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.

E. coli do not count single molecules.

Organisms must perform sensory-motor behaviors to survive. What bounds or constraints limit behavioral performance? Previously, we found that the gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set by the limited information they acquire from their chemical environments (1). Here we ask what limits their sensory accuracy. Past theoretical analyses have shown that the stochasticity of single molecule arrivals sets a fundamental limit on the precision of chemical sensing (2). Although it has been argued that bacteria approach this limit, direct evidence is lacking. Here, using information theory and quantitative experiments, we find that E. coli's chemosensing is not limited by the physics of particle counting. First, we derive the physical limit on the behaviorally-relevant information that any sensor can get about a changing chemical concentration, assuming that every molecule arriving at the sensor is recorded. Then, we derive and measure how much information E. coli's signaling pathway encodes during chemotaxis. We find that E. coli encode two orders of magnitude less information than an ideal sensor limited only by shot noise in particle arrivals. These results strongly suggest that constraints other than particle arrival noise limit E. coli's sensory fidelity.

E. coli do not count single molecules.

Organisms must perform sensory-motor behaviors to survive. What bounds or constraints limit behavioral performance? Previously, we found that the gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set by the limited information they acquire from their chemical environments (1). Here we ask what limits their sensory accuracy. Past theoretical analyses have shown that the stochasticity of single molecule arrivals sets a fundamental limit on the precision of chemical sensing (2). Although it has been argued that bacteria approach this limit, direct evidence is lacking. Here, using information theory and quantitative experiments, we find that E. coli's chemosensing is not limited by the physics of particle counting. First, we derive the physical limit on the behaviorally-relevant information that any sensor can get about a changing chemical concentration, assuming that every molecule arriving at the sensor is recorded. Then, we derive and measure how much information E. coli's signaling pathway encodes during chemotaxis. We find that E. coli encode two orders of magnitude less information than an ideal sensor limited only by shot noise in particle arrivals. These results strongly suggest that constraints other than particle arrival noise limit E. coli's sensory fidelity.

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.

Bifurcation enhances temporal information encoding in the olfactory periphery.

Living systems continually respond to signals from the surrounding environment. Survival requires that their responses adapt quickly and robustly to the changes in the environment. One particularly challenging example is olfactory navigation in turbulent plumes, where animals experience highly intermittent odor signals while odor concentration varies over many length- and timescales. Here, we show theoretically that Drosophila olfactory receptor neurons (ORNs) can exploit proximity to a bifurcation point of their firing dynamics to reliably extract information about the timing and intensity of fluctuations in the odor signal, which have been shown to be critical for odor-guided navigation. Close to the bifurcation, the system is intrinsically invariant to signal variance, and information about the timing, duration, and intensity of odor fluctuations is transferred efficiently. Importantly, we find that proximity to the bifurcation is maintained by mean adaptation alone and therefore does not require any additional feedback mechanism or fine-tuning. Using a biophysical model with calcium-based feedback, we demonstrate that this mechanism can explain the measured adaptation characteristics of Drosophila ORNs.

Bifurcation enhances temporal information encoding in the olfactory periphery.

Living systems continually respond to signals from the surrounding environment. Survival requires that their responses adapt quickly and robustly to the changes in the environment. One particularly challenging example is olfactory navigation in turbulent plumes, where animals experience highly intermittent odor signals while odor concentration varies over many length- and timescales. Here, we show theoretically that Drosophila olfactory receptor neurons (ORNs) can exploit proximity to a bifurcation point of their firing dynamics to reliably extract information about the timing and intensity of fluctuations in the odor signal, which have been shown to be critical for odor-guided navigation. Close to the bifurcation, the system is intrinsically invariant to signal variance, and information about the timing, duration, and intensity of odor fluctuations is transferred efficiently. Importantly, we find that proximity to the bifurcation is maintained by mean adaptation alone and therefore does not require any additional feedback mechanism or fine-tuning. Using a biophysical model with calcium-based feedback, we demonstrate that this mechanism can explain the measured adaptation characteristics of Drosophila ORNs.

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.

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

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

Non-genetic adaptation by collective migration.

Collective behaviors require coordination of individuals. Thus, a population must adjust its phenotypic distribution to adapt to changing environments. How can a population regulate its phenotypic distribution? One strategy is to utilize specialized networks for gene regulation and maintaining distinct phenotypic subsets. Another involves genetic mutations, which can be augmented by stress-response pathways. Here, we studied how a migrating bacterial population regulates its phenotypic distribution to traverse across diverse environments. We generated isogenic Escherichia coli populations with varying distributions of swimming behaviors and observed their phenotype distributions during migration in liquid and porous environments. Surprisingly, we found that during collective migration, the distributions of swimming phenotypes adapt to the environment without mutations or gene regulation. Instead, adaptation is caused by the dynamic and reversible enrichment of high-performing swimming phenotypes within each environment. This adaptation mechanism is supported by a recent theoretical study, which proposed that the phenotypic composition of a migrating population results from a balance between cell growth generating diversity and collective migration eliminating the phenotypes that are unable to keep up with the migrating group. Furthermore, by examining chemoreceptor abundance distributions during migration towards different attractants, we found that this mechanism acts on multiple chemotaxis-related traits simultaneously. Our findings reveal that collective migration itself can enable cell populations with continuous, multi-dimensional phenotypes to flexibly and rapidly adapt their phenotypic composition to diverse environmental conditions. Significance statement: Conventional cell adaptation mechanisms, like gene regulation and random phenotypic switching, act swiftly but are limited to a few traits, while mutation-driven adaptations unfold slowly. By quantifying phenotypic diversity during bacterial collective migration, we discovered an adaptation mechanism that rapidly and reversibly adjusts multiple traits simultaneously. By dynamically balancing the elimination of phenotypes unable to keep pace with generation of diversity through growth, this process enables populations to tune their phenotypic composition based on the environment, without the need for gene regulation or mutations. Given the prevalence of collective migration in microbes, cancers, and embryonic development, non-genetic adaptation through collective migration may be a universal mechanism for populations to navigate diverse environments, offering insights into broader applications across various fields.

Extracting spatial information from temporal odor patterns: insights from insects.

Extracting spatial information from temporal stimulus patterns is essential for sensory perception (e.g. visual motion direction detection or concurrent sound segregation), but this process remains understudied in olfaction. Animals rely on olfaction to locate resources and dangers. In open environments, where odors are dispersed by turbulent wind, detection of wind direction seems crucial for odor source localization. However, recent studies showed that insects can extract spatial information from the odor stimulus itself, independently from sensing wind direction. This remarkable ability is achieved by detecting the fine-scale temporal pattern of odor encounters, which contains information about the location and size of an odor source, and the distance between different odor sources.

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

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

Temporal novelty detection and multiple timescale integration drive Drosophila orientation dynamics in temporally diverse olfactory environments.

To survive, insects must effectively navigate odor plumes to their source. In natural plumes, turbulent winds break up smooth odor regions into disconnected patches, so navigators encounter brief bursts of odor interrupted by bouts of clean air. The timing of these encounters plays a critical role in navigation, determining the direction, rate, and magnitude of insects' orientation and speed dynamics. Disambiguating the specific role of odor timing from other cues, such as spatial structure, is challenging due to natural correlations between plumes' temporal and spatial features. Here, we use optogenetics to isolate temporal features of odor signals, examining how the frequency and duration of odor encounters shape the navigational decisions of freely-walking Drosophila. We find that fly angular velocity depends on signal frequency and intermittency-the fraction of time signal can be detected-but not directly on durations. Rather than switching strategies when signal statistics change, flies smoothly transition between signal regimes, by combining an odor offset response with a frequency-dependent novelty-like response. In the latter, flies are more likely to turn in response to each odor hit only when the hits are sparse. Finally, the upwind bias of individual turns relies on a filtering scheme with two distinct timescales, allowing rapid and sustained responses in a variety of signal statistics. A quantitative model incorporating these ingredients recapitulates fly orientation dynamics across a wide range of environments and shows that temporal novelty detection, when combined with odor motion detection, enhances odor plume navigation.

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.

Sensory diversity and precise adaptation enable independent bet-hedging strategies for multiple signals at the same time.

While navigating their environments, cells encounter many different signals at once. In the face of uncertain conditions, diversifying the sensitivity to different signals across the population can be useful. Previous studies established that one of the simplest sensory systems, the chemotaxis network of Escherichia coli , can switch between a high diversity bet-hedging strategy, and a low diversity tracking strategy for a ligand as that ligand becomes prevalent. Here, we combine mathematical modeling and single-cell experiments to show that populations of chemotactic bacteria make this transition for each ligand independently. That is, transitioning to tracking one ligand does not compromise the population’s ability to hedge its bets across other future ligands. Remarkably, we found that this independence holds even if those ligands compete for receptor binding sites with the background ligand being tracked. The independence of this transition between two diversity regimes is explained by a simple allosteric model of chemoreceptor clusters with negative integral feedback, which accurately predicts the observed diversity in sensitivity under various background stimulus conditions. Our mathematical analysis shows that similar transitions from bet-hedging to tracking also arise in feed-forward network architectures capable of precise adaptation, suggesting that environment-dependent modulation of diversity may occur in many cell types.

Odour motion sensing enhances navigation of complex plumes.

Odour plumes in the wild are spatially complex and rapidly fluctuating structures carried by turbulent airflows1-4. To successfully navigate plumes in search of food and mates, insects must extract and integrate multiple features of the odour signal, including odour identity5, intensity6 and timing6-12. Effective navigation requires balancing these multiple streams of olfactory information and integrating them with other sensory inputs, including mechanosensory and visual cues9,12,13. Studies dating back a century have indicated that, of these many sensory inputs, the wind provides the main directional cue in turbulent plumes, leading to the longstanding model of insect odour navigation as odour-elicited upwind motion6,8-12,14,15. Here we show that Drosophila melanogaster shape their navigational decisions using an additional directional cue-the direction of motion of odours-which they detect using temporal correlations in the odour signal between their two antennae. Using a high-resolution virtual-reality paradigm to deliver spatiotemporally complex fictive odours to freely walking flies, we demonstrate that such odour-direction sensing involves algorithms analogous to those in visual-direction sensing16. Combining simulations, theory and experiments, we show that odour motion contains valuable directional information that is absent from the airflow alone, and that both Drosophila and virtual agents are aided by that information in navigating naturalistic plumes. The generality of our findings suggests that odour-direction sensing may exist throughout the animal kingdom and could improve olfactory robot navigation in uncertain environments.

Where is that smell coming from?

Computational model reveals why pausing to sniff the air helps animals track a scent when they are far away from the source.

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

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

Sensing complementary temporal features of odor signals enhances navigation of diverse turbulent plumes.

We and others have shown that during odor plume navigation, walking Drosophila melanogaster bias their motion upwind in response to both the frequency of their encounters with the odor (Demir et al., 2020) and the intermittency of the odor signal, which we define to be the fraction of time the signal is above a detection threshold (Alvarez-Salvado et al., 2018). Here, we combine and simplify previous mathematical models that recapitulated these data to investigate the benefits of sensing both of these temporal features and how these benefits depend on the spatiotemporal statistics of the odor plume. Through agent-based simulations, we find that navigators that only use frequency or intermittency perform well in some environments - achieving maximal performance when gains are near those inferred from experiment - but fail in others. Robust performance across diverse environments requires both temporal modalities. However, we also find a steep trade-off when using both sensors simultaneously, suggesting a strong benefit to modulating how much each sensor is weighted, rather than using both in a fixed combination across plumes. Finally, we show that the circuitry of the Drosophila olfactory periphery naturally enables simultaneous intermittency and frequency sensing, enhancing robust navigation through a diversity of odor environments. Together, our results suggest that the first stage of olfactory processing selects and encodes temporal features of odor signals critical to real-world navigation tasks.

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior.

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

A Primed Subpopulation of Bacteria Enables Rapid Expression of the Type 3 Secretion System in Pseudomonas aeruginosa.

Type 3 secretion systems (T3SS) are complex nanomachines that span the cell envelope and play a central role in the biology of Gram-negative pathogens and symbionts. In Pseudomonas aeruginosa, T3SS expression is strongly associated with human disease severity and with mortality in murine acute pneumonia models. Uniform exposure of isogenic cells to T3SS-activating signal results in heterogeneous expression of this critical virulence trait. To understand the function of such diversity, we measured the production of the T3SS master regulator ExsA and the expression of T3SS genes using fluorescent reporters. We found that heterogeneous expression of ExsA in the absence of activating signal generates a "primed" subpopulation of cells that can rapidly induce T3SS gene expression in response to signal. T3SS expression is accompanied by a reproductive trade-off as measured by increased division time of T3SS-expressing cells. Although T3SS-primed cells are a minority of the population, they compose the majority of T3SS-expressing cells for several hours following activation. The primed state therefore allows P. aeruginosa to maximize reproductive fitness while maintaining the capacity to quickly express the T3SS. As T3SS effectors can serve as shared public goods for nonproducing cells, this division of labor benefits the population as a whole. IMPORTANCE The expression of specific virulence traits is strongly associated with Pseudomonas aeruginosa's success in establishing acute infections but is thought to carry a cost for bacteria. Producing multiprotein secretion systems or motility organelles is metabolically expensive and can target a cell for recognition by innate immune system receptors that recognize structural components of the type 3 secretion system (T3SS) or flagellum. These acute virulence factors are also negatively selected when P. aeruginosa establishes chronic infections in the lung. We demonstrate a regulatory mechanism by which only a minority subpopulation of genetically identical P. aeruginosa cells is "primed" to respond to signals that turn on T3SS expression. This phenotypic heterogeneity allows the population to maximize the benefit of rapid T3SS effector production while maintaining a rapidly growing and nonexpressing reservoir of cells that perpetuates this genotype within the population.