Non-genetic diversity modulates population performance

The ability to sense the environment is heterogeneously distributed in cell populations

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information-theoretic framework to quantify the distribution of sensing abilities from single-cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an 'average cell'. We verify these predictions using live-cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information-theoretic framework will significantly improve our understanding of how cells sense in their environment.

Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Chemotactic bacteria not only navigate chemical gradients, but also shape their environments by consuming and secreting attractants. Investigating how these processes influence the dynamics of bacterial populations has been challenging because of a lack of experimental methods for measuring spatial profiles of chemoattractants in real time. Here, we use a fluorescent sensor for aspartate to directly measure bacterially generated chemoattractant gradients during collective migration. Our measurements show that the standard Patlak-Keller-Segel model for collective chemotactic bacterial migration breaks down at high cell densities. To address this, we propose modifications to the model that consider the impact of cell density on bacterial chemotaxis and attractant consumption. With these changes, the model explains our experimental data across all cell densities, offering insight into chemotactic dynamics. Our findings highlight the significance of considering cell density effects on bacterial behavior, and the potential for fluorescent metabolite sensors to shed light on the complex emergent dynamics of bacterial communities.

Non-genetic adaptation by collective migration

Collective behaviors require coordination of individuals. Thus, a population must adjust its phenotypic distribution to adapt to changing environments. How can a population regulate its phenotypic distribution? One strategy is to utilize specialized networks for gene regulation and maintaining distinct phenotypic subsets. Another involves genetic mutations, which can be augmented by stress-response pathways. Here, we studied how a migrating bacterial population regulates its phenotypic distribution to traverse across diverse environments. We generated isogenic Escherichia coli populations with varying distributions of swimming behaviors and observed their phenotype distributions during migration in liquid and porous environments. Surprisingly, we found that during collective migration, the distributions of swimming phenotypes adapt to the environment without mutations or gene regulation. Instead, adaptation is caused by the dynamic and reversible enrichment of high-performing swimming phenotypes within each environment. This adaptation mechanism is supported by a recent theoretical study, which proposed that the phenotypic composition of a migrating population results from a balance between cell growth generating diversity and collective migration eliminating the phenotypes that are unable to keep up with the migrating group. Furthermore, by examining chemoreceptor abundance distributions during migration towards different attractants, we found that this mechanism acts on multiple chemotaxis-related traits simultaneously. Our findings reveal that collective migration itself can enable cell populations with continuous, multi-dimensional phenotypes to flexibly and rapidly adapt their phenotypic composition to diverse environmental conditions.

Significance statement

Conventional cell adaptation mechanisms, like gene regulation and random phenotypic switching, act swiftly but are limited to a few traits, while mutation-driven adaptations unfold slowly. By quantifying phenotypic diversity during bacterial collective migration, we discovered an adaptation mechanism that rapidly and reversibly adjusts multiple traits simultaneously. By dynamically balancing the elimination of phenotypes unable to keep pace with generation of diversity through growth, this process enables populations to tune their phenotypic composition based on the environment, without the need for gene regulation or mutations. Given the prevalence of collective migration in microbes, cancers, and embryonic development, non-genetic adaptation through collective migration may be a universal mechanism for populations to navigate diverse environments, offering insights into broader applications across various fields.

Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Chemotactic bacteria not only navigate chemical gradients, but also shape their environments by consuming and secreting attractants. Investigating how these processes influence the dynamics of bacterial populations has been challenging because of a lack of experimental methods for measuring spatial profiles of chemoattractants in real time. Here, we use a fluorescent sensor for aspartate to directly measure bacterially generated chemoattractant gradients during collective migration. Our measurements show that the standard Patlak-Keller-Segel model for collective chemotactic bacterial migration breaks down at high cell densities. To address this, we propose modifications to the model that consider the impact of cell density on bacterial chemotaxis and attractant consumption. With these changes, the model explains our experimental data across all cell densities, offering new insight into chemotactic dynamics. Our findings highlight the significance of considering cell density effects on bacterial behavior, and the potential for fluorescent metabolite sensors to shed light on the complex emergent dynamics of bacterial communities.

Collective behavior and nongenetic inheritance allow bacterial populations to adapt to changing environments

Collective behaviors require coordination among a group of individuals. As a result, individuals that are too phenotypically different from the rest of the group can be left out, reducing heterogeneity, but increasing coordination. If individuals also reproduce, the offspring can have different phenotypes from their parent(s). This raises the question of how these two opposing processes-loss of diversity by collective behaviors and generation of it through growth and inheritance-dynamically shape the phenotypic composition of an isogenic population. We examine this question theoretically using collective migration of chemotactic bacteria as a model system, where cells of different swimming phenotypes are better suited to navigate in different environments. We find that the differential loss of phenotypes caused by collective migration is environment-dependent. With cell growth, this differential loss enables migrating populations to dynamically adapt their phenotype compositions to the environment, enhancing migration through multiple environments. Which phenotypes are produced upon cell division depends on the level of nongenetic inheritance, and higher inheritance leads to larger composition adaptation and faster migration at steady state. However, this comes at the cost of slower responses to new environments. Due to this trade-off, there is an optimal level of inheritance that maximizes migration speed through changing environments, which enables a diverse population to outperform a nondiverse one. Growing populations might generally leverage the selection-like effects provided by collective behaviors to dynamically shape their own phenotype compositions, without mutations.

Imaging whole-brain activity to understand behavior

The brain evolved to produce behaviors that help an animal inhabit the natural world. During natural behaviors, the brain is engaged in many levels of activity from the detection of sensory inputs to decision-making to motor planning and execution. To date, most brain studies have focused on small numbers of neurons that interact in limited circuits. This allows analyzing individual computations or steps of neural processing. During behavior, however, brain activity must integrate multiple circuits in different brain regions. The activities of different brain regions are not isolated, but may be contingent on one another. Coordinated and concurrent activity within and across brain areas is organized by (1) sensory information from the environment, (2) the animal's internal behavioral state, and (3) recurrent networks of synaptic and non-synaptic connectivity. Whole-brain recording with cellular resolution provides a new opportunity to dissect the neural basis of behavior, but whole-brain activity is also mutually contingent on behavior itself. This is especially true for natural behaviors like navigation, mating, or hunting, which require dynamic interaction between the animal, its environment, and other animals. In such behaviors, the sensory experience of an unrestrained animal is actively shaped by its movements and decisions. Many of the signaling and feedback pathways that an animal uses to guide behavior only occur in freely moving animals. Recent technological advances have enabled whole-brain recording in small behaving animals including nematodes, flies, and zebrafish. These whole-brain experiments capture neural activity with cellular resolution spanning sensory, decision-making, and motor circuits, and thereby demand new theoretical approaches that integrate brain dynamics with behavioral dynamics. Here, we review the experimental and theoretical methods that are being employed to understand animal behavior and whole-brain activity, and the opportunities for physics to contribute to this emerging field of systems neuroscience.

The ecological roles of bacterial chemotaxis

How bacterial chemotaxis is performed is much better understood than why. Traditionally, chemotaxis has been understood as a foraging strategy by which bacteria enhance their uptake of nutrients and energy, yet it has remained puzzling why certain less nutritious compounds are strong chemoattractants and vice versa. Recently, we have gained increased understanding of alternative ecological roles of chemotaxis, such as navigational guidance in colony expansion, localization of hosts or symbiotic partners and contribution to microbial diversity by the generation of spatial segregation in bacterial communities. Although bacterial chemotaxis has been observed in a wide range of environmental settings, insights into the phenomenon are mostly based on laboratory studies of model organisms. In this Review, we highlight how observing individual and collective migratory behaviour of bacteria in different settings informs the quantification of trade-offs, including between chemotaxis and growth. We argue that systematically mapping when and where bacteria are motile, in particular by transgenerational bacterial tracking in dynamic environments and in situ approaches from guts to oceans, will open the door to understanding the rich interplay between metabolism and growth and the contribution of chemotaxis to microbial life.

Bayesian-based decipherment of in-depth information in bacterial chemical sensing beyond pleasant/unpleasant responses

Chemical sensing is vital to the survival of all organisms. Bacterial chemotaxis is conducted by multiple receptors that sense chemicals to regulate a single signalling system controlling the transition between the direction (clockwise vs. counterclockwise) of flagellar rotation. Such an integrated system seems better suited to judge chemicals as either favourable or unfavourable, but not for identification purposes though differences in their affinities to the receptors may cause difference in response strength. Here, an experimental setup was developed to monitor behaviours of multiple cells stimulated simultaneously as well as a statistical framework based on Bayesian inferences. Although responses of individual cells varied substantially, ensemble averaging of the time courses seemed characteristic to attractant species, indicating we can extract information of input chemical species from responses of the bacterium. Furthermore, two similar, but distinct, beverages elicited attractant responses of cells with profiles distinguishable with the Bayesian procedure. These results provide a basis for novel bio-inspired sensors that could be used with other cell types to sense wider ranges of chemicals.

Escherichia coli chemotaxis is information limited

Organisms acquire and use information from their environment to guide their behaviour. However, it is unclear whether this information quantitatively limits their behavioural performance. Here, we relate information to the ability of Escherichia coli to navigate up chemical gradients, the behaviour known as chemotaxis. First, we derive a theoretical limit on the speed with which cells climb gradients, given the rate at which they acquire information. Next, we measure cells' gradient-climbing speeds and the rate of information acquisition by their chemotaxis signaling pathway. We find that E. coli make behavioural decisions with much less than the one bit required to determine whether they are swimming up-gradient. Some of this information is irrelevant to gradient climbing, and some is lost in communication to behaviour. Despite these limitations, E. coli climb gradients at speeds within a factor of two of the theoretical bound. Thus, information can limit the performance of an organism, and sensory-motor pathways may have evolved to efficiently use information acquired from the environment.

Multiple functions of flagellar motility and chemotaxis in bacterial physiology

Most swimming bacteria are capable of following gradients of nutrients, signaling molecules and other environmental factors that affect bacterial physiology. This tactic behavior became one of the most-studied model systems for signal transduction and quantitative biology, and underlying molecular mechanisms are well characterized in Escherichia coli and several other model bacteria. In this review, we focus primarily on less understood aspect of bacterial chemotaxis, namely its physiological relevance for individual bacterial cells and for bacterial populations. As evident from multiple recent studies, even for the same bacterial species flagellar motility and chemotaxis might serve multiple roles, depending on the physiological and environmental conditions. Among these, finding sources of nutrients and more generally locating niches that are optimal for growth appear to be one of the major functions of bacterial chemotaxis, which could explain many chemoeffector preferences as well as flagellar gene regulation. Chemotaxis might also generally enhance efficiency of environmental colonization by motile bacteria, which involves intricate interplay between individual and collective behaviors and trade-offs between growth and motility. Finally, motility and chemotaxis play multiple roles in collective behaviors of bacteria including swarming, biofilm formation and autoaggregation, as well as in their interactions with animal and plant hosts.

Spatial modulation of individual behaviors enables an ordered structure of diverse phenotypes during bacterial group migration

Coordination of diverse individuals often requires sophisticated communications and high-order computational abilities. Microbial populations can exhibit diverse individualistic behaviors, and yet can engage in collective migratory patterns with a spatially sorted arrangement of phenotypes. However, it is unclear how such spatially sorted patterns emerge from diverse individuals without complex computational abilities. Here, by investigating the single-cell trajectories during group migration, we discovered that, despite the constant migrating speed of a group, the drift velocities of individual bacteria decrease from the back to the front. With a Langevin-type modeling framework, we showed that this decreasing profile of drift velocities implies the spatial modulation of individual run-and-tumble random motions, and enables the bacterial population to migrate as a pushed wave front. Theoretical analysis and stochastic simulations further predicted that the pushed wave front can help a diverse population to stay in a tight group, while diverse individuals perform the same type of mean reverting processes around centers orderly aligned by their chemotactic abilities. This mechanism about the emergence of orderly collective migration from diverse individuals is experimentally demonstrated by titration of bacterial chemoreceptor abundance. These results reveal a simple computational principle for emergent ordered behaviors from heterogeneous individuals.

Organisms living in large groups often have to move together in order to navigate, forage for food, and increase their roaming range. Such groups are often made up of distinct individuals that must integrate their different behaviors in order to migrate in the same direction at a similar pace. For instance, for the bacteria Escherichia coli to travel as a condensed group, they must coordinate their response to a set of chemical signals called chemoattractants that tell them where to go.

The chemoattractants surrounding the bacteria are unequally distributed so that there is more of them at the front than the back of the group. During migration, each bacterium moves towards this concentration gradient in a distinct way, spontaneously rotating its direction in a ‘run-and-tumble’ motion that guides it towards areas where there are high levels of these chemical signals. In addition to this variability, how well individual bacteria are able to swim up the gradient also differs within the population. Bacteria that are better at sensing the chemoattractant gradient are placed at the front of the group, while those that are worst are shifted towards the back. This spatial arrangement is thought to help the bacteria migrate together. But how E. coli organize themselves in to this pattern is unclear, especially as they cannot communicate directly with one another and display such diverse, randomized behaviors.

To help answer this question, Bai, He et al. discovered a general principle that describes how single bacterial cells move within a group. The results showed that E. coli alter their run-and-tumble motion depending on where they reside within the population: individuals at the rear drift faster so they can catch up with the group, while those leading the group drift slower to draw themselves back. This ‘reversion behavior’ allows the migrating bacteria to travel at a constant speed around a mean position relative to the group.

A cell’s drifting speed is determined by how well it moves towards the chemoattractant and its response to the concentration gradient. As a result, the mean position around which the bacterium accelerates or deaccelerates will vary depending on how sensitive it is to the chemoattractant gradient. The E. coli therefore spatially arrange themselves so that the more sensitive bacteria are located at the front of the group where the gradient is shallower; and cells that are less sensitive are located towards the back where the gradient is steeper.

These findings suggest a general principle for how bacteria form ordered patterns whilst migrating as a collective group. This behavior could also apply to other populations of distinct individuals, such as ants following a trail or flocks of birds migrating in between seasons.

Effect of inoculum size and antibiotics on bacterial traveling bands in a thin microchannel defined by optical adhesive

Phenotypic diversity in bacterial flagella-induced motility leads to complex collective swimming patterns, appearing as traveling bands with transient locally enhanced cell densities. Traveling bands are known to be a bacterial chemotactic response to self-generated nutrient gradients during growth in resource-limited microenvironments. In this work, we studied different parameters of Escherichia coli (E. coli) collective migration, in particular the quantity of bacteria introduced initially in a microfluidic chip (inoculum size) and their exposure to antibiotics (ampicillin, ciprofloxacin, and gentamicin). We developed a hybrid polymer-glass chip with an intermediate optical adhesive layer featuring the microfluidic channel, enabling high-content imaging of the migration dynamics in a single bacterial layer, i.e., bacteria are confined in a quasi-2D space that is fully observable with a high-magnification microscope objective. On-chip bacterial motility and traveling band analysis was performed based on individual bacterial trajectories by means of custom-developed algorithms. Quantifications of swimming speed, tumble bias and effective diffusion properties allowed the assessment of phenotypic heterogeneity, resulting in variations in transient cell density distributions and swimming performance. We found that incubation of isogeneic E. coli with different inoculum sizes eventually generated different swimming phenotype distributions. Interestingly, incubation with antimicrobials promoted bacterial chemotaxis in specific cases, despite growth inhibition. Moreover, E. coli filamentation in the presence of antibiotics was assessed, and the impact on motility was evaluated. We propose that the observation of traveling bands can be explored as an alternative for fast antimicrobial susceptibility testing.

Leave or Stay: Simulating Motility and Fitness of Microorganisms in Dynamic Aquatic Ecosystems

Motility is a key adaptation factor in scarce marine environments inhabited by bacteria. The question of how a capacity for adaptive migrations influences the success of a microbial population in various conditions is a challenge addressed in this study. We employed the agent-based model of competition of motile and sedentary microbial populations in a confined aquatic environment supplied with a periodic batch nutrient source to assess the fitness of both. Such factors as nutrient concentration in a batch, batch period, mortality type and energetic costs of migration were considered to determine the conditions favouring different strategies: Nomad of a motile population and Settler of a sedentary one. The modelling results demonstrate that dynamic and nutrient-scarce environments favour motile populations, whereas nutrient-rich and stagnant environments promote sedentary microorganisms. Energetic costs of migration determine whether or not the Nomad strategy of the motile population is successful, though it also depends on such conditions as nutrient availability. Even without penalties for migration, under certain conditions, the sedentary Settler population dominates in the ecosystem. It is achieved by decreasing the local nutrient availability near the nutrient source, as motile populations relying on a local optimizing strategy tend to follow benign conditions and fail, enduring stress associated with crossing the valleys of suboptimal nutrient availability.

Temporal fluctuations in chemotaxis gain implement a simulated-tempering strategy for efficient navigation in complex environments

Bacterial chemotaxis is a major testing ground for systems biology, including the role of fluctuations and individual variation. Individual bacteria vary in their tumbling frequency and adaptation time. Recently, large cell-cell variation was also discovered in chemotaxis gain, which determines the sensitivity of the tumbling rate to attractant gradients. Variation in gain is puzzling, because low gain impairs chemotactic velocity. Here, we provide a functional explanation for gain variation by establishing a formal analogy between chemotaxis and algorithms for sampling probability distributions. We show that temporal fluctuations in gain implement simulated tempering, which allows sampling of attractant distributions with many local peaks. Periods of high gain allow bacteria to detect and climb gradients quickly, and periods of low gain allow them to move to new peaks. Gain fluctuations thus allow bacteria to thrive in complex environments, and more generally they may play an important functional role for organism navigation.

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior

Non-genetic phenotypic diversity plays a significant role in the chemotactic behavior of bacteria, influencing how populations sense and respond to chemical stimuli. First, we review the molecular mechanisms that generate phenotypic diversity in bacterial chemotaxis. Next, we discuss the functional consequences of phenotypic diversity for the chemosensing and chemotactic performance of single cells and populations. Finally, we discuss mechanisms that modulate the amount of phenotypic diversity in chemosensory parameters in response to changes in the environment.

A multiscale 3D chemotaxis assay reveals bacterial navigation mechanisms

How motile bacteria navigate environmental chemical gradients has implications ranging from health to climate science, but the underlying behavioral mechanisms are unknown for most species. The well-studied navigation strategy of Escherichia coli forms a powerful paradigm that is widely assumed to translate to other bacterial species. This assumption is rarely tested because of a lack of techniques capable of bridging scales from individual navigation behavior to the resulting population-level chemotactic performance. Here, we present such a multiscale 3D chemotaxis assay by combining high-throughput 3D bacterial tracking with microfluidically created chemical gradients. Large datasets of 3D trajectories yield the statistical power required to assess chemotactic performance at the population level, while simultaneously resolving the underlying 3D navigation behavior for every individual. We demonstrate that surface effects confound typical 2D chemotaxis assays, and reveal that, contrary to previous reports, Caulobacter crescentus breaks with the E. coli paradigm.

Connection between the Bacterial Chemotactic Network and Optimal Filtering

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.

Nongenetic individuality, changeability, and inheritance in bacterial behavior

Isogenic microbial populations in constant and homogeneous environments can display remarkable levels of phenotypic diversity. Quantitative understanding of how such diversity is generated and maintained in populations is, however, experimentally and theoretically challenging. We focus on the swimming behavior of Escherichia coli as a model system of phenotypic diversity and show that, despite temporal changes in behavior that each individual undergoes, significant differences between individuals persist throughout most of their lifetimes. While the behavior of even closely related bacteria can be remarkably different, the behavioral variations produced by nongenetic mechanisms are inherited across generations. The general experimental and theoretical framework developed here can be applied to study quantitative aspects of phenotypic diversity in many biological systems.

Isogenic populations often display remarkable levels of phenotypic diversity even in constant, homogeneous environments. Such diversity results from differences between individuals (“nongenetic individuality”) as well as changes during individuals’ lifetimes (“changeability”). Yet, studies that capture and quantify both sources of diversity are scarce. Here we measure the swimming behavior of hundreds of Escherichia coli bacteria continuously over two generations and use a model-independent method for quantifying behavior to show that the behavioral space of E. coli is low-dimensional, with variations occurring mainly along two independent and interpretable behavioral traits. By statistically decomposing the diversity in these two traits, we find that individuality is the main source of diversity, while changeability makes a smaller but significant contribution. Finally, we show that even though traits of closely related individuals can be remarkably different, they exhibit positive correlations across generations that imply nongenetic inheritance. The model-independent experimental and theoretical framework developed here paves the way for more general studies of microbial behavioral diversity.

Wide lag time distributions break a trade-off between reproduction and survival in bacteria

Many microorganisms face a fundamental trade-off between reproduction and survival: Rapid growth boosts population size but makes microorganisms sensitive to external stressors. Here, we show that starved bacteria encountering new resources can break this trade-off by evolving phenotypic heterogeneity in lag time. We quantify the distribution of single-cell lag times of populations of starved Escherichia coli and show that population growth after starvation is primarily determined by the cells with shortest lag due to the exponential nature of bacterial population dynamics. As a consequence, cells with long lag times have no substantial effect on population growth resumption. However, we observe that these cells provide tolerance to stressors such as antibiotics. This allows an isogenic population to break the trade-off between reproduction and survival. We support this argument with an evolutionary model which shows that bacteria evolve wide lag time distributions when both rapid growth resumption and survival under stressful conditions are under selection. Our results can explain the prevalence of antibiotic tolerance by lag and demonstrate that the benefits of phenotypic heterogeneity in fluctuating environments are particularly high when minorities with extreme phenotypes dominate population dynamics.

Genomic, metabolic and phenotypic variability shapes ecological differentiation and intraspecies interactions of Alteromonas macleodii

Ecological differentiation between strains of bacterial species is shaped by genomic and metabolic variability. However, connecting genotypes to ecological niches remains a major challenge. Here, we linked bacterial geno- and phenotypes by contextualizing pangenomic, exometabolomic and physiological evidence in twelve strains of the marine bacterium Alteromonas macleodii, illuminating adaptive strategies of carbon metabolism, microbial interactions, cellular communication and iron acquisition. In A. macleodii strain MIT1002, secretion of amino acids and the unique capacity for phenol degradation may promote associations with Prochlorococcus cyanobacteria. Strain 83-1 and three novel Pacific isolates, featuring clonal genomes despite originating from distant locations, have profound abilities for algal polysaccharide utilization but without detrimental implications for Ecklonia macroalgae. Degradation of toluene and xylene, mediated via a plasmid syntenic to terrestrial Pseudomonas, was unique to strain EZ55. Benzoate degradation by strain EC673 related to a chromosomal gene cluster shared with the plasmid of A. mediterranea EC615, underlining that mobile genetic elements drive adaptations. Furthermore, we revealed strain-specific production of siderophores and homoserine lactones, with implications for nutrient acquisition and cellular communication. Phenotypic variability corresponded to different competitiveness in co-culture and geographic distribution, indicating linkages between intraspecific diversity, microbial interactions and biogeography. The finding of "ecological microdiversity" helps understanding the widespread occurrence of A. macleodii and contributes to the interpretation of bacterial niche specialization, population ecology and biogeochemical roles.

Microfluidic techniques for separation of bacterial cells via taxis

The microbial environment is typically within a fluid and the key processes happen at the microscopic scale where viscosity dominates over inertial forces. Microfluidic tools are thus well suited to study microbial motility because they offer precise control of spatial structures and are ideal for the generation of laminar fluid flows with low Reynolds numbers at microbial lengthscales. These tools have been used in combination with microscopy platforms to visualise and study various microbial taxes. These include establishing concentration and temperature gradients to influence motility via chemotaxis and thermotaxis, or controlling the surrounding microenvironment to influence rheotaxis, magnetotaxis, and phototaxis. Improvements in microfluidic technology have allowed fine separation of cells based on subtle differences in motility traits and have applications in synthetic biology, directed evolution, and applied medical microbiology.

Chemotaxis in external fields: Simulations for active magnetic biological matter

The movement of microswimmers is often described by active Brownian particle models. Here we introduce a variant of these models with several internal states of the swimmer to describe stochastic strategies for directional swimming such as run and tumble or run and reverse that are used by microorganisms for chemotaxis. The model includes a mechanism to generate a directional bias for chemotaxis and interactions with external fields (e.g., gravity, magnetic field, fluid flow) that impose forces or torques on the swimmer. We show how this modified model can be applied to various scenarios: First, the run and tumble motion of E. coli is used to establish a paradigm for chemotaxis and investigate how it is affected by external forces. Then, we study magneto-aerotaxis in magnetotactic bacteria, which is biased not only by an oxygen gradient towards a preferred concentration, but also by magnetic fields, which exert a torque on an intracellular chain of magnets. We study the competition of magnetic alignment with active reorientation and show that the magnetic orientation can improve chemotaxis and thereby provide an advantage to the bacteria, even at rather large inclination angles of the magnetic field relative to the oxygen gradient, a case reminiscent of what is expected for the bacteria at or close to the equator. The highest gain in chemotactic velocity is obtained for run and tumble with a magnetic field parallel to the gradient, but in general a mechanism for reverse motion is necessary to swim against the magnetic field and a run and reverse strategy is more advantageous in the presence of a magnetic torque. This finding is consistent with observations that the dominant mode of directional changes in magnetotactic bacteria is reversal rather than tumbles. Moreover, it provides guidance for the design of future magnetic biohybrid swimmers.

In this paper, we propose a modified Active Brownian particle model to describe bacterial swimming behavior under the influence of external forces and torques, in particular of a magnetic torque. This type of interaction is particularly important for magnetic biohybrids (i.e. motile bacteria coupled to a synthetic magnetic component) and for magnetotactic bacteria (i.e. bacteria with a natural intracellular magnetic chain), which perform chemotaxis to swim along chemical gradients, but are also directed by an external magnetic field. The model allows us to investigate the benefits and disadvantages of such coupling between two different directionality mechanisms. In particular we show that the magnetic torque can speed chemotaxis up in some conditions, while it can hinder it in other cases. In addition to an understanding of the swimming strategies of naturally magnetotactic organisms, the results may guide the design of future biomedical devices.

Chemotaxis as a navigation strategy to boost range expansion

Bacterial chemotaxis, the directed movement of cells along gradients of chemoattractants, is among the best-characterized subjects in molecular biology^1-10, but much less is known about its physiological roles¹¹. It is commonly seen as a starvation response when nutrients run out, or as an escape response from harmful situations^12-16. Here we identify an alternative role of chemotaxis by systematically examining the spatiotemporal dynamics of Escherichia coli in soft agar^12,17,18. Chemotaxis in nutrient-replete conditions promotes the expansion of bacterial populations into unoccupied territories well before nutrients run out in the current environment. Low levels of chemoattractants act as aroma-like cues in this process, establishing the direction and enhancing the speed of population movement along the self-generated attractant gradients. This process of navigated range expansion spreads faster and yields larger population gains than unguided expansion following the canonical Fisher-Kolmogorov dynamics^19,20 and is therefore a general strategy to promote population growth in spatially extended, nutrient-replete environments.

Phenotypic heterogeneity of microbial populations under nutrient limitation

Phenotypic heterogeneity is a phenomenon in which genetically identical individuals have different characteristics. This behavior can also be found in bacteria, even if they grow as monospecies in well-mixed environments such as bioreactors. Here it is discussed how phenotypic heterogeneity is generated by internal factors and how it is promoted under nutrient-limited growth conditions. A better understanding of the molecular levels that control phenotypic heterogeneity could improve biotechnological production processes.

An evolutionarily stable strategy to colonize spatially extended habitats

The ability of a species to colonize newly available habitats is crucial to its overall fitness1-3. In general, motility and fast expansion are expected to be beneficial for colonization and hence for the fitness of an organism4-7. Here we apply an evolution protocol to investigate phenotypical requirements for colonizing habitats of different sizes during range expansion by chemotaxing bacteria8. Contrary to the intuitive expectation that faster is better, we show that there is an optimal expansion speed for a given habitat size. Our analysis showed that this effect arises from interactions among pioneering cells at the front of the expanding population, and revealed a simple, evolutionarily stable strategy for colonizing a habitat of a specific size: to expand at a speed given by the product of the growth rate and the habitat size. These results illustrate stability-to-invasion as a powerful principle for the selection of phenotypes in complex ecological processes.

Evolution at the Edge of Expanding Populations

Predicting the evolution of expanding populations is critical to controlling biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of evolution where organisms pay a reproductive cost to disperse faster. When does selection favor this "survival of the fastest"? We searched for a simple rule, motivated by evolution experiments where swarming bacteria evolved into a hyperswarmer mutant that disperses ∼100% faster but pays a growth cost of ∼10% to make many copies of its flagellum. We analyzed a two-species model based on the Fisher equation to explain this observation: the population expansion rate (v) results from an interplay of growth (r) and dispersal (D) and is independent of the carrying capacity: v = 2 ( rD ) 1 / 2 . A mutant can take over the edge only if its expansion rate (v2) exceeds the expansion rate of the established species (v1); this simple condition ( v 2 > v 1 ) determines the maximum cost in slower growth that a faster mutant can pay and still be able to take over. Numerical simulations and time-course experiments where we tracked evolution by imaging bacteria suggest that our findings are general: less favorable conditions delay but do not entirely prevent the success of the fastest. Thus, the expansion rate defines a traveling wave fitness, which could be combined with trade-offs to predict evolution of expanding populations.

Signal integration and information transfer in an allosterically regulated network

A biological reaction network may serve multiple purposes, processing more than one input and impacting downstream processes via more than one output. These networks operate in a dynamic cellular environment in which the levels of network components may change within cells and across cells. Recent evidence suggests that protein concentration variability could explain cell fate decisions. However, systems with multiple inputs, multiple outputs, and changing input concentrations have not been studied in detail due to their complexity. Here, we take a systems biochemistry approach, combining physiochemical modeling and information theory, to investigate how cyclooxygenase-2 (COX-2) processes simultaneous input signals within a complex interaction network. We find that changes in input levels affect the amount of information transmitted by the network, as does the correlation between those inputs. This, and the allosteric regulation of COX-2 by its substrates, allows it to act as a signal integrator that is most sensitive to changes in relative input levels.

Bacteria push the limits of chemotactic precision to navigate dynamic chemical gradients

Ephemeral aggregations of bacteria are ubiquitous in the environment, where they serve as hotbeds of metabolic activity, nutrient cycling, and horizontal gene transfer. In many cases, these regions of high bacterial concentration are thought to form when motile cells use chemotaxis to navigate to chemical hotspots. However, what governs the dynamics of bacterial aggregations is unclear. Here, we use an experimental platform to create realistic submillimeter-scale nutrient pulses with controlled nutrient concentrations. By combining experiments, mathematical theory, and agent-based simulations, we show that individual Vibrio ordalii bacteria begin chemotaxis toward hotspots of dissolved organic matter (DOM) when the magnitude of the chemical gradient rises sufficiently far above the sensory noise that is generated by stochastic encounters with chemoattractant molecules. Each DOM hotspot is surrounded by a dynamic ring of chemotaxing cells, which congregate in regions of high DOM concentration before dispersing as DOM diffuses and gradients become too noisy for cells to respond to. We demonstrate that V. ordalii operates close to the theoretical limits on chemotactic precision. Numerical simulations of chemotactic bacteria, in which molecule counting noise is explicitly taken into account, point at a tradeoff between nutrient acquisition and the cost of chemotactic precision. More generally, our results illustrate how limits on sensory precision can be used to understand the location, spatial extent, and lifespan of bacterial behavioral responses in ecologically relevant environments.

Axon growth regulation by a bistable molecular switch

For the brain to function properly, its neurons must make the right connections during neural development. A key aspect of this process is the tight regulation of axon growth as axons navigate towards their targets. Neuronal growth cones at the tips of developing axons switch between growth and paused states during axonal pathfinding, and this switching behaviour determines the heterogeneous axon growth rates observed during brain development. The mechanisms controlling this switching behaviour, however, remain largely unknown. Here, using mathematical modelling, we predict that the molecular interaction network involved in axon growth can exhibit bistability, with one state representing a fast-growing growth cone state and the other a paused growth cone state. Owing to stochastic effects, even in an unchanging environment, model growth cones reversibly switch between growth and paused states. Our model further predicts that environmental signals could regulate axon growth rate by controlling the rates of switching between the two states. Our study presents a new conceptual understanding of growth cone switching behaviour, and suggests that axon guidance may be controlled by both cell-extrinsic factors and cell-intrinsic growth regulatory mechanisms.

Stochastic protein multimerization, activity, and fitness

Many proteins assemble into homomultimeric structures, with a number of subunits that can vary substantially among phylogenetic lineages. As protein-protein interactions require productive encounters among subunits, such variation might partially be explained by variation in cellular protein abundance. Protein abundance in turn depends on the intrinsic rates of production and decay of mRNA and protein molecules, as well as rates of cell growth and division. Using a stochastic framework for prediction of the multimeric state of a protein as a function of these processes and the free energy associated with interface-interface binding, we demonstrate agreement with a wide class of proteins using E. coli proteome data. As such, this platform, which links protein quaternary structure with biochemical rates governing gene expression, protein association and dissociation, and cell growth and division, can be extended to evolutionary models for the emergence and diversification of multimers. While it is tempting to think of multimerization as adaptive, the diversity of multimeric states raises the question of its functional role and impact on fitness. As a force driving selection, we consider the possible increase in enzymatic activity of proteins arising strictly as a consequence of interface-interface binding-namely, enhanced stability to degradation, substrate binding affinity, or catalytic rate of multimers with respect to monomers without invoking further conformational changes, as in allostery. For fixed cost of protein production, we find a benefit conferred by multimers that is dependent on context and can therefore become different in diverging lineages.

Spatial self-organization resolves conflicts between individuality and collective migration

Collective behavior can spontaneously emerge when individuals follow common rules of interaction. However, the behavior of each individual differs due to existing genetic and non-genetic variation within the population. It remains unclear how this individuality is managed to achieve collective behavior. We quantify individuality in bands of clonal Escherichia coli cells that migrate collectively along a channel by following a self-generated gradient of attractant. We discover that despite substantial differences in individual chemotactic abilities, the cells are able to migrate as a coherent group by spontaneously sorting themselves within the moving band. This sorting mechanism ensures that differences between individual chemotactic abilities are compensated by differences in the local steepness of the traveling gradient each individual must navigate, and determines the minimum performance required to travel with the band. By resolving conflicts between individuality and collective migration, this mechanism enables populations to maintain advantageous diversity while on the move.

How bacteria migrate collectively despite individual phenotypic variation is not understood. Here, the authors show that cells spontaneously sort themselves within moving bands such that variations in individual tumble bias, a determinant of gradient climbing speed, are compensated by the local gradient steepness experienced by individuals.

Behavioral Variability and Phenotypic Diversity in Bacterial Chemotaxis

Living cells detect and process external signals using signaling pathways that are affected by random fluctuations. These variations cause the behavior of individual cells to fluctuate over time (behavioral variability) and generate phenotypic differences between genetically identical individuals (phenotypic diversity). These two noise sources reduce our ability to predict biological behavior because they diversify cellular responses to identical signals. Here, we review recent experimental and theoretical advances in understanding the mechanistic origin and functional consequences of such variation in Escherichia coli chemotaxis-a well-understood model of signal transduction and behavior. After briefly summarizing the architecture and logic of the chemotaxis system, we discuss determinants of behavior and chemotactic performance of individual cells. Then, we review how cell-to-cell differences in protein abundance map onto differences in individual chemotactic abilities and how phenotypic variability affects the performance of the population. We conclude with open questions to be addressed by future research.

Tuning dCas9's ability to block transcription enables robust, noiseless knockdown of bacterial genes

Over the past few years, tools that make use of the Cas9 nuclease have led to many breakthroughs, including in the control of gene expression. The catalytically dead variant of Cas9 known as dCas9 can be guided by small RNAs to block transcription of target genes, in a strategy also known as CRISPRi. Here, we reveal that the level of complementarity between the guide RNA and the target controls the rate at which RNA polymerase "kicks out" dCas9 from the target and completes transcription. We use this mechanism to precisely and robustly reduce gene expression by defined relative amounts. Alternatively, tuning repression by changing dCas9 concentration is noisy and promoter-strength dependent. We demonstrate broad applicability of this method to the study of genetic regulation and cellular physiology. First, we characterize feedback strength of a model auto-repressor. Second, we study the impact of amount variations of cell-wall synthesizing enzymes on cell morphology. Finally, we multiplex the system to obtain any combination of fractional repression of two genes.

Complexity-aware simple modeling

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches.

Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.

Phenotypic diversity and temporal variability in a bacterial signaling network revealed by single-cell FRET

We present in vivo single-cell FRET measurements in the Escherichia coli chemotaxis system that reveal pervasive signaling variability, both across cells in isogenic populations and within individual cells over time. We quantify cell-to-cell variability of adaptation, ligand response, as well as steady-state output level, and analyze the role of network design in shaping this diversity from gene expression noise. In the absence of changes in gene expression, we find that single cells demonstrate strong temporal fluctuations. We provide evidence that such signaling noise can arise from at least two sources: (i) stochastic activities of adaptation enzymes, and (ii) receptor-kinase dynamics in the absence of adaptation. We demonstrate that under certain conditions, (ii) can generate giant fluctuations that drive signaling activity of the entire cell into a stochastic two-state switching regime. Our findings underscore the importance of molecular noise, arising not only in gene expression but also in protein networks.

Applications of Microfluidics in Quantitative Biology

Quantitative biology is dedicated to taking advantage of quantitative reasoning and advanced engineering technologies to make biology more predictable. Microfluidics, as an emerging technique, provides new approaches to precisely control fluidic conditions on small scales and collect data in high-throughput and quantitative manners. In this review, the authors present the relevant applications of microfluidics to quantitative biology based on two major categories (channel-based microfluidics and droplet-based microfluidics), and their typical features. We also envision some other microfluidic techniques that may not be employed in quantitative biology right now, but have great potential in the near future.

Drift and Behavior of E. coli Cells

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. Whereas maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

Emergent properties of bacterial chemotaxis pathway

The chemotaxis pathway of Escherichia coli is the most studied sensory system in prokaryotes. The highly conserved general architecture of this pathway consists of two modules which mediate signal transduction and adaptation. The signal transduction module detects and amplifies changes in environmental conditions and rapidly transmits these signals to control bacterial swimming behavior. The adaptation module gradually resets the activity and sensitivity of the first module after initial stimulation and thereby enables the temporal comparisons necessary for bacterial chemotaxis. Recent experimental and theoretical work has unraveled multiple quantitative features emerging from the interplay between these two modules. This has laid the groundwork for rationalization of these emerging properties in the context of the evolutionary optimization of the chemotactic behavior.

Taking chances and making mistakes: non-genetic phenotypic heterogeneity and its consequences for surviving in dynamic environments

Natural selection has shaped the strategies for survival and growth of microorganisms. The success of microorganisms depends not only on slow evolutionary tuning but also on the ability to adapt to unpredictable changes in their environment. In principle, adaptive strategies range from purely deterministic mechanisms to those that exploit the randomness intrinsic to many cellular and molecular processes. Depending on the environment and selective pressures, particular strategies can lie somewhere along this continuum. In recent years, non-genetic cell-to-cell differences have received a lot of attention, not least because of their potential impact on the ability of microbial populations to survive in dynamic environments. Using several examples, we describe the origins of spontaneous and induced mechanisms of phenotypic adaptation. We identify some of the commonalities of these examples and consider the potential role of chance and constraints in microbial phenotypic adaptation.

Recent advances and future prospects in bacterial and archaeal locomotion and signal transduction

Unraveling the structure and function of two-component and chemotactic signaling along with different aspects related to motility of bacteria and archaea are key research areas in modern microbiology. Escherichia coli is the traditional model organism to study chemotaxis signaling and motility. However, the recent study of a wide range of bacteria and even some archaea with different lifestyles has provided new insight into the eco-physiology of chemotaxis, which is essential for the host establishment of different pathogens or beneficial bacteria. The expanded range of model organisms has also permitted the study of chemosensory pathways unrelated to chemotaxis, multiple chemotaxis pathways within an organism, and new types of chemoreceptors. This research has greatly benefitted from technical advances in the field of cryo-microscopy that continues to reveal with increasing resolution the complexity and diversity of large protein complexes like the flagellar motor or chemoreceptor arrays. In addition, sensitive instruments now allow for an increasing number of experiments to be conducted at the single-cell level, thereby revealing information that is beginning to bridge the gap between individual cells and population behavior. Evidence has also accumulated showing that bacteria have evolved different mechanisms for surface sensing, which appears to be mediated by flagella and possibly type IV pili, and that the downstream signaling involves chemosensory pathways and two-component system based processes. Herein we summarize the recent advances and research tendencies in this field as presented at the latest Bacterial Locomotion and Signal Transduction (BLAST XIV) conference.

Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation

Many organisms navigate gradients by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles whenever attractant signal increases. This induces a functional coupling between movement and sensation, since tumbling probability is controlled by the internal state of the organism which, in turn, depends on previous signal levels. Although a negative feedback tends to maintain this internal state close to adapted levels, positive feedback can arise when motion up the gradient reduces tumbling probability, further boosting drift up the gradient. Importantly, such positive feedback can drive large fluctuations in the internal state, complicating analytical approaches. Previous studies focused on what happens when the negative feedback dominates the dynamics. By contrast, we show here that there is a large portion of physiologically-relevant parameter space where the positive feedback can dominate, even when gradients are relatively shallow. We demonstrate how large transients emerge because of non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the positive feedback, and further identify a fundamental nonlinearity that strongly amplifies their effect. Most importantly, this amplification is asymmetric, elongating runs in favorable directions and abbreviating others. The result is a “ratchet-like” gradient climbing behavior with drift speeds that can approach half the maximum run speed of the organism. Our results thus show that the classical drawback of run-and-tumble navigation—wasteful runs in the wrong direction—can be mitigated by exploiting the non-normal dynamics implicit in the run-and-tumble strategy.

Countless bacteria, larvae and even larger organisms (and robots) navigate gradients by alternating periods of straight motion (runs) with random reorientation events (tumbles). Control of the tumble probability is based on previously-encountered signals. A drawback of this run-and-tumble strategy is that occasional runs in the wrong direction are wasteful. Here we show that there is an operating regime within the organism’s internal parameter space where run-and-tumble navigation can be extremely efficient. We characterize how the positive feedback between behavior and sensed signal results in a type of non-equilibrium dynamics, with the organism rapidly tumbling after moving in the wrong direction and extending motion in the right ones. For a distant source, then, the organism can find it fast.

Stochastic gene expression: bacterial elites in chemotaxis

Even in the absence of genetic or environmental differences, cells differ from each other in their molecular make‐up. The consequences of these phenotypic differences are often not well understood. New work by Waite et al (2016) directly links variation in the molecular composition of individual bacterial cells to their population‐level performance.

Non-genetic diversity modulates population performance

Biological functions are typically performed by groups of cells that express predominantly the same genes, yet display a continuum of phenotypes. While it is known how one genotype can generate such non-genetic diversity, it remains unclear how different phenotypes contribute to the performance of biological function at the population level. We developed a microfluidic device to simultaneously measure the phenotype and chemotactic performance of tens of thousands of individual, freely swimming Escherichia coli as they climbed a gradient of attractant. We discovered that spatial structure spontaneously emerged from initially well-mixed wild-type populations due to non-genetic diversity. By manipulating the expression of key chemotaxis proteins, we established a causal relationship between protein expression, non-genetic diversity, and performance that was theoretically predicted. This approach generated a complete phenotype-to-performance map, in which we found a nonlinear regime. We used this map to demonstrate how changing the shape of a phenotypic distribution can have as large of an effect on collective performance as changing the mean phenotype, suggesting that selection could act on both during the process of adaptation.