Feedback control architecture and the bacterial chemotaxis network.

PMCID: PMC3088647This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance

NO PLIF Visualizations of the Orion Capsule in LENS-I

Planar laser-induced fluorescence (PLIF) of nitric oxide (NO) was used to visualize the interaction of reaction-control-system (RCS) jet flows in the wake of a hypersonic capsule reentry vehicle. The tests were performed at the Calspan University at Buffalo Research Center's (CUBRC) LENS-I reflected shock tunnel facility. This was the first application of PLIF to study RCS jets in a large-scale pulsed hypersonic facility. The LENS-I facility allowed RCS jet flows to be studied while varying the flow enthalpy, Reynolds number, angle of attack and jet configuration. The interaction of pitch and roll jets with the flowfield was investigated. Additionally, thin film sensors were used to monitor heat transfer on the surface of the model to detect any localized heating resulting from the firing of the RCS jets. Tests were conducted with the model held at angles of attack of 18deg and 22deg. The nominal Mach number in all tests was 8, while Reynolds number based on model diameter ranged from 2.2x10(exp 6) - 1.5x10(exp 7). Images were processed using the Virtual Diagnostics Interface (ViDI) system developed at NASA Langley Research Center to provide a three-dimensional display of the experimental data

Chemotactic response and adaptation dynamics in Escherichia coli

Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from repellents. Its biochemical mechanism based on methylation and demethylation of chemoreceptors has long been known. Despite the importance of adaptation for cell memory and behavior, the dynamics of adaptation are difficult to reconcile with current models of precise adaptation. Here, we follow time courses of signaling in response to concentration step changes of attractant using in vivo fluorescence resonance energy transfer measurements. Specifically, we use a condensed representation of adaptation time courses for efficient evaluation of different adaptation models. To quantitatively explain the data, we finally develop a dynamic model for signaling and adaptation based on the attractant flow in the experiment, signaling by cooperative receptor complexes, and multiple layers of feedback regulation for adaptation. We experimentally confirm the predicted effects of changing the enzyme-expression level and bypassing the negative feedback for demethylation. Our data analysis suggests significant imprecision in adaptation for large additions. Furthermore, our model predicts highly regulated, ultrafast adaptation in response to removal of attractant, which may be useful for fast reorientation of the cell and noise reduction in adaptation.Comment: accepted for publication in PLoS Computational Biology; manuscript (19 pages, 5 figures) and supplementary information; added additional clarification on alternative adaptation models in supplementary informatio

A Minimal Model of Metabolism Based Chemotaxis

Since the pioneering work by Julius Adler in the 1960's, bacterial chemotaxis has been predominantly studied as metabolism-independent. All available simulation models of bacterial chemotaxis endorse this assumption. Recent studies have shown, however, that many metabolism-dependent chemotactic patterns occur in bacteria. We hereby present the simplest artificial protocell model capable of performing metabolism-based chemotaxis. The model serves as a proof of concept to show how even the simplest metabolism can sustain chemotactic patterns of varying sophistication. It also reproduces a set of phenomena that have recently attracted attention on bacterial chemotaxis and provides insights about alternative mechanisms that could instantiate them. We conclude that relaxing the metabolism-independent assumption provides important theoretical advances, forces us to rethink some established pre-conceptions and may help us better understand unexplored and poorly understood aspects of bacterial chemotaxis

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area

Evolution of Taxis Responses in Virtual Bacteria: Non-Adaptive Dynamics

Bacteria are able to sense and respond to a variety of external stimuli, with responses that vary from stimuli to stimuli and from species to species. The best-understood is chemotaxis in the model organism Escherichia coli, where the dynamics and the structure of the underlying pathway are well characterised. It is not clear, however, how well this detailed knowledge applies to mechanisms mediating responses to other stimuli or to pathways in other species. Furthermore, there is increasing experimental evidence that bacteria integrate responses from different stimuli to generate a coherent taxis response. We currently lack a full understanding of the different pathway structures and dynamics and how this integration is achieved. In order to explore different pathway structures and dynamics that can underlie taxis responses in bacteria, we perform a computational simulation of the evolution of taxis. This approach starts with a population of virtual bacteria that move in a virtual environment based on the dynamics of the simple biochemical pathways they harbour. As mutations lead to changes in pathway structure and dynamics, bacteria better able to localise with favourable conditions gain a selective advantage. We find that a certain dynamics evolves consistently under different model assumptions and environments. These dynamics, which we call non-adaptive dynamics, directly couple tumbling probability of the cell to increasing stimuli. Dynamics that are adaptive under a wide range of conditions, as seen in the chemotaxis pathway of E. coli, do not evolve in these evolutionary simulations. However, we find that stimulus scarcity and fluctuations during evolution results in complex pathway dynamics that result both in adaptive and non-adaptive dynamics depending on basal stimuli levels. Further analyses of evolved pathway structures show that effective taxis dynamics can be mediated with as few as two components. The non-adaptive dynamics mediating taxis responses provide an explanation for experimental observations made in mutant strains of E. coli and in wild-type Rhodobacter sphaeroides that could not be explained with standard models. We speculate that such dynamics exist in other bacteria as well and play a role linking the metabolic state of the cell and the taxis response. The simplicity of mechanisms mediating such dynamics makes them a candidate precursor of more complex taxis responses involving adaptation. This study suggests a strong link between stimulus conditions during evolution and evolved pathway dynamics. When evolution was simulated under conditions of scarce and fluctuating stimulus conditions, the evolved pathway contained features of both adaptive and non-adaptive dynamics, suggesting that these two types of dynamics can have different advantages under distinct environmental circumstances

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

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 {\it 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 does. 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 of 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 manuscript closes by discussing intercell variability of total protein concentration as means of ensuring the overall survival of a population as cells are subjected to different environments

Mystery Solved: The Identification of the Two Missing Romanov Children Using DNA Analysis

One of the greatest mysteries for most of the twentieth century was the fate of the Romanov family, the last Russian monarchy. Following the abdication of Tsar Nicholas II, he and his wife, Alexandra, and their five children were eventually exiled to the city of Yekaterinburg. The family, along with four loyal members of their staff, was held captive by members of the Ural Soviet. According to historical reports, in the early morning hours of July 17, 1918 the entire family along with four loyal members of their staff was executed by a firing squad. After a failed attempt to dispose of the remains in an abandoned mine shaft, the bodies were transported to an open field only a few kilometers from the mine shaft. Nine members of the group were buried in one mass grave while two of the children were buried in a separate grave. With the official discovery of the larger mass grave in 1991, and subsequent DNA testing to confirm the identities of the Tsar, the Tsarina, and three of their daughters – doubt persisted that these remains were in fact those of the Romanov family. In the summer of 2007, a group of amateur archeologists discovered a collection of remains from the second grave approximately 70 meters from the larger grave. We report forensic DNA testing on the remains discovered in 2007 using mitochondrial DNA (mtDNA), autosomal STR, and Y- STR testing. Combined with additional DNA testing of material from the 1991 grave, we have virtually irrefutable evidence that the two individuals recovered from the 2007 grave are the two missing children of the Romanov family: the Tsarevich Alexei and one of his sisters