Predicted Auxiliary Navigation Mechanism of Peritrichously Flagellated Chemotactic Bacteria

Chemotactic movement of Escherichia coli is one of the most thoroughly studied paradigms of simple behavior. Due to significant competitive advantage conferred by chemotaxis and to high evolution rates in bacteria, the chemotaxis system is expected to be strongly optimized. Bacteria follow gradients by performing temporal comparisons of chemoeffector concentrations along their runs, a strategy which is most efficient given their size and swimming speed. Concentration differences are detected by a sensory system and transmitted to modulate rotation of flagellar motors, decreasing the probability of a tumble and reorientation if the perceived concentration change during a run is positive. Such regulation of tumble probability is of itself sufficient to explain chemotactic drift of a population up the gradient, and is commonly assumed to be the only navigation mechanism of chemotactic E. coli. Here we use computer simulations to predict existence of an additional mechanism of gradient navigation in E. coli. Based on the experimentally observed dependence of cell tumbling angle on the number of switching motors, we suggest that not only the tumbling probability but also the degree of reorientation during a tumble depend on the swimming direction along the gradient. Although the difference in mean tumbling angles up and down the gradient predicted by our model is small, it results in a dramatic enhancement of the cellular drift velocity along the gradient. We thus demonstrate a new level of optimization in E. coli chemotaxis, which arises from the switching of several flagellar motors and a resulting fine tuning of tumbling angle. Similar strategy is likely to be used by other peritrichously flagellated bacteria, and indicates yet another level of evolutionary development of bacterial chemotaxis

Modeling E. coli Tumbles by Rotational Diffusion. Implications for Chemotaxis

The bacterium Escherichia coli in suspension in a liquid medium swims by a succession of runs and tumbles, effectively describing a random walk. The tumbles randomize incompletely, i.e. with a directional persistence, the orientation taken by the bacterium. Here, we model these tumbles by an active rotational diffusion process characterized by a diffusion coefficient and a diffusion time. In homogeneous media, this description accounts well for the experimental reorientations. In shallow gradients of nutrients, tumbles are still described by a unique rotational diffusion coefficient. Together with an increase in the run length, these tumbles significantly contribute to the net chemotactic drift via a modulation of their duration as a function of the direction of the preceding run. Finally, we discuss the limits of this model in propagating concentration waves characterized by steep gradients. In that case, the effective rotational diffusion coefficient itself varies with the direction of the preceding run. We propose that this effect is related to the number of flagella involved in the reorientation process

Stochastic model for the CheY-P molarity in the neighbourhood of E. coli flagella motors

E.coli serves as prototype for the study of peritrichous enteric bacteria that perform runs and tumbles alternately. Bacteria run forward as a result of the counterclockwise (CCW) rotation of their flagella bundle and perform tumbles when at least one of their flagella rotates clockwise (CW), moving away from the bundle. The flagella are hooked to molecular rotary motors of nanometric diameter able to make transitions between CCW and CW rotations that last up to one hundredth of a second. At the same time, flagella move or rotate the bacteria's body microscopically during lapses that range between a tenth and ten seconds. We assume that the transitions between CCW and CW rotations occur solely by fluctuations of CheY-P molarity in the presence of two threshold values, and that a veto rule selects the run or tumble motions. We present Langevin eqs for the CheY-P molarity in the vicinity of each molecular motor. This model allows to obtain the run- or tumble-time distribution as a linear combination of decreasing exponentials that is a function of the steady molarity of CheY-P in the neighbourhood of the molecular motor, which fits experimental data. In turn, if the internal signaling system is unstimulated, we show that the runtime distributions reach power-law behaviour, a characteristic of self-organized systems, in some time range and, afterwards, exponential cutoff. In addition, our model explains without any fitting parameters the ultrasensitivity of the flagella motors as a function of the steady state of CheY-P molarity. In addition, we show that the tumble bias for peritrichous bacterium has a similar sigmoid-shape to the CW bias, although shifted to lower concentrations when the flagella number increases. Thus, the increment in the flagella number allows lower operational values for each motor increasing amplification and robustness of the chemotatic pathway.Comment: 13 pages, 7 figure

Multiscale Modeling of Bacterial Chemotaxis

One of the central questions of modern systems biology is the role of microscopic parameters of a single cell in the behavior of a cell population. Multiscale models help to address this problem, allowing to understand population behavior from the information about single-cell molecular components and reactions. This goal requires models that are sufficiently detailed to capture central intracellular processes, but at the same time enable simulation of entire cell populations. In this work a novel multiscale (hybrid) model is presented, which describes chemotactic Escherichia coli bacterium by a combination of heterogeneous mathematical approaches in one platform: rapid-equilibrium (algebraic) models, ordinary differential equations, and stochastic processes. The multiscale approach is based on time-scale separation of key reactions. The resulting model of chemotactic bacterium describes signal processing by mixed chemoreceptor clusters (MWC model), adaptation through methylation, running and tumbling of a cell with several flagellar motors. The model is implemented in a program RapidCell. It outperforms the present simulation software in reproducing the experimental data on pathway sensitivity, and simulates bacterial populations in a computationally efficient way. The model was used to investigate chemotaxis in different gradients. A theoretical analysis of the receptor cluster (MWC) model suggested a new, constant-activity type of gradient to systematically study chemotactic behavior of bacteria in silico. Using the unique properties of this gradient, it is shown that the optimal chemotaxis is observed in a narrow range of CheA kinase activity, where concentration of the response regulator CheYp falls into the operating range of flagellar motors. Simulations further confirm that the CheB phosphorylation feedback improves chemotactic efficiency in a number of gradients by shifting the average CheYp concentration to fit the motor operating range. Comparative simulations of motility in liquid and porous media suggest that adaptation time required for optimal chemotaxis depends on the medium. In liquid medium, the variability in adaptation times among cells may be evolutionary favourable to ensure co-existence of subpopulations that will be optimally tactic in different gradients. However, in a porous medium (agar) such variability appears to be less important, because agar structure poses mainly negative selection, against subpopulations with low levels of adaptation enzymes. A detailed model of cell motion predicts existence of an additional mechanism of gradient navigation in E. coli. Based on the experimentally observed dependence of cell tumbling angle on the number of clockwise-rotating motors, the model suggests that not only the tumbling frequency, but also the angle of reorientation during a tumble depends on the swimming direction along the gradient. Although the difference in mean tumbling angles up and down the gradient predicted by the model is small, it results in a dramatic enhancement of the cellular drift velocity along the gradient. This result demonstrates a new level of optimization in E. coli chemotaxis, which arises from collective switching of several flagellar motors and a resulting fine tuning of tumbling angle. Similar strategy is likely to be used by other peritrichously flagellated bacteria, and indicates a yet another level of evolutionary optimization in bacterial chemotaxis. Concluding, multiscale models as the one presented here can be an important research instrument for understanding the cell behavior. They reflect the most important experimental knowledge about the biological system, and allow to carry out computational experiments of high complexity, which may be too complicated for experimental trials. Currently, there is abundant experimental data on signal transduction in living organisms, but there is no general mathematical framework to integrate heterogeneous models over the wide range of scales present in most biological systems. This thesis is a new stone in the work aimed to "bridge the scales" in biology

Sensing and adhesion are adaptive functions in the plant pathogenic xanthomonads

<p>Abstract</p> <p>Background</p> <p>Bacterial plant pathogens belonging to the <it>Xanthomonas </it>genus are tightly adapted to their host plants and are not known to colonise other environments. The host range of each strain is usually restricted to a few host plant species. Bacterial strains responsible for the same type of symptoms on the same host range cluster in a pathovar. The phyllosphere is a highly stressful environment, but it provides a selective habitat and a source of substrates for these bacteria. Xanthomonads colonise host phylloplane before entering leaf tissues and engaging in an invasive pathogenic phase. Hence, these bacteria are likely to have evolved strategies to adapt to life in this environment. We hypothesised that determinants responsible for bacterial host adaptation are expressed starting from the establishment of chemotactic attraction and adhesion on host tissue.</p> <p>Results</p> <p>We established the distribution of 70 genes coding sensors and adhesins in a large collection of xanthomonad strains. These 173 strains belong to different pathovars of <it>Xanthomonas </it>spp and display different host ranges. Candidate genes are involved in chemotactic attraction (25 genes), chemical environment sensing (35 genes), and adhesion (10 genes). Our study revealed that candidate gene repertoires comprised core and variable gene suites that likely have distinct roles in host adaptation. Most pathovars were characterized by unique repertoires of candidate genes, highlighting a correspondence between pathovar clustering and repertoires of sensors and adhesins. To further challenge our hypothesis, we tested for molecular signatures of selection on candidate genes extracted from sequenced genomes of strains belonging to different pathovars. We found strong evidence of adaptive divergence acting on most candidate genes.</p> <p>Conclusions</p> <p>These data provide insight into the potential role played by sensors and adhesins in the adaptation of xanthomonads to their host plants. The correspondence between repertoires of sensor and adhesin genes and pathovars and the rapid evolution of sensors and adhesins shows that, for plant pathogenic xanthomonads, events leading to host specificity may occur as early as chemotactic attraction by host and adhesion to tissues.</p

Statistical abstraction for multi-scale spatio-temporal systems

Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a prototypic scenario where spatially distributed agents decide their movement based on external inputs and a fast-equilibrating internal computation. We propose a generally applicable strategy based on statistically abstracting the internal system using Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning. We show on a running example of bacterial chemotaxis that this approach leads to accurate and much faster simulations in a variety of scenarios.Comment: 14th International Conference on Quantitative Evaluation of SysTems (QEST 2017

Swimming of multi-flagellated bacteria

Many prokaryotes employ rotating helical appendages known as flagella to swim in an aqueous medium. We studied differentially flagellated B. subtilis strains as model systems study the dynamics of swimming bacteria with numerous flagella. We found out that decreasing the number of flagella of individual cells reduces the average turning angle after the tumbling, enhances the run time and directional persistency of the run phase. Consequently, having a few flagella is beneficial for the fast spreading, while having many flagella is advantageous for the processes which require slower spreading. The results of numerical simulations based on the two-state model were used to discuss the search efficiency of different strains. Fluorescence microscopy shows that B. subtilis can make several bundles during the run phase, where the probability distribution of the number of bundles is similar for all strains independent of the flagellar number. The angle between the bundles on the observation plane widens with increasing the number of flagella, which leads to a slight modification of the effective cell aspect ratio while the other bundle properties do not significantly change. The collective motion of dense suspension of bacteria was also investigated to understand how the swimming persistency of individual cells and their geometrical properties can influence characteristic features of the collective behavior. The results show that the characteristic time and length scale of the collective motion are robust to these parameters.Viele Bakterien nutzen Flagellen - kleine spiralförmige Anhänge - um sich zu bewegen. Beispielsweise können E. coli Bakterien ihre Flagellen synchronisieren und bündeln um aktiv zu schwimmen. Die Auswirkungen der Flagellenanzahl auf die Dynamik der Bakterien ist nicht genau verstanden. Daher haben wir Bakterien der Art B. Subtilis mit verschiedener Anzahl an Flagellen untersucht. Die Verringerung der Flagellenanzahl reduziert den mittleren Änderungswinkel zwischen aufeinanderfolgenden Renn-Phassen und erhöht die Renn-Zeit sowie die Richtungsbeständigkeit. Eine geringe Anzahl von Flagellen ist daher vorteilhaft für Transportprozesse, wohingegen eine hohe Anzahl von Flagellen vorteilhaft für eine langsamere Verteilung wichtig ist (Entstehung von Biofilmen). Wir haben ein Zwei-Zustands Random-Walk Modell entwickelt, welches einen exakten analytischen Ausdruck für die Transporteigenschaften liefert. Die Ergebnisse der numerischen Simulationen dienten als Grundlage für die Diskussion der Such-Effizienz verschiedener Stämme. Wir konnten beobachten, dass verschiedene Flagellen-Bündel während der Renn-Phase entstehen. Außerdem untersuchten wir die kollektive Bewegung in einer dichten Suspension von Bakterien. Die Ergebnisse zeigen, dass innerhalb der Reichweite unserer experimentellen Parameter die charakteristische Zeit- und Länge-Skalen der kollektiven Bewegung stabil gegenüber Form- und Persistenzänderungen einzelner Bakterien sind