Changing Cellular Location of CheZ Predicted by Molecular Simulations

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

Detailed simulations of cell biology with Smoldyn 2.1.

Most cellular processes depend on intracellular locations and random collisions of individual protein molecules. To model these processes, we developed algorithms to simulate the diffusion, membrane interactions, and reactions of individual molecules, and implemented these in the Smoldyn program. Compared to the popular MCell and ChemCell simulators, we found that Smoldyn was in many cases more accurate, more computationally efficient, and easier to use. Using Smoldyn, we modeled pheromone response system signaling among yeast cells of opposite mating type. This model showed that secreted Bar1 protease might help a cell identify the fittest mating partner by sharpening the pheromone concentration gradient. This model involved about 200,000 protein molecules, about 7000 cubic microns of volume, and about 75 minutes of simulated time; it took about 10 hours to run. Over the next several years, as faster computers become available, Smoldyn will allow researchers to model and explore systems the size of entire bacterial and smaller eukaryotic cells

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

Noise characteristics of the Escherichia coli rotary motor

The chemotaxis pathway in the bacterium Escherichia coli allows cells to detect changes in external ligand concentration (e.g. nutrients). The pathway regulates the flagellated rotary motors and hence the cells' swimming behaviour, steering them towards more favourable environments. While the molecular components are well characterised, the motor behaviour measured by tethered cell experiments has been difficult to interpret. Here, we study the effects of sensing and signalling noise on the motor behaviour. Specifically, we consider fluctuations stemming from ligand concentration, receptor switching between their signalling states, adaptation, modification of proteins by phosphorylation, and motor switching between its two rotational states. We develop a model which includes all signalling steps in the pathway, and discuss a simplified version, which captures the essential features of the full model. We find that the noise characteristics of the motor contain signatures from all these processes, albeit with varying magnitudes. This allows us to address how cell-to-cell variation affects motor behaviour and the question of optimal pathway design. A similar comprehensive analysis can be applied to other two-component signalling pathways.Comment: 22 pages, 7 figures, 3 tutorials, supplementary information; submitted manuscrip

Spatial regulation of dual flagellar systems

Many cellular processes are highly spatially ordered, with spatial separation regulated by cellular factors called landmark proteins. Examples of compartmentalized processes are those involved in bacterial motility. In bacteria, swimming and swarming require the formation of flagella - long, rotating, helical filaments driven by a membrane-embedded motor. Landmark proteins likely regulate the numerous flagellation patterns found in a variety of bacterial species. In polarly flagellated bacteria, primarily encountered in marine habitats, the SRP-like GTPase FlhF and the MinD-like ATPase FlhG are known to control flagellar positioning and number. HubP, another polar factor identified in Vibrio cholerae, was shown to be involved in the localization of proteins which are a part of other cellular processes such as chemotaxis, enabling the cell to navigate efficiently towards more favorable conditions. The polarly flagellated gammaproteobacterium Shewanella putrefaciens CN-32 possesses two flagellar systems encoded in two gene clusters, enabling the cell to form a single polar and multiple lateral flagella. However, genes for only a single chemotaxis system are located on the chromosome. The primary polar system is required for the main propulsion of the cell. Since only the motor switch protein of the polar system, FliM1, harbors the binding domain of the chemotaxis response regulator CheY, the chemotaxis system also acts exclusively on this flagellar motor. Secondary, lateral flagella enable the cell to turn more efficiently by biasing the directional changes of the swimming cell towards smaller turn angles. This leads to a higher directional persistence in the swimming path of the cell. Since the positions of both the polar and lateral flagella play key roles in this special movement pattern, the mode of action of the regulators FlhF and FlhG on the dual flagellation was examined. While FlhF determinates the position of the nascent flagellum by recruiting flagellar components to the cell pole, direct interaction, likely at the cell pole, of FlhF and FlhG estricts polar accumulation of FlhF by stimulating its GTPase activity. The placement of the lateral flagellar system seems to be FlhF-independent. In addition to interaction with FlhF, FlhG was shown to be involved in the assembly of the cytoplasmic portion of the flagellar motor. For this purpose, FlhG binds FliM1 at the binding motif also recognized by CheY. As the motor switch protein of the lateral system, FliM2, lacks this binding domain, lateral flagella assemble independently of FlhG. Since FlhG was also shown to act on flagellar transcription, polar localization of FlhG might form a part of a feedback loop regulating flagellar transcription and assembly. In V. cholerae, the polar landmark HubP was shown to interact with both FlhF and FlhG. The ortholog of V. cholerae HubP was identified in S. putrefaciens and affected its flagella-mediated motility. In addition to its interaction with FlhFG and the chemotaxis system, SpHubP and VcHubP appears to be involved in chromosome segregation and polar recruitment of other yet unidentified factors. These results indicate that the polar flagellar system requires the presence of several factors to assemble a functional flagellum and to function in concert with the chemotaxis system. These factors do not affect assembly and function of the lateral flagellum, which seems to assemble stochastically and independently

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

Bacterial chemotaxis: sensory adaptation, noise filtering, and information transmission

Chemotaxis is a fundamental cellular process by which cells sense and navigate in their environment. The molecular signalling pathway in the bacterium Escherichia coli is experimentally well-characterised and, hence, ideal for quantitative analysis and modelling. Chemoreceptors sense gradients of a multitude of substances and regulate an intracellular signalling pathway, which modulates the swimming behaviour. We studied the chemotaxis pathway in E. coli (i) to quantitatively understand molecular interactions in the signalling network, (ii) to gain a systems view of the workings of the pathway, including the effects of noise generated by biomolecular reactions during signalling, and (iii) to understand general design principles relevant for many sensory systems. Specifically, we investigated the adaptation dynamics due to covalent chemoreceptor modification, which includes numerous layers of feedback regulation. In collaboration with an experimental group, we undertook quantitative experiments using wild-type cells and mutants for proteins involved in adaptation using in vivo fluorescence resonance transfer (FRET). We developed a dynamical model for chemotactic signalling based on cooperative chemoreceptors and adaptation of the sensory response. This model quantitatively explains an interesting asymmetry of the response to favourable and unfavourable stimuli observed in the experiments. In a whole-pathway description, we further studied the response to controlled concentration stimuli, as well as how fluctuations from the environment and due to intracellular signalling affect the detection of input signals. Finally, the chemotaxis pathway is characterised by high sensitivity, a wide dynamic range and the need for information transmission, properties shared with many other sensory systems. Based on FRET data, we investigated the emergence, limits and biological significance of Weber’s law which predicts that the system detects stimuli relative to the background stimulus. Furthermore, we studied the information transmission from input concentrations into intracellular signals. We connect Weber’s law, as well as information transmission, to swimming bacteria and predict typically encountered chemical inputs