selection acts on the shape of response function only.

Sources and sinks: a stochastic model of evolution in heterogeneous environments.

We study evolution driven by spatial heterogeneity in a stochastic model of source-sink ecologies. A sink is a habitat where mortality exceeds reproduction so that a local population persists only due to immigration from a source. Immigrants can, however, adapt to conditions in the sink by mutation. To characterize the adaptation rate, we derive expressions for the first arrival time of adapted mutants. The joint effects of migration, mutation, birth, and death result in two distinct parameter regimes. These results may pertain to the rapid evolution of drug-resistant pathogens and insects.

Chance and necessity in chromosomal gene distributions.

By analyzing the spacing of genes on chromosomes, we find that transcriptional and RNA-processing regulatory sequences outside coding regions leave footprints on the distribution of intergenic distances. Using analogies between genes on chromosomes and one-dimensional gases, we constructed a statistical null model. We used this to estimate typical upstream and downstream regulatory sequence sizes in various species. Deviations from this model reveal bi-directional transcriptional regulatory regions in Saccharomyces cerevisiae and bi-directional terminators in Escherichia coli.

Transcriptional regulation by competing transcription factor modules.

Gene regulatory networks lie at the heart of cellular computation. In these networks, intracellular and extracellular signals are integrated by transcription factors, which control the expression of transcription units by binding to cis-regulatory regions on the DNA. The designs of both eukaryotic and prokaryotic cis-regulatory regions are usually highly complex. They frequently consist of both repetitive and overlapping transcription factor binding sites. To unravel the design principles of these promoter architectures, we have designed in silico prokaryotic transcriptional logic gates with predefined input-output relations using an evolutionary algorithm. The resulting cis-regulatory designs are often composed of modules that consist of tandem arrays of binding sites to which the transcription factors bind cooperatively. Moreover, these modules often overlap with each other, leading to competition between them. Our analysis thus identifies a new signal integration motif that is based upon the interplay between intramodular cooperativity and intermodular competition. We show that this signal integration mechanism drastically enhances the capacity of cis-regulatory domains to integrate signals. Our results provide a possible explanation for the complexity of promoter architectures and could be used for the rational design of synthetic gene circuits.