A novel multiobjective optimization algorithm based on bacterial chemotaxis

In this article a novel algorithm based on the chemotaxis process of Echerichia coil is developed to solve multiobjective optimization problems. The algorithm uses fast nondominated sorting procedure, communication between the colony members and a simple chemotactical strategy to change the bacterial positions in order to explore the search space to find several optimal solutions. The proposed algorithm is validated using 11 benchmark problems and implementing three different performance measures to compare its performance with the NSGA-II genetic algorithm and with the particle swarm-based algorithm NSPSO. (C) 2009 Elsevier Ltd. All rights reserved.

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.

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1168 For further resources related to this article, please visit the WIREs website.

Two binding modes reveal flexibility in kinase/response regulator interactions in the bacterial chemotaxis pathway

The crystal structure at 2.0-Å resolution of the complex of the Escherichia coli chemotaxis response regulator CheY and the phosphoacceptor-binding domain (P2) of the kinase CheA is presented. The binding interface involves the fourth and fifth helices and fifth β-strand of CheY and both helices of P2. Surprisingly, the two heterodimers in the asymmetric unit have two different binding modes involving the same interface, suggesting some flexibility in the binding regions. Significant conformational changes have occurred in CheY compared with previously determined unbound structures. The active site of CheY is exposed by the binding of the kinase domain, possibly to enhance phosphotransfer from CheA to CheY. The conformational changes upon complex formation as well as the observation that there are two different binding modes suggest that the plasticity of CheY is an essential feature of response regulator function.

A model of excitation and adaptation in bacterial chemotaxis

Bacterial chemotaxis is widely studied because of its accessibility and because it incorporates processes that are important in a number of sensory systems: signal transduction, excitation, adaptation, and a change in behavior, all in response to stimuli. Quantitative data on the change in behavior are available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. We have incorporated recent biochemical data into a mathematical model that can reproduce many of the major features of the intracellular response, including the change in the level of chemotactic proteins to step and ramp stimuli such as those used in experimental protocols. The interaction of the chemotactic proteins with the motor is not modeled, but we can estimate the degree of cooperativity needed to produce the observed gain under the assumption that the chemotactic proteins interact directly with the motor proteins.

Signal termination in bacterial chemotaxis: CheZ mediates dephosphorylation of free rather than switch-bound CheY.

Chemotaxis in bacteria is controlled by regulating the direction of flagellar rotation. The regulation is carried out by the chemotaxis protein CheY. When phosphorylated, CheY binds to FliM, which is one of the proteins that constitute the "gear box" (or "switch") of the flagellar motor. Consequently, the motor shifts from the default direction of rotation, counterclockwise, to clockwise rotation. This biased rotation is terminated when CheY is dephosphorylated either spontaneously or, faster, by a specific phosphatase, CheZ. Logically, one might expect CheZ to act directly on FliM-bound CheY. However, here we provide direct biochemical evidence that, in contrast to this expectation, phosphorylated CheY (CheY approximately P), bound to FliM, is protected from dephosphorylation by CheZ. The complex between CheY approximately P and FliM was trapped by cross-linking with dimethylsuberimidate, and its susceptibility to CheZ was measured. CheY approximately P complexed with FliM, unlike free CheY approximately P, was not dephosphorylated by CheZ. However, it did undergo spontaneous dephosphorylation. Nonspecific cross-linked CheY dimers, measured as a control, were dephosphorylated by CheZ. No significant binding between CheZ and any of the switch proteins was detected. It is concluded that, in the termination mechanism of signal transduction in bacterial chemotaxis, CheZ acts only on free CheY approximately P. We suggest that CheZ affects switch-bound CheY approximately P by shifting the equilibrium between bound and free CheY approximately P.

Modeling chemotaxis reveals the role of reversed phosphotransfer and a bi-functional kinase-phosphatase

Understanding how multiple signals are integrated in living cells to produce a balanced response is a major challenge in biology. Two-component signal transduction pathways, such as bacterial chemotaxis, comprise histidine protein kinases (HPKs) and response regulators (RRs). These are used to sense and respond to changes in the environment. Rhodobacter sphaeroides has a complex chemosensory network with two signaling clusters, each containing a HPK, CheA. Here we demonstrate, using a mathematical model, how the outputs of the two signaling clusters may be integrated. We use our mathematical model supported by experimental data to predict that: (1) the main RR controlling flagellar rotation, CheY6, aided by its specific phosphatase, the bifunctional kinase CheA3, acts as a phosphate sink for the other RRs; and (2) a phosphorelay pathway involving CheB2 connects the cytoplasmic cluster kinase CheA3 with the polar localised kinase CheA2, and allows CheA3-P to phosphorylate non-cognate chemotaxis RRs. These two mechanisms enable the bifunctional kinase/phosphatase activity of CheA3 to integrate and tune the sensory output of each signaling cluster to produce a balanced response. The signal integration mechanisms identified here may be widely used by other bacteria, since like R. sphaeroides, over 50% of chemotactic bacteria have multiple cheA homologues and need to integrate signals from different sources.

Response kinetics in the complex chemotaxis signalling pathway of Rhodobacter sphaeroides

Chemotaxis is one of the best characterised signalling systems in biology. It is the mechanism by which bacteria move towards optimal environments and is implicated in biofilm formation, pathogenesis and symbiosis. The properties of the bacterial chemosensory response have been described in detail for the single chemosensory pathway of Escherichia coli. We have characterised the properties of the chemosensory response of Rhodobacter sphaeroides, an -proteobacterium with multiple chemotaxis pathways, under two growth conditions allowing the effects of protein expression levels and cell architecture to be investigated. Using tethered cell assays we measured the responses of the system to step changes in concentration of the attractant propionate and show that, independently of the growth conditions, R. sphaeroides is chemotactic over at least five orders of magnitude and has a sensing profile following Weber’s law. Mathematical modelling also shows that, like E. coli, R. sphaeroides is capable of showing Fold-Change Detection (FCD). Our results indicate that general features of bacterial chemotaxis such as the range and sensitivity of detection, adaptation times, adherence to Weber’s law and the presence of FCD may be integral features of chemotaxis systems in general, regardless of network complexity, protein expression levels and cellular architecture across different species.

Conformational coupling in the chemotaxis response regulator CheY

CheY, a response regulator protein in bacterial chemotaxis, serves as a prototype for the analysis of response regulator function in two-component signal transduction. Phosphorylation of a conserved aspartate at the active site mediates a conformational change at a distal signaling surface that modulates interactions with the flagellar motor component FliM, the sensor kinase CheA, and the phosphatase CheZ. The objective of this study was to probe the conformational coupling between the phosphorylation site and the signaling surface of CheY in the reverse direction by quantifying phosphorylation activity in the presence and absence of peptides of CheA, CheZ, and FliM that specifically interact with CheY. Binding of these peptides dramatically impacted autophosphorylation of CheY by small molecule phosphodonors, which is indicative of reverse signal propagation in CheY. Autodephosphorylation and substrate affinity, however, were not significantly affected. Kinetic characterization of several CheY mutants suggested that conserved residues Thr-87, Tyr-106, and Lys-109, implicated in the activation mechanism, are not essential for conformational coupling. These findings provide structural and conceptual insights into the mechanism of CheY activation. Our results are consistent with a multistate thermodynamic model of response regulator activation.

Light regulation of type IV pilus-dependent motility by chemosensor-like elements in Synechocystis PCC6803

To optimize photosynthesis, cyanobacteria move toward or away from a light source by a process known as phototaxis. Phototactic movement of the cyanobacterium Synechocystis PCC6803 is a surface-dependent phenomenon that requires type IV pili, cellular appendages implicated in twitching and social motility in a range of bacteria. To elucidate regulation of cyanobacterial motility, we generated transposon-tagged mutants with aberrant phototaxis; mutants were either nonmotile or exhibited an “inverted motility response” (negative phototaxis) relative to wild-type cells. Several mutants contained transposons in genes similar to those involved in bacterial chemotaxis. Synechocystis PCC6803 has three loci with chemotaxis-like genes, of which two, Tax1 and Tax3, are involved in phototaxis. Transposons interrupting the Tax1 locus yielded mutants that exhibited an inverted motility response, suggesting that this locus is involved in controlling positive phototaxis. However, a strain null for taxAY1 was nonmotile and hyperpiliated. Interestingly, whereas the C-terminal region of the TaxD1 polypeptide is similar to the signaling domain of enteric methyl-accepting chemoreceptor proteins, the N terminus has two domains resembling chromophore-binding domains of phytochrome, a photoreceptor in plants. Hence, TaxD1 may play a role in perceiving the light stimulus. Mutants in the Tax3 locus are nonmotile and do not make type IV pili. These findings establish links between chemotaxis-like regulatory elements and type IV pilus-mediated phototaxis.

C factor, a cell-surface-associated intercellular signaling protein, stimulates the cytoplasmic Frz signal transduction system in Myxococcus xanthus.

C factor, an intercellular signaling protein, is required for aggregation and sporulation of the social bacterium, Myxococcus xanthus. We report that C factor, which normally is associated with the cell surface, provides input to the Frz signal transduction cascade. Elements of this cascade have sequence homology to bacterial chemotaxis systems and are known to control the frequency of gliding reversal. Exposure of developing cells of a C-factor-less mutant (csgA) to purified C factor increases the ratio of methylated to nonmethylated FrzCD protein, the Frz homolog of the methyl-accepting chemotaxis proteins. Methylation depends on the cognate methyltransferase FrzF, and its extent increases with the concentration of C factor. C-factor-induced methylation also depends on the product of a gene, called class II, which is necessary in vivo for all known responses to C factor. A model for aggregation is proposed in which C factor stimulates the Frz cascade and thereby decreases cell reversals in a way that preferentially leads cells into an aggregate.

Molecular mechanism of transmembrane signaling by the aspartate receptor: a model.

The aspartate receptor of bacterial chemotaxis is representative of a large class of membrane-spanning receptors found in prokaryotic and eukaryotic organisms. These receptors, which regulate histidine kinase pathways and possess two putative transmembrane helices per subunit, appear to control a wide variety of cellular processes. The best characterized subgroup of the two-helix receptor class is the homologous family of chemosensory receptors from Escherichia coli and Salmonella typhimurium, including the aspartate receptor. This receptor binds aspartate, an attractant, in the periplasmic compartment and undergoes an intramolecular, transmembrane conformational change, thereby modulating the autophosphorylation rate of a bound histidine kinase in the cytoplasm. Here, we analyze recent results from x-ray crystallographic, solution 19F NMR, and engineered disulfide studies probing the aspartate-induced structural change within the periplasmic and transmembrane regions of the receptor. Together, these approaches provide evidence that aspartate binding triggers a "swinging-piston" displacement of the second membrane-spanning helix, which is proposed to communicate the signal across the bilayer.