A modular gradient-sensing network for chemotaxis in Escherichia coli revealed by responses to time-varying stimuli

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.

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.

Signal integration in chemoreceptor complexes

Motile bacteria use large receptor arrays to detect chemical and physical stimuli in their environment, process this complex information, and accordingly bias their swimming in a direction they deem favorable. The chemoreceptor molecules form tripod-like trimers of receptor dimers through direct contacts between their cytoplasmic tips. A pair of trimers, together with a dedicated kinase enzyme, form a core signaling complex. Hundreds of core complexes network to form extended arrays. While considerable progress has been made in revealing the hierarchical structure of the array, the molecular properties underlying signal processing in these structures remain largely unclear. Here we analyzed the signaling properties of nonnetworked core complexes in live cells by following both conformational and kinase control responses to attractant stimuli and to output-biasing lesions at various locations in the receptor molecule. Contrary to the prevailing view that individual receptors are binary two-state devices, we demonstrate that conformational coupling between the ligand binding and the kinase-control receptor domains is, in fact, only moderate. In addition, we demonstrate communication between neighboring receptors through their trimer-contact domains that biases them to adopt similar signaling states. Taken together, these data suggest a view of signaling in receptor trimers that allows significant signal integration to occur within individual core complexes.

Chemotactic Micro/Nanomotors for Biomedical Applications

In nature, many organisms respond chemotactically to external chemical stimuli in order to extract nutrients or avoid danger. Inspired by this natural chemotaxis, micro/nanomotors with chemotactic properties have been developed and applied to study a variety of disease models. This chemotactic strategy has shown promising results and has attracted the attention of an increasing number of researchers. This paper mainly reviews the construction methods of different types of chemotactic micro/nanomotors, the mechanism of chemotaxis, and the potential applications in biomedicine. First, based on the classification of materials, the construction methods and therapeutic effects of chemotactic micro/nanomotors based on natural cells and synthetic materials in cellular and animal experiments will be elaborated in detail. Second, the mechanism of chemotaxis of micro/nanomotors is elaborated in detail: chemical reaction induced chemotaxis and physical process driven chemotaxis. In particular, the main differences and significant advantages between chemotactic micro/nanomotors and magnetic, electrical and optical micro/nanomotors are described. The applications of chemotactic micro/nanomotors in the biomedical fields in recent years are then summarized, focusing on the mechanism of action and therapeutic effects in cancer and cardiovascular disease. Finally, the authors are looking forward to the future development of chemotactic micro/nanomotors in the biomedical fields.

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.

Phenotypic consequences of logarithmic signaling in MAPK stress response

How cells respond to dynamic environmental changes is crucial for understanding fundamental biological processes and cell physiology. In this study, we developed an experimental and quantitative analytical framework to explore how dynamic stress gradients that change over time regulate cellular volume, signaling activation, and growth phenotypes. Our findings reveal that gradual stress conditions substantially enhance cell growth compared to conventional acute stress. This growth advantage correlates with a minimal reduction in cell volume dependent on the dynamic of stress. We explain the growth phenotype with our finding of a logarithmic signal transduction mechanism in the yeast Mitogen-Activated Protein Kinase (MAPK) osmotic stress response pathway. These insights into the interplay between gradual environments, cell volume change, dynamic cell signaling, and growth, advance our understanding of fundamental cellular processes in gradual stress environments.

Tethered particle motion of the adaptation enzyme CheR in bacterial chemotaxis

Bacteria perform chemotactic adaptation by sequential modification of multiple modifiable sites on chemoreceptors through stochastic action of tethered adaptation enzymes (CheR and CheB). To study the molecular kinetics of this process, we measured the response to different concentrations of MeAsp for the Tar-only Escherichia coli strain. We found a strong dependence of the methylation rate on the methylation level and established a new mechanism of adaptation kinetics due to tethered particle motion of the methylation enzyme CheR. Experiments with various lengths of the C-terminal flexible chain in the Tar receptor further validated this mechanism. The tethered particle motion resulted in a CheR concentration gradient that ensures encounter-rate matching of the sequential modifiable sites. An analytical model of multisite catalytic reaction showed that this enables robustness of methylation to fluctuations in receptor activity or cell-to-cell variations in the expression of adaptation enzymes and reduces the variation in methylation level among individual receptors.

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.

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.

Rate thresholds in cell signaling have functional and phenotypic consequences in non-linear time-dependent environments

All cells employ signal transduction pathways to respond to physiologically relevant extracellular cytokines, stressors, nutrient levels, hormones, morphogens, and other stimuli that vary in concentration and rate in healthy and diseased states. A central unsolved fundamental question in cell signaling is whether and how cells sense and integrate information conveyed by changes in the rate of extracellular stimuli concentrations, in addition to the absolute difference in concentration. We propose that different environmental changes over time influence cell behavior in addition to different signaling molecules or different genetic backgrounds. However, most current biomedical research focuses on acute environmental changes and does not consider how cells respond to environments that change slowly over time. As an example of such environmental change, we review cell sensitivity to environmental rate changes, including the novel mechanism of rate threshold. A rate threshold is defined as a threshold in the rate of change in the environment in which a rate value below the threshold does not activate signaling and a rate value above the threshold leads to signal activation. We reviewed p38/Hog1 osmotic stress signaling in yeast, chemotaxis and stress response in bacteria, cyclic adenosine monophosphate signaling in Amoebae, growth factors signaling in mammalian cells, morphogen dynamics during development, temporal dynamics of glucose and insulin signaling, and spatio-temproral stressors in the kidney. These reviewed examples from the literature indicate that rate thresholds are widespread and an underappreciated fundamental property of cell signaling. Finally, by studying cells in non-linear environments, we outline future directions to understand cell physiology better in normal and pathophysiological conditions.

A negative feedback loop in the GPCR pathway underlies efficient coding of external stimuli

Efficient navigation based on chemical cues is an essential feature shared by all animals. These cues may be encountered in complex spatiotemporal patterns and with orders of magnitude varying intensities. Nevertheless, sensory neurons accurately extract the relevant information from such perplexing signals. Here, we show how a single sensory neuron in Caenorhabditis elegans animals can cell-autonomously encode complex stimulus patterns composed of instantaneous sharp changes and of slowly changing continuous gradients. This encoding relies on a simple negative feedback in the G-protein-coupled receptor (GPCR) signaling pathway in which TAX-6/Calcineurin plays a key role in mediating the feedback inhibition. This negative feedback supports several important coding features that underlie an efficient navigation strategy, including exact adaptation and adaptation to the magnitude of the gradient's first derivative. A simple mathematical model explains the fine neural dynamics of both wild-type and tax-6 mutant animals, further highlighting how the calcium-dependent activity of TAX-6/Calcineurin dictates GPCR inhibition and response dynamics. As GPCRs are ubiquitously expressed in all sensory neurons, this mechanism may be a general solution for efficient cell-autonomous coding of external stimuli.

A biophysical threshold for biofilm formation

Bacteria are ubiquitous in our daily lives, either as motile planktonic cells or as immobilized surface-attached biofilms. These different phenotypic states play key roles in agriculture, environment, industry, and medicine; hence, it is critically important to be able to predict the conditions under which bacteria transition from one state to the other. Unfortunately, these transitions depend on a dizzyingly complex array of factors that are determined by the intrinsic properties of the individual cells as well as those of their surrounding environments, and are thus challenging to describe. To address this issue, here, we develop a generally-applicable biophysical model of the interplay between motility-mediated dispersal and biofilm formation under positive quorum sensing control. Using this model, we establish a universal rule predicting how the onset and extent of biofilm formation depend collectively on cell concentration and motility, nutrient diffusion and consumption, chemotactic sensing, and autoinducer production. Our work thus provides a key step toward quantitatively predicting and controlling biofilm formation in diverse and complex settings.

Influence of confinement on the spreading of bacterial populations

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings—despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading via motility that also incorporates cellular growth and division, and explicitly considers the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading—eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.

The spreading of bacteria through their environments critically impacts our everyday lives; it can be harmful, underlying the progression of infections and spoilage of foods, or can be beneficial, enabling the delivery of therapeutics, sustaining plant growth, and remediating polluted terrain. In all these cases, bacteria typically inhabit crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and regulate their spreading. However, existing models of spreading typically focus on cells in unconfined settings, and thus are frequently not applicable to cells in more complex environments. Here, we address this gap in knowledge by extending the classic Keller-Segel model of bacterial spreading via motility to also incorporate cellular growth and division, and explicitly consider the influence of confinement. Through numerical simulations of this extended model, we show how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations—in particular, driving a transition from chemotactic spreading of motile cells to growth-driven spreading via a slower, jammed front. These results provide a foundation for further investigations of the influence of confinement on bacterial spreading, both by yielding testable predictions for future experiments, and by providing guidelines to predict and control the dynamics of bacterial populations in complex and crowded environments.

A new mode of swimming in singly flagellated Pseudomonas aeruginosa

SignificanceThe monotrichous Pseudomonas aeruginosa was usually thought to swim in a pattern of "run and reverse" (possibly with pauses in between), where straight runs alternated with reverses with angular changes of swimming direction near 180°. Here, by simultaneously tracking the cell swimming and the morphology of its flagellum, we discovered a swimming mode in P. aeruginosa-the wrap mode, during which the flagellar filament wrapped around the cell body and induced large fluctuation of the body orientation. The wrap mode randomized swimming direction, resulting in a broad distribution of angular changes over 0 to 180° with a peak near 90°. This allowed the bacterium to explore the environment more efficiently, which we confirmed by stochastic simulations of P. aeruginosa chemotaxis.

Chemotactic smoothing of collective migration

Collective migration-the directed, coordinated motion of many self-propelled agents-is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient-revealing a population-scale consequence of the manner in which individual cells transduce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.

Hexameric rings of the scaffolding protein CheW enhance response sensitivity and cooperativity in Escherichia coli chemoreceptor arrays

The Escherichia coli chemoreceptor array is a supramolecular assembly that enables cells to respond to extracellular cues dynamically and with great precision and sensitivity. In the array, transmembrane receptors organized as trimers of dimers are connected at their cytoplasmic tips by hexameric rings of alternating subunits of the kinase CheA and the scaffolding protein CheW (CheA-CheW rings). Interactions of CheW molecules with the members of receptor trimers not directly bound to CheA-CheW rings may lead to the formation of hexameric CheW rings in the chemoreceptor array. Here, we detected such CheW rings with a cellular cysteine-directed cross-linking assay and explored the requirements for their formation and their participation in array assembly. We found that CheW ring formation varied with cellular CheW abundance, depended on the presence of receptors capable of a trimer-of-dimers arrangement, and did not require CheA. Cross-linking studies of a CheA~CheW fusion protein incapable of forming homomeric CheW oligomers demonstrated that CheW rings were not essential for the assembly of CheA-containing arrays. Förster resonance energy transfer (FRET)-based kinase assays of arrays containing variable amounts of CheW rings revealed that CheW rings enhanced the cooperativity and the sensitivity of the responses to attractants. We propose that six-membered CheW rings provide the additional interconnectivity required for optimal signaling and gradient tracking performance by chemosensory arrays.

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.

Biomolecular mechanisms for signal differentiation

Cells can sense temporal changes of molecular signals, allowing them to predict environmental variations and modulate their behavior. This paper elucidates biomolecular mechanisms of time derivative computation, facilitating the design of reliable synthetic differentiator devices for a variety of applications, ultimately expanding our understanding of cell behavior. In particular, we describe and analyze three alternative biomolecular topologies that are able to work as signal differentiators to input signals around their nominal operation. We propose strategies to preserve their performance even in the presence of high-frequency input signal components which are detrimental to the performance of most differentiators. We find that the core of the proposed topologies appears in natural regulatory networks and we further discuss their biological relevance. The simple structure of our designs makes them promising tools for realizing derivative control action in synthetic biology.

Genes and knowledge: Response to Baverstock, K. the gene an appraisal. https://doi.org/10.1016/j.pbiomolbio.2021.04.005

This response aims to expand on some of the issues raised by Keith Baverstock's The Gene: An Appraisal, especially on the evolution and nature of knowledge in living things. In contrast to the simple associationism envisaged in "genetic information", it emphasises the dynamic complexity and changeability of most natural environments, and, therefore, predictability based on underlying statistical structures. That seems to be the basis of the "cognitive" functions increasingly being reported about cellular, as well as more evolved, functions, and of the autonomous agency of organisms thriving creatively in complex environments.

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.

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.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.

Chemotactic migration of bacteria in porous media

Chemotactic migration of bacteria-their ability to direct multicellular motion along chemical gradients-is central to processes in agriculture, the environment, and medicine. However, current understanding of migration is based on studies performed in bulk liquid, despite the fact that many bacteria inhabit tight porous media such as soils, sediments, and biological gels. Here, we directly visualize the chemotactic migration of Escherichia coli populations in well-defined 3D porous media in the absence of any other imposed external forcing (e.g., flow). We find that pore-scale confinement is a strong regulator of migration. Strikingly, cells use a different primary mechanism to direct their motion in confinement than in bulk liquid. Furthermore, confinement markedly alters the dynamics and morphology of the migrating population-features that can be described by a continuum model, but only when standard motility parameters are substantially altered from their bulk liquid values to reflect the influence of pore-scale confinement. Our work thus provides a framework to predict and control the migration of bacteria, and active matter in general, in complex environments.

An Automated Tabletop Continuous Culturing System with Multicolor Fluorescence Monitoring for Microbial Gene Expression and Long-Term Population Dynamics

Real-time monitoring of gene expression dynamics and population levels in a multispecies microbial community could enable the study of the role of changing gene expression patterns on eco-evolutionary outcomes. Here we report the design and validation of a unique experimental platform with an in situ fluorescence measurement system that has high dynamic range and temporal resolution and is capable of monitoring multiple fluorophores for long-term gene expression and population dynamics experiments. We demonstrate the capability of our system to capture gene expression dynamics in response to external perturbations in two synthetic genetic systems: a simple inducible genetic circuit and a bistable toggle switch. Finally, in exploring the population dynamics of a two species microbial community, we show that our system can capture the switch between competitive exclusion and long-term coexistence in response to different nutrient conditions.

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.

Collective motion enhances chemotaxis in a two-dimensional bacterial swarm

In a dilute liquid environment in which cell-cell interaction is negligible, flagellated bacteria, such as Escherichia coli, perform chemotaxis by biased random walks alternating between run-and-tumble. In a two-dimensional crowded environment, such as a bacterial swarm, the typical behavior of run-and-tumble is absent, and this raises the question whether and how bacteria can perform chemotaxis in a swarm. Here, by examining the chemotactic behavior as a function of the cell density, we showed that chemotaxis is surprisingly enhanced because of cell crowding in a bacterial swarm, and this enhancement is correlated with increase in the degree of cell body alignment. Cells tend to form clusters that move collectively in a swarm with increased effective run length, and we showed analytically that this resulted in increased drift velocity toward attractants. We also explained the enhancement by stochastically simulating bacterial chemotaxis in a swarm. We found that cell crowding in a swarm enhances chemotaxis if the cell-cell interactions used in the simulation induce cell-cell alignment, but it impedes chemotaxis if the interactions are collisions that randomize cell moving direction. Therefore, collective motion in a bacterial swarm enhances chemotaxis.

Theory for the optimal detection of time-varying signals in cellular sensing systems

Living cells often need to measure chemical concentrations that vary in time, yet how accurately they can do so is poorly understood. Here, we present a theory that fully specifies, without any adjustable parameters, the optimal design of a canonical sensing system in terms of two elementary design principles: (1) there exists an optimal integration time, which is determined by the input statistics and the number of receptors; and (2) in the optimally designed system, the number of independent concentration measurements as set by the number of receptors and the optimal integration time equals the number of readout molecules that store these measurements and equals the work to store these measurements reliably; no resource is then in excess and hence wasted. Applying our theory to the Escherichia coli chemotaxis system indicates that its integration time is not only optimal for sensing shallow gradients but also necessary to enable navigation in these gradients.

Sensitivity minimization, biological homeostasis and information theory

All organisms must be able to adapt to changes in the environment. To this end, they have developed sophisticated regulatory mechanisms to ensure homeostasis. Control engineers, who must design similar regulatory systems, have developed a number of general principles that govern feedback regulation. These lead to constraints which impose trade-offs that arise when developing controllers to minimize the effect of external disturbances on systems. Here, we review some of these trade-offs, particularly Bode's integral formula. We also highlight its connection to information theory, by showing that the constraints in sensitivity minimization can be cast as limitations on the information transmission through a system, and these have their root in causality. Finally, we look at how these constraints arise in two biological systems: glycolytic oscillations and the energy cost of perfect adaptation in a bacterial chemotactic pathway.

A rate threshold mechanism regulates MAPK stress signaling and survival

Cells are exposed to changes in extracellular stimulus concentration that vary as a function of rate. However, how cells integrate information conveyed from stimulation rate along with concentration remains poorly understood. Here, we examined how varying the rate of stress application alters budding yeast mitogen-activated protein kinase (MAPK) signaling and cell behavior at the single-cell level. We show that signaling depends on a rate threshold that operates in conjunction with stimulus concentration to determine the timing of MAPK signaling during rate-varying stimulus treatments. We also discovered that the stimulation rate threshold and stimulation rate-dependent cell survival are sensitive to changes in the expression levels of the Ptp2 phosphatase, but not of another phosphatase that similarly regulates osmostress signaling during switch-like treatments. Our results demonstrate that stimulation rate is a regulated determinant of cell behavior and provide a paradigm to guide the dissection of major stimulation rate dependent mechanisms in other systems.

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.

Diverse Cell Stimulation Kinetics Identify Predictive Signal Transduction Models

Computationally understanding the molecular mechanisms that give rise to cell signaling responses upon different environmental, chemical, and genetic perturbations is a long-standing challenge that requires models that fit and predict quantitative responses for new biological conditions. Overcoming this challenge depends not only on good models and detailed experimental data but also on the rigorous integration of both. We propose a quantitative framework to perturb and model generic signaling networks using multiple and diverse changing environments (hereafter "kinetic stimulations") resulting in distinct pathway activation dynamics. We demonstrate that utilizing multiple diverse kinetic stimulations better constrains model parameters and enables predictions of signaling dynamics that would be impossible using traditional dose-response or individual kinetic stimulations. To demonstrate our approach, we use experimentally identified models to predict signaling dynamics in normal, mutated, and drug-treated conditions upon multitudes of kinetic stimulations and quantify which proteins and reaction rates are most sensitive to which extracellular stimulations.

Constrained optimal foraging by marine bacterioplankton on particulate organic matter

Patch use theory predicts that organisms foraging in a heterogeneous resource landscape balance their residence time on a patch yielding diminishing returns with the sum of the metabolic, predation, and opportunity costs of foraging. By combining single-cell tracking with mathematical modeling, we show that bacteria foraging on seascapes of organic particles switch between attached and planktonic lifestyles and tune the time spent on particles to increase individual fitness. As predicted by patch use theory, bacteria remain longer on particles of higher quality and in poor environments, or when search times for fresh particles are longer. These results show that patch use theory can be a valuable framework to understand not only animals, but also microorganisms, and ultimately their ecosystem-level consequences.

Optimal foraging theory provides a framework to understand how organisms balance the benefits of harvesting resources within a patch with the sum of the metabolic, predation, and missed opportunity costs of foraging. Here, we show that, after accounting for the limited environmental information available to microorganisms, optimal foraging theory and, in particular, patch use theory also applies to the behavior of marine bacteria in particle seascapes. Combining modeling and experiments, we find that the marine bacterium Vibrio ordalii optimizes nutrient uptake by rapidly switching between attached and planktonic lifestyles, departing particles when their nutrient concentration is more than hundredfold higher than background. In accordance with predictions from patch use theory, single-cell tracking reveals that bacteria spend less time on nutrient-poor particles and on particles within environments that are rich or in which the travel time between particles is smaller, indicating that bacteria tune the nutrient concentration at detachment to increase their fitness. A mathematical model shows that the observed behavioral switching between exploitation and dispersal is consistent with foraging optimality under limited information, namely, the ability to assess the harvest rate of nutrients leaking from particles by molecular diffusion. This work demonstrates how fundamental principles in behavioral ecology traditionally applied to animals can hold right down to the scale of microorganisms and highlights the exquisite adaptations of marine bacterial foraging. The present study thus provides a blueprint for a mechanistic understanding of bacterial uptake of dissolved organic matter and bacterial production in the ocean—processes that are fundamental to the global carbon cycle.

Modeling navigation by weaver ants in an unfamiliar, featureless environment

The motion of individual weaver ants from Oecophylla smaragdina was tracked within a small arena to study the algorithm that these ants use for navigation. The arena, a floor tile, was either clean or partly covered by a mild chemical repellent. Statistical properties of the observed motion of the ant can be described by a model that is analogous to the Langevin theory of the motion of Brownian particles. With each time step, the velocity of the ant changes by a random vector with a robust probability distribution. When the average ant encounters the chemical repellent it responds, like a particle seeing a potential energy barrier, by initially slowing before recovering towards its equilibrium state of motion. The model accounts for most qualitative properties of motion with a small number of parameters.

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

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

Sequential modification of bacterial chemoreceptors is key for achieving both accurate adaptation and high gain

Many regulatory and signaling proteins have multiple modification sites. In bacterial chemotaxis, each chemoreceptor has multiple methylation sites that are responsible for adaptation. However, whether the ordering of the multisite methylation process affects adaptation remains unclear. Furthermore, the benefit of having multiple modification sites is also unclear. Here, we show that sequentially ordered methylation/demethylation is critical for perfect adaptation; adaptation accuracy decreases as randomness in the multisite methylation process increases. A tradeoff between adaptation accuracy and response gain is discovered. We find that this accuracy-gain tradeoff is lifted significantly by having more methylation sites, but only when the multisite modification process is sequential. Our study suggests that having multiple modification sites and a sequential modification process constitute a general strategy to achieve both accurate adaptation and high response gain simultaneously. Our theory agrees with existing data and predictions are made to help identify the molecular mechanism underlying ordered covalent modifications.

Bacterial chemoreceptors have multiple methylation sites, but whether the order of methylation matters is unclear. Here, the authors show that sequentially ordered methylation is critical for perfect adaptation and for attenuating the trade-off between accurate adaptation and high response gain.

Emergence of collective oscillations in adaptive cells

Collective oscillations of cells in a population appear under diverse biological contexts. Here, we establish a set of common principles by categorising the response of individual cells against a time-varying signal. A positive intracellular signal relay of sufficient gain from participating cells is required to sustain the oscillations, together with phase matching. The two conditions yield quantitative predictions for the onset cell density and frequency in terms of measured single-cell and signal response functions. Through mathematical constructions, we show that cells that adapt to a constant stimulus fulfil the phase requirement by developing a leading phase in an active frequency window that enables cell-to-signal energy flow. Analysis of dynamical quorum sensing in several cellular systems with increasing biological complexity reaffirms the pivotal role of adaptation in powering oscillations in an otherwise dissipative cell-to-cell communication channel. The physical conditions identified also apply to synthetic oscillatory systems.

There are many examples of cell populations exhibiting density-dependent collective oscillatory behaviour. Here, the authors show that sustained collective oscillations emerge when cells anticipate variation in signal and attempt to amplify it, a property that can be linked to adaptation.

Under Elevated c-di-GMP in Escherichia coli, YcgR Alters Flagellar Motor Bias and Speed Sequentially, with Additional Negative Control of the Flagellar Regulon via the Adaptor Protein RssB

In Escherichia coli and Salmonella, the c-di-GMP effector YcgR inhibits flagellar motility by interacting directly with the motor to alter both its bias and speed. Here, we demonstrate that in both of these bacteria, YcgR acts sequentially, altering motor bias first and then decreasing motor speed. We show that when c-di-GMP levels are high, deletion of ycgR restores wild-type motor behavior in E. coli, indicating that YcgR is the only motor effector in this bacterium. Yet, motility and chemotaxis in soft agar do not return to normal, suggesting that there is a second mechanism that inhibits motility under these conditions. In Salmonella, c-di-GMP-induced synthesis of extracellular cellulose has been reported to entrap flagella and to be responsible for the YcgR-independent motility defect. We found that this is not the case in E. coli Instead, we found through reversion analysis that deletion of rssB, which codes for a response regulator/adaptor protein that normally directs ClpXP protease to target σ^S for degradation, restored wild-type motility in the ycgR mutant. Our data suggest that high c-di-GMP levels may promote altered interactions between these proteins to downregulate flagellar gene expression.IMPORTANCE Flagellum-driven motility has been studied in E. coli and Salmonella for nearly half a century. Over 60 genes control flagellar assembly and function. The expression of these genes is regulated at multiple levels in response to a variety of environmental signals. Cues that elevate c-di-GMP levels, however, inhibit motility by direct binding of the effector YcgR to the flagellar motor. In this study conducted mainly in E. coli, we show that YcgR is the only effector of motor control and tease out the order of YcgR-mediated events. In addition, we find that the σ^S regulator protein RssB contributes to negative regulation of flagellar gene expression when c-di-GMP levels are elevated.

An Adaptive-Threshold Mechanism for Odor Sensation and Animal Navigation

Identifying the environmental information and computations that drive sensory detection is key for understanding animal behavior. Using experimental and theoretical analysis of AWC^ON, a well-described olfactory neuron in C. elegans, here we derive a general and broadly useful model that matches stimulus history to odor sensation and behavioral responses. We show that AWC^ON sensory activity is regulated by an absolute signal threshold that continuously adapts to odor history, allowing animals to compare present and past odor concentrations. The model predicts sensory activity and probabilistic behavior during animal navigation in different odor gradients and across a broad stimulus regime. Genetic studies demonstrate that the cGMP-dependent protein kinase EGL-4 determines the timescale of threshold adaptation, defining a molecular basis for a critical model feature. The adaptive threshold model efficiently filters stimulus noise, allowing reliable sensation in fluctuating environments, and represents a feedforward sensory mechanism with implications for other sensory systems.

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.

Optimal compressed sensing strategies for an array of nonlinear olfactory receptor neurons with and without spontaneous activity

There are numerous different odorant molecules in nature but only a relatively small number of olfactory receptor neurons (ORNs) in brains. This "compressed sensing" challenge is compounded by the constraint that ORNs are nonlinear sensors with a finite dynamic range. Here, we investigate possible optimal olfactory coding strategies by maximizing mutual information between odor mixtures and ORNs' responses with respect to the bipartite odor-receptor interaction network (ORIN) characterized by sensitivities between all odorant-ORN pairs. For ORNs without spontaneous (basal) activity, we find that the optimal ORIN is sparse-a finite fraction of sensitives are zero, and the nonzero sensitivities follow a broad distribution that depends on the odor statistics. We show analytically that sparsity in the optimal ORIN originates from a trade-off between the broad tuning of ORNs and possible interference. Furthermore, we show that the optimal ORIN enhances performances of downstream learning tasks (reconstruction and classification). For ORNs with a finite basal activity, we find that having inhibitory odor-receptor interactions increases the coding capacity and the fraction of inhibitory interactions increases with the ORN basal activity. We argue that basal activities in sensory receptors in different organisms are due to the trade-off between the increase in coding capacity and the cost of maintaining the spontaneous basal activity. Our theoretical findings are consistent with existing experiments and predictions are made to further test our theory. The optimal coding model provides a unifying framework to understand the peripheral olfactory systems across different organisms.

Regulation of the chemotaxis histidine kinase CheA: A structural perspective

Bacteria sense and respond to their environment through a highly conserved assembly of transmembrane chemoreceptors (MCPs), the histidine kinase CheA, and the coupling protein CheW, hereafter termed "the chemosensory array". In recent years, great strides have been made in understanding the architecture of the chemosensory array and how this assembly engenders sensitive and cooperative responses. Nonetheless, a central outstanding question surrounds how receptors modulate the activity of the CheA kinase, the enzymatic output of the sensory system. With a focus on recent advances, we summarize the current understanding of array structure and function to comment on the molecular mechanism by which CheA, receptors and CheW generate the high sensitivity, gain and dynamic range emblematic of bacterial chemotaxis. The complexity of the chemosensory arrays has motivated investigation with many different approaches. In particular, structural methods, genetics, cellular activity assays, nanodisc technology and cryo-electron tomography have provided advances that bridge length scales and connect molecular mechanism to cellular function. Given the high degree of component integration in the chemosensory arrays, we ultimately aim to understand how such networked molecular interactions generate a whole that is truly greater than the sum of its parts. This article is part of a Special Issue entitled: Molecular biophysics of membranes and membrane proteins.

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.

Hard Limits and Performance Tradeoffs in a Class of Antithetic Integral Feedback Networks

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism called antithetic integral feedback, which can be implemented using the binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of antithetic integral feedback and contribute to a more general theory of biological control systems.

Communication codes in developmental signaling pathways

A handful of core intercellular signaling pathways play pivotal roles in a broad variety of developmental processes. It has remained puzzling how so few pathways can provide the precision and specificity of cell-cell communication required for multicellular development. Solving this requires us to quantitatively understand how developmentally relevant signaling information is actively sensed, transformed and spatially distributed by signaling pathways. Recently, single cell analysis and cell-based reconstitution, among other approaches, have begun to reveal the 'communication codes' through which information is represented in the identities, concentrations, combinations and dynamics of extracellular ligands. They have also revealed how signaling pathways decipher these features and control the spatial distribution of signaling in multicellular contexts. Here, we review recent work reporting the discovery and analysis of communication codes and discuss their implications for diverse developmental processes.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

Biological signal generators: integrating synthetic biology tools and in silico control

Biological networks sense extracellular stimuli and generate appropriate outputs within the cell that determine cellular response. Biological signal generators are becoming an important tool for understanding how information is transmitted in these networks and controlling network behavior. Signal generators produce well-defined, dynamic, intracellular signals of important network components, such as kinase activity or the concentration of a specific transcription factor. Synthetic biology tools coupled with in silico control have enabled the construction of these sophisticated biological signal generators. Here we review recent advances in biological signal generator construction and their use in systems biology studies. Challenges for constructing signal generators for a wider range of biological networks and generalizing their use are discussed.