Limits of feedback control in bacterial chemotaxis

Inputs to signaling pathways can have complex statistics that depend on the environment and on the behavioral response to previous stimuli. Such behavioral feedback is particularly important in navigation. Successful navigation relies on proper coupling between sensors, which gather information during motion, and actuators, which control behavior. Because reorientation conditions future inputs, behavioral feedback can place sensors and actuators in an operational regime different from the resting state. How then can organisms maintain proper information transfer through the pathway while navigating diverse environments? In bacterial chemotaxis, robust performance is often attributed to the zero integral feedback control of the sensor, which guarantees that activity returns to resting state when the input remains constant. While this property provides sensitivity over a wide range of signal intensities, it remains unclear how other parameters affect chemotactic performance, especially when considering that the swimming behavior of the cell determines the input signal. Using analytical models and simulations that incorporate recent experimental evidences about behavioral feedback and flagellar motor adaptation we identify an operational regime of the pathway that maximizes drift velocity for various environments and sensor adaptation rates. This optimal regime is outside the dynamic range of the motor response, but maximizes the contrast between run duration up and down gradients. In steep gradients, the feedback from chemotactic drift can push the system through a bifurcation. This creates a non-chemotactic state that traps cells unless the motor is allowed to adapt. Although motor adaptation helps, we find that as the strength of the feedback increases individual phenotypes cannot maintain the optimal operational regime in all environments, suggesting that diversity could be beneficial.Comment: Corrected one typo. First two authors contributed equally. Notably, there were various typos in the values of the parameters in the model of motor adaptation. The results remain unchange

Hook length of the bacterial flagellum is optimized for maximal stability of the flagellar bundle

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook- length variants of Salmonella enterica. Measurements of plate-assay motility, single- cell swimming speed, and directional persistence in quasi-2D and population- averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild-type hook length. We conclude that too-short hooks may be too stiff to function as a junction and too-long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant but robust mechanisms to maximize their fitness under specific environmental constraints

Reconstruction of the Core and Extended Regulons of Global Transcription Factors

The processes underlying the evolution of regulatory networks are unclear. To address this question, we used a comparative genomics approach that takes advantage of the large number of sequenced bacterial genomes to predict conserved and variable members of transcriptional regulatory networks across phylogenetically related organisms. Specifically, we developed a computational method to predict the conserved regulons of transcription factors across α-proteobacteria. We focused on the CRP/FNR super-family of transcription factors because it contains several well-characterized members, such as FNR, FixK, and DNR. While FNR, FixK, and DNR are each proposed to regulate different aspects of anaerobic metabolism, they are predicted to recognize very similar DNA target sequences, and they occur in various combinations among individual α-proteobacterial species. In this study, the composition of the respective FNR, FixK, or DNR conserved regulons across 87 α-proteobacterial species was predicted by comparing the phylogenetic profiles of the regulators with the profiles of putative target genes. The utility of our predictions was evaluated by experimentally characterizing the FnrL regulon (a FNR-type regulator) in the α-proteobacterium Rhodobacter sphaeroides. Our results show that this approach correctly predicted many regulon members, provided new insights into the biological functions of the respective regulons for these regulators, and suggested models for the evolution of the corresponding transcriptional networks. Our findings also predict that, at least for the FNR-type regulators, there is a core set of target genes conserved across many species. In addition, the members of the so-called extended regulons for the FNR-type regulators vary even among closely related species, possibly reflecting species-specific adaptation to environmental and other factors. The comparative genomics approach we developed is readily applicable to other regulatory networks

The SuperCam Instrument Suite on the Mars 2020 Rover: Science Objectives and Mast-Unit Description

On the NASA 2020 rover mission to Jezero crater, the remote determination of the texture, mineralogy and chemistry of rocks is essential to quickly and thoroughly characterize an area and to optimize the selection of samples for return to Earth. As part of the Perseverance payload, SuperCam is a suite of five techniques that provide critical and complementary observations via Laser-Induced Breakdown Spectroscopy (LIBS), Time-Resolved Raman and Luminescence (TRR/L), visible and near-infrared spectroscopy (VISIR), high-resolution color imaging (RMI), and acoustic recording (MIC). SuperCam operates at remote distances, primarily 2-7 m, while providing data at sub-mm to mm scales. We report on SuperCam's science objectives in the context of the Mars 2020 mission goals and ways the different techniques can address these questions. The instrument is made up of three separate subsystems: the Mast Unit is designed and built in France; the Body Unit is provided by the United States; the calibration target holder is contributed by Spain, and the targets themselves by the entire science team. This publication focuses on the design, development, and tests of the Mast Unit; companion papers describe the other units. The goal of this work is to provide an understanding of the technical choices made, the constraints that were imposed, and ultimately the validated performance of the flight model as it leaves Earth, and it will serve as the foundation for Mars operations and future processing of the data.In France was provided by the Centre National d'Etudes Spatiales (CNES). Human resources were provided in part by the Centre National de la Recherche Scientifique (CNRS) and universities. Funding was provided in the US by NASA's Mars Exploration Program. Some funding of data analyses at Los Alamos National Laboratory (LANL) was provided by laboratory-directed research and development funds

Tumble Suppression Is a Conserved Feature of Swarming Motility

Bacteria within a swarm move characteristically in packs, displaying an intricate swirling motion in which hundreds of dynamic rafts continuously form and dissociate as the swarm colonizes an increasing expanse of territory. The demonstrated property of E. coli to reduce its tumble bias and hence increase its run duration during swarming is expected to maintain and promote side-by-side alignment and cohesion within the bacterial packs. In this study, we observed a similar low tumble bias in five different bacterial species, both Gram positive and Gram negative, each inhabiting a unique habitat and posing unique problems to our health. The unanimous display of an altered run-tumble bias in swarms of all species examined in this investigation suggests that this behavioral adaptation is crucial for swarming.Many bacteria use flagellum-driven motility to swarm or move collectively over a surface terrain. Bacterial adaptations for swarming can include cell elongation, hyperflagellation, recruitment of special stator proteins, and surfactant secretion, among others. We recently demonstrated another swarming adaptation in Escherichia coli, wherein the chemotaxis pathway is remodeled to decrease tumble bias (increase run durations), with running speeds increased as well. We show here that the modification of motility parameters during swarming is not unique to E. coli but is shared by a diverse group of bacteria we examined—Proteus mirabilis, Serratia marcescens, Salmonella enterica, Bacillus subtilis, and Pseudomonas aeruginosa—suggesting that increasing run durations and speeds are a cornerstone of swarming

Dynamical coupling between the sensor and the actuator in the bacterial chemotaxis system.

<p><b>A.</b> The bacterial chemotaxis system is composed of a sensor module (receptor-kinase complexes) and an actuator module (flagellar motors) coupled through the phosphorylated form of CheY. Both modules are ultra-sensitive and adapt to their respective input signals. Maintaining the output of the sensor within the right range relative to the actuator is critical for chemotaxis performance. <b>B.</b> Diagrams of the CheY-P concentration response to different signals. First line: when cells are immobilized onto a slide, a step stimulus of attractant (e.g. methylaspartate) causes a sudden decrease in CheY-P concentration followed by a slower adaptation. Because of the negative integral feedback architecture of the sensor module, CheY-P adapts back to its pre-stimulus level, the adapted CheY-P concentration, <i>Y₀</i>. Second line: when immobilized cells are exposed to an exponential ramp in time of the same stimulus, the system, which is log sensing, experiences a constant “force” and adapts towards an operational CheY-P concentration, <i>Y_m</i>, lower than the adapted level <i>Y₀</i>. This deviation of CheY-P activity from <i>Y₀</i> to <i>Y_m</i> changes the coupling between sensor and actuator. Third line: when cells are swimming in a gradient of attractant, their biased random walk causes them to climb the gradient. The average drift velocity of the cell up a chemical gradient affects the average input signal experienced by the cell. This creates a feedback of the behavior onto the input signal, which in turn can significantly affect the operating concentration of CheY-P and thus the coupling between sensor and actuator.</p

Effect of motor adaptation on drift velocity <i>V_D</i> in exponential gradients.

<p><b>A.</b> Motor CW bias response curve as function of CheY-P concentration when the motor is allowed to adapt (solid line) fitted to data from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi.1003694-Cluzel1" target="_blank">[19]</a> (circles; derivation in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#s4" target="_blank">Materials and Methods</a>). <b>B.</b> Average drift velocity as a function of operational CheY-P concentration <i>Y_m</i>, in a shallow gradient. Same adaptation times and gradient steepness as <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi-1003694-g002" target="_blank">Figure 2A</a>. Lines: analytical solutions; circles: stochastic simulations (averages between <i>t</i> = 10 and 15 min are used to calculate <i>V_D</i> (<i>Y_m</i>)). <b>C.</b> Same as <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi-1003694-g004" target="_blank">Figure 4B</a> but with motor adaptation. The drift velocity has only one stable steady sate (<i>Y_m</i> = 1.6 µM, black dot). Motor adaptation eliminated the other states present in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi-1003694-g004" target="_blank">Fig. 4B</a>.</p

Non‐genetic diversity modulates population performance

Abstract 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

Simulated and theoretical drift velocity <i>V_D</i> in exponential gradient of aspartate <i>L₀e^gx</i>.

<p><b>A. </b><i>V_D</i> as a function of the adapted CheY-P concentration <i>Y₀</i>, in a shallow gradient (<i>L₀</i> = 200 µM and <i>g</i>⁻¹ = 5,000 µm) for cells with adaptation times <i>τ</i> = 5 (blue), 10 (green), and 30 seconds (red). <i>V_D</i> is the average velocity of 10,000 identical cells between <i>t</i> = 60 and 300 seconds (dots: stochastic simulations; lines: analytical solution from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi.1003694.e015" target="_blank">Eq. (3)</a>; grey: motor CW bias response curve. <b>B.</b> Expected trajectories of CheY-P concentration <i>Y</i>(<i>F</i>(<i>t</i>)) for cells running in one dimension up (green) or down (red) in a gradient (integration of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi.1003694.e007" target="_blank">Eqs. (2)</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi.1003694.e040" target="_blank">(5)</a>, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003694#pcbi.1003694.s007" target="_blank">Text S1</a>; <i>τ</i> = 30 s, <i>g</i>⁻¹ = 5,000 µm, <i>Y</i>(<i>F_i</i>) = 2.4 µM and 3 µM). Expected run, (dotted line), and tumble, (dashed line), durations as a function of <i>Y₀</i>. Expected run duration along a given direction <i>τ_R0 = (2D_r+λ_R0)⁻¹</i> (solid black line) is limited by rotational diffusion (<i>D_r</i> = 0.062 rad² s⁻¹). Grey: motor CW bias. <b>C.</b> Same as A (τ = 10 <i>s</i>) but with the rotational diffusion constant <i>D_r</i> = 0.031 (red), 0.062 (green), and 0.124 (blue) rad² s⁻¹. Dotted lines: expected run duration in a given direction. <b>D.</b> Same as A (τ = 10 <i>s</i>) but with the motor switching rate <i>ω</i> = 2.6 (red), 1.3 (green), and 0.65 (blue) s⁻¹. Dotted lines: expected run duration in a given direction.</p