Predicting chemical environments of bacteria from receptor signaling

Persistent pseudopod splitting is an effective chemotaxis strategy in shallow gradients

Single-cell organisms and various cell types use a range of motility modes when following a chemical gradient, but it is unclear which mode is best suited for different gradients. Here, we model directional decision-making in chemotactic amoeboid cells as a stimulus-dependent actin recruitment contest. Pseudopods extending from the cell body compete for a finite actin pool to push the cell in their direction until one pseudopod wins and determines the direction of movement. Our minimal model provides a quantitative understanding of the strategies cells use to reach the physical limit of accurate chemotaxis, aligning with data without explicit gradient sensing or cellular memory for persistence. To generalize our model, we employ reinforcement learning optimization to study the effect of pseudopod suppression, a simple but effective cellular algorithm by which cells can suppress possible directions of movement. Different pseudopod-based chemotaxis strategies emerge naturally depending on the environment and its dynamics. For instance, in static gradients, cells can react faster at the cost of pseudopod accuracy, which is particularly useful in noisy, shallow gradients where it paradoxically increases chemotactic accuracy. In contrast, in dynamics gradients, cells form de novo pseudopods. Overall, our work demonstrates mechanical intelligence for high chemotaxis performance with minimal cellular regulation.

Design patterns of biological cells

Design patterns are generalized solutions to frequently recurring problems. They were initially developed by architects and computer scientists to create a higher level of abstraction for their designs. Here, we extend these concepts to cell biology to lend a new perspective on the evolved designs of cells' underlying reaction networks. We present a catalog of 21 design patterns divided into three categories: creational patterns describe processes that build the cell, structural patterns describe the layouts of reaction networks, and behavioral patterns describe reaction network function. Applying this pattern language to the E. coli central metabolic reaction network, the yeast pheromone response signaling network, and other examples lends new insights into these systems.

Network topology-directed design of molecular CPU for cell-like dynamic information processing

Natural cells (NCs) can automatically and continuously respond to fluctuant external information and distinguish meaningful stimuli from weak noise depending on their powerful genetic and protein networks. We herein report a network topology-directed design of dynamic molecular processing system (DMPS) as a molecular central processing unit that powers an artificial cell (AC) able to process fluctuant information in its immediate environment similar to NCs. By constructing a mixed cell community, ACs and NCs have synchronous response to fluctuant extracellular stimuli under physiological condition and in a blood vessel-mimic circulation system. We also show that fluctuant bioinformation released by NCs can be received and processed by ACs. The molecular design of DMPS-powered AC is expected to allow a profound understanding of biological systems, advance the construction of intelligent molecular systems, and promote more elegant bioengineering applications.

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.

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.

Limnohabitans radicicola sp. nov., a slow-growing bacterium isolated from rhizosphere of rice plant and emended description of the genus Limnohabitans

In the present study, in an attempt to explore the diversity of bacteria in the roots of rice plants, a Gram-stain-negative, motile, facultatively anaerobic, non-pigmented, catalase-positive, oxidase-negative and rod-shaped bacterium with polar flagella was isolated. Phylogenetic analysis based on 16S rRNA gene sequences revealed highest sequence similarity to Limnohabitans parvus KCTC 42859^T (98.2%) followed by Limnohabitans curvus KCTC 42562^T (98%), Limnohabitans planktonicicus II-D5^T (97.9%) and Limnohabitans australis MWH-BRAZ-DAM2D^T (97.4%). Growth of strain JUR4^T occurred at 10-37 °C (optimum, 30 °C), at pH 5.5-8.0 (optimum, 6.5-7) and in the presence of 0-0.2% NaCl (optimum, 0%, w/v). The genome size of strain JUR4^T was found to be 3.34 Mb containing 3139 predicted protein-coding genes with a DNA G+C content of 61.5 mol%. The digital DNA-DNA hybridization and average nucleotide identity values between the genome sequence of strain JUR4^T and closely related reference strains were 21.0-24.8% and 74.7-81.4%, respectively. Strain JUR4^T contained diphosphatidylglycerol, phoshatidylethanolamine, one unidentified phosphoglycolipid, one unidentified aminophosphoglycolipid, one unidentified phospholipid and seven unidentified glycolipids. The major fatty acids were C_16:0 and summed feature 3 (comprising C_16:1 ω7c and/or C_16:1 ω6c), and ubiquinone Q-8 was the sole isoprenoid quinone. So far, all species belonging to the genus Limnohabitans have been described as non-motile and devoid of flagella. All species were isolated from freshwater and are therefore denoted as planktonic bacteria. This present study introduces a novel motile member of Limnohabitans isolated from the root of rice plant, and introduces the genes associated with motility and methyl-accepting chemotaxis proteins. Phylogenetic, phenotypic, chemotaxonomic and genotypic data clearly indicates that strain JUR4^T represents a novel species of the genus Limnohabitans for which the name Limnohabitans radicicola sp. nov. is proposed. The type strain is JUR4^T (=KACC 21745^T=NBRC 114484^T).

Multi-bit Boolean model for chemotactic drift of Escherichia coli

Dynamic biological systems can be modelled to an equivalent modular structure using Boolean networks (BNs) due to their simple construction and relative ease of integration. The chemotaxis network of the bacterium Escherichia coli (E. coli) is one of the most investigated biological systems. In this study, the authors developed a multi-bit Boolean approach to model the drifting behaviour of the E. coli chemotaxis system. Their approach, which is slightly different than the conventional BNs, is designed to provide finer resolution to mimic high-level functional behaviour. Using this approach, they simulated the transient and steady-state responses of the chemoreceptor sensory module. Furthermore, they estimated the drift velocity under conditions of the exponential nutrient gradient. Their predictions on chemotactic drifting are in good agreement with the experimental measurements under similar input conditions. Taken together, by simulating chemotactic drifting, they propose that multi-bit Boolean methodology can be used for modelling complex biological networks. Application of the method towards designing bio-inspired systems such as nano-bots is discussed.

A Multi-Scale Approach to Modeling E. coli Chemotaxis

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

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.

Applying machine learning to the flagellar motor for biosensing

Escherichia coli detects and follows chemical gradients in its environment in a process known as chemotaxis. The performance of chemotaxis approaches fundamental biosensor speed and sensitivity limits, but there have been relatively few attempts to incorporate the response into a functional biosensor. Toward that end, we have developed software to process digital microscope images of a large number of tethered E. coli responding to different chemical perturbations. Upwards of fifty cells can be recorded in one experiment, allowing for rapid labeling of the chemotactic responses of multiple cells. After we collected hundreds of wild-type chemotactic E. coli motor responses to dilutions of aspartate and leucine, we trained a support vector classifier (SVC) to estimate the order of magnitude of aspartate concentration between 0M, 100nM, and 1μM with a single cell classification subset accuracy of 69%. We trained another SVC to differentiate between aspartate and leucine with a single cell classification subset accuracy of 83%. Using a majority-vote method on a bacterial population of size N, estimates have 95% confidence for N = 27 bacteria for concentration detection and N = 9 bacteria for chemical differentiation. These methods are a step towards adaptable chemotaxis-based biosensing.

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

We present in vivo single-cell FRET measurements in the Escherichia coli chemotaxis system that reveal pervasive signaling variability, both across cells in isogenic populations and within individual cells over time. We quantify cell-to-cell variability of adaptation, ligand response, as well as steady-state output level, and analyze the role of network design in shaping this diversity from gene expression noise. In the absence of changes in gene expression, we find that single cells demonstrate strong temporal fluctuations. We provide evidence that such signaling noise can arise from at least two sources: (i) stochastic activities of adaptation enzymes, and (ii) receptor-kinase dynamics in the absence of adaptation. We demonstrate that under certain conditions, (ii) can generate giant fluctuations that drive signaling activity of the entire cell into a stochastic two-state switching regime. Our findings underscore the importance of molecular noise, arising not only in gene expression but also in protein networks.

Drift and Behavior of E. coli Cells

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. Whereas maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

Emergent properties of bacterial chemotaxis pathway

The chemotaxis pathway of Escherichia coli is the most studied sensory system in prokaryotes. The highly conserved general architecture of this pathway consists of two modules which mediate signal transduction and adaptation. The signal transduction module detects and amplifies changes in environmental conditions and rapidly transmits these signals to control bacterial swimming behavior. The adaptation module gradually resets the activity and sensitivity of the first module after initial stimulation and thereby enables the temporal comparisons necessary for bacterial chemotaxis. Recent experimental and theoretical work has unraveled multiple quantitative features emerging from the interplay between these two modules. This has laid the groundwork for rationalization of these emerging properties in the context of the evolutionary optimization of the chemotactic behavior.

Stochastic feeding dynamics arise from the need for information and energy

Animals regulate their food intake in response to the available level of food. Recent observations of feeding dynamics in small animals showed feeding patterns of bursts and pauses, but their function is unknown. Here, we present a data-driven decision-theoretical model of feeding in Caenorhabditis elegans Our central assumption is that food intake serves a dual purpose: to gather information about the external food level and to ingest food when the conditions are good. The model recapitulates experimentally observed feeding patterns. It naturally implements trade-offs between speed versus accuracy and exploration versus exploitation in responding to a dynamic environment. We find that the model predicts three distinct regimes in responding to a dynamical environment, with a transition region where animals respond stochastically to periodic signals. This stochastic response accounts for previously unexplained experimental data.

A Boolean approach to bacterial chemotaxis

Bacterium such as Escherichia coli (E. coli) show biased Brownian motion in different chemical concentration gradients. This chemical sensitive motility or chemotaxis has gained considerable interest among scientists for some remarkable features such as chemo-sensory dynamic range, adaptation, diffusion and drift. A Boolean model of the whole chemotaxis process has been developed in this manuscript. The response of the circuit is in accordance with the experimental results available in the literature, providing indirect validation of the model. This simple Boolean network (BN) can be easily integrated into the paradigm of modular whole cell modelling. Another crucial application is in designing bio-inspired micro-robots to detect certain spatio-temporal chemical signatures.

Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation

Many organisms navigate gradients by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles whenever attractant signal increases. This induces a functional coupling between movement and sensation, since tumbling probability is controlled by the internal state of the organism which, in turn, depends on previous signal levels. Although a negative feedback tends to maintain this internal state close to adapted levels, positive feedback can arise when motion up the gradient reduces tumbling probability, further boosting drift up the gradient. Importantly, such positive feedback can drive large fluctuations in the internal state, complicating analytical approaches. Previous studies focused on what happens when the negative feedback dominates the dynamics. By contrast, we show here that there is a large portion of physiologically-relevant parameter space where the positive feedback can dominate, even when gradients are relatively shallow. We demonstrate how large transients emerge because of non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the positive feedback, and further identify a fundamental nonlinearity that strongly amplifies their effect. Most importantly, this amplification is asymmetric, elongating runs in favorable directions and abbreviating others. The result is a “ratchet-like” gradient climbing behavior with drift speeds that can approach half the maximum run speed of the organism. Our results thus show that the classical drawback of run-and-tumble navigation—wasteful runs in the wrong direction—can be mitigated by exploiting the non-normal dynamics implicit in the run-and-tumble strategy.

Countless bacteria, larvae and even larger organisms (and robots) navigate gradients by alternating periods of straight motion (runs) with random reorientation events (tumbles). Control of the tumble probability is based on previously-encountered signals. A drawback of this run-and-tumble strategy is that occasional runs in the wrong direction are wasteful. Here we show that there is an operating regime within the organism’s internal parameter space where run-and-tumble navigation can be extremely efficient. We characterize how the positive feedback between behavior and sensed signal results in a type of non-equilibrium dynamics, with the organism rapidly tumbling after moving in the wrong direction and extending motion in the right ones. For a distant source, then, the organism can find it fast.

The Role of Adaptation in Bacterial Speed Races

Evolution of biological sensory systems is driven by the need for efficient responses to environmental stimuli. A paradigm among prokaryotes is the chemotaxis system, which allows bacteria to navigate gradients of chemoattractants by biasing their run-and-tumble motion. A notable feature of chemotaxis is adaptation: after the application of a step stimulus, the bacterial running time relaxes to its pre-stimulus level. The response to the amino acid aspartate is precisely adapted whilst the response to serine is not, in spite of the same pathway processing the signals preferentially sensed by the two receptors Tar and Tsr, respectively. While the chemotaxis pathway in E. coli is well characterized, the role of adaptation, its functional significance and the ecological conditions where chemotaxis is selected, are largely unknown. Here, we investigate the role of adaptation in the climbing of gradients by E. coli. We first present theoretical arguments that highlight the mechanisms that control the efficiency of the chemotactic up-gradient motion. We discuss then the limitations of linear response theory, which motivate our subsequent experimental investigation of E. coli speed races in gradients of aspartate, serine and combinations thereof. By using microfluidic techniques, we engineer controlled gradients and demonstrate that bacterial fronts progress faster in equal-magnitude gradients of serine than aspartate. The effect is observed over an extended range of concentrations and is not due to differences in swimming velocities. We then show that adding a constant background of serine to gradients of aspartate breaks the adaptation to aspartate, which results in a sped-up progression of the fronts and directly illustrate the role of adaptation in chemotactic gradient-climbing.

Biological sensory pathways are presumed to evolve for the processing of environmental information, yet quantitative evidence is scant. Chemotaxis allows bacteria to sense chemical gradients but their ecological distribution, e.g. whether natural gradients sensed by E. coli change slowly or rapidly in space and time, is unknown. That distribution matters, as it controls constraints and selective pressure acting on the pathway. We used microfluidic devices to generate controlled chemoattractant gradients and measure the speed of bacterial climbing of those gradients. We could thereby assay the impact of adaptation properties of the chemotaxis pathway onto the progression of gradient climbing. We specifically show that loss of adaptation, induced by adding a background of serine to gradients of aspartate, leads to a faster progression of the bacteria along the chemoattractant gradient. We finally discuss why our experiments suggest that ecological conditions are likely to involve chemoattractant profiles more complex than constant gradients usually considered in the laboratory.

Bacterial chemotaxis: information processing, thermodynamics, and behavior

Escherichia coli has long been used as a model organism due to the extensive experimental characterization of its pathways and molecular components. Take chemotaxis as an example, which allows bacteria to sense and swim in response to chemicals, such as nutrients and toxins. Many of the pathway's remarkable sensing and signaling properties are now concisely summarized in terms of design (or engineering) principles. More recently, new approaches from information theory and stochastic thermodynamics have begun to address how pathways process environmental stimuli and what the limiting factors are. However, to fully capitalize on these theoretical advances, a closer connection with single-cell experiments will be required.

The Good, the Bad, and the Tiny: A Simple, Mechanistic-Probabilistic Model of Virus-Nutrient Colimitation in Microbes

For phytoplankton and other microbes, nutrient receptors are often the passages through which viruses invade. This presents a bottom-up vs. top-down, co-limitation scenario; how do these would-be-hosts balance minimizing viral susceptibility with maximizing uptake of limiting nutrient(s)? This question has been addressed in the biological literature on evolutionary timescales for populations, but a shorter timescale, mechanistic perspective is lacking, and marine viral literature suggests the strong influence of additional factors, e.g. host size; while the literature on both nutrient uptake and host-virus interactions is expansive, their intersection, of ubiquitous relevance to marine environments, is understudied. I present a simple, mechanistic model from first principles to analyze the effect of this co-limitation scenario on individual growth, which suggests that in environments with high risk of viral invasion or spatial/temporal heterogeneity, an individual host’s growth rate may be optimized with respect to receptor coverage, producing top-down selective pressure on short timescales. The model has general applicability, is suggestive of hypotheses for empirical exploration, and can be extended to theoretical studies of more complex behaviors and systems.