Behaviors and strategies of bacterial navigation in chemical and nonchemical gradients

Collective condensation and auto-aggregation of Escherichia coli in uniform acidic environments

Chemotaxis-the movement of cells along chemical gradients-leads to collective behaviors when cells coordinate their movements. Here, using Escherichia coli as a model, we demonstrate a distinct type of bacterial collective response in acidic environments containing organic acids. Bacterial populations immersed in such environments collectively condensed into millimeter-sized focal points. Furthermore, this bacterial condensation fostered the formation of small, tightly packed cell aggregates, resembling non-surface-attached biofilms. These cell aggregates were physically displaced by the free-swimming condensing cells, leading to the segregation of the two cell populations. Bacterial condensation relied on feedback between the tendency of these bacteria to neutralize the pH and their chemotactic repulsion from low pH. Sustained cell condensation occurred when the bacteria occupied only part of the acidic environment, either dynamically or due to physical constraints. Such condensed bacterial populations can mitigate acid stress more efficiently, a principle that may be applicable to other stress conditions.

Potassium-mediated bacterial chemotactic response

Bacteria in biofilms secrete potassium ions to attract free swimming cells. However, the basis of chemotaxis to potassium remains poorly understood. Here, using a microfluidic device, we found that Escherichia coli can rapidly accumulate in regions of high potassium concentration on the order of millimoles. Using a bead assay, we measured the dynamic response of individual flagellar motors to stepwise changes in potassium concentration, finding that the response resulted from the chemotaxis signaling pathway. To characterize the chemotactic response to potassium, we measured the dose-response curve and adaptation kinetics via an Förster resonance energy transfer (FRET) assay, finding that the chemotaxis pathway exhibited a sensitive response and fast adaptation to potassium. We further found that the two major chemoreceptors Tar and Tsr respond differently to potassium. Tar receptors exhibit a biphasic response, whereas Tsr receptors respond to potassium as an attractant. These different responses were consistent with the responses of the two receptors to intracellular pH changes. The sensitive response and fast adaptation allow bacteria to sense and localize small changes in potassium concentration. The differential responses of Tar and Tsr receptors to potassium suggest that cells at different growth stages respond differently to potassium and may have different requirements for potassium.

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 responses of bacteria to a local source of conflicting effectors

To cope in complex environments, motile bacteria have developed a chemosensory system that integrates multiple cues and directs their motion toward regions that it deems favorable. However, we have a limited understanding of the principles that govern bacterial behavior in complex stimuli fields. Here, we followed the spatial redistribution of E. coli cells in perplexing environments created by a local source of both beneficial (nutrients) and hazardous (low pH or indole) effectors. We identified two fundamentally distinct collective responses: a ‘trade-off’ response, in which bacteria sharply accumulated at a distance from the source that reflected a trade-off between the propagating effectors, and a ‘bet-hedging’ response, in which part of the bacteria accumulated away from the source, avoiding the hazardous effector, while the other part evaded the repulsive force and accumulated at the source. In addition, we demonstrate that cells lacking the Tsr sensor swim toward both repellents and, surprisingly, even toward pH values well below 7. Using a numerical analysis, we could correlate the collective bacterial responses with fundamentally distinct chemotactic force fields created along the channel by the propagation of the effectors and their unique perception by the chemosensory system.

pH-taxis drives aerobic bacteria in duodenum to migrate into the pancreas with tumors

As oral or intestinal bacteria have been found in pancreatic cystic fluid and tumors, understanding bacterial migration from the duodenum into the pancreas via hepato-pancreatic duct is critical. Mathematical models of migration of aerobic bacteria from the duodenum to the pancreas with tumors were developed. Additionally, the bacterial distributions under the pH gradient and those under flow were measured in double-layer flow based microfluidic device and T-shaped cylinders. Migration of aerobic bacteria from the duodenum into pancreas is counteracted by bile and pancreatic juice flow but facilitated by pH-taxis from acidic duodenum fluid toward more favorable slightly alkaline pH in pancreatic juice. Additionally, the reduced flow velocity in cancer patients, due to compressed pancreatic duct by solid tumor, facilitates migration. Moreover, measured distribution of GFP E. coli under the pH gradient in a microfluidic device validated pH-tactic behaviors. Furthermore, Pseudomonas fluorescens in hydrochloride solution, but not in bicarbonate solution, migrated upstream against bicarbonate flow of > 20 μm/s, with an advancement at approximately 50 μm/s.

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

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.

Theoretical Constraints Imposed by Gradient Detection and Dispersal on Microbial Size in Astrobiological Environments

The capacity to sense gradients efficiently and acquire information about the ambient environment confers many advantages such as facilitating movement toward nutrient sources or away from toxic chemicals. The amplified dispersal evinced by organisms endowed with motility is possibly beneficial in related contexts. Hence, the connections between information acquisition, motility, and microbial size are explored from an explicitly astrobiological standpoint. By using prior theoretical models, the constraints on organism size imposed by gradient detection and motility are elucidated in the form of simple heuristic scaling relations. It is argued that environments such as alkaline hydrothermal vents, which are distinguished by the presence of steep gradients, might be conducive to the existence of "small" microbes (with radii of ≳0.1 μm) in principle, when only the above two factors are considered; other biological functions (e.g., metabolism and genetic exchange) could, however, regulate the lower bound on microbial size and elevate it. The derived expressions are potentially applicable to a diverse array of settings, including those entailing solvents other than water; for example, the lakes and seas of Titan. The article concludes with a brief exposition of how this formalism may be of practical and theoretical value to astrobiology.

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.

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.

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.

Escape band in Escherichia coli chemotaxis in opposing attractant and nutrient gradients

It is commonly believed that bacterial chemotaxis helps cells find food. However, not all attractants are nutrients, and not all nutrients are strong attractants. Here, by using microfluidic experiments, we studied Escherichia coli chemotaxis behavior in the presence of a strong chemoattractant (e.g., aspartate or methylaspartate) gradient and an opposing gradient of diluted tryptone broth (TB) growth medium. Our experiments showed that cells initially accumulate near the strong attractant source. However, after the peak cell density (h) reaches a critical value [Formula: see text], the cells form a "escape band" (EB) that moves toward the chemotactically weaker but metabolically richer nutrient source. By using various mutant strains and varying experimental conditions, we showed that the competition between Tap and Tar receptors is the key molecular mechanism underlying the formation of the escape band. A mathematical model combining chemotaxis signaling and cell growth was developed to explain the experiments quantitatively. The model also predicted that the width w and the peak position [Formula: see text] of EB satisfy two scaling relations: [Formula: see text] and [Formula: see text], where l is the channel length. Both scaling relations were verified by experiments. Our study shows that the combination of nutrient consumption, population growth, and chemotaxis with multiple receptors allows cells to search for optimal growth condition in complex environments with conflicting sources.

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.

Meaning, Autonomy, Symbolic Causality, and Free Will

As physical entities that translate symbols into physical actions, computers offer insights into the nature of meaning and agency. Physical symbol systems, generically known as agents, link abstractions to material actions. The meaning of a symbol is defined as the physical actions an agent takes when the symbol is encountered. An agent has autonomy when it has the power to select actions based on internal decision processes. Autonomy offers a partial escape from constraints imposed by direct physical influences such as gravity and the transfer of momentum. Swimming upstream is an example. Symbols are names that can designate other entities. It appears difficult to explain the use of names and symbols in terms of more primitive functionality. The ability to use names and symbols, that is, symbol grounding, may be a fundamental cognitive building block. The standard understanding of causality—wiggling X results in Y wiggling—applies to both physical causes (e.g., one billiard ball hitting another) and symbolic causes (e.g., a traffic light changing color). Because symbols are abstract, they cannot produce direct physical effects. For a symbol to be a cause requires that the affected entity determine its own response. This is called autonomous causality. This analysis of meaning and autonomy offers new perspectives on free will.

Stimulus sensing and signal processing in bacterial chemotaxis

Motile bacteria use chemotaxis to migrate towards environments that are favorable for growth and survival. The signaling pathway that mediates this behavior is largely conserved among prokaryotes, with Escherichia coli chemotaxis system being one of the simplest and the best studied. At the core of this pathway are the arrays of clustered chemoreceptors that detect, amplify and integrate various stimuli. Recent work provided deeper understanding of spatial organization and signal processing by these clusters and uncovered the variety of sensory mechanisms used to detect environmental stimuli. Moreover, studies of bacteria with different lifestyles have led to new insights into the diversity and evolutionary conservation of the chemotaxis pathway, as well as the physiological relevance of chemotactic behavior in different environments.

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.

Mobile microrobots for bioengineering applications

Untethered micron-scale mobile robots can navigate and non-invasively perform specific tasks inside unprecedented and hard-to-reach inner human body sites and inside enclosed organ-on-a-chip microfluidic devices with live cells. They are aimed to operate robustly and safely in complex physiological environments where they will have a transforming impact in bioengineering and healthcare. Research along this line has already demonstrated significant progress, increasing attention, and high promise over the past several years. The first-generation microrobots, which could deliver therapeutics and other cargo to targeted specific body sites, have just been started to be tested inside small animals toward clinical use. Here, we review frontline advances in design, fabrication, and testing of untethered mobile microrobots for bioengineering applications. We convey the most impactful and recent strategies in actuation, mobility, sensing, and other functional capabilities of mobile microrobots, and discuss their potential advantages and drawbacks to operate inside complex, enclosed and physiologically relevant environments. We lastly draw an outlook to provide directions in the veins of more sophisticated designs and applications, considering biodegradability, immunogenicity, mobility, sensing, and possible medical interventions in complex microenvironments.

Barrier Crossing in Escherichia coli Chemotaxis

We study cell navigation in spatiotemporally complex environments by developing a microfluidic racetrack device that creates a traveling wave with multiple peaks and a tunable wave speed. We find that while the population-averaged chemotaxis drift speed increases with wave speed for low wave speed, it decreases sharply for high wave speed. This reversed dependence of population-averaged chemotaxis drift speed on wave speed is caused by a "barrier-crossing" phenomenon, where a cell hops backwards from one peak attractant location to the peak behind by crossing an unfavorable (barrier) region with low attractant concentrations. By using a coarse-grained model of chemotaxis, we map bacterial motility in an attractant field to the random motion of an overdamped particle in an effective potential. The observed barrier-crossing phenomenon of living cells and its dependence on the spatiotemporal profile of attractant concentration are explained quantitatively by Kramers reaction rate theory.

Interplay of chemical and thermal gradient on bacterial migration in a diffusive microfluidic device

Living systems are constantly under different combinations of competing gradients of chemical, thermal, pH, and mechanical stresses allied. The present work is about competing chemical and thermal gradients imposed on E. coli in a diffusive stagnant microfluidic environment. The bacterial cells were exposed to opposing and aligned gradients of an attractant (1 mM sorbitol) or a repellant (1 mM NiSO4) and temperature. The effects of the repellant/attractant and temperature on migration behavior, migration rate, and initiation time for migration have been reported. It has been observed that under competing gradients of an attractant and temperature, the nutrient gradient (gradient generated by cells itself) initiates directed migration, which, in turn, is influenced by temperature through the metabolic rate. Exposure to competing gradients of an inhibitor and temperature leads to the imposed chemical gradient governing the directed cell migration. The cells under opposing gradients of the repellant and temperature have experienced the longest decision time (∼60 min). The conclusion is that in a competing chemical and thermal gradient environment in the range of experimental conditions used in the present work, the migration of E. coli is always initiated and governed by chemical gradients (either generated by the cells in situ or imposed upon externally), but the migration rate and percentage of migration of cells are influenced by temperature, shedding insights into the importance of such gradients in deciding collective dynamics of such cells in physiological conditions.

Networked Chemoreceptors Benefit Bacterial Chemotaxis Performance

Motile bacteria use large receptor arrays to detect and follow chemical gradients in their environment. Extended receptor arrays, composed of networked signaling complexes, promote cooperative stimulus control of their associated signaling kinases. Here, we used structural lesions at the communication interface between core complexes to create an Escherichia coli strain with functional but dispersed signaling complexes. This strain allowed us to directly study how networking of signaling complexes affects chemotactic signaling and gradient-tracking performance. We demonstrate that networking of receptor complexes provides bacterial cells with about 10-fold-heightened detection sensitivity to attractants while maintaining a wide dynamic range over which receptor adaptational modifications can tune response sensitivity. These advantages proved especially critical for chemotaxis toward an attractant source under conditions in which bacteria are unable to alter the attractant gradient.

Chemoreceptor arrays are found in many motile bacteria. However, although our understanding of bacterial chemotaxis is quite detailed, the signaling and behavioral advantages of networked receptor arrays had not been directly studied in cells. We have recently shown that lesions in a key interface of the E. coli receptor array diminish physical connections and functional coupling between core signaling complexes while maintaining their basic signaling capacity. In this study, we exploited an interface 2 mutant to show, for the first time, that coupling between core complexes substantially enhances stimulus detection and chemotaxis performance.

Precision and variability in bacterial temperature sensing

In Escherichia coli, the ratio of the two most abundant chemoreceptors, Tar/Tsr, has become the focus of much attention in bacterial taxis studies. This ratio has been shown to change under various growth conditions and to determine the response of the bacteria to the environment. Here, we present a study that makes a quantitative link between the ratio Tar/Tsr and the favored temperature of the cell in a temperature gradient and in various chemical environments. From the steady-state density-profile of bacteria with one dominant thermo-sensor, Tar or Tsr, we deduce the response function of each receptor to temperature changes. Using the response functions of both receptors, we determine the relationship between the favored temperature of wild-type bacteria with mixed clusters of receptors and the receptor ratio. Our model is based on the assumption that the behavior of a wild-type bacterium in a temperature gradient is determined by a linear combination of the independent responses of the two receptors, factored by the receptor's relative abundance in the bacterium. This is confirmed by comparing our model predictions with measurements of the steady-state density-profile of several bacterial populations in a temperature gradient. Our results reveal that the density-profile of wild-type bacteria can be accurately described by measuring the distribution of the ratio Tar/Tsr in the population, which is then used to divide the population into groups with distinct Tar/Tsr values, whose behavior can be described in terms of independent Gaussian distributions. Each of these Gaussians is centered about the favored temperature of the subpopulation, which is determined by the receptor ratio, and has a width defined by the temperature-dependent speed and persistence time.

pH-Taxis of Biohybrid Microsystems

The last decade has seen an increasing number of studies developing bacteria and other cell-integrated biohybrid microsystems. However, the highly stochastic motion of these microsystems severely limits their potential use. Here, we present a method that exploits the pH sensing of flagellated bacteria to realize robust drift control of multi-bacteria propelled microrobots. Under three specifically configured pH gradients, we demonstrate that the microrobots exhibit both unidirectional and bidirectional pH-tactic behaviors, which are also observed in free-swimming bacteria. From trajectory analysis, we find that the swimming direction and speed biases are two major factors that contribute to their tactic drift motion. The motion analysis of microrobots also sheds light on the propulsion dynamics of the flagellated bacteria as bioactuators. It is expected that similar driving mechanisms are shared among pH-taxis, chemotaxis, and thermotaxis. By identifying the mechanism that drives the tactic behavior of bacteria-propelled microsystems, this study opens up an avenue towards improving the control of biohybrid microsystems. Furthermore, assuming that it is possible to tune the preferred pH of bioactuators by genetic engineering, these biohybrid microsystems could potentially be applied to sense the pH gradient induced by cancerous cells in stagnant fluids inside human body and realize targeted drug delivery.

Predicting chemical environments of bacteria from receptor signaling

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.

Outside the laboratory, bacteria live in complex microenvironments characterized by competition for space and available nutrients. Although often inaccessible by experiments, understanding the spatio-temporal dynamics of bacterial microenvironments is biomedically important. For instance, the chemical environment that symbiotic Escherichia coli encounter in the human gut relates to health of the gastrointestinal tract, gut metabolism, immune response, and tissue homeostasis. Other complex microenvironments include soil and biofilms. Assuming that bacterial sensory systems have evolved to optimally sense typical gradients, we treat signaling data, the signaling pathway with its architecture and reaction rates, and computer simulations of swimming bacteria in different gradients as “prior knowledge” to “reverse engineer” E. coli's habitat. Our identified gradients are exponentially shaped with wide-ranging rate values. These microenvironments most likely stem from local fluctuating nutrient sources and degradation by competing species, in which bacteria have evolved to swim with optimal performance.