Dependence of bacterial chemotaxis on gradient shape and adaptation rate

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.

Strong chemotaxis by marine bacteria towards polysaccharides is enhanced by the abundant organosulfur compound DMSP

The ability of marine bacteria to direct their movement in response to chemical gradients influences inter-species interactions, nutrient turnover, and ecosystem productivity. While many bacteria are chemotactic towards small metabolites, marine organic matter is predominantly composed of large molecules and polymers. Yet, the signalling role of these large molecules is largely unknown. Using in situ and laboratory-based chemotaxis assays, we show that marine bacteria are strongly attracted to the abundant algal polysaccharides laminarin and alginate. Unexpectedly, these polysaccharides elicited stronger chemoattraction than their oligo- and monosaccharide constituents. Furthermore, chemotaxis towards laminarin was strongly enhanced by dimethylsulfoniopropionate (DMSP), another ubiquitous algal-derived metabolite. Our results indicate that DMSP acts as a methyl donor for marine bacteria, increasing their gradient detection capacity and facilitating their access to polysaccharide patches. We demonstrate that marine bacteria are capable of strong chemotaxis towards large soluble polysaccharides and uncover a new ecological role for DMSP in enhancing this attraction. These navigation behaviours may contribute to the rapid turnover of polymers in the ocean, with important consequences for marine carbon cycling.

Individual-Based Modeling of Spatial Dynamics of Chemotactic Microbial Populations

One important direction of synthetic biology is to establish desired spatial structures from microbial populations. Underlying this structural development process are different driving factors, among which bacterial motility and chemotaxis serve as a major force. Here, we present an individual-based, biophysical computational framework for mechanistic and multiscale simulation of the spatiotemporal dynamics of motile and chemotactic microbial populations. The framework integrates cellular movement with spatial population growth, mechanical and chemical cellular interactions, and intracellular molecular kinetics. It is validated by a statistical comparison of single-cell chemotaxis simulations with reported experiments. The framework successfully captures colony range expansion of growing isogenic populations and also reveals chemotaxis-modulated, spatial patterns of a two-species amensal community. Partial differential equation-based models subsequently validate these simulation findings. This study provides a versatile computational tool to uncover the fundamentals of microbial spatial ecology as well as to facilitate the design of synthetic consortia for desired spatial patterns.

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.

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).

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.

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.

Direct Mapping from Intracellular Chemotaxis Signaling to Single-Cell Swimming Behavior

Bacterial chemotaxis allows bacteria to sense the chemical environment and modulate their swimming behavior accordingly. Although the intracellular chemotaxis signaling pathway has been studied extensively, experimental studies are still lacking that could provide direct link from the pathway output (the intracellular concentration of the phosphorylated form of the response regulator phosphorylated CheY (CheY-P)) to single-cell swimming behavior. Here, we measured the swimming behavior of individual Escherichia coli cells while simultaneously detecting the intracellular CheY-P concentration, thereby providing a direct relationship between the intracellular CheY-P concentration and the single-cell run-and-tumble behavior. The measured relationship is consistent with the ultrasensitivity of the motor switch and a "veto model" that describes the interaction among individual flagella, although contribution from the voting mechanism could not be ruled out.

A Multi-Scale Approach to Modeling E. coli Chemotaxis

The degree to which we can understand the multi-scale organization of cellular life is tied to how well our models can represent this organization and the processes that drive its evolution. This paper uses Vivarium-an engine for composing heterogeneous computational biology models into integrated, multi-scale simulations. Vivarium's approach is demonstrated by combining several sub-models of biophysical processes into a model of chemotactic E. coli that exchange molecules with their environment, express the genes required for chemotaxis, swim, grow, and divide. This model is developed incrementally, highlighting cross-compartment mechanisms that link E. coli to its environment, with models for: (1) metabolism and transport, with transport moving nutrients across the membrane boundary and metabolism converting them to useful metabolites, (2) transcription, translation, complexation, and degradation, with stochastic mechanisms that read real gene sequence data and consume base pairs and ATP to make proteins and complexes, and (3) the activity of flagella and chemoreceptors, which together support navigation in the environment.

From indication to decision: A hierarchical approach to model the chemotactic behavior of Escherichia coli

Reducing the complex behavior of living entities to its underlying physical and chemical processes is a formidable task in biology. Complex behaviors can be characterized as decision making: the ability to process the incoming information via an intracellular network and act upon this information to choose appropriate strategies. Motility is one such behavior that has been the focus many modeling efforts in the past. Our aim is to reduce the chemotactic behavior in Escherichia coli to its molecular constituents in order to paint a comprehensive and end-to-end picture of this intricate behavior. We utilize a hierarchical approach, consisting of three layers, to achieve this goal: at the first level, chemical reactions involved in chemotaxis are simulated. In the second level, the chemical reactions give rise to the mechanical movement of six independent flagella. At the last layer, the two lower layers are combined to allow a digital bacterium to receive information from its environment and swim through it with verve. Our results are in concert with the experimental studies concerning the motility of E.coli cells. In addition, we show that our detailed model of chemotaxis is reducible to a non-homogeneous Markov process.

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.

Effective Exploration Behavior for Chemical-Sensing Robots

Mobile robots that can effectively detect chemical effluents could be useful in a variety of situations, such as disaster relief or drug sniffing. Such a robot might mimic biological systems that exhibit chemotaxis, which is movement towards or away from a chemical stimulant in the environment. Some existing robotic exploration algorithms that mimic chemotaxis suffer from the problems of getting stuck in local maxima and becoming "lost", or unable to find the chemical if there is no initial detection. We introduce the use of the RapidCell algorithm for mobile robots exploring regions with potentially detectable chemical concentrations. The RapidCell algorithm mimics the biology behind the biased random walk of Escherichia coli (E. coli) bacteria more closely than traditional chemotaxis algorithms by simulating the chemical signaling pathways interior to the cell. For comparison, we implemented a classical chemotaxis controller and a controller based on RapidCell, then tested them in a variety of simulated and real environments (using phototaxis as a surrogate for chemotaxis). We also added simple obstacle avoidance behavior to explore how it affects the success of the algorithms. Both simulations and experiments showed that the RapidCell controller more fully explored the entire region of detectable chemical when compared with the classical controller. If there is no detectable chemical present, the RapidCell controller performs random walk in a much wider range, hence increasing the chance of encountering the chemical. We also simulated an environment with triple effluent to show that the RapidCell controller avoided being captured by the first encountered peak, which is a common issue for the classical controller. Our study demonstrates that mimicking the adapting sensory system of E. coli chemotaxis can help mobile robots to efficiently explore the environment while retaining their sensitivity to the chemical gradient.

Blue Light Is a Universal Signal for Escherichia coli Chemoreceptors

Blue light has been shown to elicit a tumbling response in Escherichia coli, a nonphototrophic bacterium. The exact mechanism of this phototactic response is still unknown. Here, we quantify phototaxis in E. coli by analyzing single-cell trajectories in populations of free-swimming bacteria before and after light exposure. Bacterial strains expressing only one type of chemoreceptor reveal that all five E. coli receptors (Aer, Tar, Tsr, Tap, and Trg) are capable of mediating responses to light. In particular, light exposure elicits a running response in the Tap-only strain, the opposite of the tumbling responses observed for all other strains. Therefore, light emerges as a universal stimulus for all E. coli chemoreceptors. We also show that blue light exposure causes a reversible decrease in swimming velocity, a proxy for proton motive force. This result is consistent with a previously proposed hypothesis that, rather than sensing light directly, chemoreceptors sense light-induced perturbations in proton motive force, although other factors are also likely to contribute.IMPORTANCE Our findings provide new insights into the mechanism of E. coli phototaxis, showing that all five chemoreceptor types respond to light and their interactions play an important role in cell behavior. Our results also open up new avenues for examining and manipulating E. coli taxis. Since light is a universal stimulus, it may provide a way to quantify interactions among different types of receptors. Because light is easier to control spatially and temporally than chemicals, it may be used to study swimming behavior in complex environments. Since phototaxis can cause migration of E. coli bacteria in light gradients, light may be used to control bacterial density for studying density-dependent processes in bacteria.

Effects of Advective-Diffusive Transport of Multiple Chemoattractants on Motility of Engineered Chemosensory Particles in Fluidic Environments

Motility behavior of an engineered chemosensory particle (ECP) in fluidic environments is driven by its responses to chemical stimuli. One of the challenges to understanding such behaviors lies in tracking changes in chemical signal gradients of chemoattractants and ECP-fluid dynamics as the fluid is continuously disturbed by ECP motion. To address this challenge, we introduce a new multiscale numerical model to simulate chemotactic swimming of an ECP in confined fluidic environments by accounting for motility-induced disturbances in spatiotemporal chemoattractant distributions. The model accommodates advective-diffusive transport of unmixed chemoattractants, ECP-fluid hydrodynamics at the ECP-fluid interface, and spatiotemporal disturbances in the chemoattractant concentrations due to particle motion. Demonstrative simulations are presented with an ECP, mimicking Escherichia coli (E. coli) chemotaxis, released into initially quiescent fluids with different source configurations of the chemoattractants N-methyl-L-aspartate and L-serine. Simulations demonstrate that initial distributions and temporal evolution of chemoattractants and their release modes (instantaneous vs. continuous, point source vs. distributed) dictate time histories of chemotactic motility of an ECP. Chemotactic motility is shown to be largely determined by spatiotemporal variation in chemoattractant concentration gradients due to transient disturbances imposed by ECP-fluid hydrodynamics, an observation not captured in previous numerical studies that relied on static chemoattractant concentration fields.

A hydrodynamic-stochastic model of chemotactic ciliated microorganisms

Biological systems like ciliated microorganisms are capable of responding to the external chemical gradients, a process known as chemotaxis. In this process, the internal signaling network of the microorganism is triggered due to binding of the chemoattractant molecules with the receptors on the surface of the body. This can alter the activity at the surface of the microorganism. We study the chemotaxis of ciliated microorganisms using the chiral squirmer model, a spherical body with a surface slip velocity. In the presence of a chemical gradient, the coefficients of the slip velocity get modified resulting in a change in the path followed by the body. We observe that the strength of the gradient is not the only parameter which controls the dynamics of the body but also the adaptation time plays a very significant role in the success of chemotaxis. The trajectory of the body is smooth if we ignore the discreteness in the ligand-receptor binding which is stochastic in nature. In the presence of the latter, the path is not only irregular but the whole dynamics of the body changes. We calculate the mean first passage time, by varying the strength of the chemical gradient and the adaptation time, to determine the success rate of chemotaxis.

Biophysical constraints determine the selection of phenotypic fluctuations during directed evolution

Phenotypes of individuals in a population of organisms are not fixed. Phenotypic fluctuations, which describe temporal variation of the phenotype of an individual or individual-to-individual variation across a population, are present in populations from microbes to higher animals. Phenotypic fluctuations can provide a basis for adaptation and be the target of selection. Here we present a theoretical and experimental investigation of the fate of phenotypic fluctuations in directed evolution experiments where phenotypes are subject to constraints. We show that selecting bacterial populations for fast migration through a porous environment drives a reduction in cell-to-cell variation across the population. Using sequencing and genetic engineering we study the genetic basis for this reduction in phenotypic fluctuations. We study the generality of this reduction by developing a simple, abstracted, numerical simulation model of the evolution of phenotypic fluctuations subject to constraints. Using this model we find that strong and weak selection generally lead respectively to increasing or decreasing cell-to-cell variation as a result of a bound on the selected phenotype under a wide range of parameters. However, other behaviors are also possible, and we describe the outcome of selection simulations for different model parameters and suggest future experiments. We analyze the mechanism of the observed reduction of phenotypic fluctuations in our experimental system, discuss the relevance of our abstract model to the experiment and explore its broader implications for evolution.

Quantitative Investigation of the Role of Intra-/Intercellular Dynamics in Bacterial Quorum Sensing

Bacteria utilize diffusible signals to regulate population density-dependent coordinated gene expression in a process called quorum sensing (QS). While the intracellular regulatory mechanisms of QS are well-understood, the effect of spatiotemporal changes in the population configuration on the sensitivity and robustness of the QS response remains largely unexplored. Using a microfluidic device, we quantitatively characterized the emergent behavior of a population of swimming E. coli bacteria engineered with the lux QS system and a GFP reporter. We show that the QS activation time follows a power law with respect to bacterial population density, but this trend is disrupted significantly by microscale variations in population configuration and genetic circuit noise. We then developed a computational model that integrates population dynamics with genetic circuit dynamics to enable accurate (less than 7% error) quantitation of the bacterial QS activation time. Through modeling and experimental analyses, we show that changes in spatial configuration of swimming bacteria can drastically alter the QS activation time, by up to 22%. The integrative model developed herein also enables examination of the performance robustness of synthetic circuits with respect to growth rate, circuit sensitivity, and the population's initial size and spatial structure. Our framework facilitates quantitative tuning of microbial systems performance through rational engineering of synthetic ribosomal binding sites. We have demonstrated this through modulation of QS activation time over an order of magnitude. Altogether, we conclude that predictive engineering of QS-based bacterial systems requires not only the precise temporal modulation of gene expression (intracellular dynamics) but also accounting for the spatiotemporal changes in population configuration (intercellular dynamics).

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.

FRET Analysis of the Chemotaxis Pathway Response

Most motile bacteria follow spatial gradients of chemical and physical stimuli in their environment. In Escherichia coli and other bacteria, the best characterized chemotaxis is in gradients of amino acids or sugars, but other physiological stimuli such as pH, osmolarity, redox potentials, and temperature are also known to elicit tactic responses. These multiple environmental stimuli are integrated and processed within a highly sophisticated chemotaxis network to generate coordinated chemotaxis behavior, which features high sensitivity, a wide dynamic range, and robustness against variations in background stimulation, protein levels, and temperature. Although early studies relied on behavioral analyses to characterize chemotactic responses in vivo, or on biochemical assays to study the pathway in vitro, we describe here a method to directly measure the intracellular pathway response using Förster resonance energy transfer (FRET). In E. coli, the most commonly used form of the FRET assay relies on the interaction between the phosphorylated response regulator CheY and its phosphatase CheZ to quantify activity of the histidine kinase CheA. We further describe a FRET assay for Bacillus subtilis, which employs CheY and the motor-associated phosphatase FliY as a FRET pair. In particular, we highlight the use of FRET to quantify pathway properties, including signal amplification, dynamic range, and kinetics of adaptation.

Multiple sources of slow activity fluctuations in a bacterial chemosensory network

Cellular networks are intrinsically subject to stochastic fluctuations, but analysis of the resulting noise remained largely limited to gene expression. The pathway controlling chemotaxis of Escherichia coli provides one example where posttranslational signaling noise has been deduced from cellular behavior. This noise was proposed to result from stochasticity in chemoreceptor methylation, and it is believed to enhance environment exploration by bacteria. Here we combined single-cell FRET measurements with analysis based on the fluctuation-dissipation theorem (FDT) to characterize origins of activity fluctuations within the chemotaxis pathway. We observed surprisingly large methylation-independent thermal fluctuations of receptor activity, which contribute to noise comparably to the energy-consuming methylation dynamics. Interactions between clustered receptors involved in amplification of chemotactic signals are also necessary to produce the observed large activity fluctuations. Our work thus shows that the high response sensitivity of this cellular pathway also increases its susceptibility to noise, from thermal and out-of-equilibrium processes.

A polar bundle of flagella can drive bacterial swimming by pushing, pulling, or coiling around the cell body

Bacteria swim in sequences of straight runs that are interrupted by turning events. They drive their swimming locomotion with the help of rotating helical flagella. Depending on the number of flagella and their arrangement across the cell body, different run-and-turn patterns can be observed. Here, we present fluorescence microscopy recordings showing that cells of the soil bacterium Pseudomonas putida that are decorated with a polar tuft of helical flagella, can alternate between two distinct swimming patterns. On the one hand, they can undergo a classical push-pull-push cycle that is well known from monopolarly flagellated bacteria but has not been reported for species with a polar bundle of multiple flagella. Alternatively, upon leaving the pulling mode, they can enter a third slow swimming phase, where they propel themselves with their helical bundle wrapped around the cell body. A theoretical estimate based on a random-walk model shows that the spreading of a population of swimmers is strongly enhanced when cycling through a sequence of pushing, pulling, and wrapped flagellar configurations as compared to the simple push-pull-push pattern.

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.

Predicting Escherichia coli's chemotactic drift under exponential gradient

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.

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.

Agent-based modelling in synthetic biology

Biological systems exhibit complex behaviours that emerge at many different levels of organization. These span the regulation of gene expression within single cells to the use of quorum sensing to co-ordinate the action of entire bacterial colonies. Synthetic biology aims to make the engineering of biology easier, offering an opportunity to control natural systems and develop new synthetic systems with useful prescribed behaviours. However, in many cases, it is not understood how individual cells should be programmed to ensure the emergence of a required collective behaviour. Agent-based modelling aims to tackle this problem, offering a framework in which to simulate such systems and explore cellular design rules. In this article, I review the use of agent-based models in synthetic biology, outline the available computational tools, and provide details on recently engineered biological systems that are amenable to this approach. I further highlight the challenges facing this methodology and some of the potential future directions.

Growth-dependent behavioral difference in bacterial chemotaxis

Cells can adjust to their growth environments and regulate their behavior accordingly. To study how cells accomplish this growth-dependent adjustment from the molecular to the behavioral level, we used bacterial chemotaxis as a model system to explore the behavioral difference for bacteria grown in nutrient-rich and nutrient-poor media. We found that bacteria grown in a nutrient-poor medium exhibit faster chemotaxis adaptation, and this enables them to respond more rapidly to a changing environment and increases their ability to localize to a nutrient concentration peak. We identified the molecular mechanisms behind this behavioral difference through coarse-grained modeling, and demonstrated its physiological consequences by simulating bacterial chemotactic motion in spatiotemporally varying environments and in a static environment with a nutrient concentration peak.

Environment determines evolutionary trajectory in a constrained phenotypic space

Constraints on phenotypic variation limit the capacity of organisms to adapt to the multiple selection pressures encountered in natural environments. To better understand evolutionary dynamics in this context, we select Escherichia coli for faster migration through a porous environment, a process which depends on both motility and growth. We find that a trade-off between swimming speed and growth rate constrains the evolution of faster migration. Evolving faster migration in rich medium results in slow growth and fast swimming, while evolution in minimal medium results in fast growth and slow swimming. In each condition parallel genomic evolution drives adaptation through different mutations. We show that the trade-off is mediated by antagonistic pleiotropy through mutations that affect negative regulation. A model of the evolutionary process shows that the genetic capacity of an organism to vary traits can qualitatively depend on its environment, which in turn alters its evolutionary trajectory.

DOI:http://dx.doi.org/10.7554/eLife.24669.001

In nature organisms face many challenges, and species adapt to their environment by changing heritable traits over the course of many generations. How organisms adapt is often limited by trade-offs, in which improving one trait can only come at the expense of another.

In the laboratory, scientists use well-controlled environments to study how populations adapt to specific challenges without interference from their natural habitat. Most experiments, however, only look at simple challenges and do not take into account that organisms in the wild face many pressures at the same time. Fraebel et al. wanted to know what happens when an organism’s performance depends on two traits that are restricted by a trade-off. The experiments used populations of the bacterium Escherichia coli, which can go through hundreds of generations in a week, providing ample opportunity to study mutations and their impact on heritable traits.

Through a combination of mathematical modeling and experiments, Fraebel et al. found that the environment is crucial for determining how bacteria adapt when their swimming speed and population growth rate are restricted by a trade-off. When nutrients are plentiful, E. coli populations evolve to spread faster by swimming more quickly despite growing more slowly. Yet, if nutrients are scarcer, the bacteria evolve to spread faster by growing more quickly despite swimming more slowly. In each scenario, the experiments identified single mutations that changed both swimming speed and growth rate by modifying regulatory activity in the cell.

A better understanding of how an organism’s genetic architecture, its environment and trade-offs are connected may help identify the traits that are most easily changed by mutations. The ultimate goal would be to be able to predict evolutionary responses to complex selection pressures.

DOI:http://dx.doi.org/10.7554/eLife.24669.002

A stochastic micro-machine inspired by bacterial chemotaxis

Inspired by bacterial chemotaxis, we propose and study the dynamics of a 3D hydrodynamical search-machine at micrometer scale. Chemotactic memory of the proposed system that is borrowed from bacteria, allows it to search the fluid medium and find the required target. As the motion in micron size length scale is dominated by random forces, we analyze the statistical properties of the model. Mean square displacements, orientational correlation functions and also the chemotactic index (CI) of the system are investigated in detail. Because of the chemotactic memory, the system shows superdiffusing displacements in all directions and the diffusion exponents are anisotropic for the directions along or perpendicular to a preferred direction given by the gradient of attractant molecules transmitted by the target.

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.

Perspectives in flow-based microfluidic gradient generators for characterizing bacterial chemotaxis

Chemotaxis is a phenomenon which enables cells to sense concentrations of certain chemical species in their microenvironment and move towards chemically favorable regions. Recent advances in microbiology have engineered the chemotactic properties of bacteria to perform novel functions, but traditional methods of characterizing chemotaxis do not fully capture the associated cell motion, making it difficult to infer mechanisms that link the motion to the microbiology which induces it. Microfluidics offers a potential solution in the form of gradient generators. Many of the gradient generators studied to date for this application are flow-based, where a chemical species diffuses across the laminar flow interface between two solutions moving through a microchannel. Despite significant research efforts, flow-based gradient generators have achieved mixed success at accurately capturing the highly subtle chemotactic responses exhibited by bacteria. Here we present an analysis encompassing previously published versions of flow-based gradient generators, the theories that govern their gradient-generating properties, and new, more practical considerations that result from experimental factors. We conclude that flow-based gradient generators present a challenge inherent to their design in that the residence time and gradient decay must be finely balanced, and that this significantly narrows the window for reliable observation and quantification of chemotactic motion. This challenge is compounded by the effects of shear on an ellipsoidal bacterium that causes it to preferentially align with the direction of flow and subsequently suppresses the cross-flow chemotactic response. These problems suggest that a static, non-flowing gradient generator may be a more suitable platform for chemotaxis studies in the long run, despite posing greater difficulties in design and fabrication.

Diffusion of Bacterial Cells in Porous Media

The chemotaxis signal transduction network regulates the biased random walk of many bacteria in favorable directions and away from harmful ones through modulating the frequency of directional reorientations. In mutants of diverse bacteria lacking the chemotaxis response, migration in classic motility agar, which constitutes a fluid-filled porous medium, is compromised; straight-swimming cells unable to tumble become trapped within the agar matrix. Spontaneous mutations that restore spreading have been previously observed in the enteric bacterium Escherichia coli, and recent work in other bacterial species has isolated and quantified different classes of nonchemotacting mutants exhibiting the same spreading phenotype. We present a theoretical description of bacterial diffusion in a porous medium-the natural habitat for many cell types-which elucidates how diverse modifications of the motility apparatus resulting in a nonzero tumbling frequency allows for unjamming of otherwise straight-swimming cells at internal boundaries and leads to net migration. A unique result of our analysis is increasing diffusive spread with increasing tumbling frequency in the small pore limit, consistent with earlier experimental observations but not captured by previous models. Our theoretical results, combined with a simple model of bacterial diffusion and growth in agar, are compared with our experimental measurements of swim ring expansion as a function of time, demonstrating good quantitative agreement. Our results suggest that the details of the cellular tumbling process may be adapted to enable bacteria to propagate efficiently through complex environments. For engineered, self-propelled microswimmers that navigate via alternating straight runs and changes in direction, these results suggest an optimal reorientation strategy for efficient migration in a porous environment with a given microarchitecture.

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.

Video processing analysis for the determination and evaluation of the chemotactic response in bacterial populations

The aim of the present work was to design a methodology based on video processing to obtain indicators of bacterial population motility that allow the quantitative and qualitative analysis and comparison of the chemotactic phenomenon with different attractants in the agarose-in plug bridge method. Video image sequences were processed applying Shannon's entropy to the intensity time series of each pixel, which conducted to a final pseudo colored image resembling a map of the dynamic bacterial clusters. Processed images could discriminate perfectly between positive and negative attractant responses at different periods of time from the beginning of the assay. An index of spatial and temporal motility was proposed to quantify the bacterial response. With this index, this video processing method allowed obtaining quantitative information of the dynamic changes in space and time from a traditional qualitative assay. We conclude that this computational technique, applied to the traditional agarose-in plug assay, has demonstrated good sensitivity for identifying chemotactic regions with a broad range of motility.

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.

Understanding the link between single cell and population scale responses of Escherichia coli in differing ligand gradients

We formulate an agent-based population model of Escherichia coli cells which incorporates a description of the chemotaxis signalling cascade at the single cell scale. The model is used to gain insight into the link between the signalling cascade dynamics and the overall population response to differing chemoattractant gradients. Firstly, we consider how the observed variation in total (phosphorylated and unphosphorylated) signalling protein concentration affects the ability of cells to accumulate in differing chemoattractant gradients. Results reveal that a variation in total cell protein concentration between cells may be a mechanism for the survival of cell colonies across a wide range of differing environments. We then study the response of cells in the presence of two different chemoattractants. In doing so we demonstrate that the population scale response depends not on the absolute concentration of each chemoattractant but on the sensitivity of the chemoreceptors to their respective concentrations. Our results show the clear link between single cell features and the overall environment in which cells reside.

Novel pseudotaxis mechanisms improve migration of straight-swimming bacterial mutants through a porous environment

Bacterial locomotion driven by flagella is given directionality by the chemotaxis signal transduction network. In the classic plate assays of migration in porous motility agar, efficient motility is compromised in chemotaxis mutants of diverse bacteria. Nonchemotactic mutants become trapped within the agar matrix. Suppressor mutations that prevent this entanglement but do not restore chemotaxis, a phenomenon designated pseudotaxis, were first reported to arise for Escherichia coli. In this study, novel mechanisms of pseudotaxis have been identified for the plant-pathogenic alphaproteobacterium Agrobacterium tumefaciens. Mutants with chemotaxis mutation suppressor (cms) mutations that impart enhanced migration in motility agar compared to that of their straight-swimming, nonchemotactic parent were isolated. We find that pseudotaxis in A. tumefaciens occurs most commonly via mutations in the D1 domain of the flagellar hook protein, FlgE, but it can also be found less frequently to be due to mutations in the hook length regulator, FliK, or in the motor protein, MotA. Single-cell-tracking studies of cms mutants in bulk medium clearly reveal frequent changes in the direction of swimming, similar to the swimming of strains that are proficient for chemotaxis, but independent of a sensory mechanism. Our results suggest that the tumbling process can be tuned through mutation and evolution to optimize migration through complex, porous environments.

Chemotaxis sensory networks control direct bacterial motility by modulating flagellar rotary motion, alternating cellular movement between runs and tumbles. The straight-swimming phenotype of chemotaxis-deficient cells yields nonexpanding colonies in motility agar. Enhanced, chemotaxis-independent spreading, dubbed pseudotaxis, has been observed in Escherichia coli mutants. We have identified novel pseudotaxis mutations in Agrobacterium tumefaciens that alter the flagellar hook structure or motor, leading to randomly occurring reorientations observed in single-cell tracking studies in bulk medium. These directional changes allow the cells to migrate more efficiently than the parent strain through the agar matrix, independently of the chemotaxis process. These findings reveal that tumbling can be tuned for effective navigation in complex porous environments, analogous to the natural habitats for many bacteria, and provide evidence for the strong selective pressure exerted by the external environment on the basal pattern of motility, even in the absence of chemotaxis.

Universal response-adaptation relation in bacterial chemotaxis

The bacterial strategy of chemotaxis relies on temporal comparisons of chemical concentrations, where the probability of maintaining the current direction of swimming is modulated by changes in stimulation experienced during the recent past. A short-term memory required for such comparisons is provided by the adaptation system, which operates through the activity-dependent methylation of chemotaxis receptors. Previous theoretical studies have suggested that efficient navigation in gradients requires a well-defined adaptation rate, because the memory time scale needs to match the duration of straight runs made by bacteria. Here we demonstrate that the chemotaxis pathway of Escherichia coli does indeed exhibit a universal relation between the response magnitude and adaptation time which does not depend on the type of chemical ligand. Our results suggest that this alignment of adaptation rates for different ligands is achieved through cooperative interactions among chemoreceptors rather than through fine-tuning of methylation rates for individual receptors. This observation illustrates a yet-unrecognized function of receptor clustering in bacterial chemotaxis.

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.

Adaptability of non-genetic diversity in bacterial chemotaxis

Bacterial chemotaxis systems are as diverse as the environments that bacteria inhabit, but how much environmental variation can cells tolerate with a single system? Diversification of a single chemotaxis system could serve as an alternative, or even evolutionary stepping-stone, to switching between multiple systems. We hypothesized that mutations in gene regulation could lead to heritable control of chemotactic diversity. By simulating foraging and colonization of E. coli using a single-cell chemotaxis model, we found that different environments selected for different behaviors. The resulting trade-offs show that populations facing diverse environments would ideally diversify behaviors when time for navigation is limited. We show that advantageous diversity can arise from changes in the distribution of protein levels among individuals, which could occur through mutations in gene regulation. We propose experiments to test our prediction that chemotactic diversity in a clonal population could be a selectable trait that enables adaptation to environmental variability.

DOI:http://dx.doi.org/10.7554/eLife.03526.001

Bacterial colonies are generally made up of genetically identical cells. Despite this, a closer look at the members of a bacterial colony shows that these cells can have very different behaviors. For example, some cells may grow more quickly than others, or be more resistant to antibiotics. The mechanisms driving this diversity are only beginning to be identified and understood.

Escherichia coli bacteria can move towards, or away from, certain chemicals in their surrounding environment to help them navigate toward favorable conditions. This behavior is known as chemotaxis. The signals from all of these chemicals are processed in E. coli by just one set of proteins, which control the different behaviors that are needed for the bacteria to follow them. Different numbers of these proteins are found in different—but genetically identical—bacteria, and the number of proteins is linked to how the bacteria perform these behaviors.

It has been suggested that diversity can be beneficial to the overall bacterial population, as it helps the population survive environmental changes. This suggests that the level of diversity in the population should adapt to the level of diversity in the environment. However, it remains unknown how this adaptation occurs.

Frankel et al. developed and combined several models and simulations to investigate whether differences in chemotaxis protein production help an E. coli colony to survive. The models show that in different environments, it can be beneficial for the population as a whole if different cells have different responses to the chemicals present. For example, if a lot of a useful chemical is present, bacteria are more likely to survive by heading straight to the source. If not much chemical is detected, the bacteria may need to move in a more exploratory manner.

Frankel et al. find that different amounts of chemotaxis proteins produce these different behaviors. To survive in a changing environment, it is therefore best for the E. coli colony to contain cells that have different amounts of these proteins. Frankel et al. propose that the variability of chemotaxis protein levels between genetically identical cells can change through mutations in the genes that control how many of the proteins are produced, and predict that such mutations allow populations to adapt to environmental changes.

The environments simulated in the model were much simpler than would be found in the real world, and Frankel et al. describe experiments that are now being performed to confirm and expand on their results. The model could be used in the future to shed light on the behavior of other cells that are genetically identical but exhibit diverse behaviors, from other bacterial species to more complex cancer cells.

DOI:http://dx.doi.org/10.7554/eLife.03526.002

Cooperative target tracking by a mobile bionanosensor network

This paper describes a mobile bionanosensor network designed for target tracking. The mobile bionanosensor network is composed of bacterium-based autonomous biosensors that coordinate their movement through the use of two types of signaling molecules, repellents and attractants. In search of a target, the bacterium-based autonomous biosensors release repellents to quickly spread over the environment, while, upon detecting a target, they release attractants to recruit other biosensors in the environment toward the location around the target. A mobility model of bacterium-based autonomous biosensors is first developed based on the rotational diffusion model of bacterial chemotaxis, and from this their collective movement to track a moving target is demonstrated. In simulation experiments, the mobile bionanosensor network is evaluated based on the mean tracking time. Simulation results show a set of parameter values that can optimize the mean tracking time, providing an insight into how bacterium-based autonomous biosensors may be designed and engineered for target tracking.

Limits of feedback control in bacterial chemotaxis

Inputs to signaling pathways can have complex statistics that depend on the environment and on the behavioral response to previous stimuli. Such behavioral feedback is particularly important in navigation. Successful navigation relies on proper coupling between sensors, which gather information during motion, and actuators, which control behavior. Because reorientation conditions future inputs, behavioral feedback can place sensors and actuators in an operational regime different from the resting state. How then can organisms maintain proper information transfer through the pathway while navigating diverse environments? In bacterial chemotaxis, robust performance is often attributed to the zero integral feedback control of the sensor, which guarantees that activity returns to resting state when the input remains constant. While this property provides sensitivity over a wide range of signal intensities, it remains unclear how other parameters such as adaptation rate and adapted activity affect chemotactic performance, especially when considering that the swimming behavior of the cell determines the input signal. We examine this issue using analytical models and simulations that incorporate recent experimental evidences about behavioral feedback and flagellar motor adaptation. By focusing on how sensory information carried by the response regulator is best utilized by the motor, we identify an operational regime that maximizes drift velocity along chemical concentration gradients for a wide range of environments and sensor adaptation rates. This optimal regime is outside the dynamic range of the motor response, but maximizes the contrast between run duration up and down gradients. In steep gradients, the feedback from chemotactic drift can push the system through a bifurcation. This creates a non-chemotactic state that traps cells unless the motor is allowed to adapt. Although motor adaptation helps, we find that as the strength of the feedback increases individual phenotypes cannot maintain the optimal operational regime in all environments, suggesting that diversity could be beneficial.

The biased random walk is a fundamental strategy used by many organisms to navigate their environment. Drift along the desired direction is achieved by reducing the probability to reorient whenever conditions improve. In the chemotaxis system of Escherichia coli, this is accomplished with a sensory module that implements negative integral feedback control, the output of which is relayed to the flagellar motors (the actuators) by a response regulator to control the probability to change direction. The proper dynamical coupling between sensor and actuator is critical for the performance of the random walker. Here, we identify an optimal regime for this coupling that maximizes drift velocity in the direction of the gradient in multiple environments. Our analysis reveals that feedback of the behavior onto the system in steep gradients can constrain individual cell performance, by causing bi-stable behavior that can trap cells in non-chemotactic states. These limitations are inherent in the biased random walk strategy with integral feedback control, but can be alleviated if the output of the pathway adapts, as recently characterized for the flagellar motors in Escherichia coli.

Analytical modeling and experimental characterization of chemotaxis in Serratia marcescens

This paper presents a modeling and experimental framework to characterize the chemotaxis of Serratia marcescens (S. marcescens) relying on two-dimensional and three-dimensional tracking of individual bacteria. Previous studies mainly characterized bacterial chemotaxis based on population density analysis. Instead, this study focuses on single-cell tracking and measuring the chemotactic drift velocity V(C) from the biased tumble rate of individual bacteria on exposure to a concentration gradient of l-aspartate. The chemotactic response of S. marcescens is quantified over a range of concentration gradients (10^{-3} to 5 mM/mm) and average concentrations (0.5 × 10(-3) to 2.5 mM). Through the analysis of a large number of bacterial swimming trajectories, the tumble rate is found to have a significant bias with respect to the swimming direction. We also verify the relative gradient sensing mechanism in the chemotaxis of S. marcescens by measuring the change of V(C) with the average concentration and the gradient. The applied full pathway model with fitted parameters matches the experimental data. Finally, we show that our measurements based on individual bacteria lead to the determination of the motility coefficient μ (7.25 × 10(-6) cm(2)/s) of a population. The experimental characterization and simulation results for the chemotaxis of this bacterial species contribute towards using S. marcescens in chemically controlled biohybrid systems.

Escherichia coli swimming is robust against variations in flagellar number

Bacterial chemotaxis is a paradigm for how environmental signals modulate cellular behavior. Although the network underlying this process has been studied extensively, we do not yet have an end-to-end understanding of chemotaxis. Specifically, how the rotational states of a cell’s flagella cooperatively determine whether the cell ‘runs’ or ‘tumbles’ remains poorly characterized. Here, we measure the swimming behavior of individual E. coli cells while simultaneously detecting the rotational states of each flagellum. We find that a simple mathematical expression relates the cell’s run/tumble bias to the number and average rotational state of its flagella. However, due to inter-flagellar correlations, an ‘effective number’ of flagella—smaller than the actual number—enters into this relation. Data from a chemotaxis mutant and stochastic modeling suggest that fluctuations of the regulator CheY-P are the source of flagellar correlations. A consequence of inter-flagellar correlations is that run/tumble behavior is only weakly dependent on number of flagella.

DOI:http://dx.doi.org/10.7554/eLife.01916.001

Escherichia coli is a rod-shaped bacterium commonly found in the lower intestines of humans and other warm-blooded animals. While most strains of E. coli are harmless, including most of those found in the human gut, some can cause diseases such as food poisoning. Due to its close association with humans and the fact that it is easy to grow and work with in the laboratory, E. coli has been intensively studied for over 60 years.

Many bacteria are capable of ‘swimming’ by using one or more flagella. These rotating whip-like structures are each driven by a reversible motor, and they act a bit like a propeller on a boat. While some bacteria have only a single flagellum, others, such as E. coli, have multiple flagella distributed over the cell surface. Rotating all their flagella in a counterclockwise direction allows the bacterium to swim—and it has been proposed that the clockwise movement of at least one flagellum will cause the bacterium cell to stop swimming and start tumbling.

E. coli is able to control the time it spends swimming or tumbling to move towards a nutrient, such as glucose, or away from certain harmful chemicals. However, the details of how the number of flagella and the direction of rotation (clockwise or counterclockwise) influence the motion of the bacterium are not fully understood.

Now, Mears et al. have used ‘optical tweezers’ to immobilize individual E. coli cells under a microscope, and then track both their swimming behavior and the movements of their flagella. This revealed that the individual flagella on the same cell tend to move in a coordinated way. Therefore, whilst tumbling could be caused by a single flagellum stopping swimming behavior, it often involved a concerted effort by many of the cell’s flagella.

After observing that E. coli cells with more flagella spent less time tumbling than would be predicted if a single flagella always ‘vetoed’ swimming, Mears et al. propose a new mathematical relationship between the number of flagella on the cell, the direction of rotation, and the resulting probability that the cell will tumble. This work shows that swimming behavior in bacteria is less affected by variations in the number of flagella than previously thought—and this phenomenon may provide evolutionary advantages to E. coli. The next step is to explore the mechanism by which bacteria coordinate their flagella.

DOI:http://dx.doi.org/10.7554/eLife.01916.002

Imprecision of adaptation in Escherichia coli chemotaxis

Adaptability is an essential property of many sensory systems, enabling maintenance of a sensitive response over a range of background stimulus levels. In bacterial chemotaxis, adaptation to the preset level of pathway activity is achieved through an integral feedback mechanism based on activity-dependent methylation of chemoreceptors. It has been argued that this architecture ensures precise and robust adaptation regardless of the ambient ligand concentration, making perfect adaptation a celebrated property of the chemotaxis system. However, possible deviations from such ideal adaptive behavior and its consequences for chemotaxis have not been explored in detail. Here we show that the chemotaxis pathway in Escherichia coli shows increasingly imprecise adaptation to higher concentrations of attractants, with a clear correlation between the time of adaptation to a step-like stimulus and the extent of imprecision. Our analysis suggests that this imprecision results from a gradual saturation of receptor methylation sites at high levels of stimulation, which prevents full recovery of the pathway activity by violating the conditions required for precise adaptation. We further use computer simulations to show that limited imprecision of adaptation has little effect on the rate of chemotactic drift of a bacterial population in gradients, but hinders precise accumulation at the peak of the gradient. Finally, we show that for two major chemoeffectors, serine and cysteine, failure of adaptation at concentrations above 1 mM might prevent bacteria from accumulating at toxic concentrations of these amino acids.

Adaptation dynamics in densely clustered chemoreceptors

In many sensory systems, transmembrane receptors are spatially organized in large clusters. Such arrangement may facilitate signal amplification and the integration of multiple stimuli. However, this organization likely also affects the kinetics of signaling since the cytoplasmic enzymes that modulate the activity of the receptors must localize to the cluster prior to receptor modification. Here we examine how these spatial considerations shape signaling dynamics at rest and in response to stimuli. As a model system, we use the chemotaxis pathway of Escherichia coli, a canonical system for the study of how organisms sense, respond, and adapt to environmental stimuli. In bacterial chemotaxis, adaptation is mediated by two enzymes that localize to the clustered receptors and modulate their activity through methylation-demethylation. Using a novel stochastic simulation, we show that distributive receptor methylation is necessary for successful adaptation to stimulus and also leads to large fluctuations in receptor activity in the steady state. These fluctuations arise from noise in the number of localized enzymes combined with saturated modification kinetics between the localized enzymes and the receptor substrate. An analytical model explains how saturated enzyme kinetics and large fluctuations can coexist with an adapted state robust to variation in the expression levels of the pathway constituents, a key requirement to ensure the functionality of individual cells within a population. This contrasts with the well-mixed covalent modification system studied by Goldbeter and Koshland in which mean activity becomes ultrasensitive to protein abundances when the enzymes operate at saturation. Large fluctuations in receptor activity have been quantified experimentally and may benefit the cell by enhancing its ability to explore empty environments and track shallow nutrient gradients. Here we clarify the mechanistic relationship of these large fluctuations to well-studied aspects of the chemotaxis system, precise adaptation and functional robustness.