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

Signal integration and adaptive sensory diversity tuning in Escherichia coli chemotaxis

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

Signal Integration and Adaptive Sensory Diversity Tuning in Escherichia coli Chemotaxis

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

Lattice ultrasensitivity produces large gain in E. coli chemosensing

E. coli use a regular lattice of receptors and attached kinases to detect and amplify faint chemical signals. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in ligand concentration. These characteristics are well described by models which achieve their gain through equilibrium cooperativity. But these models are challenged by two experimental results. First, neither adaptation nor large gain are present in receptor binding assays. Second, in cells lacking adaptation machinery, fluctuations can sometimes be enormous, with essentially all kinases transitioning together. Here we introduce a far-from equilibrium model in which receptors gate the spread of activity between neighboring kinases. This model achieves large gain through a mechanism we term lattice ultrasensitivity (LU). In our LU model, kinase and receptor states are separate degrees of freedom, and kinase kinetics are dominated by chemical rates far-from-equilibrium rather than by equilibrium allostery. The model recapitulates the successes of past models, but also matches the challenging experimental findings. Importantly, unlike past lattice critical models, our LU model does not require parameters to be fine tuned for function.

Non-genetic adaptation by collective migration

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

Significance statement

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

Adaptation of a Commercial Qualitative BAX® Real-Time PCR Assay to Quantify Campylobacter spp. in Whole Bird Carcass Rinses

Poultry is the primary reservoir of Campylobacter, a leading cause of gastroenteritis in the United States. Currently, the selective plating methodology using selective agars, Campy Cefex and Modified Charcoal Cefoperazone Deoxycholate agar, is preferentially used for the quantification of Campylobacter spp. among poultry products. Due to the specific nature of Campylobacter, this methodology is not sensitive, which can lead to skewed detection and quantification results. Therefore, Campylobacter detection and quantification methods are urgently needed. The objective was to develop a shortened enrichment-based quantification method for Campylobacter (CampyQuant™) in post-chill poultry rinsates using the BAX® System Real-Time PCR assay for Campylobacter. The specificity and sensitivity for the detection of C. jejuni, C. coli, and C. lari in pure culture were determined. The BAX® System Real-Time PCR assay consistently detected and identified each species 100% of the time with an enumeration range of 4.00 to 9.00 Log10 CFU/mL. Enrichment time parameters for low-level concentrations (0.00, 1.00, and 2.00 Log10 CFU/mL) of Campylobacter using the BAX® System Real-Time PCR assay were elucidated. It was determined that an enrichment time of 20 h was needed to detect at least 1.00 Log10 CFU/mL of Campylobacter spp. Using the BAX® System Real-Time PCR assay for Campylobacter. As a result, time of detection, detection limits, and enrichment parameters were used to develop the CampyQuant™ linear standard curve using the detected samples from the BAX® System Real-Time PCR assay to quantify the levels in post-chill poultry rinsates. A linear fit equation was generated for each Campylobacter species using the cycle threshold from the BAX® System Real-Time PCR assay to estimate a pre-enrichment of 1.00 to 4.00 Log10 CFU/mL of rinsates detected. The statistical analyses of each equation yielded an R2 of 0.93, 0.76, and 0.94 with a Log10 RMSE of 0.64, 1.09, and 0.81 from C. jejuni, C. coli, and C. lari, respectively. The study suggests that the BAX® System Real-Time PCR assay for Campylobacter is a more rapid, accurate, and efficient alternative method for Campylobacter enumeration.

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.

Hierarchical network structure as the source of hierarchical dynamics (power-law frequency spectra) in living and non-living systems: How state-trait continua (body plans, personalities) emerge from first principles in biophysics

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine.

A nonequilibrium allosteric model for receptor-kinase complexes: The role of energy dissipation in chemotaxis signaling

The Escherichia coli chemotaxis signaling pathway has served as a model system for the adaptive sensing of environmental signals by large protein complexes. The chemoreceptors control the kinase activity of CheA in response to the extracellular ligand concentration and adapt across a wide concentration range by undergoing methylation and demethylation. Methylation shifts the kinase response curve by orders of magnitude in ligand concentration while incurring a much smaller change in the ligand binding curve. Here, we show that the disproportionate shift in binding and kinase response is inconsistent with equilibrium allosteric models. To resolve this inconsistency, we present a nonequilibrium allosteric model that explicitly includes the dissipative reaction cycles driven by adenosine triphosphate (ATP) hydrolysis. The model successfully explains all existing joint measurements of ligand binding, receptor conformation, and kinase activity for both aspartate and serine receptors. Our results suggest that the receptor complex acts as an enzyme: Receptor methylation modulates the ON-state kinetics of the kinase (e.g., phosphorylation rate), while ligand binding controls the equilibrium balance between kinase ON/OFF states. Furthermore, sufficient energy dissipation is responsible for maintaining and enhancing the sensitivity range and amplitude of the kinase response. We demonstrate that the nonequilibrium allosteric model is broadly applicable to other sensor-kinase systems by successfully fitting previously unexplained data from the DosP bacterial oxygen-sensing system. Overall, this work provides a nonequilibrium physics perspective on cooperative sensing by large protein complexes and opens up research directions for understanding their microscopic mechanisms through simultaneous measurements and modeling of ligand binding and downstream responses.

Dynamic fluctuations in a bacterial metabolic network

The operation of the central metabolism is typically assumed to be deterministic, but dynamics and high connectivity of the metabolic network make it potentially prone to generating fluctuations. However, time-resolved measurements of metabolite levels in individual cells that are required to characterize such fluctuations remained a challenge, particularly in small bacterial cells. Here we use single-cell metabolite measurements based on Förster resonance energy transfer, combined with computer simulations, to explore the real-time dynamics of the metabolic network of Escherichia coli. We observe that steplike exposure of starved E. coli to glycolytic carbon sources elicits large periodic fluctuations in the intracellular concentration of pyruvate in individual cells. These fluctuations are consistent with predicted oscillatory dynamics of E. coli metabolic network, and they are primarily controlled by biochemical reactions around the pyruvate node. Our results further indicate that fluctuations in glycolysis propagate to other cellular processes, possibly leading to temporal heterogeneity of cellular states within a population.

Optimal inference of molecular interaction dynamics in FRET microscopy

Intensity-based time-lapse fluorescence resonance energy transfer (FRET) microscopy has been a major tool for investigating cellular processes, converting otherwise unobservable molecular interactions into fluorescence time series. However, inferring the molecular interaction dynamics from the observables remains a challenging inverse problem, particularly when measurement noise and photobleaching are nonnegligible-a common situation in single-cell analysis. The conventional approach is to process the time-series data algebraically, but such methods inevitably accumulate the measurement noise and reduce the signal-to-noise ratio (SNR), limiting the scope of FRET microscopy. Here, we introduce an alternative probabilistic approach, B-FRET, generally applicable to standard 3-cube FRET-imaging data. Based on Bayesian filtering theory, B-FRET implements a statistically optimal way to infer molecular interactions and thus drastically improves the SNR. We validate B-FRET using simulated data and then apply it to real data, including the notoriously noisy in vivo FRET time series from individual bacterial cells to reveal signaling dynamics otherwise hidden in the noise.

Calcineurin Signalling in Astrocytes: From Pathology to Physiology and Control of Neuronal Functions

Calcineurin (CaN), a Ca²⁺/calmodulin-activated serine/threonine phosphatase, acts as a Ca²⁺-sensitive switch regulating cellular functions through protein dephosphorylation and activation of gene transcription. In astrocytes, the principal homeostatic cells in the CNS, over-activation of CaN is known to drive pathological transcriptional remodelling, associated with neuroinflammation in diseases such as Alzheimer's disease, epilepsy and brain trauma. Recent reports suggest that, in physiological conditions, the activity of CaN in astrocytes is transcription-independent and is required for maintenance of basal protein synthesis rate and activation of astrocytic Na⁺/K⁺ pump thereby contributing to neuronal functions such as neuronal excitability and memory formation. In this contribution we overview the role of Ca²⁺ and CaN signalling in astroglial pathophysiology focusing on the emerging physiological role of CaN in astrocytes. We propose a model for the context-dependent switch of CaN activity from the post-transcriptional regulation of cell proteostasis in healthy astrocytes to the CaN-dependent transcriptional activation in neuroinflammation-associated diseases.

The Chemoreceptor Sensory Adaptation System Produces Coordinated Reversals of the Flagellar Motors on an Escherichia coli Cell

In isotropic environments, an Escherichia coli cell exhibits coordinated rotational switching of its flagellar motors, produced by fluctuations in the intracellular concentration of phosphorylated CheY (CheY-P) emanating from chemoreceptor signaling arrays. In this study, we show that these CheY-P fluctuations arise through modifications of chemoreceptors by two sensory adaptation enzymes: the methyltransferase CheR and the methylesterase CheB. A cell containing CheR, CheB, and the serine chemoreceptor Tsr exhibited motor synchrony, whereas a cell lacking CheR and CheB or containing enzymatically inactive forms did not. Tsr variants with different combinations of methylation-mimicking Q residues at the adaptation sites also failed to show coordinated motor switching in cells lacking CheR and CheB. Cells containing CheR, CheB, and Tsr [NDND], a variant in which the adaptation site residues are not substrates for CheR or CheB modifications, also lacked motor synchrony. TsrΔNWETF, which lacks a C-terminal pentapeptide-binding site for CheR and CheB, and the ribose-galactose receptor Trg, which natively lacks this motif, failed to produce coordinated motor switching, despite the presence of CheR and CheB. However, addition of the NWETF sequence to Trg enabled Trg-NWETF to produce motor synchrony, as the sole receptor type in cells containing CheR and CheB. Finally, CheBc, the catalytic domain of CheB, supported motor coordination in combination with CheR and Tsr. These results indicate that the coordination of motor switching requires CheR/CheB-mediated changes in receptor modification state. We conclude that the opposing receptor substrate-site preferences of CheR and CheB produce spontaneous blinking of the chemoreceptor array's output activity. IMPORTANCE Under steady-state conditions with no external stimuli, an Escherichia coli cell coordinately switches the rotational direction of its flagellar motors. Here, we demonstrate that the CheR and CheB enzymes of the chemoreceptor sensory adaptation system mediate this coordination. Stochastic fluctuations in receptor adaptation states trigger changes in signal output from the receptor array, and this array blinking generates fluctuations in CheY-P concentration that coordinate directional switching of the flagellar motors. Thus, in the absence of chemoeffector gradients, the sensory adaptation system controls run-tumble swimming of the cell, its optimal foraging strategy.

The ecological roles of bacterial chemotaxis

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

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

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

Suppression of cell-cell variation by cooperative interaction of phosphatase and response regulator

In bacterial chemotaxis, the output of chemosensing, the concentration of the response regulator CheY-P that was constantly adjusted by the opposing action of the kinase CheA and the phosphatase CheZ, serves as the input of the ultrasensitive flagellar motor that drives bacterial motility. The steady-state kinase activity exhibits large cell-to-cell variation that may result in similar variation in CheY-P concentration. Here, we found that the in vivo phosphatase activity is highly cooperative with respect to CheY-P concentration, and this suppresses the cell-to-cell variation of CheY-P concentration so that it falls within the operational range of the flagellar motor. Therefore, the cooperativity of the CheZ and CheY-P interaction we identified here provided a mechanism of robust coupling between the output of chemosensing and the input of the flagellar motor. Suppression of cell heterogeneity by cooperativity of protein-protein interaction is likely a common feature in many biological signaling systems.

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

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

Escherichia coli chemotaxis is information limited

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

Multiple functions of flagellar motility and chemotaxis in bacterial physiology

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

Single-Cell Technologies to Study Phenotypic Heterogeneity and Bacterial Persisters

Antibiotic persistence is a phenomenon in which rare cells of a clonal bacterial population can survive antibiotic doses that kill their kin, even though the entire population is genetically susceptible. With antibiotic treatment failure on the rise, there is growing interest in understanding the molecular mechanisms underlying bacterial phenotypic heterogeneity and antibiotic persistence. However, elucidating these rare cell states can be technically challenging. The advent of single-cell techniques has enabled us to observe and quantitatively investigate individual cells in complex, phenotypically heterogeneous populations. In this review, we will discuss current technologies for studying persister phenotypes, including fluorescent tags and biosensors used to elucidate cellular processes; advances in flow cytometry, mass spectrometry, Raman spectroscopy, and microfluidics that contribute high-throughput and high-content information; and next-generation sequencing for powerful insights into genetic and transcriptomic programs. We will further discuss existing knowledge gaps, cutting-edge technologies that can address them, and how advances in single-cell microbiology can potentially improve infectious disease treatment outcomes.

From Information and Quantum Physics to Consciousness and Reality

How does the world around us work and what is real? This question has preoccupied humanity since its beginnings. From the 16th century onwards, it has periodically been necessary to revise the prevailing worldview—but things became very strange at the beginning of the 20th century with the advent of relativity theory and quantum physics. The current focus is on the role of information, there being a debate about whether this is ontological or epistemological. A theory has recently been formulated in which spacetime and gravity emerges from microscopic quantum information—more specifically from quantum entanglement via entanglement entropy. A recent theory describes the emergence of reality itself through first-person perspective experiences and algorithmic information theory. In quantum physics, perception and observation play a central role. Perception of and interaction with the environment require an exchange of information. Via biochemical projection, information is given an interpretation that is necessary to make life and consciousness possible. The world around us is not at all what it seems.

Individual based models exhibiting Lévy-flight type movement induced by intracellular noise

We use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the intrinsic noise plays a central role. Compared with previous work in Perthame et al. (Z Angew Math Phys 69(3):1-15, 2018), in which the parametric assumptions are mainly targeted for mathematical convenience but not well-suited for numerical simulations or comparison with experimental results, our current paper makes use of biologically meaningful pathways and tumbling kernels. The main contribution of this current work is bridging the gap between the theoretical results and experimentally available data. Some particular forms of how the tumbling frequency depends on the internal variable are proposed. Moreover, we propose two individual-based models, one for the tumbling frequency and the other for the receptor activity, and perform numerical simulations. Power-law decay of the run length distribution, which corresponds to Lévy-type motions, is observed in our numerical results. The particular decay rate agrees quantitatively with the analytical result.

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

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

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior

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

Effect of receptor clustering on chemotactic performance of E. coli: Sensing versus adaptation

We show how the competition between sensing and adaptation can result in a performance peak in Escherichia coli chemotaxis using extensive numerical simulations in a detailed theoretical model. Receptor clustering amplifies the input signal coming from ligand binding which enhances chemotactic efficiency. But large clusters also induce large fluctuations in total activity since the number of clusters goes down. The activity and hence the run-tumble motility now gets controlled by methylation levels which are part of adaptation module rather than ligand binding. This reduces chemotactic efficiency.

Connection between the Bacterial Chemotactic Network and Optimal Filtering

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

Alternative Architecture of the E. coli Chemosensory Array

Chemotactic responses in motile bacteria are the result of sophisticated signal transduction by large, highly organized arrays of sensory proteins. Despite tremendous progress in the understanding of chemosensory array structure and function, a structural basis for the heightened sensitivity of networked chemoreceptors is not yet complete. Here, we present cryo-electron tomography visualisations of native-state chemosensory arrays in E. coli minicells. Strikingly, these arrays appear to exhibit a p2-symmetric array architecture that differs markedly from the p6-symmetric architecture previously described in E. coli. Based on this data, we propose molecular models of this alternative architecture and the canonical p6-symmetric assembly. We evaluate our observations and each model in the context of previously published data, assessing the functional implications of an alternative architecture and effects for future studies.

Pulses and delays, anticipation and memory: seeing bacterial stress responses from a single-cell perspective

Stress responses are crucial for bacteria to survive harmful conditions that they encounter in the environment. Although gene regulatory mechanisms underlying stress responses in bacteria have been thoroughly characterised for decades, recent advances in imaging technologies helped to uncover previously hidden dynamics and heterogeneity that become visible at the single-cell level. Despite the diversity of stress response mechanisms, certain dynamic regulatory features are frequently seen in single cells, such as pulses, delays, stress anticipation and memory effects. Often, these dynamics are highly variable across cells. While any individual cell may not achieve an optimal stress response, phenotypic diversity can provide a benefit at the population level. In this review, we highlight microscopy studies that offer novel insights into how bacteria sense stress, regulate protective mechanisms, cope with response delays and prepare for future environmental challenges. These studies showcase developments in the single-cell imaging toolbox including gene expression reporters, FRET, super-resolution microscopy and single-molecule tracking, as well as microfluidic techniques to manipulate cells and create defined stress conditions.

Swimming Escherichia coli Cells Explore the Environment by Lévy Walk

Escherichia coli cells swim in aqueous environment in a random walk of alternating runs and tumbles. The diffusion characteristics of this random walk remains unclear. In this study, by tracking the swimming of wild-type cells in a three-dimensional (3D) homogeneous environment, we found that their trajectories are superdiffusive, consistent with Lévy walk behavior. For comparison, we tracked the swimming of mutant cells that lack the chemotaxis signaling noise (the steady-state fluctuation of the concentration of the chemotaxis response regulator CheY-P) and found that their trajectories are normal diffusive. Therefore, wild-type E. coli cells explore the environment by Lévy walk, which originates from the chemotaxis signaling noise. This Lévy walk pattern enhances their efficiency in environmental exploration.IMPORTANCE E. coli cells explore the environment in a random walk of alternating runs and tumbles. By tracking the 3D trajectories of E. coli cells in an aqueous environment, we found that their trajectories are superdiffusive, with a power-law shape for the distribution of run lengths, which is characteristics of Lévy walk. We further show that this Lévy walk behavior is due to the random fluctuation of the output level of the bacterial chemotaxis pathway, and it enhances the efficiency of the bacteria in exploring the environment.

Fluctuations in Intracellular CheY-P Concentration Coordinate Reversals of Flagellar Motors in E. coli

Signal transduction utilizing membrane-spanning receptors and cytoplasmic regulator proteins is a fundamental process for all living organisms, but quantitative studies of the behavior of signaling proteins, such as their diffusion within a cell, are limited. In this study, we show that fluctuations in the concentration of the signaling molecule, phosphorylated CheY, constitute the basis of chemotaxis signaling. To analyze the propagation of the CheY-P signal quantitatively, we measured the coordination of directional switching between flagellar motors on the same cell. We analyzed the time lags of the switching of two motors in both CCW-to-CW and CW-to-CCW switching (∆t_CCW-CW and ∆t_CW-CCW). In wild-type cells, both time lags increased as a function of the relative distance of two motors from the polar receptor array. The apparent diffusion coefficient estimated for ∆t values was ~9 µm²/s. The distance-dependency of ∆t_CW-CCW disappeared upon loss of polar localization of the CheY-P phosphatase, CheZ. The distance-dependency of the response time for an instantaneously applied serine attractant signal also disappeared with the loss of polar localization of CheZ. These results were modeled by calculating the diffusion of CheY and CheY-P in cells in which phosphorylation and dephosphorylation occur in different subcellular regions. We conclude that diffusion of signaling molecules and their production and destruction through spontaneous activity of the receptor array generates fluctuations in CheY-P concentration over timescales of several hundred milliseconds. Signal fluctuation coordinates rotation among flagella and regulates steady-state run-and-tumble swimming of cells to facilitate efficient responses to environmental chemical signals.

Adaptive tuning of cell sensory diversity without changes in gene expression

In the face of uncertainty, cell populations tend to diversify to enhance survival and growth. Previous studies established that cells can optimize such bet hedging upon environmental change by modulating gene expression to adapt both the average and diversity of phenotypes. Here, we demonstrate that cells can tune phenotypic diversity also using posttranslational modifications. In the chemotaxis network of Escherichia coli, we find, for both major chemoreceptors Tar and Tsr, that cell-to-cell variation in response sensitivity is dynamically modulated depending on the presence or absence of their cognate chemoeffector ligands in the environment. Combining experiments with mathematical modeling, we show that this diversity tuning requires only the environment-dependent covalent modification of chemoreceptors and a standing cell-to-cell variation in their allosteric coupling. Thus, when environmental cues are unavailable, phenotypic diversity enhances the population's readiness for many signals. However, once a signal is perceived, the population focuses on tracking that signal.

In Vivo Feedback Control of an Antithetic Molecular-Titration Motif in Escherichia coli Using Microfluidics

We study both in silico and in vivo the real-time feedback control of a molecular titration motif that has been earmarked as a fundamental component of antithetic and multicellular feedback control schemes in E. coli. We show that an external feedback control strategy can successfully regulate the average fluorescence output of a bacterial cell population to a desired constant level in real-time. We also provide in silico evidence that the same strategy can be used to track a time-varying reference signal where the set-point is switched to a different value halfway through the experiment. We use the experimental data to refine and parametrize an in silico model of the motif that can be used as an error computation module in future embedded or multicellular control experiments.

Estimating entropy production by machine learning of short-time fluctuating currents

Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents. Since the TURs do not refer to the full details of the stochastic dynamics, it would be promising to apply the TURs for estimating the entropy production rate from a limited set of trajectory data corresponding to the dynamics. Here we investigate a theoretical framework for estimation of the entropy production rate using the TURs along with machine learning techniques without prior knowledge of the parameters of the stochastic dynamics. Specifically, we derive a TUR for the short-time region and prove that it can provide the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics, if the observed current is optimally chosen. This formulation naturally includes a generalization of the TURs with the partial entropy production of subsystems under autonomous interaction, which reveals the hierarchical structure of the estimation. We then construct estimators on the basis of the short-time TUR and machine learning techniques such as the gradient ascent. By performing numerical experiments, we demonstrate that our learning protocol performs well even in nonlinear Langevin dynamics. We also discuss the case of Markov jump processes, where the exact estimation is shown to be impossible in general. Our result provides a platform that can be applied to a broad class of stochastic dynamics out of equilibrium, including biological systems.

Drugs modulating stochastic gene expression affect the erythroid differentiation process

To better understand the mechanisms behind cells decision-making to differentiate, we assessed the influence of stochastic gene expression (SGE) modulation on the erythroid differentiation process. It has been suggested that stochastic gene expression has a role in cell fate decision-making which is revealed by single-cell analyses but studies dedicated to demonstrate the consistency of this link are still lacking. Recent observations showed that SGE significantly increased during differentiation and a few showed that an increase of the level of SGE is accompanied by an increase in the differentiation process. However, a consistent relation in both increasing and decreasing directions has never been shown in the same cellular system. Such demonstration would require to be able to experimentally manipulate simultaneously the level of SGE and cell differentiation in order to observe if cell behavior matches with the current theory. We identified three drugs that modulate SGE in primary erythroid progenitor cells. Both Artemisinin and Indomethacin decreased SGE and reduced the amount of differentiated cells. On the contrary, a third component called MB-3 simultaneously increased the level of SGE and the amount of differentiated cells. We then used a dynamical modelling approach which confirmed that differentiation rates were indeed affected by the drug treatment. Using single-cell analysis and modeling tools, we provide experimental evidence that, in a physiologically relevant cellular system, SGE is linked to differentiation.

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.

Chemotaxis as a navigation strategy to boost range expansion

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

Phenotypic heterogeneity of microbial populations under nutrient limitation

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

New Twists and Turns in Bacterial Locomotion and Signal Transduction

Prokaryotic organisms occupy the most diverse set of environments and conditions on our planet. Their ability to sense and respond to a broad range of external cues remain key research areas in modern microbiology, central to behaviors that underlie beneficial and pathogenic interactions of bacteria with multicellular organisms and within complex ecosystems. Advances in our understanding of the one- and two-component signal transduction systems that underlie these sensing pathways have been driven by advances in imaging the behavior of many individual bacterial cells, as well as visualizing individual proteins and protein arrays within living cells. Cryo-electron tomography continues to provide new insights into the structure and function of chemosensory receptors and flagellar motors, while advances in protein labeling and tracking are applied to understand information flow between receptor and motor. Sophisticated microfluidics allow simultaneous analysis of the behavior of thousands of individual cells, increasing our understanding of how variance between individuals is generated, regulated and employed to maximize fitness of a population. In vitro experiments have been complemented by the study of signal transduction and motility in complex in vivo models, allowing investigators to directly address the contribution of motility, chemotaxis and aggregation/adhesion on virulence during infection. Finally, systems biology approaches have demonstrated previously uncharted areas of protein space in which novel two-component signal transduction pathways can be designed and constructed de novo These exciting experimental advances were just some of the many novel findings presented at the 15^th Bacterial Locomotion and Signal Transduction conference (BLAST XV) in January 2019.

Conformational shifts in a chemoreceptor helical hairpin control kinase signaling in Escherichia coli

Motile bacteria use chemoreceptor signaling arrays to track chemical gradients with high precision. The Escherichia coli chemotaxis system offers an ideal model for probing the molecular mechanisms of transmembrane and intracellular signaling. In this study, we characterized the signaling properties of mutant E. coli receptors that had amino acid replacements in residues that form a salt-bridge connection between the cytoplasmic tips of receptor molecules. The mutant signaling defects suggested that the chemoreceptor tip operates as a two-state device with discrete active and inactive conformations and that the level of output activity modulates connections between receptor signaling units that produce highly cooperative responses to attractant stimuli. These findings shed important light on the nature and control of receptor signaling states.

Motile Escherichia coli cells use chemoreceptor signaling arrays to track chemical gradients with exquisite precision. Highly conserved residues in the cytoplasmic hairpin tip of chemoreceptor molecules promote assembly of trimer-based signaling complexes and modulate the activity of their CheA kinase partners. To explore hairpin tip output states in the serine receptor Tsr, we characterized the signaling consequences of amino acid replacements at the salt-bridge residue pair E385-R388. All mutant receptors assembled trimers and signaling complexes, but most failed to support serine chemotaxis in soft agar assays. Small side-chain replacements at either residue produced OFF- or ON-shifted outputs that responded to serine stimuli in wild-type fashion, suggesting that these receptors, like the wild-type, operate as two-state signaling devices. Larger aliphatic or aromatic side chains caused slow or partial kinase control responses that proved dependent on the connections between core signaling units that promote array cooperativity. In a mutant lacking one of two key adapter-kinase contacts (interface 2), those mutant receptors exhibited more wild-type behaviors. Lastly, mutant receptors with charged amino acid replacements assembled signaling complexes that were locked in kinase-ON (E385K|R) or kinase-OFF (R388D|E) output. The hairpin tips of mutant receptors with these more aberrant signaling properties probably have nonnative structures or dynamic behaviors. Our results suggest that chemoeffector stimuli and adaptational modifications influence the cooperative connections between core signaling units. This array remodeling process may involve activity-dependent changes in the relative strengths of interface 1 and 2 interactions between the CheW and CheA.P5 components of receptor core signaling complexes.

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

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

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

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

Escherichia coli Remodels the Chemotaxis Pathway for Swarming

The fundamental motile behavior of E. coli is a random walk, where straight “runs” are punctuated by “tumbles.” This behavior, conferred by the chemotaxis signaling system, is used to track chemical gradients in liquid. Our study results show that when migrating collectively on surfaces, E. coli modifies its chemosensory physiology to decrease its tumble bias (and hence to increase run durations) by post-transcriptional changes that alter the levels of a key signaling protein. We speculate that the low tumble bias may contribute to the observed Lévy walk (LW) trajectories within the swarm, where run durations have a power law distribution. In animals, LW patterns are hypothesized to maximize searches in unpredictable environments. Swarming bacteria face several challenges while moving collectively over a surface—maintaining cohesion, overcoming constraints imposed by a physical substrate, searching for nutrients as a group, and surviving lethal levels of antimicrobials. The altered chemosensory behavior that we describe in this report may help with these challenges.

Many flagellated bacteria “swarm” over a solid surface as a dense consortium. In different bacteria, swarming is facilitated by several alterations such as those corresponding to increased flagellum numbers, special stator proteins, or secreted surfactants. We report here a change in the chemosensory physiology of swarming Escherichia coli which alters its normal “run tumble” bias. E. coli bacteria taken from a swarm exhibit more highly extended runs (low tumble bias) and higher speeds than E. coli bacteria swimming individually in a liquid medium. The stability of the signaling protein CheZ is higher in swarmers, consistent with the observed elevation of CheZ levels and with the low tumble bias. We show that the tumble bias displayed by wild-type swarmers is the optimal bias for maximizing swarm expansion. In assays performed in liquid, swarm cells have reduced chemotactic performance. This behavior is specific to swarming, is not specific to growth on surfaces, and persists for a generation. Therefore, the chemotaxis signaling pathway is reprogrammed for swarming.

Propagation of regulatory fluctuations induces coordinated switching of flagellar motors in chemotaxis signaling pathway of single bacteria

The random motion of E. coli is driven by multiple flagella motors. When all motors rotate in the counter clockwise direction, the bacteria swims smoothly. A recent experimental report by Terasawa et al. [Biophys J,100,2193,(2011)] demonstrated that a coordination of the motors can occur through signaling pathways, and perturbation of a regulatory molecule disrupted the coordination. Here, we develop a mathematical model to show that a large temporal fluctuation in the regulator concentration can induce a correlated switching of the multiple motors. Such a large fluctuation is generated by a chemotaxis receptor cluster in unilateral cell pole, which then exhibits a spatial propagation through the cytoplasm from the receptor position to the motor around cell periphery. Our numerical simulation successfully reproduces synchronized switching and the lag time in the motions of two distant motors, which has been observed experimentally. We further show that the large fluctuation in the regulator concentration at the motor positions can expand the dynamic range that the motor can respond, which confers robustness to the signaling system.

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.

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.