Escherichia coli chemotaxis is information limited

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.

MCP5, a methyl-accepting chemotaxis protein regulated by both the Hk1-Rrp1 and Rrp2-RpoN-RpoS pathways, is required for the immune evasion of Borrelia burgdorferi

Borrelia (or Borreliella) burgdorferi, the causative agent of Lyme disease, is a motile and invasive zoonotic pathogen, adept at navigating between its arthropod vector and mammalian host. While motility and chemotaxis are well established as essential for its enzootic cycle, the function of methyl-accepting chemotaxis proteins (MCPs) in the infectious cycle of B. burgdorferi remains unclear. In this study, we demonstrate that MCP5, one of the most abundant MCPs in B. burgdorferi, is differentially expressed in response to environmental signals as well as at different stages of the pathogen's enzootic cycle. Specifically, the expression of mcp5 is regulated by the Hk1-Rrp1 and Rrp2-RpoN-RpoS pathways, which are critical for the spirochete's colonization of the tick vector and mammalian host, respectively. Infection experiments with an mcp5 mutant revealed that spirochetes lacking MCP5 could not establish infections in either C3H/HeN mice or Severe Combined Immunodeficiency (SCID) mice, which are defective in adaptive immunity, indicating the essential role of MCP5 in mammalian infection. However, the mcp5 mutant could establish infection and disseminate in NOD SCID Gamma (NSG) mice, which are deficient in both adaptive and most innate immune responses, suggesting a crucial role of MCP5 in evading host innate immunity. In the tick vector, the mcp5 mutants survived feeding but failed to transmit to mice, highlighting the importance of MCP5 in transmission. Our findings reveal that MCP5, regulated by the Rrp1 and Rrp2 pathways, is critical for the establishment of infection in mammalian hosts by evading host innate immunity and is important for the transmission of spirochetes from ticks to mammalian hosts, underscoring its potential as a target for intervention strategies.

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.

Deposited footprints let cells switch between confined, oscillatory, and exploratory migration

For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix (ECM). Cells may also deposit ECM components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cell lines on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional (2D) substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs. exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.

Deposited footprints let cells switch between confined, oscillatory, and exploratory migration

For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix. Cells may also deposit extracellular matrix components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cells on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion.

Smart active particles learn and transcend bacterial foraging strategies

Throughout evolution, bacteria and other microorganisms have learned efficient foraging strategies that exploit characteristic properties of their unknown environment. While much research has been devoted to the exploration of statistical models describing the dynamics of foraging bacteria and other (micro-) organisms, little is known, regarding the question of how good the learned strategies actually are. This knowledge gap is largely caused by the absence of methods allowing to systematically develop alternative foraging strategies to compare with. In the present work, we use deep reinforcement learning to show that a smart run-and-tumble agent, which strives to find nutrients for its survival, learns motion patterns that are remarkably similar to the trajectories of chemotactic bacteria. Strikingly, despite this similarity, we also find interesting differences between the learned tumble rate distribution and the one that is commonly assumed for the run and tumble model. We find that these differences equip the agent with significant advantages regarding its foraging and survival capabilities. Our results uncover a generic route to use deep reinforcement learning for discovering search and collection strategies that exploit characteristic but initially unknown features of the environment. These results can be used, e.g., to program future microswimmers, nanorobots, and smart active particles for tasks like searching for cancer cells, micro-waste collection, or environmental remediation.

Microbes in porous environments: from active interactions to emergent feedback

Microbes thrive in diverse porous environments-from soil and riverbeds to human lungs and cancer tissues-spanning multiple scales and conditions. Short- to long-term fluctuations in local factors induce spatio-temporal heterogeneities, often leading to physiologically stressful settings. How microbes respond and adapt to such biophysical constraints is an active field of research where considerable insight has been gained over the last decades. With a focus on bacteria, here we review recent advances in self-organization and dispersal in inorganic and organic porous settings, highlighting the role of active interactions and feedback that mediates microbial survival and fitness. We discuss open questions and opportunities for using integrative approaches to advance our understanding of the biophysical strategies which microbes employ at various scales to make porous settings habitable.

The ability to sense the environment is heterogeneously distributed in cell populations

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information-theoretic framework to quantify the distribution of sensing abilities from single-cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an 'average cell'. We verify these predictions using live-cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information-theoretic framework will significantly improve our understanding of how cells sense in their environment.

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.

Information Transmission via Molecular Communication in Astrobiological Environments

The ubiquity of information transmission via molecular communication between cells is comprehensively documented on Earth; this phenomenon might even have played a vital role in the origin(s) and early evolution of life. Motivated by these considerations, a simple model for molecular communication entailing the diffusion of signaling molecules from transmitter to receiver is elucidated. The channel capacity C (maximal rate of information transmission) and an optimistic heuristic estimate of the actual information transmission rate ℐ are derived for this communication system; the two quantities, especially the latter, are demonstrated to be broadly consistent with laboratory experiments and more sophisticated theoretical models. The channel capacity exhibits a potentially weak dependence on environmental parameters, whereas the actual information transmission rate may scale with the intercellular distance d as ℐ ∝ d-4 and could vary substantially across settings. These two variables are roughly calculated for diverse astrobiological environments, ranging from Earth's upper oceans (C ∼ 3.1 × 103 bits/s; ℐ ∼ 4.7 × 10-2 bits/s) and deep sea hydrothermal vents (C ∼ 4.2 × 103 bits/s; ℐ ∼ 1.2 × 10-1 bits/s) to the hydrocarbon lakes and seas of Titan (C ∼ 3.8 × 103 bits/s; ℐ ∼ 2.6 × 10-1 bits/s).

Connecting theory and experiment in cell and tissue mechanics

Understanding complex living systems, which are fundamentally constrained by physical phenomena, requires combining experimental data with theoretical physical and mathematical models. To develop such models, collaborations between experimental cell biologists and theoreticians are increasingly important but these two groups often face challenges achieving mutual understanding. To help navigate these challenges, this Perspective discusses different modelling approaches, including bottom-up hypothesis-driven and top-down data-driven models, and highlights their strengths and applications. Using cell mechanics as an example, we explore the integration of specific physical models with experimental data from the molecular, cellular and tissue level up to multiscale input. We also emphasize the importance of constraining model complexity and outline strategies for crosstalk between experimental design and model development. Furthermore, we highlight how physical models can provide conceptual insights and produce unifying and generalizable frameworks for biological phenomena. Overall, this Perspective aims to promote fruitful collaborations that advance our understanding of complex biological systems.

Physical limits on galvanotaxis

Eukaryotic cells can polarize and migrate in response to electric fields via "galvanotaxis," which aids wound healing. Experimental evidence suggests cells sense electric fields via molecules on the cell's surface redistributing via electrophoresis and electroosmosis, though the sensing species has not yet been conclusively identified. We develop a model that links sensor redistribution and galvanotaxis using maximum likelihood estimation. Our model predicts a single universal curve for how galvanotactic directionality depends on field strength. We can collapse measurements of galvanotaxis in keratocytes, neural crest cells, and granulocytes to this curve, suggesting that stochasticity due to the finite number of sensors may limit galvanotactic accuracy. We find cells can achieve experimentally observed directionalities with either a few (∼100) highly polarized sensors or many (∼10^{4}) sensors with an ∼6-10% change in concentration across the cell. We also identify additional signatures of galvanotaxis via sensor redistribution, including the presence of a tradeoff between accuracy and variance in cells being controlled by rapidly switching fields. Our approach shows how the physics of noise at the molecular scale can limit cell-scale galvanotaxis, providing important constraints on sensor properties and allowing for new tests to determine the specific molecules underlying galvanotaxis.

Construction of an Engineered Escherichia coli with Efficient Chemotactic and Metabolizing Ability toward Tetrathionate

The emergence of genetically engineered bacteria has provided a new means for the diagnosis and treatment of diseases. However, in vivo applications of these engineered bacteria are hindered by their inefficient accumulation in areas of inflammation. In this study, we constructed an engineered Escherichia coli (E. coli) for directional migration toward tetrathionate (a biomarker of gut inflammation), which is regulated by the TtrSR two-component system (TCS) from Shewanella baltica OS195 (S. baltica). Specifically, we removed endogenous cheZ to control the motility of E. coli. Moreover, we introduced the reductase gene cluster (ttrBCA) from Salmonella enterica serotype typhimurium (S. typhimurium), a major pathogen causing gut inflammation, into E. coli to metabolize tetrathionate. The resulting strain was tested for its motility along the gradients of tetrathionate; the engineered strain exhibits tropism to tetrathionate compared with the original strain. Furthermore, the engineered E. coli could only restore its smooth swimming ability when tetrathionate existed. With these modifications enabling tetrathionate-mediated chemotactic and metabolizing activity, this strategy with therapeutic elements will provide a great potential opportunity for target treatment of various diseases by swapping the corresponding genetic circuits.

Trade-offs between cost and information in cellular prediction

Living cells can leverage correlations in environmental fluctuations to predict the future environment and mount a response ahead of time. To this end, cells need to encode the past signal into the output of the intracellular network from which the future input is predicted. Yet, storing information is costly while not all features of the past signal are equally informative on the future input signal. Here, we show for two classes of input signals that cellular networks can reach the fundamental bound on the predictive information as set by the information extracted from the past signal: Push-pull networks can reach this information bound for Markovian signals, while networks that take a temporal derivative can reach the bound for predicting the future derivative of non-Markovian signals. However, the bits of past information that are most informative about the future signal are also prohibitively costly. As a result, the optimal system that maximizes the predictive information for a given resource cost is, in general, not at the information bound. Applying our theory to the chemotaxis network of Escherichia coli reveals that its adaptive kernel is optimal for predicting future concentration changes over a broad range of background concentrations, and that the system has been tailored to predicting these changes in shallow gradients.

Planetary Scale Information Transmission in the Biosphere and Technosphere: Limits and Evolution

Information transmission via communication between agents is ubiquitous on Earth, and is a vital facet of living systems. In this paper, we aim to quantify this rate of information transmission associated with Earth's biosphere and technosphere (i.e., a measure of global information flow) by means of a heuristic order-of-magnitude model. By adopting ostensibly conservative values for the salient parameters, we estimate that the global information transmission rate for the biosphere might be ∼1024 bits/s, and that it may perhaps exceed the corresponding rate for the current technosphere by ∼9 orders of magnitude. However, under the equivocal assumption of sustained exponential growth, we find that information transmission in the technosphere can potentially surpass that of the biosphere ∼90 years in the future, reflecting its increasing dominance.

Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit

Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in k_{B}T/bit, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.

Continuous odor profile monitoring to study olfactory navigation in small animals

Olfactory navigation is observed across species and plays a crucial role in locating resources for survival. In the laboratory, understanding the behavioral strategies and neural circuits underlying odor-taxis requires a detailed understanding of the animal's sensory environment. For small model organisms like Caenorhabditis elegans and larval Drosophila melanogaster, controlling and measuring the odor environment experienced by the animal can be challenging, especially for airborne odors, which are subject to subtle effects from airflow, temperature variation, and from the odor's adhesion, adsorption, or reemission. Here, we present a method to control and measure airborne odor concentration in an arena compatible with an agar substrate. Our method allows continuous controlling and monitoring of the odor profile while imaging animal behavior. We construct stationary chemical landscapes in an odor flow chamber through spatially patterned odorized air. The odor concentration is measured with a spatially distributed array of digital gas sensors. Careful placement of the sensors allows the odor concentration across the arena to be continuously inferred in space and monitored through time. We use this approach to measure the odor concentration that each animal experiences as it undergoes chemotaxis behavior and report chemotaxis strategies for C. elegans and D. melanogaster larvae populations as they navigate spatial odor landscapes.

Multiplexed microfluidic screening of bacterial chemotaxis

Microorganism sensing of and responding to ambient chemical gradients regulates a myriad of microbial processes that are fundamental to ecosystem function and human health and disease. The development of efficient, high-throughput screening tools for microbial chemotaxis is essential to disentangling the roles of diverse chemical compounds and concentrations that control cell nutrient uptake, chemorepulsion from toxins, and microbial pathogenesis. Here, we present a novel microfluidic multiplexed chemotaxis device (MCD) which uses serial dilution to simultaneously perform six parallel bacterial chemotaxis assays that span five orders of magnitude in chemostimulant concentration on a single chip. We first validated the dilution and gradient generation performance of the MCD, and then compared the measured chemotactic response of an established bacterial chemotaxis system (Vibrio alginolyticus) to a standard microfluidic assay. Next, the MCD's versatility was assessed by quantifying the chemotactic responses of different bacteria (Psuedoalteromonas haloplanktis, Escherichia coli) to different chemoattractants and chemorepellents. The MCD vastly accelerates the chemotactic screening process, which is critical to deciphering the complex sea of chemical stimuli underlying microbial responses.

Biphasic Chemokinesis of Mammalian Sperm

The female reproductive tract (FRT) continuously modulates mammalian sperm motion by releasing various clues as sperm migrate toward the fertilization site. An existing gap in our understanding of sperm migration within the FRT is a quantitative picture of how sperm respond to and navigate the biochemical clues within the FRT. In this experimental study, we have found that in response to biochemical clues, mammalian sperm display two distinct chemokinetic behaviors which are dependent upon the rheological properties of the media: chiral, characterized by swimming in circles; and hyperactive, characterized by random reorientation events. We used minimal theoretical modeling, along with statistical characterization of the chiral and hyperactive trajectories, to show that the effective diffusivity of these motion phases decreases with increasing concentration of chemical stimulant. In the context of navigation this concentration dependent chemokinesis suggests that the chiral or hyperactive motion refines the sperm search area within different FRT functional regions. Further, the ability to switch between phases indicates that sperm may use various stochastic navigational strategies, such as run and tumble or intermittent search, within the fluctuating and spatially heterogeneous environment of the FRT.

The MAPK/ERK channel capacity exceeds 6 bit/hour

Living cells utilize signaling pathways to sense, transduce, and process information. As the extracellular stimulation often has rich temporal characteristics which may govern dynamic cellular responses, it is important to quantify the rate of information flow through the signaling pathways. In this study, we used an epithelial cell line expressing a light-activatable FGF receptor and an ERK activity reporter to assess the ability of the MAPK/ERK pathway to transduce signal encoded in a sequence of pulses. By stimulating the cells with random light pulse trains, we demonstrated that the MAPK/ERK channel capacity is at least 6 bits per hour. The input reconstruction algorithm detects the light pulses with 1-min accuracy 5 min after their occurrence. The high information transmission rate may enable the pathway to coordinate multiple processes including cell movement and respond to rapidly varying stimuli such as chemoattracting gradients created by other cells.

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.

Smart micro- and nanorobots for water purification

Less than 1% of Earth's freshwater reserves is accessible. Industrialization, population growth and climate change are further exacerbating clean water shortage. Current water-remediation treatments fail to remove most pollutants completely or release toxic by-products into the environment. The use of self-propelled programmable micro- and nanoscale synthetic robots is a promising alternative way to improve water monitoring and remediation by overcoming diffusion-limited reactions and promoting interactions with target pollutants, including nano- and microplastics, persistent organic pollutants, heavy metals, oils and pathogenic microorganisms. This Review introduces the evolution of passive micro- and nanomaterials through active micro- and nanomotors and into advanced intelligent micro- and nanorobots in terms of motion ability, multifunctionality, adaptive response, swarming and mutual communication. After describing removal and degradation strategies, we present the most relevant improvements in water treatment, highlighting the design aspects necessary to improve remediation efficiency for specific contaminants. Finally, open challenges and future directions are discussed for the real-world application of smart micro- and nanorobots.

Colossal Power Extraction from Active Cyclic Brownian Information Engines

Brownian information engines can extract work from thermal fluctuations by utilizing information. To date, the studies on Brownian information engines consider the system in a thermal bath; however, many processes in nature occur in a nonequilibrium setting, such as the suspensions of self-propelled microorganisms or cellular environments called an active bath. Here, we introduce an archetypal model for a Maxwell-demon type cyclic Brownian information engine operating in a Gaussian correlated active bath capable of extracting more work than its thermal counterpart. We obtain a general integral fluctuation theorem for the active engine that includes additional mutual information gained from the active bath with a unique effective temperature. This effective description modifies the generalized second law and provides a new upper bound for the extracted work. Unlike the passive information engine operating in a thermal bath, the active information engine extracts colossal power that peaks at the finite cycle period. Our study provides fundamental insights into the design and functioning of synthetic and biological submicrometer motors in active baths under measurement and feedback control.

Information thermodynamics for deterministic chemical reaction networks

Information thermodynamics relates the rate of change of mutual information between two interacting subsystems to their thermodynamics when the joined system is described by a bipartite stochastic dynamics satisfying local detailed balance. Here, we expand the scope of information thermodynamics to deterministic bipartite chemical reaction networks, namely, composed of two coupled subnetworks sharing species but not reactions. We do so by introducing a meaningful notion of mutual information between different molecular features that we express in terms of deterministic concentrations. This allows us to formulate separate second laws for each subnetwork, which account for their energy and information exchanges, in complete analogy with stochastic systems. We then use our framework to investigate the working mechanisms of a model of chemically driven self-assembly and an experimental light-driven bimolecular motor. We show that both systems are constituted by two coupled subnetworks of chemical reactions. One subnetwork is maintained out of equilibrium by external reservoirs (chemostats or light sources) and powers the other via energy and information flows. In doing so, we clarify that the information flow is precisely the thermodynamic counterpart of an information ratchet mechanism only when no energy flow is involved.

Cellular Sensing Governs the Stability of Chemotactic Fronts

In contexts ranging from embryonic development to bacterial ecology, cell populations migrate chemotactically along self-generated chemical gradients, often forming a propagating front. Here, we theoretically show that the stability of such chemotactic fronts to morphological perturbations is determined by limitations in the ability of individual cells to sense and thereby respond to the chemical gradient. Specifically, cells at bulging parts of a front are exposed to a smaller gradient, which slows them down and promotes stability, but they also respond more strongly to the gradient, which speeds them up and promotes instability. We predict that this competition leads to chemotactic fingering when sensing is limited at too low chemical concentrations. Guided by this finding and by experimental data on E. coli chemotaxis, we suggest that the cells' sensory machinery might have evolved to avoid these limitations and ensure stable front propagation. Finally, as sensing of any stimuli is necessarily limited in living and active matter in general, the principle of sensing-induced stability may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.

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.

Perpetuating enzymatically-induced spatiotemporal pH and catalytic heterogeneity of a hydrogel by nanoparticles

The attainment of spatiotemporally inhomogeneous chemical and physical properties within a system is gaining attention across disciplines due to the resemblance to environmental and biological heterogeneity. Notably, the origin of natural pH gradients and how they have been incorporated in cellular systems is one of the most important questions in understanding the prebiotic origin of life. Herein, we have demonstrated a spatiotemporal pH gradient formation pattern on a hydrogel surface by employing two different enzymatic reactions, namely, the reactions of glucose oxidase (pH decreasing) and urease (pH increasing). We found here a generic pattern of spatiotemporal change in pH and proton transfer catalytic activity that was completely altered in a cationic gold nanoparticle containing hydrogel. In the absence of nanoparticles, the gradually generated macroscopic pH gradient slowly diminished with time, whereas the presence of nanoparticles helped to perpetuate the generated gradient effect. This behavior is due to the differential responsiveness of the interface of the cationic nanoparticle in temporally changing surroundings with increasing or decreasing pH or ionic contents. Moreover, the catalytic proton transfer ability of the nanoparticle showed a concerted kinetic response following the spatiotemporal pH dynamics in the gel matrix. Notably, this nanoparticle-driven spatiotemporally resolved gel matrix will find applicability in the area of the membrane-free generation and control of spatially segregated chemistry at the macroscopic scale.

This work reports perpetuating effect in enzymatically generated spatiotemporal pH gradient across a hydrogel in presence of cationic gold nanoparticle; showing a new route in spatially resolved chemistry in a membrane-free environment.