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

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.

Motor Adaptive Remodeling Speeds Up Bacterial Chemotactic Adaptation

Bacterial chemotaxis is a canonical system for the study of signal transduction. One of the hallmarks of this system is its robust adaptive behavior. However, how fast the system adapts remains controversial. The adaptation time measured at the level of the kinase activity was tens of seconds, whereas that measured at the level of the flagellar motor was <10 s. The flagellar motor was recently shown to exhibit adaptive remodeling, its main physiological function being to provide a robust match between the chemoreceptor output and the motor input, whereas its adaptation timescale was thought to be too slow to contribute much to the overall adaptation timescale of the chemotaxis system. Here, through theoretical modeling of the motor adaptive remodeling and experimental tests, we show that this motor adaptation contributes significantly to speeding up the overall chemotactic adaptation, thereby resolving the previous inconsistency.

Run-and-tumble motion with steplike responses to a stochastic input

We study a simple run-and-tumble random walk whose switching frequencies between run mode and tumble mode depend on a stochastic signal. We consider a particularly sharp, steplike dependence, where the run-to-tumble switching probability jumps from zero to one as the signal crosses a particular value (say y_{1}) from below. Similarly, tumble-to-run switching probability also shows a jump like this as the signal crosses another value (y_{2}<y_{1}) from above. We are interested in characterizing the effect of signaling noise on the long-time behavior of the random walker. We consider two different time-evolutions of the stochastic signal. In one case, the signal dynamics is an independent stochastic process and does not depend on the run-and-tumble motion. In this case we can analytically calculate the mean value and the complete distribution function of the run duration and tumble duration. In the second case, we assume that the signal dynamics is influenced by the spatial location of the random walker. For this system, we numerically measure the steady state position distribution of the random walker. We discuss some similarities and differences between our system and Escherichia coli chemotaxis, which is another well-known run-and-tumble motion encountered in nature.

Programming Bacteria With Light-Sensors and Applications in Synthetic Biology

Photo-receptors are widely present in both prokaryotic and eukaryotic cells, which serves as the foundation of tuning cell behaviors with light. While practices in eukaryotic cells have been relatively established, trials in bacterial cells have only been emerging in the past few years. A number of light sensors have been engineered in bacteria cells and most of them fall into the categories of two-component and one-component systems. Such a sensor toolbox has enabled practices in controlling synthetic circuits at the level of transcription and protein activity which is a major topic in synthetic biology, according to the central dogma. Additionally, engineered light sensors and practices of tuning synthetic circuits have served as a foundation for achieving light based real-time feedback control. Here, we review programming bacteria cells with light, introducing engineered light sensors in bacteria and their applications, including tuning synthetic circuits and achieving feedback controls over microbial cell culture.

Optimal methylation noise for best chemotactic performance of E. coli

In response to a concentration gradient of chemoattractant, E. coli bacterium modulates the rotational bias of flagellar motors which control its run-and-tumble motion, to migrate towards regions of high chemoattractant concentration. Presence of stochastic noise in the biochemical pathway of the cell has important consequences on the switching mechanism of motor bias, which in turn affects the runs and tumbles of the cell in a significant way. We model the intracellular reaction network in terms of coupled time evolution of three stochastic variables-kinase activity, methylation level, and CheY-P protein level-and study the effect of methylation noise on the chemotactic performance of the cell. In presence of a spatially varying nutrient concentration profile, a good chemotactic performance allows the cell to climb up the concentration gradient quickly and localize in the nutrient-rich regions in the long time limit. Our simulations show that the best performance is obtained at an optimal noise strength. While it is expected that chemotaxis will be weaker for very large noise, it is counterintuitive that the performance worsens even when noise level falls below a certain value. We explain this striking result by detailed analysis of CheY-P protein level statistics for different noise strengths. We show that when the CheY-P level falls below a certain (noise-dependent) threshold the cell tends to move down the concentration gradient of the nutrient, which has a detrimental effect on its chemotactic response. This threshold value decreases as noise is increased, and this effect is responsible for noise-induced enhancement of chemotactic performance. In a harsh chemical environment, when the nutrient degrades with time, the amount of nutrient intercepted by the cell trajectory is an effective performance criterion. In this case also, depending on the nutrient lifetime, we find an optimum noise strength when the performance is at its best.

Sign epistasis caused by hierarchy within signalling cascades

Sign epistasis is a central evolutionary constraint, but its causal factors remain difficult to predict. Here we use the notion of parameterised optima to explain epistasis within a signalling cascade, and test these predictions in Escherichia coli. We show that sign epistasis arises from the benefit of tuning phenotypic parameters of cascade genes with respect to each other, rather than from their complex and incompletely known genetic bases. Specifically, sign epistasis requires only that the optimal phenotypic parameters of one gene depend on the phenotypic parameters of another, independent of other details, such as activating or repressing nature, position within the cascade, intra-genic pleiotropy or genotype. Mutational effects change sign more readily in downstream genes, indicating that optimising downstream genes is more constrained. The findings show that sign epistasis results from the inherent upstream-downstream hierarchy between signalling cascade genes, and can be addressed without exhaustive genotypic mapping.

Sign epistasis clearly constrains evolution, but its causes are difficult to decipher. Here, the authors study epistasis in a signalling cascade, and arrive at a general criterion and understanding of sign epistasis as arising from the inherent hierarchy between signalling cascade components.

Behavioral Variability and Phenotypic Diversity in Bacterial Chemotaxis

Living cells detect and process external signals using signaling pathways that are affected by random fluctuations. These variations cause the behavior of individual cells to fluctuate over time (behavioral variability) and generate phenotypic differences between genetically identical individuals (phenotypic diversity). These two noise sources reduce our ability to predict biological behavior because they diversify cellular responses to identical signals. Here, we review recent experimental and theoretical advances in understanding the mechanistic origin and functional consequences of such variation in Escherichia coli chemotaxis-a well-understood model of signal transduction and behavior. After briefly summarizing the architecture and logic of the chemotaxis system, we discuss determinants of behavior and chemotactic performance of individual cells. Then, we review how cell-to-cell differences in protein abundance map onto differences in individual chemotactic abilities and how phenotypic variability affects the performance of the population. We conclude with open questions to be addressed by future research.

Adaptation of Living Systems

Adaptation refers to the biological phenomenon where living systems change their internal states in response to changes in their environments in order to maintain certain key functions critical for their survival and fitness. Adaptation is one of the most ubiquitous and arguably one of the most fundamental properties of living systems. It occurs throughout all biological scales, from adaptation of populations of species over evolutionary time to adaptation of a single cell to different environmental stresses during its life span. In this article, we review some of the recent progress made in understanding molecular mechanisms of cellular level adaptation. We take the minimalist (or the physicist) approach and study the simplest systems that exhibit generic adaptive behaviors. We focus on understanding the basic biochemical interaction networks in living matter that are responsible for adaptation dynamics. By combining theoretical modeling with quantitative experimentation, we demonstrate universal features in adaptation as well as important differences in different cellular systems, including chemotaxis in bacterium cells (Escherichia coli) and eukaryotic cells (Dictyostelium). Future work in extending the modeling framework to study adaptation in more complex systems such as sensory neurons are discussed.

Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.

Multiple sources of slow activity fluctuations in a bacterial chemosensory network

Cellular networks are intrinsically subject to stochastic fluctuations, but analysis of the resulting noise remained largely limited to gene expression. The pathway controlling chemotaxis of Escherichia coli provides one example where posttranslational signaling noise has been deduced from cellular behavior. This noise was proposed to result from stochasticity in chemoreceptor methylation, and it is believed to enhance environment exploration by bacteria. Here we combined single-cell FRET measurements with analysis based on the fluctuation-dissipation theorem (FDT) to characterize origins of activity fluctuations within the chemotaxis pathway. We observed surprisingly large methylation-independent thermal fluctuations of receptor activity, which contribute to noise comparably to the energy-consuming methylation dynamics. Interactions between clustered receptors involved in amplification of chemotactic signals are also necessary to produce the observed large activity fluctuations. Our work thus shows that the high response sensitivity of this cellular pathway also increases its susceptibility to noise, from thermal and out-of-equilibrium processes.

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.

Frequency-Domain Response Analysis for Quantitative Systems Pharmacology Models

Drug dosing regimen can significantly impact drug effect and, thus, the success of treatments. Nevertheless, trial and error is still the most commonly used method by conventional pharmacometric approaches to optimize dosing regimen. In this tutorial, we utilize four distinct classes of quantitative systems pharmacology models to introduce frequency-domain response analysis, a method widely used in electrical and control engineering that allows the analytical optimization of drug treatment regimen from the dynamics of the model.

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.

Predicting Escherichia coli's chemotactic drift under exponential gradient

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.

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.

Mechanism of bidirectional thermotaxis in Escherichia coli

In bacteria various tactic responses are mediated by the same cellular pathway, but sensing of physical stimuli remains poorly understood. Here, we combine an in-vivo analysis of the pathway activity with a microfluidic taxis assay and mathematical modeling to investigate the thermotactic response of Escherichia coli. We show that in the absence of chemical attractants E. coli exhibits a steady thermophilic response, the magnitude of which decreases at higher temperatures. Adaptation of wild-type cells to high levels of chemoattractants sensed by only one of the major chemoreceptors leads to inversion of the thermotactic response at intermediate temperatures and bidirectional cell accumulation in a thermal gradient. A mathematical model can explain this behavior based on the saturation-dependent kinetics of adaptive receptor methylation. Lastly, we find that the preferred accumulation temperature corresponds to optimal growth in the presence of the chemoattractant serine, pointing to a physiological relevance of the observed thermotactic behavior.

Many bacteria can move towards or away from chemicals, heat and other stimuli in their environment. The ability of bacteria to move in response to nutrients and other chemicals, known as chemotaxis, is the best understood of these phenomena. Bacteria generally swim in a fairly random way and frequently change direction. During chemotaxis, however, the bacteria sense changes in the concentrations of a chemical in their surroundings and this biases the direction in which they swim so that they spend more time swimming towards or away from the source of the chemical. The bacteria have various receptor proteins that can detect different chemicals. For example, the Tar and Tsr receptors can recognize chemicals called aspartate and serine, respectively, which are – amongst other things – nutrients that are used to build proteins.

Tar and Tsr are also involved in the response to temperature, referred to as thermotaxis. At low temperatures, a bacterium Escherichia coli will move towards sources of heat. Yet when the bacteria detect both serine and aspartate they may reverse the response and move towards colder areas instead. However, it was not clear why the bacteria do this, and what roles Tar and Tsr play in this response.

Paulick et al. have now combined approaches that directly visualise signalling inside living bacteria and that track the movements of individual bacterial cellswith mathematical modelling to investigate thermotaxis in E. coli. The experiments show that the bacteria’s behaviour could be explained by interplay between the responses mediated by Tar and Tsr. In the absence of both serine and aspartate, both receptors stimulate heat-seeking responses, causing the bacteria to move towards hotter areas. When only aspartate is present, Tsr continues to stimulate the heat-seeking response, but the aspartate causes Tar to switch to promoting a cold-seeking response instead. This leads to the bacteria accumulating in areas of intermediate temperature. In the presence of serine only, the bacteria behave in a similar way because the receptors swap roles so that Tsr stimulates the cold-seeking response, while Tar promotes the heat-seeking one.

The intermediate temperature at which the bacteria accumulate in response to serine is also around the optimal temperature for E.coli growth in presence of this chemical, suggesting that thermotaxis might play an important role in allowing bacteria to survive and grow in many different environments, including in the human body. Thus, understanding how chemotaxis and thermotaxis are regulated may lead to new ways to control how bacteria behave in patients and natural environments.

Olfactory receptor neurons use gain control and complementary kinetics to encode intermittent odorant stimuli

Insects find food and mates by navigating odorant plumes that can be highly intermittent, with intensities and durations that vary rapidly over orders of magnitude. Much is known about olfactory responses to pulses and steps, but it remains unclear how olfactory receptor neurons (ORNs) detect the intensity and timing of natural stimuli, where the absence of scale in the signal makes detection a formidable olfactory task. By stimulating Drosophila ORNs in vivo with naturalistic and Gaussian stimuli, we show that ORNs adapt to stimulus mean and variance, and that adaptation and saturation contribute to naturalistic sensing. Mean-dependent gain control followed the Weber-Fechner relation and occurred primarily at odor transduction, while variance-dependent gain control occurred at both transduction and spiking. Transduction and spike generation possessed complementary kinetic properties, that together preserved the timing of odorant encounters in ORN spiking, regardless of intensity. Such scale-invariance could be critical during odor plume navigation.

Noise-Induced Increase of Sensitivity in Bacterial Chemotaxis

Flagellated bacteria, like Escherichia coli, can swim toward beneficial environments by modulating the rotational direction of their flagellar motors through a chemotaxis signal transduction network. The noise of this network, the random fluctuation of the intracellular concentration of the signal protein CheY-P with time, has been identified in studies of single cell behavioral variability, and found to be important in coordination of multiple motors in a bacterium and in enhancement of bacterial drift velocity in chemical gradients. Here, by comparing the behavioral difference between motors of wild-type E. coli and mutants without signal noise, we measured the magnitude of this noise in wild-type cells, and found that the noise increases the sensitivity of the bacterial chemotaxis network downstream at the level of the flagellar motor. This provided a simple mechanism for the noise-induced enhancement of chemotactic drift, which we confirmed by simulating the E. coli chemotactic motion in various spatial profiles of chemo-attractant concentration.

Growth-dependent behavioral difference in bacterial chemotaxis

Cells can adjust to their growth environments and regulate their behavior accordingly. To study how cells accomplish this growth-dependent adjustment from the molecular to the behavioral level, we used bacterial chemotaxis as a model system to explore the behavioral difference for bacteria grown in nutrient-rich and nutrient-poor media. We found that bacteria grown in a nutrient-poor medium exhibit faster chemotaxis adaptation, and this enables them to respond more rapidly to a changing environment and increases their ability to localize to a nutrient concentration peak. We identified the molecular mechanisms behind this behavioral difference through coarse-grained modeling, and demonstrated its physiological consequences by simulating bacterial chemotactic motion in spatiotemporally varying environments and in a static environment with a nutrient concentration peak.

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.

Barrier Crossing in Escherichia coli Chemotaxis

We study cell navigation in spatiotemporally complex environments by developing a microfluidic racetrack device that creates a traveling wave with multiple peaks and a tunable wave speed. We find that while the population-averaged chemotaxis drift speed increases with wave speed for low wave speed, it decreases sharply for high wave speed. This reversed dependence of population-averaged chemotaxis drift speed on wave speed is caused by a "barrier-crossing" phenomenon, where a cell hops backwards from one peak attractant location to the peak behind by crossing an unfavorable (barrier) region with low attractant concentrations. By using a coarse-grained model of chemotaxis, we map bacterial motility in an attractant field to the random motion of an overdamped particle in an effective potential. The observed barrier-crossing phenomenon of living cells and its dependence on the spatiotemporal profile of attractant concentration are explained quantitatively by Kramers reaction rate theory.

Networked Chemoreceptors Benefit Bacterial Chemotaxis Performance

Motile bacteria use large receptor arrays to detect and follow chemical gradients in their environment. Extended receptor arrays, composed of networked signaling complexes, promote cooperative stimulus control of their associated signaling kinases. Here, we used structural lesions at the communication interface between core complexes to create an Escherichia coli strain with functional but dispersed signaling complexes. This strain allowed us to directly study how networking of signaling complexes affects chemotactic signaling and gradient-tracking performance. We demonstrate that networking of receptor complexes provides bacterial cells with about 10-fold-heightened detection sensitivity to attractants while maintaining a wide dynamic range over which receptor adaptational modifications can tune response sensitivity. These advantages proved especially critical for chemotaxis toward an attractant source under conditions in which bacteria are unable to alter the attractant gradient.

Chemoreceptor arrays are found in many motile bacteria. However, although our understanding of bacterial chemotaxis is quite detailed, the signaling and behavioral advantages of networked receptor arrays had not been directly studied in cells. We have recently shown that lesions in a key interface of the E. coli receptor array diminish physical connections and functional coupling between core signaling complexes while maintaining their basic signaling capacity. In this study, we exploited an interface 2 mutant to show, for the first time, that coupling between core complexes substantially enhances stimulus detection and chemotaxis performance.

Non-genetic diversity modulates population performance

Biological functions are typically performed by groups of cells that express predominantly the same genes, yet display a continuum of phenotypes. While it is known how one genotype can generate such non-genetic diversity, it remains unclear how different phenotypes contribute to the performance of biological function at the population level. We developed a microfluidic device to simultaneously measure the phenotype and chemotactic performance of tens of thousands of individual, freely swimming Escherichia coli as they climbed a gradient of attractant. We discovered that spatial structure spontaneously emerged from initially well-mixed wild-type populations due to non-genetic diversity. By manipulating the expression of key chemotaxis proteins, we established a causal relationship between protein expression, non-genetic diversity, and performance that was theoretically predicted. This approach generated a complete phenotype-to-performance map, in which we found a nonlinear regime. We used this map to demonstrate how changing the shape of a phenotypic distribution can have as large of an effect on collective performance as changing the mean phenotype, suggesting that selection could act on both during the process of adaptation.

Rescaling of Spatio-Temporal Sensing in Eukaryotic Chemotaxis

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient—an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies.

Direct Correlation between Motile Behavior and Protein Abundance in Single Cells

Understanding how stochastic molecular fluctuations affect cell behavior requires the quantification of both behavior and protein numbers in the same cells. Here, we combine automated microscopy with in situ hydrogel polymerization to measure single-cell protein expression after tracking swimming behavior. We characterized the distribution of non-genetic phenotypic diversity in Escherichia coli motility, which affects single-cell exploration. By expressing fluorescently tagged chemotaxis proteins (CheR and CheB) at different levels, we quantitatively mapped motile phenotype (tumble bias) to protein numbers using thousands of single-cell measurements. Our results disagreed with established models until we incorporated the role of CheB in receptor deamidation and the slow fluctuations in receptor methylation. Beyond refining models, our central finding is that changes in numbers of CheR and CheB affect the population mean tumble bias and its variance independently. Therefore, it is possible to adjust the degree of phenotypic diversity of a population by adjusting the global level of expression of CheR and CheB while keeping their ratio constant, which, as shown in previous studies, confers functional robustness to the system. Since genetic control of protein expression is heritable, our results suggest that non-genetic diversity in motile behavior is selectable, supporting earlier hypotheses that such diversity confers a selective advantage.

Cell-to-cell variations in protein numbers due to random fluctuations at the molecular level lead to cell-to-cell variations in behavior. To maintain predictable responses, signaling networks have evolved robustness against noise, but in some situations phenotypic diversity in a clonal population can be beneficial as a bet hedging or division of labor strategy. Investigating of how random molecular fluctuations affect cell behavior requires to measure biological parameters at different scales. Here, we report a new experiment that allows the measure of both protein numbers and behavior in cells that are free to move in their environment. Using Escherichia coli, a model system for the study of cellular behavior, we investigated the effects variations in the numbers of the chemo-receptor modification enzymes on single-cell swimming behavior. We found that the mean and variance of the behavior can be adjusted independently in the population by adjusting protein expression. This mechanism allows for the genetic selection of phenotypic diversity without disrupting correlations in protein expression that are important for the overall robustness of the chemotaxis system.

Allosteric proteins as logarithmic sensors

Many sensory systems, from vision and hearing in animals to signal transduction in cells, respond to fold changes in signal relative to background. Responding to fold change requires that the system senses signal on a logarithmic scale, responding identically to a change in signal level from 1 to 3, or from 10 to 30. It is an ongoing search in the field to understand the ways in which a logarithmic sensor can be implemented at the molecular level. In this work, we present evidence that logarithmic sensing can be implemented with a single protein, by means of allosteric regulation. Specifically, we find that mathematical models show that allosteric proteins can respond to stimuli on a logarithmic scale. Next, we present evidence from measurements in the literature that some allosteric proteins do operate in a parameter regime that permits logarithmic sensing. Finally, we present examples suggesting that allosteric proteins are indeed used in this capacity: allosteric proteins play a prominent role in systems where fold-change detection has been proposed. This finding suggests a role as logarithmic sensors for the many allosteric proteins across diverse biological processes.

Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella

Cilia and flagella are model systems for studying how mechanical forces control morphology. The periodic bending motion of cilia and flagella is thought to arise from mechanical feedback: dynein motors generate sliding forces that bend the flagellum, and bending leads to deformations and stresses, which feed back and regulate the motors. Three alternative feedback mechanisms have been proposed: regulation by the sliding forces, regulation by the curvature of the flagellum, and regulation by the normal forces that deform the cross-section of the flagellum. In this work, we combined theoretical and experimental approaches to show that the curvature control mechanism is the one that accords best with the bending waveforms of Chlamydomonas flagella. We make the surprising prediction that the motors respond to the time derivative of curvature, rather than curvature itself, hinting at an adaptation mechanism controlling the flagellar beat.

DOI:http://dx.doi.org/10.7554/eLife.13258.001

Information processing in bacteria: memory, computation, and statistical physics: a key issues review

Living systems have to constantly sense their external environment and adjust their internal state in order to survive and reproduce. Biological systems, from as complex as the brain to a single E. coli cell, have to process these data in order to make appropriate decisions. How do biological systems sense external signals? How do they process the information? How do they respond to signals? Through years of intense study by biologists, many key molecular players and their interactions have been identified in different biological machineries that carry out these signaling functions. However, an integrated, quantitative understanding of the whole system is still lacking for most cellular signaling pathways, not to say the more complicated neural circuits. To study signaling processes in biology, the key thing to measure is the input-output relationship. The input is the signal itself, such as chemical concentration, external temperature, light (intensity and frequency), and more complex signals such as the face of a cat. The output can be protein conformational changes and covalent modifications (phosphorylation, methylation, etc), gene expression, cell growth and motility, as well as more complex output such as neuron firing patterns and behaviors of higher animals. Due to the inherent noise in biological systems, the measured input-output dependence is often noisy. These noisy data can be analysed by using powerful tools and concepts from information theory such as mutual information, channel capacity, and the maximum entropy hypothesis. This information theory approach has been successfully used to reveal the underlying correlations between key components of biological networks, to set bounds for network performance, and to understand possible network architecture in generating observed correlations. Although the information theory approach provides a general tool in analysing noisy biological data and may be used to suggest possible network architectures in preserving information, it does not reveal the underlying mechanism that leads to the observed input-output relationship, nor does it tell us much about which information is important for the organism and how biological systems use information to carry out specific functions. To do that, we need to develop models of the biological machineries, e.g. biochemical networks and neural networks, to understand the dynamics of biological information processes. This is a much more difficult task. It requires deep knowledge of the underlying biological network-the main players (nodes) and their interactions (links)-in sufficient detail to build a model with predictive power, as well as quantitative input-output measurements of the system under different perturbations (both genetic variations and different external conditions) to test the model predictions to guide further development of the model. Due to the recent growth of biological knowledge thanks in part to high throughput methods (sequencing, gene expression microarray, etc) and development of quantitative in vivo techniques such as various florescence technology, these requirements are starting to be realized in different biological systems. The possible close interaction between quantitative experimentation and theoretical modeling has made systems biology an attractive field for physicists interested in quantitative biology. In this review, we describe some of the recent work in developing a quantitative predictive model of bacterial chemotaxis, which can be considered as the hydrogen atom of systems biology. Using statistical physics approaches, such as the Ising model and Langevin equation, we study how bacteria, such as E. coli, sense and amplify external signals, how they keep a working memory of the stimuli, and how they use these data to compute the chemical gradient. In particular, we will describe how E. coli cells avoid cross-talk in a heterogeneous receptor cluster to keep a ligand-specific memory. We will also study the thermodynamic costs of adaptation for cells to maintain an accurate memory. The statistical physics based approach described here should be useful in understanding design principles for cellular biochemical circuits in general.

Dose-Response Analysis of Chemotactic Signaling Response in Salmonella typhimurium LT2 upon Exposure to Cysteine/Cystine Redox Pair

The chemotaxis system enables motile bacteria to search for an optimum level of environmental factors. Salmonella typhimurium senses the amino acid cysteine as an attractant and its oxidized dimeric form, cystine, as a repellent. We investigated the dose-response dependence of changes in chemotactic signaling activity upon exposure to cysteine and cystine of S. typhimurium LT2 using in vivo fluorescence resonance energy transfer (FRET) measurements. The dose-response curve of the attractant response to cysteine had a sigmoidal shape, typical for receptor-ligand interactions. However, in a knockout strain of the chemoreceptor genes tsr and tar, we detected a repellent response to cysteine solutions, scaling linearly with the logarithm of the cysteine concentration. Interestingly, the magnitude of the repellent response to cystine also showed linear dependence to the logarithm of the cystine concentration. This linear dependence was observed over more than four orders of magnitude, where detection started at nanomolar concentrations. Notably, low concentrations of another oxidized compound, benzoquinone, triggered similar responses. In contrast to S. typhimurium 14028, where no response to cystine was observed in a knockout strain of chemoreceptor genes mcpB and mcpC, here we showed that McpB/McpC-independent responses to cystine existed in the strain S. typhimurium LT2 even at nanomolar concentrations. Additionally, knocking out mcpB and mcpC did not affect the linear dose-response dependence, whereas enhanced responses were only observed to solutions that where not pH neutral (>100 μM cystine) in the case of McpC overexpression. We discuss that the linear dependence of the response on the logarithm of cystine concentrations could be a result of a McpB/C-independent redox-sensing pathway that exists in S. typhimurium LT2. We supported this hypothesis with experiments with defined cysteine/cystine mixed solutions, where a transition from repellent to attractant response occurred depending on the estimated redox potential.

Singly Flagellated Pseudomonas aeruginosa Chemotaxes Efficiently by Unbiased Motor Regulation

Pseudomonas aeruginosa is an opportunistic human pathogen that has long been known to chemotax. More recently, it has been established that chemotaxis is an important factor in the ability of P. aeruginosa to make biofilms. Genes that allow P. aeruginosa to chemotax are homologous with genes in the paradigmatic model organism for chemotaxis, Escherichia coli. However, P. aeruginosa is singly flagellated and E. coli has multiple flagella. Therefore, the regulation of counterclockwise/clockwise flagellar motor bias that allows E. coli to efficiently chemotax by runs and tumbles would lead to inefficient chemotaxis by P. aeruginosa, as half of a randomly oriented population would respond to a chemoattractant gradient in the wrong sense. How P. aeruginosa regulates flagellar rotation to achieve chemotaxis is not known. Here, we analyze the swimming trajectories of single cells in microfluidic channels and the rotations of cells tethered by their flagella to the surface of a variable-environment flow cell. We show that P. aeruginosa chemotaxes by symmetrically increasing the durations of both counterclockwise and clockwise flagellar rotations when swimming up the chemoattractant gradient and symmetrically decreasing rotation durations when swimming down the chemoattractant gradient. Unlike the case for E. coli, the counterclockwise/clockwise bias stays constant for P. aeruginosa. We describe P. aeruginosa’s chemotaxis using an analytical model for symmetric motor regulation. We use this model to do simulations that show that, given P. aeruginosa’s physiological constraints on motility, its distinct, symmetric regulation of motor switching optimizes chemotaxis.

Chemotaxis has long been known to strongly affect biofilm formation by the opportunistic human pathogen P. aeruginosa, whose essential chemotaxis genes have homologues in E. coli, which achieves chemotaxis by biasing the relative probability of counterclockwise and clockwise flagellar rotation. However, the physiological difference between multiflagellated E. coli and singly flagellated P. aeruginosa implies that biased motor regulation should prevent P. aeruginosa populations from chemotaxing efficiently. Here, we used experiments, analytical modeling, and simulations to demonstrate that P. aeruginosa uses unbiased, symmetric regulation of the flagellar motor to maximize its chemotaxis efficiency. This mode of chemotaxis was not previously known and demonstrates a new variant of a paradigmatic signaling system in an important human pathogen.

Kinetics of Reactive Modules Adds Discriminative Dimensions for Selective Cell Imaging

Living cells are chemical mixtures of exceptional interest and significance, whose investigation requires the development of powerful analytical tools fulfilling the demanding constraints resulting from their singular features. In particular, multiplexed observation of a large number of molecular targets with high spatiotemporal resolution appears highly desirable. One attractive road to address this analytical challenge relies on engaging the targets in reactions and exploiting the rich kinetic signature of the resulting reactive module, which originates from its topology and its rate constants. This review explores the various facets of this promising strategy. We first emphasize the singularity of the content of a living cell as a chemical mixture and suggest that its multiplexed observation is significant and timely. Then, we show that exploiting the kinetics of analytical processes is relevant to selectively detect a given analyte: upon perturbing the system, the kinetic window associated to response read-out has to be matched with that of the targeted reactive module. Eventually, we introduce the state-of-the-art of cell imaging exploiting protocols based on reaction kinetics and draw some promising perspectives.

Fundamental constraints on the abundances of chemotaxis proteins

Flagellated bacteria, such as Escherichia coli, perform directed motion in gradients of concentration of attractants and repellents in a process called chemotaxis. The E. coli chemotaxis signaling pathway is a model for signal transduction, but it has unique features. We demonstrate that the need for fast signaling necessitates high abundances of the proteins involved in this pathway. We show that further constraints on the abundances of chemotaxis proteins arise from the requirements of self-assembly both of flagellar motors and of chemoreceptor arrays. All these constraints are specific to chemotaxis, and published data confirm that chemotaxis proteins tend to be more highly expressed than their homologs in other pathways. Employing a chemotaxis pathway model, we show that the gain of the pathway at the level of the response regulator CheY increases with overall chemotaxis protein abundances. This may explain why, at least in one E. coli strain, the abundance of all chemotaxis proteins is higher in media with lower nutrient content. We also demonstrate that the E. coli chemotaxis pathway is particularly robust to abundance variations of the motor protein FliM.

Protein Connectivity in Chemotaxis Receptor Complexes

The chemotaxis sensory system allows bacteria such as Escherichia coli to swim towards nutrients and away from repellents. The underlying pathway is remarkably sensitive in detecting chemical gradients over a wide range of ambient concentrations. Interactions among receptors, which are predominantly clustered at the cell poles, are crucial to this sensitivity. Although it has been suggested that the kinase CheA and the adapter protein CheW are integral for receptor connectivity, the exact coupling mechanism remains unclear. Here, we present a statistical-mechanics approach to model the receptor linkage mechanism itself, building on nanodisc and electron cryotomography experiments. Specifically, we investigate how the sensing behavior of mixed receptor clusters is affected by variations in the expression levels of CheA and CheW at a constant receptor density in the membrane. Our model compares favorably with dose-response curves from in vivo Förster resonance energy transfer (FRET) measurements, demonstrating that the receptor-methylation level has only minor effects on receptor cooperativity. Importantly, our model provides an explanation for the non-intuitive conclusion that the receptor cooperativity decreases with increasing levels of CheA, a core signaling protein associated with the receptors, whereas the receptor cooperativity increases with increasing levels of CheW, a key adapter protein. Finally, we propose an evolutionary advantage as explanation for the recently suggested CheW-only linker structures.

Receptor clusters of the bacterial chemotaxis sensory system act as antennae to amplify tiny changes in concentrations in the chemical environment of the cell, ultimately steering the cell towards nutrients and away from toxins. Despite bacterial chemotaxis being the most widely studied sensory pathway, the exact architecture of the receptor clusters remains speculative, with understanding suffering from a number of paradoxical observations. To address these issues with respect to the protein arrangement in the linkers connecting receptors, we present a statistical-mechanics model that combines insights from electron cryotomography on the linker architecture with results from fluorescence imaging of signaling in living cells. Although the signaling data for different expression levels of key molecular components in the linkers seems contradictory at first, our model reconciles these predictions with structural and biochemical data. Finally, we provide an evolutionary explanation for the observation that some of the incorporated linkers do not seem to transmit signals from the receptors.

A spatiotemporally controllable chemical gradient generator via acoustically oscillating sharp-edge structures

The ability to generate stable, spatiotemporally controllable concentration gradients is critical for resolving the dynamics of cellular response to a chemical microenvironment. Here we demonstrate an acoustofluidic gradient generator based on acoustically oscillating sharp-edge structures, which facilitates in a step-wise fashion the rapid mixing of fluids to generate tunable, dynamic chemical gradients. By controlling the driving voltage of a piezoelectric transducer, we demonstrated that the chemical gradient profiles can be conveniently altered (spatially controllable). By adjusting the actuation time of the piezoelectric transducer, moreover, we generated pulsatile chemical gradients (temporally controllable). With these two characteristics combined, we have developed a spatiotemporally controllable gradient generator. The applicability and biocompatibility of our acoustofluidic gradient generator are validated by demonstrating the migration of human dermal microvascular endothelial cells (HMVEC-d) in response to a generated vascular endothelial growth factor (VEGF) gradient, and by preserving the viability of HMVEC-d cells after long-term exposure to an acoustic field. Our device features advantages such as simple fabrication and operation, compact and biocompatible device, and generation of spatiotemporally tunable gradients.

Response thresholds in bacterial chemotaxis

Stimulation of Escherichia coli by exponential ramps of chemoattractants generates step changes in the concentration of the response regulator, CheY-P. Because flagellar motors are ultrasensitive, this should change the fraction of time that motors spin clockwise, the CWbias. However, early work failed to show changes in CWbias when ramps were shallow. This was explained by a model for motor remodeling that predicted plateaus in plots of CWbias versus [CheY-P]. We looked for these plateaus by examining distributions of CWbias in populations of cells with different mean [CheY-P]. We did not find such plateaus. Hence, we repeated the work on shallow ramps and found that motors did indeed respond. These responses were quantitatively described by combining motor remodeling with ultrasensitivity in a model that exhibited high sensitivities over a wide dynamic range.

Adaptive Responses Limited by Intrinsic Noise

Sensory systems have mechanisms to respond to the external environment and adapt to them. Such adaptive responses are effective for a wide dynamic range of sensing and perception of temporal change in stimulus. However, noise generated by the adaptation system itself as well as extrinsic noise in sensory inputs may impose a limit on the ability of adaptation systems. The relation between response and noise is well understood for equilibrium systems in the form of fluctuation response relation. However, the relation for nonequilibrium systems, including adaptive systems, are poorly understood. Here, we systematically explore such a relation between response and fluctuation in adaptation systems. We study the two network motifs, incoherent feedforward loops (iFFL) and negative feedback loops (nFBL), that can achieve perfect adaptation. We find that the response magnitude in adaption systems is limited by its intrinsic noise, implying that higher response would have higher noise component as well. Comparing the relation of response and noise in iFFL and nFBL, we show that whereas iFFL exhibits adaptation over a wider parameter range, nFBL offers higher response to noise ratio than iFFL. We also identify the condition that yields the upper limit of response for both network motifs. These results may explain the reason of why nFBL seems to be more abundant in nature for the implementation of adaption systems.

Chemotactic Motility of Pseudomonas fluorescens F113 under Aerobic and Denitrification Conditions

The sequence of the genome of Pseudomonas fluorescens F113 has shown the presence of multiple traits relevant for rhizosphere colonization and plant growth promotion. Among these traits are denitrification and chemotactic motility. Besides aerobic growth, F113 is able to grow anaerobically using nitrate and nitrite as final electron acceptors. F113 is able to perform swimming motility under aerobic conditions and under anaerobic conditions when nitrate is used as the electron acceptor. However, nitrite can not support swimming motility. Regulation of swimming motility is similar under aerobic and anaerobic conditions, since mutants that are hypermotile under aerobic conditions, such as gacS, sadB, kinB, algU and wspR, are also hypermotile under anaerobic conditions. However, chemotactic behavior is different under aerobic and denitrification conditions. Unlike most pseudomonads, the F113 genome encode three complete chemotaxis systems, Che1, Che2 and Che3. Mutations in each of the cheA genes of the three Che systems has shown that the three systems are functional and independent. Mutation of the cheA1 gene completely abolished swimming motility both under aerobic and denitrification conditions. Mutation of the cheA2 gene, showed only a decrease in swimming motility under both conditions, indicating that this system is not essential for chemotactic motility but is necessary for optimal motility. Mutation of the cheA3 gene abolished motility under denitrification conditions but only produced a decrease in motility under aerobic conditions. The three Che systems proved to be implicated in competitive rhizosphere colonization, being the cheA1 mutant the most affected.

Maxwell's demon in biochemical signal transduction with feedback loop

Signal transduction in living cells is vital to maintain life itself, where information transfer in noisy environment plays a significant role. In a rather different context, the recent intensive research on ‘Maxwell's demon'—a feedback controller that utilizes information of individual molecules—have led to a unified theory of information and thermodynamics. Here we combine these two streams of research, and show that the second law of thermodynamics with information reveals the fundamental limit of the robustness of signal transduction against environmental fluctuations. Especially, we find that the degree of robustness is quantitatively characterized by an informational quantity called transfer entropy. Our information-thermodynamic approach is applicable to biological communication inside cells, in which there is no explicit channel coding in contrast to artificial communication. Our result could open up a novel biophysical approach to understand information processing in living systems on the basis of the fundamental information–thermodynamics link.

The connection between information and thermodynamics is embodied in the figure of Maxwell's demon, a feedback controller. Here, the authors apply thermodynamics of information to signal transduction in chemotaxis of E. coli, predicting that its robustness is quantified by transfer entropy.

A Trigger Residue for Transmembrane Signaling in the Escherichia coli Serine Chemoreceptor

The transmembrane Tsr protein of Escherichia coli mediates chemotactic responses to environmental serine gradients. Serine binds to the periplasmic domain of the homodimeric Tsr molecule, promoting a small inward displacement of one transmembrane helix (TM2). TM2 piston displacements, in turn, modulate the structural stability of the Tsr-HAMP domain on the cytoplasmic side of the membrane to control the autophosphorylation activity of the signaling CheA kinase bound to the membrane-distal cytoplasmic tip of Tsr. A five-residue control cable segment connects TM2 to the AS1 helix of HAMP and transmits stimulus and sensory adaptation signals between them. To explore the possible role of control cable helicity in transmembrane signaling by Tsr, we characterized the signaling properties of mutant receptors with various control cable alterations. An all-alanine control cable shifted Tsr output toward the kinase-on state, whereas an all-glycine control cable prevented Tsr from reaching either a fully on or fully off output state. Restoration of the native isoleucine (I214) in these synthetic control cables largely alleviated their signaling defects. Single amino acid replacements at Tsr-I214 shifted output toward the kinase-off (L, N, H, and R) or kinase-on (A and G) states, whereas other control cable residues tolerated most amino acid replacements with little change in signaling behavior. These findings indicate that changes in control cable helicity might mediate transitions between the kinase-on and kinase-off states during transmembrane signaling by chemoreceptors. Moreover, the Tsr-I214 side chain plays a key role, possibly through interaction with the membrane interfacial environment, in triggering signaling changes in response to TM2 piston displacements.

IMPORTANCE

The Tsr protein of E. coli mediates chemotactic responses to environmental serine gradients. Stimulus signals from the Tsr periplasmic sensing domain reach its cytoplasmic kinase control domain through piston displacements of a membrane-spanning helix and an adjoining five-residue control cable segment. We characterized the signaling properties of Tsr variants to elucidate the transmembrane signaling role of the control cable, an element present in many microbial sensory proteins. Both the kinase-on and kinase-off output states of Tsr depended on control cable helicity, but only one residue, I214, was critical for triggering responses to attractant inputs. These findings suggest that signal transmission in Tsr involves modulation of control cable helicity through interaction of the I214 side chain with the cytoplasmic membrane.

Computations underlying Drosophila photo-taxis, odor-taxis, and multi-sensory integration

To better understand how organisms make decisions on the basis of temporally varying multi-sensory input, we identified computations made by Drosophila larvae responding to visual and optogenetically induced fictive olfactory stimuli. We modeled the larva's navigational decision to initiate turns as the output of a Linear-Nonlinear-Poisson cascade. We used reverse-correlation to fit parameters to this model; the parameterized model predicted larvae's responses to novel stimulus patterns. For multi-modal inputs, we found that larvae linearly combine olfactory and visual signals upstream of the decision to turn. We verified this prediction by measuring larvae's responses to coordinated changes in odor and light. We studied other navigational decisions and found that larvae integrated odor and light according to the same rule in all cases. These results suggest that photo-taxis and odor-taxis are mediated by a shared computational pathway.

DOI:http://dx.doi.org/10.7554/eLife.06229.001

Living organisms can sense cues from their surroundings and respond in appropriate ways. For example, animals will often move towards the smell of food or away from potential threats, such as predators. However, it is not fully understood how an animal's nervous system is set up to allow sensory information to control how the animal navigates its environment. It is also not clear how animals ‘decide’ what to do when they receive conflicting information from different senses.

Optogenetics is a technique that allows neuroscientists to control the activities of individual nerve cells simply by shining light on to them. Fruit fly larvae have a simple but well-studied nervous system, and they are nearly transparent, so scientists can use optogenetics to activate nerve cells in freely moving larvae.

Fruit fly larvae move in a series of forward ‘runs’ and direction-changing ‘turns’ and use sensory cues to decide when to turn, how large of a turn to make, and whether to turn left or right. Gepner, Mihovilovic Skanata et al. used optogenetics to stimulate different combinations of sensory nerve cells in larvae, while tracking the larvae's movements to discover exactly what information they used to make these decisions. An independent study by Hernandez-Nunez et al. also used a similar approach.

Fruit fly larvae are attracted towards scents from rotting fruit and are repelled by light—in particular, larvae are most sensitive to blue light but cannot detect red light. Therefore, Gepner, Mihovilovic Skanata et al. could expose the larvae to blue light to activate light-sensing nerve cells as normal, and use red light to activate odor-sensing nerve cells via optogenetics. These experiments showed that larvae changed direction more often when the level of blue light was increased or when the level of red light (which simulated the detection of odors from rotting fruits) was decreased.

Analysis of the data from these experiments revealed that larvae essentially assign negative values to the blue light and positive values to the ‘odor-mimicking’ red light. The larvae then use the sum of these two values to dictate their next move. This suggests that navigation in response to both light and odors is supported by the same pathways in a larva's nervous system.

The approach of using optogenetics in combination with quantitative analysis, as used in these two independent studies, is now opening the door to a more complete understanding of the connections between the activities of sensory nerve cells and perception and behavior.

DOI:http://dx.doi.org/10.7554/eLife.06229.002

Comparison of adaptation motifs: temporal, stochastic and spatial responses

The cells' ability to adapt to changes in the external environment is crucial for the survival of many organisms. There are two broad classes of signalling networks that achieve perfect adaptation. Both rely on complementary regulation of the response by an external signal and an inhibitory process. In one class of systems, inhibition comes about from the response itself, closing a negative feedback (NFB) loop. In the other, the inhibition comes directly from the external signal in what is referred to as an incoherent feedforward (IFF) loop. Although both systems show adaptive behaviour to constant changes in the level of the stimulus, their response to other forms of stimuli can differ. Here the authors consider the respective response to various such disturbances, including ramp increases, removal of the stimulus and pulses. The authors also consider the effect of stochastic fluctuations in signalling that come about from the interaction of the signalling elements. Finally, the authors consider the possible effect of spatially varying signals. The authors show that both the NFB and the IFF motifs can be used to sense static spatial gradients, under a local excitation, global inhibition assumption. The results may help experimentalists develop protocols that can discriminate between the two adaptation motifs.

Elements of the cellular metabolic structure

A large number of studies have demonstrated the existence of metabolic covalent modifications in different molecular structures, which are able to store biochemical information that is not encoded by DNA. Some of these covalent mark patterns can be transmitted across generations (epigenetic changes). Recently, the emergence of Hopfield-like attractor dynamics has been observed in self-organized enzymatic networks, which have the capacity to store functional catalytic patterns that can be correctly recovered by specific input stimuli. Hopfield-like metabolic dynamics are stable and can be maintained as a long-term biochemical memory. In addition, specific molecular information can be transferred from the functional dynamics of the metabolic networks to the enzymatic activity involved in covalent post-translational modulation, so that determined functional memory can be embedded in multiple stable molecular marks. The metabolic dynamics governed by Hopfield-type attractors (functional processes), as well as the enzymatic covalent modifications of specific molecules (structural dynamic processes) seem to represent the two stages of the dynamical memory of cellular metabolism (metabolic memory). Epigenetic processes appear to be the structural manifestation of this cellular metabolic memory. Here, a new framework for molecular information storage in the cell is presented, which is characterized by two functionally and molecularly interrelated systems: a dynamic, flexible and adaptive system (metabolic memory) and an essentially conservative system (genetic memory). The molecular information of both systems seems to coordinate the physiological development of the whole cell.

How to train your microbe: methods for dynamically characterizing gene networks

Gene networks regulate biological processes dynamically. However, researchers have largely relied upon static perturbations, such as growth media variations and gene knockouts, to elucidate gene network structure and function. Thus, much of the regulation on the path from DNA to phenotype remains poorly understood. Recent studies have utilized improved genetic tools, hardware, and computational control strategies to generate precise temporal perturbations outside and inside of live cells. These experiments have, in turn, provided new insights into the organizing principles of biology. Here, we introduce the major classes of dynamical perturbations that can be used to study gene networks, and discuss technologies available for creating them in a wide range of microbial pathways.

Absolute quantitation of protein posttranslational modification isoform

Mass spectrometry has been widely applied in characterization and quantification of proteins from complex biological samples. Because the numbers of absolute amounts of proteins are needed in construction of mathematical models for molecular systems of various biological phenotypes and phenomena, a number of quantitative proteomic methods have been adopted to measure absolute quantities of proteins using mass spectrometry. The liquid chromatography-tandem mass spectrometry (LC-MS/MS) coupled with internal peptide standards, i.e., the stable isotope-coded peptide dilution series, which was originated from the field of analytical chemistry, becomes a widely applied method in absolute quantitative proteomics research. This approach provides more and more absolute protein quantitation results of high confidence. As quantitative study of posttranslational modification (PTM) that modulates the biological activity of proteins is crucial for biological science and each isoform may contribute a unique biological function, degradation, and/or subcellular location, the absolute quantitation of protein PTM isoforms has become more relevant to its biological significance. In order to obtain the absolute cellular amount of a PTM isoform of a protein accurately, impacts of protein fractionation, protein enrichment, and proteolytic digestion yield should be taken into consideration and those effects before differentially stable isotope-coded PTM peptide standards are spiked into sample peptides have to be corrected. Assisted with stable isotope-labeled peptide standards, the absolute quantitation of isoforms of posttranslationally modified protein (AQUIP) method takes all these factors into account and determines the absolute amount of a protein PTM isoform from the absolute amount of the protein of interest and the PTM occupancy at the site of the protein. The absolute amount of the protein of interest is inferred by quantifying both the absolute amounts of a few PTM-site-independent peptides in the total cellular protein and their peptide yields. The PTM occupancy determination is achieved by measuring the absolute amounts of both PTM and non-PTM peptides from the highly purified protein sample expressed in transgenic organisms or directly isolated from an organism using affinity purification. The absolute amount of each PTM isoform in the total cellular protein extract is finally calculated from these two variables. Following this approach, the ion intensities given by mass spectrometers are used to calculated the peptide amounts, from which the amounts of protein isoforms are then deduced. In this chapter, we describe the principles underlying the experimental design and procedures used in AQUIP method. This quantitation method basically employs stable isotope-labeled peptide standards and affinity purification from a tagged recombinant protein of interest. Other quantitation strategies and purification techniques related to this method are also discussed.

Thermodynamic costs of information processing in sensory adaptation

Biological sensory systems react to changes in their surroundings. They are characterized by fast response and slow adaptation to varying environmental cues. Insofar as sensory adaptive systems map environmental changes to changes of their internal degrees of freedom, they can be regarded as computational devices manipulating information. Landauer established that information is ultimately physical, and its manipulation subject to the entropic and energetic bounds of thermodynamics. Thus the fundamental costs of biological sensory adaptation can be elucidated by tracking how the information the system has about its environment is altered. These bounds are particularly relevant for small organisms, which unlike everyday computers, operate at very low energies. In this paper, we establish a general framework for the thermodynamics of information processing in sensing. With it, we quantify how during sensory adaptation information about the past is erased, while information about the present is gathered. This process produces entropy larger than the amount of old information erased and has an energetic cost bounded by the amount of new information written to memory. We apply these principles to the E. coli's chemotaxis pathway during binary ligand concentration changes. In this regime, we quantify the amount of information stored by each methyl group and show that receptors consume energy in the range of the information-theoretic minimum. Our work provides a basis for further inquiries into more complex phenomena, such as gradient sensing and frequency response.

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.

Acoustofluidic chemical waveform generator and switch

Eliciting a cellular response to a changing chemical microenvironment is central to many biological processes including gene expression, cell migration, differentiation, apoptosis, and intercellular signaling. The nature and scope of the response is highly dependent upon the spatiotemporal characteristics of the stimulus. To date, studies that investigate this phenomenon have been limited to digital (or step) chemical stimulation with little control over the temporal counterparts. Here, we demonstrate an acoustofluidic (i.e., fusion of acoustics and microfluidics) approach for generating programmable chemical waveforms that permits continuous modulation of the signal characteristics including the amplitude (i.e., sample concentration), shape, frequency, and duty cycle, with frequencies reaching up to 30 Hz. Furthermore, we show fast switching between multiple distinct stimuli, wherein the waveform of each stimulus is independently controlled. Using our device, we characterized the frequency-dependent activation and internalization of the β2-adrenergic receptor (β2-AR), a prototypic G-protein coupled receptor (GPCR), using epinephrine. The acoustofluidic-based programmable chemical waveform generation and switching method presented herein is expected to be a powerful tool for the investigation and characterization of the kinetics and other dynamic properties of many biological and biochemical processes.