Bacterial chemotaxis and the question of gain

Chemotactic Interactions Drive Migration of Membraneless Active Droplets

In nature, chemotactic interactions are ubiquitous and play a critical role in driving the collective behavior of living organisms. Reproducing these interactions in vitro is still a paramount challenge due to the complexity of mimicking and controlling cellular features, such as tangled metabolic networks, cytosolic macromolecular crowding, and cellular migration, on a microorganism size scale. Here, we generate enzymatically active cell-sized droplets able to move freely, and by following a chemical gradient, able to interact with the surrounding droplets in a collective manner. The enzyme within the droplets generates a pH gradient that extends outside the edge of the droplets. We discovered that the external pH gradient triggers droplet migration and controls its directionality, which is selectively toward the neighboring droplets. Hence, by changing the enzyme activity inside the droplet, we tuned the droplet migration speed. Furthermore, we showed that these cellular-like features can facilitate the reconstitution of a simple and linear protometabolic pathway and increase the final reaction product generation. Our work suggests that simple and stable membraneless droplets can reproduce complex biological phenomena, opening new perspectives as bioinspired materials and synthetic biology tools.

Signal integration and integral feedback control with biochemical reaction networks

Biochemical reaction networks perform a variety of signal processing functions, one of which is computing the integrals of signal values. This is often used in integral feedback control, where it enables a system's output to respond to changing inputs, but to then return exactly back to some pre-determined setpoint value afterward. To gain a deeper understanding of how biochemical networks are able to both integrate signals and perform integral feedback control, we investigated these abilities for several simple reaction networks. We found imperfect overlap between these categories, with some networks able to perform both tasks, some able to perform integration but not integral feedback control, and some the other way around. Nevertheless, networks that could either integrate or perform integral feedback control shared key elements. In particular, they included a chemical species that was neutrally stable in the open loop system (no feedback), meaning that this species does not have a unique stable steady-state concentration. Neutral stability could arise from zeroth order decay reactions, binding to a partner that was produced at a constant rate (which occurs in antithetic control), or through a long chain of covalent cycles. Mathematically, it arose from rate equations for the reaction network that were underdetermined when evaluated at steady-state.

Jeongeuplla avenae gen. nov., sp. nov., a novel β-carotene-producing bacterium that alleviates salinity stress in Arabidopsis

A novel endophytic bacterium, designated DY-R2A-6T, was isolated from oat (Avena sativa L.) seeds and found to produces β-carotene. Phylogenetic analysis based on 16S rRNA gene sequences revealed that strain DY-R2A-6T had 96.3% similarity with Jiella aquimaris LZB041T, 96.0% similarity with Aurantimonas aggregate R14M6T and Aureimonas frigidaquae JCM 14755T, and less than 95.8% similarity with other genera in the family Aurantimonadaceae. The complete genome of strain DY-R2A-6T comprised 5,929,370 base pairs, consisting of one full chromosome (5,909,198 bp) and one plasmid (20,172 bp), with a G + C content was 69.1%. The overall genome-related index (OGRI), including digital DNA-DNA hybridization (<20.5%), ANI (<79.2%), and AAI (<64.2%) values, all fell below the thresholds set for novel genera. The major cellular fatty acids (>10%) of strain DY-R2A-6T were C16:0, C19:0 cyclo ω8c, and summed feature 8 (C18:1ω7c and/or C18:1ω6c). Ubiquinone-10 was the main respiratory quinone. We identified the gene cluster responsible for carotenoid biosynthesis in the genome and found that the pink-pigment produced by strain DY-R2A-6T is β-carotene. In experiment with Arabidopsis seedlings, co-cultivation with strain DY-R2A-6T led to a 1.4-fold increase in plant biomass and chlorophyll content under salt stress conditions, demonstrating its capacity to enhance salt stress tolerance in plants. Moreover, external application of β-carotene to Arabidopsis seedlings under salt stress conditions also mitigated the stress significantly. Based on these findings, strain DY-R2A-6T is proposed to represent a novel genus and species in the family Aurantimonadaceae, named Jeongeuplla avenae gen. nov., sp. nov. The type strain is DY-R2A-6T (= KCTC 82985T = GDMCC 1.3014T). This study not only identified a new taxon but also utilized genome analysis to predict and confirm the production of β-carotene by strain DY-R2A-6T. It also demonstrated the ability of this strain to enhance salt stress tolerance in plants, suggesting potential application in agriculture to mitigate environmental stress in crops.

A Reduction of Transcriptional Regulation in Aquatic Oligotrophic Microorganisms Enhances Fitness in Nutrient-Poor Environments

In this review, we consider the regulatory strategies of aquatic oligotrophs, microbial cells that are adapted to thrive under low-nutrient concentrations in oceans, lakes, and other aquatic ecosystems. Many reports have concluded that oligotrophs use less transcriptional regulation than copiotrophic cells, which are adapted to high nutrient concentrations and are far more common subjects for laboratory investigations of regulation. It is theorized that oligotrophs have retained alternate mechanisms of regulation, such as riboswitches, that provide shorter response times and smaller amplitude responses and require fewer cellular resources. We examine the accumulated evidence for distinctive regulatory strategies in oligotrophs. We explore differences in the selective pressures copiotrophs and oligotrophs encounter and ask why, although evolutionary history gives copiotrophs and oligotrophs access to the same regulatory mechanisms, they might exhibit distinctly different patterns in how these mechanisms are used. We discuss the implications of these findings for understanding broad patterns in the evolution of microbial regulatory networks and their relationships to environmental niche and life history strategy. We ask whether these observations, which have emerged from a decade of increased investigation of the cell biology of oligotrophs, might be relevant to recent discoveries of many microbial cell lineages in nature that share with oligotrophs the property of reduced genome size.

Azospirillum brasilense AerC and Tlp4b Cytoplasmic Chemoreceptors Are Promiscuous and Interact with the Two Membrane-Bound Chemotaxis Signaling Clusters Mediating Chemotaxis Responses

Chemotaxis in Bacteria and Archaea depends on the presence of hexagonal polar arrays composed of membrane-bound chemoreceptors that interact with rings of baseplate signaling proteins. In the alphaproteobacterium Azospirillum brasilense, chemotaxis is controlled by two chemotaxis signaling systems (Che1 and Che4) that mix at the baseplates of two spatially distinct membrane-bound chemoreceptor arrays. The subcellular localization and organization of transmembrane chemoreceptors in chemotaxis signaling clusters have been well characterized but those of soluble chemoreceptors remain relatively underexplored. By combining mutagenesis, microscopy, and biochemical assays, we show that the cytoplasmic chemoreceptors AerC and Tlp4b function in chemotaxis and localize to and interact with membrane-bound chemoreceptors and chemotaxis signaling proteins from both polar arrays, indicating that soluble chemoreceptors are promiscuous. The interactions of AerC and Tlp4b with polar chemotaxis signaling clusters are not equivalent and suggest distinct functions. Tlp4b, but not AerC, modulates the abundance of chemoreceptors within the signaling clusters through an unknown mechanism. The AerC chemoreceptor, but not Tlp4b, is able to traffic in and out of chemotaxis signaling clusters depending on its level of expression. We also identify a role of the chemoreceptor composition of chemotaxis signaling clusters in regulating their polar subcellular organization. The organization of chemotaxis signaling proteins as large membrane-bound arrays underlies chemotaxis sensitivity. Our findings suggest that the composition of chemoreceptors may fine-tune chemotaxis signaling not only through their chemosensory specificity but also through their role in the organization of polar chemotaxis signaling clusters. IMPORTANCE Cytoplasmic chemoreceptors represent about 14% of all chemoreceptors encoded in bacterial and archaeal genomes, but little is known about how they interact with and function in large polar assemblies of membrane-bound chemotaxis signaling clusters. Here, we show that two soluble chemoreceptors with a role in chemotaxis are promiscuous and interact with two distinct membrane-bound chemotaxis signaling clusters that control all chemotaxis responses in Azospirillum brasilense. We also found that any change in the chemoreceptor composition of chemotaxis signaling clusters alters their polar organization, suggesting a dynamic interplay between the sensory specificity of chemotaxis signaling clusters and their polar membrane organization.

Precision of morphogen gradients in neural tube development

Morphogen gradients encode positional information during development. How high patterning precision is achieved despite natural variation in both the morphogen gradients and in the readout process, is still largely elusive. Here, we show that the positional error of gradients in the mouse neural tube has previously been overestimated, and that the reported accuracy of the central progenitor domain boundaries in the mouse neural tube can be achieved with a single gradient, rather than requiring the simultaneous readout of opposing gradients. Consistently and independently, numerical simulations based on measured molecular noise levels likewise result in lower gradient variabilities than reported. Finally, we show that the patterning mechanism yields progenitor cell numbers with even greater precision than boundary positions, as gradient amplitude changes do not affect interior progenitor domain sizes. We conclude that single gradients can yield the observed developmental precision, which provides prospects for tissue engineering.

Protein rings are critical to the remarkable signaling properties of bacterial chemotaxis nanoarrays

Bacteria build an extensive sensory nanoarray to collect information that guides their swimming. In this issue of Science Signaling, Piñas et al. demonstrate that a key element of these arrays that enhances chemotaxis responses are hexameric rings of CheW, one of two types of rings that couple the responses of core signaling units to achieve remarkable signaling properties such as single-molecule detection.

Cell-cell communication, chemotaxis and recruitment in Vibrio parahaemolyticus

Motile bacteria are proficient at finding optimal environments for colonization. Often, they use chemotaxis to sense nutrient availability and dangerous concentrations of toxic chemicals. For many bacteria, the repertoire of chemoreceptors is large, suggesting they possess a broad palate with respect to sensing. However, knowledge of the molecules detected by chemotaxis signal transduction systems is limited. Some bacteria, like Vibrio parahaemolyticus, are social and swarm in groups on surfaces. This marine bacterium and human pathogen secretes the S signal autoinducer, which cues degradation of intracellular c-di-GMP leading to transcription of the swarming program. Here, we report that the S signal also directs motility at a behavioral level by serving as a chemoattractant. The data demonstrate that V. parahaemolyticus senses the S signal using SscL and SscS, homologous methyl-accepting chemotaxis proteins. SscL is required by planktonic bacteria for S signal chemotaxis. SscS plays a role during swarming, and mutants lacking this chemoreceptor swarm faster and produce colonies with more deeply branched swarming fronts than the wild type or the sscL mutant. Other Vibrio species can swim toward the S signal, suggesting a recruitment role for this cell-cell communication molecule in the context of polymicrobial marine communities.

Modelling non-Markovian fluctuations in intracellular biomolecular transport

To model non-Markovian fluctuations arising in biomolecular transport, we introduce a stochastic process with memory where Brownian motion is modulated sinusoidally. The probability density function and moments of this non-Markovian process are evaluated analytically as Hida stochastic functional integrals. Comparison of graphs of computed variance vis-á-vis empirical data for protein diffusion coefficients closely match with both exhibiting emergent superdiffusive then subdiffusive behavior for longer proteins.

Campylobacter jejuni transducer like proteins: Chemotaxis and beyond

Chemotaxis, a process that mediates directional motility toward or away from chemical stimuli (chemoeffectors/ligands that can be attractants or repellents) in the environment, plays an important role in the adaptation of Campylobacter jejuni to disparate niches. The chemotaxis system consists of core signal transduction proteins and methyl-accepting-domain-containing Transducer like proteins (Tlps). Ligands binding to Tlps relay a signal to chemotaxis proteins in the cytoplasm which initiate a signal transduction cascade, culminating into a directional flagellar movement. Tlps facilitate substrate-specific chemotaxis in C. jejuni, which plays an important role in the pathogen's adaptation, pathobiology and colonization of the chicken gastrointestinal tract. However, the role of Tlps in C. jejuni's host tissue specific colonization, physiology and virulence remains not completely understood. Based on recent studies, it can be predicted that Tlps might be important targets for developing strategies to control C. jejuni via vaccines and antimicrobials.

How Biophysics May Help Us Understand the Flagellar Motor of Bacteria Which Cause Infections

Motor proteins are molecules which convert chemical energy to mechanical work and are responsible for motility across all levels: for transport within a cell, for the motion of an individual cell in its surroundings, and for movement in multicellular aggregates, such as muscles. The bacterial flagellar motor is one of the canonical examples of a molecular complex made from several motor proteins, which self-assembles on demand and provides the locomotive force for bacteria. This locomotion provides a key aspect of bacteria's prevalence. Here, we outline the biophysics behind the assembly, the energetics, the switching and the rotation of this remarkable nanoscale electric motor that is Nature's first wheel.

A Delicate Nanoscale Motor Made by Nature-The Bacterial Flagellar Motor

The bacterial flagellar motor (BFM) is a molecular complex ca. 45 nm in diameter that rotates the propeller that makes nearly all bacteria swim. The motor self-assembles out of ca. 20 different proteins and can not only rotate at up to 50 000 rpm, but can also switch rotational direction in milliseconds and navigate its environment to maneuver, on average, towards regions of greater benefit. The BFM is a pinnacle of evolution that informs and inspires the design of novel nanotechnology in the new era of synthetic biology.

The role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices

In vivo fluorescence microscopy and electron cryo-tomography have revealed that chemoreceptors self-assemble into extended honeycomb lattices of chemoreceptor trimers with a well-defined relative orientation of trimers. The signaling response of the observed chemoreceptor lattices is remarkable for its extreme sensitivity, which relies crucially on cooperative interactions among chemoreceptor trimers. In common with other membrane proteins, chemoreceptor trimers are expected to deform the surrounding lipid bilayer, inducing membrane-mediated anisotropic interactions between neighboring trimers. Here we introduce a biophysical model of bilayer-chemoreceptor interactions, which allows us to quantify the role of membrane-mediated interactions in the assembly and architecture of chemoreceptor lattices. We find that, even in the absence of direct protein-protein interactions, membrane-mediated interactions can yield assembly of chemoreceptor lattices at very dilute trimer concentrations. The model correctly predicts the observed honeycomb architecture of chemoreceptor lattices as well as the observed relative orientation of chemoreceptor trimers, suggests a series of “gateway” states for chemoreceptor lattice assembly, and provides a simple mechanism for the localization of large chemoreceptor lattices to the cell poles. Our model of bilayer-chemoreceptor interactions also helps to explain the observed dependence of chemotactic signaling on lipid bilayer properties. Finally, we consider the possibility that membrane-mediated interactions might contribute to cooperativity among neighboring chemoreceptor trimers.

The chemotaxis system allows bacteria to respond to minute changes in chemical concentration, and serves as a paradigm for biological signal processing and the self-assembly of large protein lattices in living cells. The sensitivity of the chemotaxis system relies crucially on cooperative interactions among chemoreceptor trimers, which are organized into intricate honeycomb lattices. Chemoreceptors are membrane proteins and, hence, are expected to deform the surrounding lipid bilayer, leading to membrane-mediated interactions between chemoreceptor trimers. Using a biophysical model of bilayer-chemoreceptor interactions we show that the membrane-mediated interactions induced by chemoreceptor trimers provide a mechanism for the observed self-assembly of chemoreceptor lattices. We find that the directionality of membrane-mediated interactions between trimers complements protein-protein interactions in the stabilization of the observed honeycomb architecture of chemoreceptor lattices. Our results suggest that the symmetry of membrane protein complexes such as chemoreceptor trimers is reflected in the anisotropy of membrane-mediated interactions, yielding a general mechanism for the self-assembly of ordered protein lattices in cell membranes.

Motility and chemotaxis in Campylobacter and Helicobacter

Flagellar motility of Campylobacter jejuni and Helicobacter pylori influences host colonization by promoting migration through viscous milieus such as gastrointestinal mucus. This review explores mechanisms C. jejuni and H. pylori employ to control flagellar biosynthesis and chemotactic responses. These microbes tightly control the activities of σ(54) and σ(28) to mediate ordered flagellar gene expression. In addition to phase-variable and posttranslational mechanisms, flagellar biosynthesis is regulated spatially and numerically so that only a certain number of organelles are placed at polar sites. To mediate chemotaxis, C. jejuni and H. pylori combine basic chemotaxis signal transduction components with several accessory proteins. H. pylori is unusual in that it lacks a methylation-based adaptation system and produces multiple CheV coupling proteins. Chemoreceptors in these bacteria contain nonconserved ligand binding domains, with several chemoreceptors matched to environmental signals. Together, these mechanisms allow for swimming motility that is essential for colonization.

Exploring the spatial and temporal organization of a cell's proteome

To increase our current understanding of cellular processes, such as cell signaling and division, knowledge is needed about the spatial and temporal organization of the proteome at different organizational levels. These levels cover a wide range of length and time scales: from the atomic structures of macromolecules for inferring their molecular function, to the quantitative description of their abundance, and spatial distribution in the cell. Emerging new experimental technologies are greatly increasing the availability of such spatial information on the molecular organization in living cells. This review addresses three fields that have significantly contributed to our understanding of the proteome's spatial and temporal organization: first, methods for the structure determination of individual macromolecular assemblies, specifically the fitting of atomic structures into density maps generated from electron microscopy techniques; second, research that visualizes the spatial distributions of these complexes within the cellular context using cryo electron tomography techniques combined with computational image processing; and third, methods for the spatial modeling of the dynamic organization of the proteome, specifically those methods for simulating reaction and diffusion of proteins and complexes in crowded intracellular fluids. The long-term goal is to integrate the varied data about a proteome's organization into a spatially explicit, predictive model of cellular processes.

Studying adaptation and homeostatic behaviors of kinetic networks by using MATLAB

Organisms have the ability to counteract environmental perturbations and keep certain components within a cell homeostatically regulated. Closely related to homeostasis is the behavior of perfect adaptation where an organism responds to a step-wise perturbation by regulating some of its components, after a transient period, to their original pre-perturbation values. A particular interesting type of model relates to the so-called robust behavior where the homeostatic or perfect adaptation property is independent of the magnitude of the applied step-wise perturbation. It has been shown that this type of behavior is related to the control-theoretic concept of integral feedback (or integral control). Using downloadable MATLAB examples, we demonstrate how robust perfect adaptation sites can be identified in reaction kinetic networks by linearizing the system, applying the Laplace transform and inspecting the transfer function. We also show how the homeostatic set point in perfect adaptation is related to the presence of zero-order fluxes.

CheV: CheW-like coupling proteins at the core of the chemotaxis signaling network

Microbes have chemotactic signaling systems that enable them to detect and follow chemical gradients in their environments. The core of these sensory systems consists of chemoreceptor proteins coupled to the CheA kinase via the scaffold or coupler protein CheW. Some bacterial chemotaxis systems replace or augment CheW with a related protein, CheV, which is less well understood. CheV consists of a CheW domain fused to a receiver domain that is capable of being phosphorylated. Our review of the literature, as well as comparisons of the CheV and CheW sequence and structure, suggest that CheV proteins conserve CheW residues that are crucial for coupling. Phosphorylation of the CheV receiver domain might adjust the efficiency of its coupling and thus allow the system to modulate the response to chemical stimuli in an adaptation process.

An agent-based model of signal transduction in bacterial chemotaxis

We report the application of agent-based modeling to examine the signal transduction network and receptor arrays for chemotaxis in Escherichia coli, which are responsible for regulating swimming behavior in response to environmental stimuli. Agent-based modeling is a stochastic and bottom-up approach, where individual components of the modeled system are explicitly represented, and bulk properties emerge from their movement and interactions. We present the Chemoscape model: a collection of agents representing both fixed membrane-embedded and mobile cytoplasmic proteins, each governed by a set of rules representing knowledge or hypotheses about their function. When the agents were placed in a simulated cellular space and then allowed to move and interact stochastically, the model exhibited many properties similar to the biological system including adaptation, high signal gain, and wide dynamic range. We found the agent based modeling approach to be both powerful and intuitive for testing hypotheses about biological properties such as self-assembly, the non-linear dynamics that occur through cooperative protein interactions, and non-uniform distributions of proteins in the cell. We applied the model to explore the role of receptor type, geometry and cooperativity in the signal gain and dynamic range of the chemotactic response to environmental stimuli. The model provided substantial qualitative evidence that the dynamic range of chemotactic response can be traced to both the heterogeneity of receptor types present, and the modulation of their cooperativity by their methylation state.

Conformational spread as a mechanism for cooperativity in the bacterial flagellar switch

The bacterial flagellar switch that controls the direction of flagellar rotation during chemotaxis has a highly cooperative response. This has previously been understood in terms of the classic two-state, concerted model of allosteric regulation. Here, we used high-resolution optical microscopy to observe switching of single motors and uncover the stochastic multistate nature of the switch. Our observations are in detailed quantitative agreement with a recent general model of allosteric cooperativity that exhibits conformational spread--the stochastic growth and shrinkage of domains of adjacent subunits sharing a particular conformational state. We expect that conformational spread will be important in explaining cooperativity in other large signaling complexes.

The asymmetric flagellar distribution and motility of Escherichia coli

Rod-shaped bacteria such as Escherichia coli divide by binary fission. They inherit an old pole from the parent cell. The new pole is recently derived from the septum. Because the chemoreceptor accumulates linearly with time on the cell pole, the old pole carries more receptors than does the new pole. Here, further evidence is provided that the old pole appears more frequently at the rear when bacteria swim. This phenomenon had been observed, yet not extensively explored in the literature. The biased swimming orientation is the consequence of the asymmetric distribution of flagella over the cell surface. On about 75% of cells, there are more flagella on the old-pole half of the cell than on the new-pole half, regardless of growth conditions. Most flagella are lateral, and few were found on the cell pole per se. The asymmetric flagellar distribution makes cells more efficient in chemotaxis. Both swimming orientation and receptor localization are components of chemotaxis, by which bacteria follow environmental stimuli. If unipolarly flagellated cells, such as the swarmer cells of Caulobacter crescentus, are regarded as 100% polar with respect to chemotaxis, E. coli is about 75%. The difference is quantitative. The peritrichous flagellation might enhance the motility and chemotaxis in the viscous environment of enteric bacteria.

Biomimetic control based on a model of chemotaxis in Escherichia coli

In the field of molecular biology, extending now to the more comprehensive area of systems biology, the development of computer models for synthetic cell simulation has accelerated extensively and has begun to be used for various purposes, such as biochemical analysis. These models, describing the highly efficient environmental searching mechanisms and adaptability of living organisms, can be used as machine-control algorithms in the field of systems engineering. To realize this biomimetic intelligent control, we require a stripped-down model that expresses a series of information-processing tasks from stimulation input to movement. Here we selected the bacterium Escherichia coli as a target organism because it has a relatively simple molecular and organizational structure, which can be characterized using biochemical and genetic analyses. We particularly focused on a motility response known as chemotaxis and developed a computer model that includes not only intracellular information processing but also motor control. After confirming the effectiveness and validity of the proposed model by a series of computer simulations, we applied it to a mobile robot control problem. This is probably the first study showing that a bacterial model can be used as an autonomous control algorithm. Our results suggest that many excellent models proposed thus far for biochemical purposes can be applied to problems in other fields.

Signal amplification in a lattice of coupled protein kinases

The bacterium Escherichia coli detects chemical attractants and repellents by means of a cluster of transmembrane receptors and associated molecules. Experiments have shown that this cluster amplifies the signal about 35-fold and current models attribute this amplification to cooperative interactions between neighbouring receptors. However, when applied to the mixed population of receptors of wild-type E. coli, these models lead to indiscriminate methylation of all receptor types rather than the selective methylation observed experimentally. In this paper, we propose that cooperative interactions occur not between receptors but in the underlying lattice of CheA molecules. In our model, each CheA molecule is stimulated by its neighbours via their flexible P1 domains and modulated by the ligand binding and methylation states of associated receptors. We test this idea with detailed, molecular-based stochastic simulations and show that it gives an accurate reproduction of signalling in this system, including ligand-specific adaptation.

The gain paradox

Chemoreceptors in Escherichia coli control the activity of a kinase that phosphorylates a response regulator that, in turn, biases the direction of rotation of flagellar motors, affecting the manner in which cells swim. A small change in receptor occupancy induces a large change in kinase activity. This gain is generated by allosteric interactions between receptors, which are arranged in clusters. The idea that such amplification might occur was advanced by Dennis Bray in 1998, and confirmed experimentally in 2002.

Predicting perfect adaptation motifs in reaction kinetic networks

Adaptation and compensation mechanisms are important to keep organisms fit in a changing environment. "Perfect adaptation" describes an organism's response to an external stepwise perturbation by resetting some of its variables precisely to their original preperturbation values. Examples of perfect adaptation are found in bacterial chemotaxis, photoreceptor responses, or MAP kinase activities. Two concepts have evolved for how perfect adaptation may be understood. In one approach, so-called "robust perfect adaptation", the adaptation is a network property (due to integral feedback control), which is independent of rate constant values. In the other approach, which we have termed "nonrobust perfect adaptation", a fine-tuning of rate constant values is needed to show perfect adaptation. Although integral feedback describes robust perfect adaptation in general terms, it does not directly show where in a network perfect adaptation may be observed. Using control theoretic methods, we are able to predict robust perfect adaptation sites within reaction kinetic networks and show that a prerequisite for robust perfect adaptation is that the network is open and irreversible. We applied the method on various reaction schemes and found that new (robust) perfect adaptation motifs emerge when considering suggested models of bacterial and eukaryotic chemotaxis.

Computing algebraic functions with biochemical reaction networks

In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.

Adaptive dynamics with a single two-state protein

An important step towards understanding biological systems is to relate simple biochemical elements to dynamics. Here, we present the arguably simplest dynamical element in biochemical networks. It consists of a single protein with two states (active and inactive) and an external signal that catalyses the conversion between these two states. Further, there is steady synthesis and degradation of the inactive and active forms, respectively. As this element captures both structural and dynamical features of biochemical networks at the lowest level, we refer to it as a biochemical network unit (BioNetUnit). Using both simulations and mathematical analysis, we find that BioNetUnit shows perfect adaptation that leads to temporal responses to step changes in the incoming signal. Compared with a well-described adaptive system, which is found in bacterial chemotaxis, BioNetUnit has lower sensitivity and its adaptation time is less robust to the base signal levels. We show that these dynamical limitations lead to 'once-and-only-once' responses for certain signal sequences. These findings demonstrate that BioNetUnit is relevant in adaptive and cyclic processes. In particular, it could be seen as a generic representation for ligand-activated receptors that are desensitized upon continuous activation. The analysis of coupled BioNetUnits will show how the presented dynamics at single unit will change upon increased system complexity and how such systems would mediate biological functions.

How the "melting" and "freezing" of protein molecules may be used in cell signaling

The motile response of Escherichia coli bacteria to attractants and repellents is one of the best-understood examples of a signal transduction pathway. A number of recent studies suggest that the receptors in this system undergo major changes in both their degree of structural order and their state of aggregation in the membrane. We discuss the thermodynamic basis for this effect and argue that the "freezing" or "melting" of protein structure may be the language of signaling.

Bacteria are small but not stupid: cognition, natural genetic engineering and socio-bacteriology

Forty years' experience as a bacterial geneticist has taught me that bacteria possess many cognitive, computational and evolutionary capabilities unimaginable in the first six decades of the twentieth century. Analysis of cellular processes such as metabolism, regulation of protein synthesis, and DNA repair established that bacteria continually monitor their external and internal environments and compute functional outputs based on information provided by their sensory apparatus. Studies of genetic recombination, lysogeny, antibiotic resistance and my own work on transposable elements revealed multiple widespread bacterial systems for mobilizing and engineering DNA molecules. Examination of colony development and organization led me to appreciate how extensive multicellular collaboration is among the majority of bacterial species. Contemporary research in many laboratories on cell-cell signaling, symbiosis and pathogenesis show that bacteria utilise sophisticated mechanisms for intercellular communication and even have the ability to commandeer the basic cell biology of 'higher' plants and animals to meet their own needs. This remarkable series of observations requires us to revise basic ideas about biological information processing and recognise that even the smallest cells are sentient beings.

Intrinsic fluctuations, robustness, and tunability in signaling cycles

Covalent modification cycles (e.g., phosphorylation-dephosphorylation) underlie most cellular signaling and control processes. Low molecular copy number, arising from compartmental segregation and slow diffusion between compartments, potentially renders these cycles vulnerable to intrinsic chemical fluctuations. How can a cell operate reliably in the presence of this inherent stochasticity? How do changes in extrinsic parameters lead to variability of response? Can cells exploit these parameters to tune cycles to different ranges of stimuli? We study the dynamics of an isolated phosphorylation cycle. Our model shows that the cycle transmits information reliably if it is tuned to an optimal parameter range, despite intrinsic fluctuations and even for small input signal amplitudes. At the same time, the cycle is sensitive to changes in the concentration and activity of kinases and phosphatases. This sensitivity can lead to significant cell-to-cell response variability. It also provides a mechanism to tune the cycle to transmit signals in various amplitude ranges. Our results show that signaling cycles possess a surprising combination of robustness and tunability. This combination makes them ubiquitous in eukaryotic signaling, optimizing signaling in the presence of fluctuations using their inherent flexibility. On the other hand, cycles tuned to suppress intrinsic fluctuations can be vulnerable to changes in the number and activity of kinases and phosphatases. Such trade-offs in robustness to intrinsic and extrinsic fluctuations can influence the evolution of signaling cascades, making them the weakest links in cellular circuits.

Stimulus perception in bacterial signal-transducing histidine kinases

Two-component signal-transducing systems are ubiquitously distributed communication interfaces in bacteria. They consist of a histidine kinase that senses a specific environmental stimulus and a cognate response regulator that mediates the cellular response, mostly through differential expression of target genes. Histidine kinases are typically transmembrane proteins harboring at least two domains: an input (or sensor) domain and a cytoplasmic transmitter (or kinase) domain. They can be identified and classified by virtue of their conserved cytoplasmic kinase domains. In contrast, the sensor domains are highly variable, reflecting the plethora of different signals and modes of sensing. In order to gain insight into the mechanisms of stimulus perception by bacterial histidine kinases, we here survey sensor domain architecture and topology within the bacterial membrane, functional aspects related to this topology, and sequence and phylogenetic conservation. Based on these criteria, three groups of histidine kinases can be differentiated. (i) Periplasmic-sensing histidine kinases detect their stimuli (often small solutes) through an extracellular input domain. (ii) Histidine kinases with sensing mechanisms linked to the transmembrane regions detect stimuli (usually membrane-associated stimuli, such as ionic strength, osmolarity, turgor, or functional state of the cell envelope) via their membrane-spanning segments and sometimes via additional short extracellular loops. (iii) Cytoplasmic-sensing histidine kinases (either membrane anchored or soluble) detect cellular or diffusible signals reporting the metabolic or developmental state of the cell. This review provides an overview of mechanisms of stimulus perception for members of all three groups of bacterial signal-transducing histidine kinases.

A hitchhiker's guide through advances and conceptual changes in chemotaxis

Chemotaxis is a basic recognition process, governed by protein network that translates molecular-based information on the surrounding environment into a guided motional response of the recipient cell or organism. This process is prevalent from bacteria to human beings. Some of the chemotaxis systems--like that of the bacterium Escherichia coli--are well established; others--like that of mammalian sperm cells--are at their relatively early stages of research. In contrast to mammalian sperm chemotaxis, where studies have so far been limited to the phenomenological level primarily, the model of bacterial chemotaxis is known down to the angstrom resolution. Despite this difference in depth of understanding, many fundamental questions are open not only in the new but also in the old chemotaxis fields of research, and recent advances in them are raising additional intriguing questions. This review summarizes some of these surprises and previously unasked or overlooked questions, and as such it offers a guided tour through conceptual changes in chemotaxis.

Changing cellular location of CheZ predicted by molecular simulations

In the chemotaxis pathway of the bacterium Escherichia coli, signals are carried from a cluster of receptors to the flagellar motors by the diffusion of the protein CheY-phosphate (CheYp) through the cytoplasm. A second protein, CheZ, which promotes dephosphorylation of CheYp, partially colocalizes with receptors in the plasma membrane. CheZ is normally dimeric in solution but has been suggested to associate into highly active oligomers in the presence of CheYp. A model is presented here and supported by Brownian dynamics simulations, which accounts for these and other experimental data: A minority component of the receptor cluster (dimers of CheA_short) nucleates CheZ oligomerization and CheZ molecules move from the cytoplasm to a bound state at the receptor cluster depending on the current level of cellular stimulation. The corresponding simulations suggest that dynamic CheZ localization will sharpen cellular responses to chemoeffectors, increase the range of detectable ligand concentrations, and make adaptation more precise and robust. The localization and activation of CheZ constitute a negative feedback loop that provides a second tier of adaptation to the system. Subtle adjustments of this kind are likely to be found in many other signaling pathways.

In order to function effectively, a living cell must not only synthesize the correct molecules but also put them in the correct place. Understanding how this positioning occurs, and what its consequences are, is a matter of great interest and concern to contemporary biologists. The author here proposes a novel mechanism that will enhance the ability of a bacterial cell to perform chemotaxis—the ability to swim toward sources of food or away from noxious substances. In this hypothesis, a key protein in the chemotaxis pathway moves dynamically between the membrane and the cytoplasm depending on the presence of attractants or repellents. This idea is explored and tested by means of detailed molecular simulations in which all of the relevant molecules are shown in their correct location in the cell. The simulations show that the proposed shift in location of the key molecule will improve the speed, range, and robustness of the cell's response. It seems likely that similar movements of proteins will occur in many other signaling pathways.

Chemosensing in Escherichia coli: two regimes of two-state receptors

The chemotaxis network in Escherichia coli is remarkable for its sensitivity to small relative changes in the concentrations of multiple chemical signals. We present a model for signal integration by mixed clusters of interacting two-state chemoreceptors. Our model results compare favorably to the results obtained by Sourjik and Berg with in vivo fluorescence resonance energy transfer. Importantly, we identify two distinct regimes of behavior, depending on the relative energies of the two states of the receptors. In regime I, coupling of receptors leads to high sensitivity, while in regime II, coupling of receptors leads to high cooperativity, i.e., high Hill coefficient. For homogeneous receptors, we predict an observable transition between regime I and regime II with increasing receptor methylation or amidation.

Simulating the evolution of signal transduction pathways

We use a generic model of a network of proteins that can activate or deactivate each other to explore the emergence and evolution of signal transduction networks and to gain a basic understanding of their general properties. Starting with a set of non-interacting proteins, we evolve a signal transduction network by random mutation and selection to fulfill a complex biological task. In order to validate this approach we base selection on a fitness function that captures the essential features of chemotactic behavior as seen in bacteria. We find that a system of as few as three proteins can evolve into a network mediating chemotaxis-like behavior by acting as a "derivative sensor". Furthermore, we find that the dynamics and topology of such networks show many similarities to the natural chemotaxis pathway, that the response magnitude can increase with increasing network size and that network behavior shows robustness towards variations in some of the internal parameters. We conclude that simulating the evolution of signal transduction networks to mediate a certain behavior may be a promising approach for understanding the general properties of the natural pathway for that behavior.

Adaptational assistance in clusters of bacterial chemoreceptors

Sensory adaptation of low-abundance chemoreceptors in Escherichia coli requires assistance from high-abundance receptors, because only high-abundance receptors carry the carboxyl-terminal pentapeptide sequence NWETF that enhances adaptational covalent modification. Using membrane vesicles containing both high-abundance receptor Tar and low-abundance receptor Trg, we observed effective assistance in vitro for all three adaptational modifications: methylation, demethylation and deamidation. These results demonstrated that adaptational assistance involves not only the previously documented assistance for methylation but also assistance for the two CheB-catalysed reactions. We determined rates of assisted methylation and demethylation at many ratios of assisting to assisted receptor. Analysis by a model of assistance indicated one Tar dimer could assist seven Trg dimers in methylation or five in demethylation, defining assistance neighbourhoods. These neighbourhoods were larger than a trimer of homodimers, required only receptors and were minimally affected by formation of signalling complexes. Time courses of assisted Trg methylation in membranes with low amounts of Tar showed that assisting receptors did not diffuse beyond initial neighbourhoods for at least two hours. Taken together, these observations indicate that chemoreceptors can form stable neighbourhoods larger than trimers in the absence of other chemotaxis proteins. Such interactions are likely to occur in natural receptor clusters in vivo.

Large increases in attractant concentration disrupt the polar localization of bacterial chemoreceptors

In bacterial chemotaxis, the chemoreceptors [methyl-accepting chemotaxis proteins (MCPs)] transduce chemotactic signals through the two-component histidine kinase CheA. At low but not high attractant concentrations, chemotactic signals must be amplified. The MCPs are organized into a polar lattice, and this organization has been proposed to be critical for signal amplification. Although evidence in support of this model has emerged, an understanding of how signals are amplified and modulated is lacking. We probed the role of MCP localization under conditions wherein signal amplification must be inhibited. We tested whether a large increase in attractant concentration (a change that should alter receptor occupancy from c. 0% to > 95%) would elicit changes in the chemoreceptor localization. We treated Escherichia coli or Bacillus subtilis with a high level of attractant, exposed cells to the cross-linking agent paraformaldehyde and visualized chemoreceptor location with an anti-MCP antibody. A marked increase in the percentage of cells displaying a diffuse staining pattern was obtained. In contrast, no increase in diffuse MCP staining is observed when cells are treated with a repellent or a low concentration of attractant. For B. subtilis mutants that do not undergo chemotaxis, the addition of a high concentration of attractant has no effect on MCP localization. Our data suggest that interactions between chemoreceptors are decreased when signal amplification is unnecessary.

Continuous-flow capillary assay for measuring bacterial chemotaxis

Bacterial chemotaxis may have a significant impact on the structure and function of bacterial communities. Quantification of chemotactic motion is necessary to identify chemoeffectors and to determine the bacterial transport parameters used in predictive models of chemotaxis. When the chemotactic bacteria consume the chemoeffector, the chemoeffector gradient to which the bacteria respond may be significantly perturbed by the consumption. Therefore, consumption of the chemoeffector can confound chemotaxis measurements if it is not accounted for. Current methods of quantifying chemotaxis use bacterial concentrations that are too high to preclude chemoeffector consumption or involve ill-defined conditions that make quantifying chemotaxis difficult. We developed a method of quantifying bacterial chemotaxis at low cell concentrations ( approximately 10(5) CFU/ml), so metabolism of the chemoeffector is minimized. The method facilitates quantification of bacterial-transport parameters by providing well-defined boundary conditions and can be used with volatile and semivolatile chemoeffectors.

An allosteric model for transmembrane signaling in bacterial chemotaxis

Bacteria are able to sense chemical gradients over a wide range of concentrations. However, calculations based on the known number of receptors do not predict such a range unless receptors interact with one another in a cooperative manner. A number of recent experiments support the notion that this remarkable sensitivity in chemotaxis is mediated by localized interactions or crosstalk between neighboring receptors. A number of simple, elegant models have proposed mechanisms for signal integration within receptor clusters. What is a lacking is a model, based on known molecular mechanisms and our accumulated knowledge of chemotaxis, that integrates data from multiple, heterogeneous sources. To address this question, we propose an allosteric mechanism for transmembrane signaling in bacterial chemotaxis based on the "trimer of dimers" model, where three receptor dimers form a stable complex with CheW and CheA. The mechanism is used to integrate a diverse set of experimental data in a consistent framework. The main predictions are: (1) trimers of receptor dimers form the building blocks for the signaling complexes; (2) receptor methylation increases the stability of the active state and retards the inhibition arising from ligand-bound receptors within the signaling complex; (3) trimer of dimer receptor complexes aggregate into clusters through their mutual interactions with CheA and CheW; (4) cooperativity arises from neighboring interaction within these clusters; and (5) cluster size is determined by the concentration of receptors, CheA, and CheW. The model is able to explain a number of seemingly contradictory experiments in a consistent manner and, in the process, explain how bacteria are able to sense chemical gradients over a wide range of concentrations by demonstrating how signals are integrated within the signaling complex.

Simulating complex intracellular processes using object-oriented computational modelling

The aim of this paper is to give an overview of computer modelling and simulation in cellular biology, in particular as applied to complex biochemical processes within the cell. This is illustrated by the use of the techniques of object-oriented modelling, where the computer is used to construct abstractions of objects in the domain being modelled, and these objects then interact within the computer to simulate the system and allow emergent properties to be observed. The paper also discusses the role of computer simulation in understanding complexity in biological systems, and the kinds of information which can be obtained about biology via simulation.

Conformational spread: the propagation of allosteric states in large multiprotein complexes

The phenomenon of allostery is conventionally described for small symmetrical oligomeric proteins such as hemoglobin. Here we review experimental evidence from a variety of systems-including bacterial chemotaxis receptors, muscle ryanodine receptors, and actin filaments-showing that conformational changes can also propagate through extended lattices of protein molecules. We explore the statistical mechanics of idealized linear and two-dimensional arrays of allosteric proteins and show that, as in the analogous Ising models, arrays of closely packed units can show large-scale integrated behavior. We also discuss proteins that undergo conformational changes driven by the hydrolysis of ATP and give examples in which these changes propagate through linear chains of molecules. We suggest that conformational spread could provide the basis of a solid-state "circuitry" in a living cell, able to integrate biochemical and biophysical events over hundreds of protein molecules.

Learning and evolution in bacterial taxis: an operational amplifier circuit modeling the computational dynamics of the prokaryotic ‘two component system’ protein network

Adaptive behavior in unicellular organisms (i.e., bacteria) depends on highly organized networks of proteins governing purposefully the myriad of molecular processes occurring within the cellular system. For instance, bacteria are able to explore the environment within which they develop by utilizing the motility of their flagellar system as well as a sophisticated biochemical navigation system that samples the environmental conditions surrounding the cell, searching for nutrients or moving away from toxic substances or dangerous physical conditions. In this paper we discuss how proteins of the intervening signal transduction network could be modeled as artificial neurons, simulating the dynamical aspects of the bacterial taxis. The model is based on the assumption that, in some important aspects, proteins can be considered as processing elements or McCulloch-Pitts artificial neurons that transfer and process information from the bacterium's membrane surface to the flagellar motor. This simulation of bacterial taxis has been carried out on a hardware realization of a McCulloch-Pitts artificial neuron using an operational amplifier. Based on the behavior of the operational amplifier we produce a model of the interaction between CheY and FliM, elements of the prokaryotic two component system controlling chemotaxis, as well as a simulation of learning and evolution processes in bacterial taxis. On the one side, our simulation results indicate that, computationally, these protein 'switches' are similar to McCulloch-Pitts artificial neurons, suggesting a bridge between evolution and learning in dynamical systems at cellular and molecular levels and the evolutive hardware approach. On the other side, important protein 'tactilizing' properties are not tapped by the model, and this suggests further complexity steps to explore in the approach to biological molecular computing.

The rotary motor of bacterial flagella

Flagellated bacteria, such as Escherichia coli, swim by rotating thin helical filaments, each driven at its base by a reversible rotary motor, powered by an ion flux. A motor is about 45 nm in diameter and is assembled from about 20 different kinds of parts. It develops maximum torque at stall but can spin several hundred Hz. Its direction of rotation is controlled by a sensory system that enables cells to accumulate in regions deemed more favorable. We know a great deal about motor structure, genetics, assembly, and function, but we do not really understand how it works. We need more crystal structures. All of this is reviewed, but the emphasis is on function.