Limits of feedback control in bacterial chemotaxis

Signal integration and adaptive sensory diversity tuning in Escherichia coli chemotaxis

In uncertain environments, phenotypic diversity can be advantageous for survival. However, as the environmental uncertainty decreases, the relative advantage of having diverse phenotypes decreases. Here, we show how populations of E. coli integrate multiple chemical signals to adjust sensory diversity in response to changes in the prevalence of each ligand in the environment. Measuring kinase activity in single cells, we quantified the sensitivity distribution to various chemoattractants in different mixtures of background stimuli. We found that when ligands bind uncompetitively, the population tunes sensory diversity to each signal independently, decreasing diversity when the signal's ambient concentration increases. However, among competitive ligands, the population can only decrease sensory diversity one ligand at a time. Mathematical modeling suggests that sensory diversity tuning benefits E. coli populations by modulating how many cells are committed to tracking each signal proportionally as their prevalence changes.

MotGen: a closed-loop bacterial motility control framework using generative adversarial networks

MOTIVATION

Many organisms' survival and behavior hinge on their responses to environmental signals. While research on bacteria-directed therapeutic agents has increased, systematic exploration of real-time modulation of bacterial motility remains limited. Current studies often focus on permanent motility changes through genetic alterations, restricting the ability to modulate bacterial motility dynamically on a large scale. To address this gap, we propose a novel real-time control framework for systematically modulating bacterial motility dynamics.

RESULTS

We introduce MotGen, a deep learning approach leveraging Generative Adversarial Networks to analyze swimming performance statistics of motile bacteria based on live cell imaging data. By tracking objects and optimizing cell trajectory mapping under environmentally altered conditions, we trained MotGen on a comprehensive statistical dataset derived from real image data. Our experimental results demonstrate MotGen's ability to capture motility dynamics from real bacterial populations with low mean absolute error in both simulated and real datasets. MotGen allows us to approach optimal swimming conditions for desired motility statistics in real-time. MotGen's potential extends to practical biomedical applications, including immune response prediction, by providing imputation of bacterial motility patterns based on external environmental conditions. Our short-term, in-situ interventions for controlling motility behavior offer a promising foundation for the development of bacteria-based biomedical applications.

AVAILABILITY AND IMPLEMENTATION

MotGen is presented as a combination of Matlab image analysis code and a machine learning workflow in Python. Codes are available at https://github.com/bgmseo/MotGen, for cell tracking and implementation of trained models to generate bacterial motility statistics.

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.

Flagellar dynamics reveal fluctuations and kinetic limit in the Escherichia coli chemotaxis network

The Escherichia coli chemotaxis network, by which bacteria modulate their random run/tumble swimming pattern to navigate their environment, must cope with unavoidable number fluctuations ("noise") in its molecular constituents like other signaling networks. The probability of clockwise (CW) flagellar rotation, or CW bias, is a measure of the chemotaxis network's output, and its temporal fluctuations provide a proxy for network noise. Here we quantify fluctuations in the chemotaxis signaling network from the switching statistics of flagella, observed using time-resolved fluorescence microscopy of individual optically trapped E. coli cells. This approach allows noise to be quantified across the dynamic range of the network. Large CW bias fluctuations are revealed at steady state, which may play a critical role in driving flagellar switching and cell tumbling. When the network is stimulated chemically to higher activity, fluctuations dramatically decrease. A stochastic theoretical model, inspired by work on gene expression noise, points to CheY activation occurring in bursts, driving CW bias fluctuations. This model also shows that an intrinsic kinetic ceiling on network activity places an upper limit on activated CheY and CW bias, which when encountered suppresses network fluctuations. This limit may also prevent cells from tumbling unproductively in steep gradients.

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.

Bacterial Proprioception: Can a Bacterium Sense Its Movement?

The evolution of the bacterial flagellum gave rise to motility and repurposing of a signaling network, now termed the chemotaxis network, enabled biasing of cell movements. This made it possible for the bacterium to seek out favorable chemical environments. To enable chemotaxis, the chemotaxis network sensitively detects extracellular chemical stimuli and appropriately modulates flagellar functions. Additionally, the flagellar motor itself is capable of detecting mechanical stimuli and adapts its structure and function in response, likely triggering a transition from planktonic to surface-associated lifestyles. Recent work has shown a link between the flagellar motor's response to mechanical stimuli and the chemotactic output. Here, we elaborate on this link and discuss how it likely helps the cell sense and adapt to changes in its swimming speeds in different environments. We discuss the mechanism whereby the motor precisely tunes its chemotaxis output under different mechanical loads, analogous to proprioception in higher order organisms. We speculate on the roles bacterial proprioception might play in a variety of phenomena including the transition to surface-associated lifestyles such as swarming and biofilms.

The dopamine circuit as a reward-taxis navigation system

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

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.

A biophysical threshold for biofilm formation

Bacteria are ubiquitous in our daily lives, either as motile planktonic cells or as immobilized surface-attached biofilms. These different phenotypic states play key roles in agriculture, environment, industry, and medicine; hence, it is critically important to be able to predict the conditions under which bacteria transition from one state to the other. Unfortunately, these transitions depend on a dizzyingly complex array of factors that are determined by the intrinsic properties of the individual cells as well as those of their surrounding environments, and are thus challenging to describe. To address this issue, here, we develop a generally-applicable biophysical model of the interplay between motility-mediated dispersal and biofilm formation under positive quorum sensing control. Using this model, we establish a universal rule predicting how the onset and extent of biofilm formation depend collectively on cell concentration and motility, nutrient diffusion and consumption, chemotactic sensing, and autoinducer production. Our work thus provides a key step toward quantitatively predicting and controlling biofilm formation in diverse and complex settings.

Influence of confinement on the spreading of bacterial populations

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings—despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading via motility that also incorporates cellular growth and division, and explicitly considers the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading—eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.

The spreading of bacteria through their environments critically impacts our everyday lives; it can be harmful, underlying the progression of infections and spoilage of foods, or can be beneficial, enabling the delivery of therapeutics, sustaining plant growth, and remediating polluted terrain. In all these cases, bacteria typically inhabit crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and regulate their spreading. However, existing models of spreading typically focus on cells in unconfined settings, and thus are frequently not applicable to cells in more complex environments. Here, we address this gap in knowledge by extending the classic Keller-Segel model of bacterial spreading via motility to also incorporate cellular growth and division, and explicitly consider the influence of confinement. Through numerical simulations of this extended model, we show how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations—in particular, driving a transition from chemotactic spreading of motile cells to growth-driven spreading via a slower, jammed front. These results provide a foundation for further investigations of the influence of confinement on bacterial spreading, both by yielding testable predictions for future experiments, and by providing guidelines to predict and control the dynamics of bacterial populations in complex and crowded environments.

The Effect of the Second Messenger c-di-GMP on Bacterial Chemotaxis in Escherichia coli

c-di-GMP is a ubiquitous bacterial second messenger that plays a central regulatory role in diverse biological processes. c-di-GMP was known to regulate chemotaxis in multiple bacterial species, but its effect on Escherichia coli chemotaxis remained unclear. As an effector of c-di-GMP in E. coli, YcgR when bound with c-di-GMP interacts with the flagellar motor to reduce its speed and its probability of rotating clockwise (CW bias). Here, we found that a significant fraction of the c-di-GMP::YcgR dynamically exchange between the motor and the cytosol. Through fluorescent measurements, we found that there was no competitive binding between the chemotaxis response regulator CheY-P and c-di-GMP::YcgR to the motor. To test the influence of elevated c-di-GMP levels on the chemotaxis pathway, we measured the chemotactic responses of E. coli cells using a FRET assay, finding that elevated c-di-GMP levels had no effect on the upstream part of chemotaxis pathway down to the level of CheY-P concentration. This suggested that the possible effect of elevated c-di-GMP levels on chemotactic motion was through regulation of motor speed and CW bias. Using stochastic simulations of chemotactic swimming, we showed that the effects of reducing motor speed and decreasing CW bias on chemotactic drift velocity are compensating for each other, resulting in minimal effect of elevated c-di-GMP levels on E. coli chemotaxis. Therefore, elevated c-di-GMP levels promote the transition from motile to sedentary forms of bacterial life by reducing the bacterial swimming speed and CW bias, while still maintaining a nearly intact chemotaxis capability in E. coli. IMPORTANCE The ubiquitous bacterial second messenger c-di-GMP was known to regulate chemotaxis in many bacterial species, but its effect on E. coli chemotaxis was unclear. Here we studied the effect of elevated c-di-GMP levels on chemotaxis in E. coli. We found that the binding of c-di-GMP::YcgR (its effector) and the chemotaxis response regulator CheY-P to the flagellar motor are noncompetitive, and elevated c-di-GMP levels do not affect the upstream part of the chemotaxis pathway down to the level of CheY-P concentration. Elevated c-di-GMP levels exert direct effects on the flagellar motor by reducing its speed and CW bias, but the resulting effects on chemotaxis performance are compensating for each other. Our findings here showed that elevated c-di-GMP levels maintain a nearly intact chemotaxis capability when promoting the transition from motile to sedentary forms of bacterial life in E. coli.

Chemotactic smoothing of collective migration

Collective migration—the directed, coordinated motion of many self-propelled agents—is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient—revealing a population-scale consequence of the manner in which individual cells transduce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.

Flocks of birds, schools of fish and herds of animals are all good examples of collective migration, where individuals co-ordinate their behavior to improve survival. This process also happens on a cellular level; for example, when bacteria consume a nutrient in their surroundings, they will collectively move to an area with a higher concentration of food via a process known as chemotaxis.

Several studies have examined how disturbing collective migration can cause populations to fall apart. However, little is known about how groups withstand these interferences. To investigate, Bhattacharjee, Amchin, Alert et al. studied bacteria called Escherichia coli as they moved through a gel towards nutrients.

The E. coli were injected into the gel using a three-dimensional printer, which deposited the bacteria into a wiggly shape that forces the cells apart, making it harder for them to move as a collective group. However, as the bacteria migrated through the gel, they smoothed out the line and gradually made it straighter so they could continue to travel together over longer distances.

Computer simulations revealed that this smoothing process is achieved by differences in how the cells respond to local nutrient levels based on their position. Bacteria towards the front of the group are exposed to more nutrients, causing them to become oversaturated and respond less effectively to the nutrient gradient. As a result, they move more slowly, allowing the cells behind them to eventually catch-up.

These findings reveal a general mechanism in which limitations in how individuals sense and respond to an external signal (in this case local nutrient concentrations) allows them to continue migrating together. This mechanism may apply to other systems that migrate via chemotaxis, as well as groups whose movement is directed by different external factors, such as temperature and light intensity.

Effect of receptor cooperativity on methylation dynamics in bacterial chemotaxis with weak and strong gradient

We study methylation dynamics of the chemoreceptors as an Escherichia coli cell moves around in a spatially varying chemoattractant environment. We consider attractant concentration with strong and weak spatial gradient. During the uphill and downhill motion of the cell along the gradient, we measure the temporal variation of average methylation level of the receptor clusters. Our numerical simulations we show that the methylation dynamics depends sensitively on the size of the receptor clusters and also on the strength of the gradient. At short times after the beginning of a run, the methylation dynamics is mainly controlled by short runs which are generally associated with high receptor activity. This results in demethylation at short times. But for intermediate or large times, long runs play an important role and depending on receptor cooperativity or gradient strength, the qualitative variation of methylation can be completely different in this time regime. For weak gradient, both for uphill and downhill runs, after the initial demethylation, we find methylation level increases steadily with time for all cluster sizes. Similar qualitative behavior is observed for strong gradient during uphill runs as well. However, the methylation dynamics for downhill runs in strong gradient show highly nontrivial dependence on the receptor cluster size. We explain this behavior as a result of interplay between the sensing and adaptation modules of the signaling network.

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.

A mathematical model for Escherichia coli chemotaxis to competing stimuli

Chemotactic bacteria sense and respond to temporal and spatial gradients of chemical cues in their surroundings. This phenomenon plays a critical role in many microbial processes such as groundwater bioremediation, microbially enhanced oil recovery, nitrogen fixation in legumes, and pathogenesis of the disease. Chemical heterogeneity in these natural systems may produce numerous competing signals from various directions. Predicting the migration behavior of bacterial populations under such conditions is necessary for designing effective treatment schemes. In this study, experimental studies and mathematical models are reported for the chemotactic response of Escherichia coli to a combination of attractant (α-methylaspartate) and repellent (NiCl₂ ), which bind to the same transmembrane receptor complex. The model describes the binding of chemoeffectors and phosphorylation of the kinase in the signal transduction mechanism. Chemotactic parameters of E. coli (signaling efficiency σ , stimuli sensitivity coefficient γ , and repellent sensitivity coefficient κ ) were determined by fitting the model with experimental results for individual stimuli. Interestingly, our model naturally identifies NiCl₂ as a repellent for κ > 1 . The model is capable of describing quantitatively the response to the individual attractant and repellent, and correctly predicts the change in direction of bacterial population migration for competing stimuli with a twofold increase in repellent concentration.

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.

Production and Characterization of Motile and Chemotactic Bacterial Minicells

Minicells are nanosized membrane vesicles produced by bacteria. Minicells are chromosome-free but contain cellular biosynthetic and metabolic machinery, and they are robust due to the protection provided by the bacterial cell envelope, which makes them potentially highly attractive in biomedical applications. However, the applicability of minicells and other nanoparticle-based delivery systems is limited by their inefficient accumulation at the target. Here we engineered the minicell-producing Escherichia coli strain to overexpress flagellar genes, which enables the generation of motile minicells. We subsequently performed an experimental and theoretical analysis of the minicell motility and their responses to gradients of chemoeffectors. Despite important differences between the motility of minicells and normal bacterial cells, minicells were able to bias their movement in chemical gradients and to accumulate toward the sources of chemoattractants. Such motile and chemotactic minicells may thus be applicable for an active effector delivery and specific targeting of tissues and cells according to their metabolic profiles.

Amylases: Biofilm Inducer or Biofilm Inhibitor?

Biofilm is a syntrophic association of sessile groups of microbial cells that adhere to biotic and abiotic surfaces with the help of pili and extracellular polymeric substances (EPS). EPSs also prevent penetration of antimicrobials/antibiotics into the sessile groups of cells. Hence, methods and agents to avoid or remove biofilms are urgently needed. Enzymes play important roles in the removal of biofilm in natural environments and may be promising agents for this purpose. As the major component of the EPS is polysaccharide, amylase has inhibited EPS by preventing the adherence of the microbial cells, thus making amylase a suitable antimicrobial agent. On the other hand, salivary amylase binds to amylase-binding protein of plaque-forming Streptococci and initiates the formation of biofilm. This review investigates the contradictory actions and microbe-associated genes of amylases, with emphasis on their structural and functional characteristics.

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.

Multi-bit Boolean model for chemotactic drift of Escherichia coli

Dynamic biological systems can be modelled to an equivalent modular structure using Boolean networks (BNs) due to their simple construction and relative ease of integration. The chemotaxis network of the bacterium Escherichia coli (E. coli) is one of the most investigated biological systems. In this study, the authors developed a multi-bit Boolean approach to model the drifting behaviour of the E. coli chemotaxis system. Their approach, which is slightly different than the conventional BNs, is designed to provide finer resolution to mimic high-level functional behaviour. Using this approach, they simulated the transient and steady-state responses of the chemoreceptor sensory module. Furthermore, they estimated the drift velocity under conditions of the exponential nutrient gradient. Their predictions on chemotactic drifting are in good agreement with the experimental measurements under similar input conditions. Taken together, by simulating chemotactic drifting, they propose that multi-bit Boolean methodology can be used for modelling complex biological networks. Application of the method towards designing bio-inspired systems such as nano-bots is discussed.

Protein Activity Sensing in Bacteria in Regulating Metabolism and Motility

Bacteria have evolved complex sensing and signaling systems to react to their changing environments, most of which are present in all domains of life. Canonical bacterial sensing and signaling modules, such as membrane-bound ligand-binding receptors and kinases, are very well described. However, there are distinct sensing mechanisms in bacteria that are less studied. For instance, the sensing of internal or external cues can also be mediated by changes in protein conformation, which can either be implicated in enzymatic reactions, transport channel formation or other important cellular functions. These activities can then feed into pathways of characterized kinases, which translocate the information to the DNA or other response units. This type of bacterial sensory activity has previously been termed protein activity sensing. In this review, we highlight the recent findings about this non-canonical sensory mechanism, as well as its involvement in metabolic functions and bacterial motility. Additionally, we explore some of the specific proteins and protein-protein interactions that mediate protein activity sensing and their downstream effects. The complex sensory activities covered in this review are important for bacterial navigation and gene regulation in their dynamic environment, be it host-associated, in microbial communities or free-living.

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.

Chemotactic behaviour of Escherichia coli at high cell density

At high cell density, swimming bacteria exhibit collective motility patterns, self-organized through physical interactions of a however still debated nature. Although high-density behaviours are frequent in natural situations, it remained unknown how collective motion affects chemotaxis, the main physiological function of motility, which enables bacteria to follow environmental gradients in their habitats. Here, we systematically investigate this question in the model organism Escherichia coli, varying cell density, cell length, and suspension confinement. The characteristics of the collective motion indicate that hydrodynamic interactions between swimmers made the primary contribution to its emergence. We observe that the chemotactic drift is moderately enhanced at intermediate cell densities, peaks, and is then strongly suppressed at higher densities. Numerical simulations reveal that this suppression occurs because the collective motion disturbs the choreography necessary for chemotactic sensing. We suggest that this physical hindrance imposes a fundamental constraint on high-density behaviours of motile bacteria, including swarming and the formation of multicellular aggregates and biofilms.

Maximal information transmission is compatible with ultrasensitive biological pathways

Cells are often considered input-output devices that maximize the transmission of information by converting extracellular stimuli (input) via signaling pathways (communication channel) to cell behavior (output). However, in biological systems outputs might feed back into inputs due to cell motility, and the biological channel can change by mutations during evolution. Here, we show that the conventional channel capacity obtained by optimizing the input distribution for a fixed channel may not reflect the global optimum. In a new approach we analytically identify both input distributions and input-output curves that optimally transmit information, given constraints from noise and the dynamic range of the channel. We find a universal optimal input distribution only depending on the input noise, and we generalize our formalism to multiple outputs (or inputs). Applying our formalism to Escherichia coli chemotaxis, we find that its pathway is compatible with optimal information transmission despite the ultrasensitive rotary motors.

Directional Switching Mechanism of the Bacterial Flagellar Motor

Bacteria sense temporal changes in extracellular stimuli via sensory signal transducers and move by rotating flagella towards into a favorable environment for their survival. Each flagellum is a supramolecular motility machine consisting of a bi-directional rotary motor, a universal joint and a helical propeller. The signal transducers transmit environmental signals to the flagellar motor through a cytoplasmic chemotactic signaling pathway. The flagellar motor is composed of a rotor and multiple stator units, each of which acts as a transmembrane proton channel to conduct protons and exert force on the rotor. FliG, FliM and FliN form the C ring on the cytoplasmic face of the basal body MS ring made of the transmembrane protein FliF and act as the rotor. The C ring also serves as a switching device that enables the motor to spin in both counterclockwise (CCW) and clockwise (CW) directions. The phosphorylated form of the chemotactic signaling protein CheY binds to FliM and FliN to induce conformational changes of the C ring responsible for switching the direction of flagellar motor rotation from CCW to CW. In this mini-review, we will describe current understanding of the switching mechanism of the bacterial flagellar motor.

Bacterial chemotaxis in a microfluidic T-maze reveals strong phenotypic heterogeneity in chemotactic sensitivity

Many microorganisms have evolved chemotactic strategies to exploit the microscale heterogeneity that frequently characterizes microbial habitats. Chemotaxis has been primarily studied as an average characteristic of a population, with little regard for variability among individuals. Here, we adopt a classic tool from animal ecology - the T-maze - and implement it at the microscale by using microfluidics to expose bacteria to a sequence of decisions, each consisting of migration up or down a chemical gradient. Single-cell observations of clonal Escherichia coli in the maze, coupled with a mathematical model, reveal that strong heterogeneity in the chemotactic sensitivity coefficient exists even within clonal populations of bacteria. A comparison of different potential sources of heterogeneity reveals that heterogeneity in the T-maze originates primarily from the chemotactic sensitivity coefficient, arising from a distribution of pathway gains. This heterogeneity may have a functional role, for example in the context of migratory bet-hedging strategies.

Bet-hedging strategies in expanding populations

In ecology, species can mitigate their extinction risks in uncertain environments by diversifying individual phenotypes. This observation is quantified by the theory of bet-hedging, which provides a reason for the degree of phenotypic diversity observed even in clonal populations. Bet-hedging in well-mixed populations is rather well understood. However, many species underwent range expansions during their evolutionary history, and the importance of phenotypic diversity in such scenarios still needs to be understood. In this paper, we develop a theory of bet-hedging for populations colonizing new, unknown environments that fluctuate either in space or time. In this case, we find that bet-hedging is a more favorable strategy than in well-mixed populations. For slow rates of variation, temporal and spatial fluctuations lead to different outcomes. In spatially fluctuating environments, bet-hedging is favored compared to temporally fluctuating environments. In the limit of frequent environmental variation, no opportunity for bet-hedging exists, regardless of the nature of the environmental fluctuations. For the same model, bet-hedging is never an advantageous strategy in the well-mixed case, supporting the view that range expansions strongly promote diversification. These conclusions are robust against stochasticity induced by finite population sizes. Our findings shed light on the importance of phenotypic heterogeneity in range expansions, paving the way to novel approaches to understand how biodiversity emerges and is maintained.

Ecological populations are often exposed to unpredictable and variable environmental conditions. A number of strategies have evolved to cope with such uncertainty. One of them is stochastic phenotypic switching, by which some individuals in the community are enabled to tackle adverse conditions, even at the price of reducing overall growth in the short term. In this paper, we study the effectiveness of these “bet-hedging” strategies for a population in the process of colonizing new territory. We show that bet-hedging is more advantageous when the environment varies spatially rather than temporally, and infrequently rather than frequently.

Optimal methylation noise for best chemotactic performance of E. coli

In response to a concentration gradient of chemoattractant, E. coli bacterium modulates the rotational bias of flagellar motors which control its run-and-tumble motion, to migrate towards regions of high chemoattractant concentration. Presence of stochastic noise in the biochemical pathway of the cell has important consequences on the switching mechanism of motor bias, which in turn affects the runs and tumbles of the cell in a significant way. We model the intracellular reaction network in terms of coupled time evolution of three stochastic variables-kinase activity, methylation level, and CheY-P protein level-and study the effect of methylation noise on the chemotactic performance of the cell. In presence of a spatially varying nutrient concentration profile, a good chemotactic performance allows the cell to climb up the concentration gradient quickly and localize in the nutrient-rich regions in the long time limit. Our simulations show that the best performance is obtained at an optimal noise strength. While it is expected that chemotaxis will be weaker for very large noise, it is counterintuitive that the performance worsens even when noise level falls below a certain value. We explain this striking result by detailed analysis of CheY-P protein level statistics for different noise strengths. We show that when the CheY-P level falls below a certain (noise-dependent) threshold the cell tends to move down the concentration gradient of the nutrient, which has a detrimental effect on its chemotactic response. This threshold value decreases as noise is increased, and this effect is responsible for noise-induced enhancement of chemotactic performance. In a harsh chemical environment, when the nutrient degrades with time, the amount of nutrient intercepted by the cell trajectory is an effective performance criterion. In this case also, depending on the nutrient lifetime, we find an optimum noise strength when the performance is at its best.

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.

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.

Quantitative Modeling of Flagellar Motor-Mediated Adaptation

The bacterial flagellar motor is capable of adapting to changes in the concentrations of extracellular chemical stimuli by changing the composition of the switch complex of the flagellar motor. Such remodeling-based adaptation complements the receptor-mediated adaptation in the chemotaxis network to help maintain high sensitivity in the response of the motor to phospho-CheY concentrations, despite cell-to-cell variability in the abundances of chemotaxis proteins. In this chapter, a modeling approach is described that explains the mechanisms of switch-remodeling and motor-mediated adaptation. The approach is based on observations of structural differences, associated with the direction of motor rotation, that modulate the strength of FliM/FliN binding within the switch. By modulating the number of CheY-P-binding sites within the motor, remodeling maximizes sensitivity over a range of signal levels.

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.

Optimal chemotactic responses in stochastic environments

Although the “adaptive” strategy used by Escherichia coli has dominated our understanding of bacterial chemotaxis, the environmental conditions under which this strategy emerged is still poorly understood. In this work, we study the performance of various chemotactic strategies under a range of stochastic time- and space-varying attractant distributions in silico. We describe a novel “speculator” response in which the bacterium compare the current attractant concentration to the long-term average; if it is higher then they tumble persistently, while if it is lower than the average, bacteria swim away in search of more favorable conditions. We demonstrate how this response explains the experimental behavior of aerobically-grown Rhodobacter sphaeroides and that under spatially complex but slowly-changing nutrient conditions the speculator response is as effective as the adaptive strategy of E. coli.

Noise-Induced Increase of Sensitivity in Bacterial Chemotaxis

Flagellated bacteria, like Escherichia coli, can swim toward beneficial environments by modulating the rotational direction of their flagellar motors through a chemotaxis signal transduction network. The noise of this network, the random fluctuation of the intracellular concentration of the signal protein CheY-P with time, has been identified in studies of single cell behavioral variability, and found to be important in coordination of multiple motors in a bacterium and in enhancement of bacterial drift velocity in chemical gradients. Here, by comparing the behavioral difference between motors of wild-type E. coli and mutants without signal noise, we measured the magnitude of this noise in wild-type cells, and found that the noise increases the sensitivity of the bacterial chemotaxis network downstream at the level of the flagellar motor. This provided a simple mechanism for the noise-induced enhancement of chemotactic drift, which we confirmed by simulating the E. coli chemotactic motion in various spatial profiles of chemo-attractant concentration.

Reconstructing the genotype-to-fitness map for the bacterial chemotaxis network and its emergent behavioural phenotypes

The signal-transduction network responsible for chemotaxis in Escherichia coli has been characterised in extraordinary detail. Yet, relatively little is known about eco-evolutionary aspects of chemotaxis, such as how the network has been shaped by selection and to what extent natural populations may fine-tune their chemotactic behaviour to the ecological conditions. To address these questions, we here develop an evolutionary-systems-biology model of the chemotaxis network of E. coli, which we apply to estimate the resource accumulation rate (here used as a proxy for fitness) of wildtype and a large number of potential mutant genotypes. Mutant genotypes differ from the wildtype in the concentrations of one or more constituent proteins of the chemotaxis signalling network or in one or more of its kinetic parameters. To guarantee model consistency across the genotype space, we explicitly incorporated biochemical constraints that underly observed phenotypic trade-offs. The model was validated by reconstructing the phenotypic properties of several known mutant genotypes. We also characterised differences in the fitness distribution between genotypes, and reconstructed adaptive walks in genotype space for populations exposed to different environmental conditions. We found that the local fitness landscape is rugged, due to non-additive interactions between mutations. When selection has a consistent direction, just a few adaptive mutations are required to reach a local peak, and different local peaks can be reached by adaptive walks starting from the same initial genotype. However, when the direction of selection is fluctuating, evolutionary paths are much longer and genotype space is explored further. Longer adaptive walks were also observed when evolution was started from a low-fitness genotype such as a CheZ knockout mutant. In line with empirical observations, the initial ΔcheZ mutant did not respond to a step-down stimulus, but a dynamic response similar to the wildtype was recovered following the fixation of compensatory mutations.

A Boolean approach to bacterial chemotaxis

Bacterium such as Escherichia coli (E. coli) show biased Brownian motion in different chemical concentration gradients. This chemical sensitive motility or chemotaxis has gained considerable interest among scientists for some remarkable features such as chemo-sensory dynamic range, adaptation, diffusion and drift. A Boolean model of the whole chemotaxis process has been developed in this manuscript. The response of the circuit is in accordance with the experimental results available in the literature, providing indirect validation of the model. This simple Boolean network (BN) can be easily integrated into the paradigm of modular whole cell modelling. Another crucial application is in designing bio-inspired micro-robots to detect certain spatio-temporal chemical signatures.

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.

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.

Direct Correlation between Motile Behavior and Protein Abundance in Single Cells

Understanding how stochastic molecular fluctuations affect cell behavior requires the quantification of both behavior and protein numbers in the same cells. Here, we combine automated microscopy with in situ hydrogel polymerization to measure single-cell protein expression after tracking swimming behavior. We characterized the distribution of non-genetic phenotypic diversity in Escherichia coli motility, which affects single-cell exploration. By expressing fluorescently tagged chemotaxis proteins (CheR and CheB) at different levels, we quantitatively mapped motile phenotype (tumble bias) to protein numbers using thousands of single-cell measurements. Our results disagreed with established models until we incorporated the role of CheB in receptor deamidation and the slow fluctuations in receptor methylation. Beyond refining models, our central finding is that changes in numbers of CheR and CheB affect the population mean tumble bias and its variance independently. Therefore, it is possible to adjust the degree of phenotypic diversity of a population by adjusting the global level of expression of CheR and CheB while keeping their ratio constant, which, as shown in previous studies, confers functional robustness to the system. Since genetic control of protein expression is heritable, our results suggest that non-genetic diversity in motile behavior is selectable, supporting earlier hypotheses that such diversity confers a selective advantage.

Cell-to-cell variations in protein numbers due to random fluctuations at the molecular level lead to cell-to-cell variations in behavior. To maintain predictable responses, signaling networks have evolved robustness against noise, but in some situations phenotypic diversity in a clonal population can be beneficial as a bet hedging or division of labor strategy. Investigating of how random molecular fluctuations affect cell behavior requires to measure biological parameters at different scales. Here, we report a new experiment that allows the measure of both protein numbers and behavior in cells that are free to move in their environment. Using Escherichia coli, a model system for the study of cellular behavior, we investigated the effects variations in the numbers of the chemo-receptor modification enzymes on single-cell swimming behavior. We found that the mean and variance of the behavior can be adjusted independently in the population by adjusting protein expression. This mechanism allows for the genetic selection of phenotypic diversity without disrupting correlations in protein expression that are important for the overall robustness of the chemotaxis system.

The Role of Adaptation in Bacterial Speed Races

Evolution of biological sensory systems is driven by the need for efficient responses to environmental stimuli. A paradigm among prokaryotes is the chemotaxis system, which allows bacteria to navigate gradients of chemoattractants by biasing their run-and-tumble motion. A notable feature of chemotaxis is adaptation: after the application of a step stimulus, the bacterial running time relaxes to its pre-stimulus level. The response to the amino acid aspartate is precisely adapted whilst the response to serine is not, in spite of the same pathway processing the signals preferentially sensed by the two receptors Tar and Tsr, respectively. While the chemotaxis pathway in E. coli is well characterized, the role of adaptation, its functional significance and the ecological conditions where chemotaxis is selected, are largely unknown. Here, we investigate the role of adaptation in the climbing of gradients by E. coli. We first present theoretical arguments that highlight the mechanisms that control the efficiency of the chemotactic up-gradient motion. We discuss then the limitations of linear response theory, which motivate our subsequent experimental investigation of E. coli speed races in gradients of aspartate, serine and combinations thereof. By using microfluidic techniques, we engineer controlled gradients and demonstrate that bacterial fronts progress faster in equal-magnitude gradients of serine than aspartate. The effect is observed over an extended range of concentrations and is not due to differences in swimming velocities. We then show that adding a constant background of serine to gradients of aspartate breaks the adaptation to aspartate, which results in a sped-up progression of the fronts and directly illustrate the role of adaptation in chemotactic gradient-climbing.

Biological sensory pathways are presumed to evolve for the processing of environmental information, yet quantitative evidence is scant. Chemotaxis allows bacteria to sense chemical gradients but their ecological distribution, e.g. whether natural gradients sensed by E. coli change slowly or rapidly in space and time, is unknown. That distribution matters, as it controls constraints and selective pressure acting on the pathway. We used microfluidic devices to generate controlled chemoattractant gradients and measure the speed of bacterial climbing of those gradients. We could thereby assay the impact of adaptation properties of the chemotaxis pathway onto the progression of gradient climbing. We specifically show that loss of adaptation, induced by adding a background of serine to gradients of aspartate, leads to a faster progression of the bacteria along the chemoattractant gradient. We finally discuss why our experiments suggest that ecological conditions are likely to involve chemoattractant profiles more complex than constant gradients usually considered in the laboratory.

Bacterial chemotaxis: information processing, thermodynamics, and behavior

Escherichia coli has long been used as a model organism due to the extensive experimental characterization of its pathways and molecular components. Take chemotaxis as an example, which allows bacteria to sense and swim in response to chemicals, such as nutrients and toxins. Many of the pathway's remarkable sensing and signaling properties are now concisely summarized in terms of design (or engineering) principles. More recently, new approaches from information theory and stochastic thermodynamics have begun to address how pathways process environmental stimuli and what the limiting factors are. However, to fully capitalize on these theoretical advances, a closer connection with single-cell experiments will be required.

Importance of Multiple Methylation Sites in Escherichia coli Chemotaxis

Bacteria navigate within inhomogeneous environments by temporally comparing concentrations of chemoeffectors over the course of a few seconds and biasing their rate of reorientations accordingly, thereby drifting towards more favorable conditions. This navigation requires a short-term memory achieved through the sequential methylations and demethylations of several specific glutamate residues on the chemotaxis receptors, which progressively adjusts the receptors' activity to track the levels of stimulation encountered by the cell with a delay. Such adaptation also tunes the receptors' sensitivity according to the background ligand concentration, enabling the cells to respond to fractional rather than absolute concentration changes, i.e. to perform logarithmic sensing. Despite the adaptation system being principally well understood, the need for a specific number of methylation sites remains relatively unclear. Here we systematically substituted the four glutamate residues of the Tar receptor of Escherichia coli by non-methylated alanine, creating a set of 16 modified receptors with a varying number of available methylation sites and explored the effect of these substitutions on the performance of the chemotaxis system. Alanine substitutions were found to desensitize the receptors, similarly but to a lesser extent than glutamate methylation, and to affect the methylation and demethylation rates of the remaining sites in a site-specific manner. Each substitution reduces the dynamic range of chemotaxis, by one order of magnitude on average. The substitution of up to two sites could be partly compensated by the adaptation system, but the full set of methylation sites was necessary to achieve efficient logarithmic sensing.

Response thresholds in bacterial chemotaxis

Stimulation of Escherichia coli by exponential ramps of chemoattractants generates step changes in the concentration of the response regulator, CheY-P. Because flagellar motors are ultrasensitive, this should change the fraction of time that motors spin clockwise, the CWbias. However, early work failed to show changes in CWbias when ramps were shallow. This was explained by a model for motor remodeling that predicted plateaus in plots of CWbias versus [CheY-P]. We looked for these plateaus by examining distributions of CWbias in populations of cells with different mean [CheY-P]. We did not find such plateaus. Hence, we repeated the work on shallow ramps and found that motors did indeed respond. These responses were quantitatively described by combining motor remodeling with ultrasensitivity in a model that exhibited high sensitivities over a wide dynamic range.