How the motility pattern of bacteria affects their dispersal and chemotaxis

A systematic review of antibiotics and antibiotic resistance genes (ARGs) in mariculture wastewater: Antibiotics removal by microalgal-bacterial symbiotic system (MBSS), ARGs characterization on the metagenomic

Antibiotic residues in mariculture wastewater seriously affect the aquatic environment. Antibiotic Resistance Genes (ARGs) produced under antibiotic stress flow through the environment and eventually enter the human body, seriously affecting human health. Microalgal-bacterial symbiotic system (MBSS) can remove antibiotics from mariculture and reduce the flow of ARGs into the environment. This review encapsulates the present scenario of mariculture wastewater, the removal mechanism of MBSS for antibiotics, and the biomolecular information under metagenomic assay. When confronted with antibiotics, there was a notable augmentation in the extracellular polymeric substances (EPS) content within MBSS, along with a concurrent elevation in the proportion of protein (PN) constituents within the EPS, which limits the entry of antibiotics into the cellular interior. Quorum sensing stimulates the microorganisms to produce biological responses (DNA synthesis - for adhesion) through signaling. Oxidative stress promotes gene expression (coupling, conjugation) to enhance horizontal gene transfer (HGT) in MBSS. The microbial community under metagenomic detection is dominated by aerobic bacteria in the bacterial-microalgal system. Compared to aerobic bacteria, anaerobic bacteria had the significant advantage of decreasing the distribution of ARGs. Overall, MBSS exhibits remarkable efficacy in mitigating the challenges posed by antibiotics and resistant genes from mariculture wastewater.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Highly biocidal poly(vinyl alcohol)-hydantoin/starch hybrid gels: A "Trojan Horse" for Bacillus subtilis

HYPOTHESIS

Poly (vinyl alcohol) (PVA) cryogels can be functionalized with n-Halamines to confer biocidal features useful for their application as wound-dressing tools. Their efficacy can be boosted by stably embedding a polymeric bacterial food source (e.g., starch) in the gel matrix. The bioavailability of the food source lures bacteria inside the gel network via chemotactic mechanisms, promoting their contact with the biocidal functionalities and their consequent inactivation.

EXPERIMENTS

The synthesis of a novel hydantoin-functionalized PVA (H-PVA-hyd) is proposed. The newly synthesized H-PVA-hyd polymer was introduced in the formulation of H-PVA-based cryogels. To promote the cryogelation of the systems we exploited phase-separation mechanisms employing either a PVA carrying residual acetate groups (L-PVA) or starch as phase-segregating components. The permanence of the biocidal functionality after swelling was investigated via proton nuclear magnetic resonance (1H NMR) and Fourier transform infrared (FT-IR) microscopy. The activated H-PVA-hyd cryogels have been tested against bacteria with amylolytic activity (Bacillus subtilis) and the outcomes were analyzed by direct observation via confocal laser scanning microscopy (CLSM).

FINDINGS

The cryogels containing starch resulted in being the most effective (up to 90% bacterial killing), despite carrying a lower amount of hydantoin groups than their starch-free counterparts, suggesting that their improved efficacy relies on a "Trojan Horse" type of mechanism.

Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions

We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type Escherichia coli obtained using differential dynamic microscopy.

Microfluidic Design of Streamlined Alginate Hydrogel Micromotors with Run and Tumble Motion Patterns

Autonomous micromotors demonstrate remarkable advancements in biomedical applications. A noteworthy example is streamlined motors, which display enhanced movement efficiency with low fluid-resistance. However, existing streamlined motors, primarily constructed from inorganic materials, present challenges due to their complex fabrication procedures and lack of a soft interface for interaction with biological systems. Herein, a novel design of biodegradable streamlined alginate hydrogel micromotors with a teardrop shape by microfluidics is introduced. The platform enables the high-throughput fabrication of monodisperse micromotors with varied dimensions. By incorporating Pt-coated Fe3 O4 nanoparticles, micromotors are equipped with dual capabilities of catalytic propulsion and accurate magnetic guidance. Through precisely tuning the localization regions of catalysts within the micromotors, the streamlined hydrogel micromotors not only exhibit enhanced propelling efficiency, but also accomplish distinct motion patterns of run and tumble. The design provides insights for developing advanced micromotors capable of executing intricate tasks across diverse application scenarios.

Optimal motility strategies for self-propelled agents to explore porous media

Microrobots for, e.g., biomedical applications, need to be equipped with motility strategies that enable them to navigate through complex environments. Inspired by biological microorganisms we re-create motility patterns such as run-and-reverse, run-and-tumble, or run-reverse-flick applied to active rodlike particles in silico. We investigate their capability to efficiently explore disordered porous environments with various porosities and mean pore sizes ranging down to the scale of the active particle. By calculating the effective diffusivity for the different patterns, we can predict the optimal one for each porous sample geometry. We find that providing the agent with very basic sensing and decision-making capabilities yields a motility pattern outperforming the biologically inspired patterns for all investigated porous samples.

Random walk and cell morphology dynamics in Naegleria gruberi

Amoeboid cell movement and migration are wide-spread across various cell types and species. Microscopy-based analysis of the model systems Dictyostelium and neutrophils over the years have uncovered generality in their overall cell movement pattern. Under no directional cues, the centroid movement can be quantitatively characterized by their persistence to move in a straight line and the frequency of re-orientation. Mathematically, the cells essentially behave as a persistent random walker with memory of two characteristic time-scale. Such quantitative characterization is important from a cellular-level ethology point of view as it has direct connotation to their exploratory and foraging strategies. Interestingly, outside the amoebozoa and metazoa, there are largely uncharacterized species in the excavate taxon Heterolobosea including amoeboflagellate Naegleria. While classical works have shown that these cells indeed show typical amoeboid locomotion on an attached surface, their quantitative features are so far unexplored. Here, we analyzed the cell movement of Naegleria gruberi by employing long-time phase contrast imaging that automatically tracks individual cells. We show that the cells move as a persistent random walker with two time-scales that are close to those known in Dictyostelium and neutrophils. Similarities were also found in the shape dynamics which are characterized by the appearance, splitting and annihilation of the curvature waves along the cell edge. Our analysis based on the Fourier descriptor and a neural network classifier point to importance of morphology features unique to Naegleria including complex protrusions and the transient bipolar dumbbell morphologies.

Motility provides specific adhesion patterns and improves Listeria monocytogenes invasion into human HEp-2 cells

Listeria monocytogenes is motile at 22°C and non-motile at 37°C. In contrast, expression of L. monocytogenes virulence factors is low at 22°C and up-regulated at 37°C. Here, we studied a character of L. monocytogenes near surface swimming (NSS) motility and its effects on adhesion patterns and invasion into epithelial cells. L. monocytogenes and its saprophytic counterpart L. innocua both grown at 22°C showed similar NSS characteristics including individual velocities, trajectory lengths, residence times, and an asymmetric distribution of velocity directions. Similar NSS patterns correlated with similar adhesion patterns. Motile bacteria, including both pathogenic and saprophytic species, showed a preference for adhering to the periphery of epithelial HEp-2 cells. In contrast, non-motile bacteria were evenly distributed across the cell surface, including areas over the nucleus. However, the uneven distribution of motile bacteria did not enhance the invasion into HEp-2 cells unless virulence factor production was up-regulated by the transient shift of the culture to 37°C. Motile L. monocytogenes grown overnight at 22°C and then shifted to 37°C for 2 h expressed invasion factors at the same level and invaded human cells up to five times more efficiently comparatively with non-motile bacteria grown overnight at 37°C. Taken together, obtained results demonstrated that (i) NSS motility and correspondent peripheral location over the cell surface did not depend on L. monocytogenes virulence traits; (ii) motility improved L. monocytogenes invasion into human HEp-2 cells within a few hours after the transition from the ambient temperature to the human body temperature.

Physiological adaptation in flagellar architecture improves Vibrio alginolyticus chemotaxis in complex environments

Bacteria navigate natural habitats with a wide range of mechanical properties, from the ocean to the digestive tract and soil, by rotating helical flagella like propellers. Species differ in the number, position, and shape of their flagella, but the adaptive value of these flagellar architectures is unclear. Many species traverse multiple types of environments, such as pathogens inside and outside a host. We investigate the hypothesis that flagellar architectures mediate environment-specific benefits in the marine pathogen Vibrio alginolyticus which exhibits physiological adaptation to the mechanical environment. In addition to its single polar flagellum, the bacterium produces lateral flagella in environments that differ mechanically from water. These are known to facilitate surface motility and attachment. We use high-throughput 3D bacterial tracking to quantify chemotactic performance of both flagellar architectures in three archetypes of mechanical environments relevant to the bacterium's native habitats: water, polymer solutions, and hydrogels. We reveal that lateral flagella impede chemotaxis in water by lowering the swimming speed but improve chemotaxis in both types of complex environments. Statistical trajectory analysis reveals two distinct underlying behavioral mechanisms: In viscous solutions of the polymer PVP K90, lateral flagella increase the swimming speed. In agar hydrogels, lateral flagella improve overall chemotactic performance, despite lowering the swimming speed, by preventing trapping in pores. Our findings show that lateral flagella are multipurpose tools with a wide range of applications beyond surfaces. They implicate flagellar architecture as a mediator of environment-specific benefits and point to a rich space of bacterial navigation behaviors in complex environments.

Encounter rates prime interactions between microorganisms

Properties of microbial communities emerge from the interactions between microorganisms and between microorganisms and their environment. At the scale of the organisms, microbial interactions are multi-step processes that are initiated by cell-cell or cell-resource encounters. Quantification and rational design of microbial interactions thus require quantification of encounter rates. Encounter rates can often be quantified through encounter kernels-mathematical formulae that capture the dependence of encounter rates on cell phenotypes, such as cell size, shape, density or motility, and environmental conditions, such as turbulence intensity or viscosity. While encounter kernels have been studied for over a century, they are often not sufficiently considered in descriptions of microbial populations. Furthermore, formulae for kernels are known only in a small number of canonical encounter scenarios. Yet, encounter kernels can guide experimental efforts to control microbial interactions by elucidating how encounter rates depend on key phenotypic and environmental variables. Encounter kernels also provide physically grounded estimates for parameters that are used in ecological models of microbial populations. We illustrate this encounter-oriented perspective on microbial interactions by reviewing traditional and recently identified kernels describing encounters between microorganisms and between microorganisms and resources in aquatic systems.

Kinetic modeling of the chemotactic process in run-and-tumble bacteria

The chemotactic process of run-and-tumble bacteria results from modulating the tumbling rate in response to changes in chemoattractant gradients felt by the bacteria. The response has a characteristic memory time and is subject to important fluctuations. These ingredients are considered in a kinetic description of chemotaxis, allowing the computation of the stationary mobility and the relaxation times needed to reach the steady state. For large memory times, these relaxation times become large, implying that finite-time measurements give rise to nonmonotonic currents as a function of the imposed chemoattractant gradient, contrary to the stationary regime where the response is monotonic. The case of an inhomogeneous signal is analyzed. Contrary to the usual Keller-Segel model, the response is nonlocal, and the bacterial profile is smoothed with a characteristic length that grows with the memory time. Finally, the case of traveling signals is considered, where appreciable differences appear compared to memoryless chemotactic descriptions.

Motility of Different Gastric Helicobacter spp

Helicobacter spp., including the well-known human gastric pathogen H. pylori, can cause gastric diseases in humans and other mammals. They are Gram-negative bacteria that colonize the gastric epithelium and use their multiple flagella to move across the protective gastric mucus layer. The flagella of different Helicobacter spp. vary in their location and number. This review focuses on the swimming characteristics of different species with different flagellar architectures and cell shapes. All Helicobacter spp. use a run-reverse-reorient mechanism to swim in aqueous solutions, as well as in gastric mucin. Comparisons of different strains and mutants of H. pylori varying in cell shape and the number of flagella show that their swimming speed increases with an increasing number of flagella and is somewhat enhanced with a helical cell body shape. The swimming mechanism of H. suis, which has bipolar flagella, is more complex than that of unipolar H. pylori. H. suis exhibits multiple modes of flagellar orientation while swimming. The pH-dependent viscosity and gelation of gastric mucin significantly impact the motility of Helicobacter spp. In the absence of urea, these bacteria do not swim in mucin gel at pH < 4, even though their flagellar bundle rotates.

Attractor-driven matter

The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate that specifies the internal state of each particle. The internal state space is typically topologically simple, in the sense that the particle's internal coordinate belongs to a suitable symmetry group. In this paper, we explore the idea of giving internal complexity to the particles, by attributing to each particle an internal state space that is represented by a point on a strange (or otherwise) attracting set. It is, of course, very well known that strange attractors arise in a variety of nonlinear dynamical systems. However, rather than considering strange attractors as emerging from complex dynamics, we may employ strange attractors to drive such dynamics. In particular, by using an attractor (strange or otherwise) to model each particle's internal state space, we present a class of matter coined "attractor-driven matter." We outline the general formalism for attractor-driven matter and explore several specific examples, some of which are reminiscent of active matter. Beyond the examples studied in this paper, our formalism for attractor-driven dynamics may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts.

Kinematics of persistent random walkers with two distinct modes of motion

We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti)persistence. We present an analytical formalism to provide a quantitative link between these two microscopic statistical properties of the trajectory and macroscopically observable transport quantities of interest. For exponentially distributed residence times in each state, we derive analytical expressions for the initial anomalous exponent, the characteristic crossover time to the asymptotic diffusive dynamics, and the long-term diffusion constant. We also obtain an exact expression for the time evolution of the mean square displacement over all timescales and provide a recipe to obtain higher displacement moments. Our approach enables us to disentangle the combined effects of velocity, persistence, and switching probabilities between the two states on the kinematics of particles in a wide range of stochastic active or passive processes and to optimize the transport quantities of interest with respect to any of the particle dynamics properties.

Direct measurement of the aerotactic response in a bacterial suspension

Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration c. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling toward the oxygen source. We compute the aerotactic response χ(c) both at the population scale, from the drift velocity in the bacterial band, and at the bacterial scale, from the angular modulation of the run times. Both methods are consistent with a power-law χ∝c^{-2}, in good agreement with existing models based on the biochemistry of bacterial membrane receptors.

The Regulatory Hierarchy Following Signal Integration by the CbrAB Two-Component System: Diversity of Responses and Functions

CbrAB is a two-component system, unique to bacteria of the family Pseudomonaceae, capable of integrating signals and involved in a multitude of physiological processes that allow bacterial adaptation to a wide variety of varying environmental conditions. This regulatory system provides a great metabolic versatility that results in excellent adaptability and metabolic optimization. The two-component system (TCS) CbrA-CbrB is on top of a hierarchical regulatory cascade and interacts with other regulatory systems at different levels, resulting in a robust output. Among the regulatory systems found at the same or lower levels of CbrAB are the NtrBC nitrogen availability adaptation system, the Crc/Hfq carbon catabolite repression cascade in Pseudomonas, or interactions with the GacSA TCS or alternative sigma ECF factor, such as SigX. The interplay between regulatory mechanisms controls a number of physiological processes that intervene in important aspects of bacterial adaptation and survival. These include the hierarchy in the use of carbon sources, virulence or resistance to antibiotics, stress response or definition of the bacterial lifestyle. The multiple actions of the CbrAB TCS result in an important competitive advantage.

Orientational memory of active particles in multistate non-Markovian processes

The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence of each state and the switching probabilities. We show how nonexponential sojourn-time distributions of interest, such as Gaussian and power-law distributions, can result from history-dependent transitions between the states. The relaxation behavior of the correlation function in such non-Markovian processes is governed by the history dependence of the switching probabilities and cannot be solely determined by the mean sojourn times of the states.

Surveying a Swarm: Experimental Techniques to Establish and Examine Bacterial Collective Motion

The survival and successful spread of many bacterial species hinges on their mode of motility. One of the most distinct of these is swarming, a collective form of motility where a dense consortium of bacteria employ flagella to propel themselves across a solid surface. Surface environments pose unique challenges, derived from higher surface friction/tension and insufficient hydration. Bacteria have adapted by deploying an array of mechanisms to overcome these challenges. Beyond allowing bacteria to colonize new terrain in the absence of bulk liquid, swarming also bestows faster speeds and enhanced antibiotic resistance to the collective. These crucial attributes contribute to the dissemination, and in some cases pathogenicity, of an array of bacteria. This mini-review highlights; 1) aspects of swarming motility that differentiates it from other methods of bacterial locomotion. 2) Facilitatory mechanisms deployed by diverse bacteria to overcome different surface challenges. 3) The (often difficult) approaches required to cultivate genuine swarmers. 4) The methods available to observe and assess the various facets of this collective motion, as well as the features exhibited by the population as a whole.

A geometric criterion for the optimal spreading of active polymers in porous media

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.

Self-generated oxygen gradients control collective aggregation of photosynthetic microbes

For billions of years, photosynthetic microbes have evolved under the variable exposure to sunlight in diverse ecosystems and microhabitats all over our planet. Their abilities to dynamically respond to alterations of the luminous intensity, including phototaxis, surface association and diurnal cell cycles, are pivotal for their survival. If these strategies fail in the absence of light, the microbes can still sustain essential metabolic functionalities and motility by switching their energy production from photosynthesis to oxygen respiration. For suspensions of motile C. reinhardtii cells above a critical density, we demonstrate that this switch reversibly controls collective microbial aggregation. Aerobic respiration dominates over photosynthesis in conditions of low light, which causes the microbial motility to sensitively depend on the local availability of oxygen. For dense microbial populations in self-generated oxygen gradients, microfluidic experiments and continuum theory based on a reaction–diffusion mechanism show that oxygen-regulated motility enables the collective emergence of highly localized regions of high and low cell densities.

Multiple functions of flagellar motility and chemotaxis in bacterial physiology

Most swimming bacteria are capable of following gradients of nutrients, signaling molecules and other environmental factors that affect bacterial physiology. This tactic behavior became one of the most-studied model systems for signal transduction and quantitative biology, and underlying molecular mechanisms are well characterized in Escherichia coli and several other model bacteria. In this review, we focus primarily on less understood aspect of bacterial chemotaxis, namely its physiological relevance for individual bacterial cells and for bacterial populations. As evident from multiple recent studies, even for the same bacterial species flagellar motility and chemotaxis might serve multiple roles, depending on the physiological and environmental conditions. Among these, finding sources of nutrients and more generally locating niches that are optimal for growth appear to be one of the major functions of bacterial chemotaxis, which could explain many chemoeffector preferences as well as flagellar gene regulation. Chemotaxis might also generally enhance efficiency of environmental colonization by motile bacteria, which involves intricate interplay between individual and collective behaviors and trade-offs between growth and motility. Finally, motility and chemotaxis play multiple roles in collective behaviors of bacteria including swarming, biofilm formation and autoaggregation, as well as in their interactions with animal and plant hosts.

Vibrio cholerae motility in aquatic and mucus-mimicking environments

Cholera disease is caused by Vibrio cholerae infecting the lining of the small intestine and results in severe diarrhea. V. cholerae’s swimming motility is known to play a crucial role in pathogenicity and may aid the bacteria in crossing the intestinal mucus barrier to reach sites of infection, but the exact mechanisms are unknown. The cell can be either pushed or pulled by its single polar flagellum, but there is no consensus on the resulting repertoire of motility behaviors. We use high-throughput three-dimensional (3D) bacterial tracking to observe V. cholerae swimming in buffer, in viscous solutions of the synthetic polymer PVP, and in mucin solutions that may mimic the host environment. We perform a statistical characterization of its motility behavior on the basis of large 3D trajectory data sets. We find that V. cholerae performs asymmetric run-reverse-flick motility, consisting of a sequence of a forward run, reversal, and a shorter backward run, followed by a turn by approximately 90°, called a flick, preceding the next forward run. Unlike many run-reverse-flick swimmers, V. cholerae’s backward runs are much shorter than its forward runs, resulting in an increased effective diffusivity. We also find that the swimming speed is not constant but subject to frequent decreases. The turning frequency in mucin matches that observed in buffer. Run-reverse-flick motility and speed fluctuations are present in all environments studied, suggesting that these behaviors also occur in natural aquatic habitats as well as the host environment.

IMPORTANCE Cholera disease produces vomiting and severe diarrhea and causes approximately 100,000 deaths per year worldwide. The disease is caused by the bacterium Vibrio cholerae colonizing the lining of the small intestine. V. cholerae’s ability to swim is known to increase its infectivity, but the underlying mechanisms are not known. One possibility is that swimming aids in crossing the protective mucus barrier that covers the lining of the small intestine. Our work characterizing how V. cholerae swims in environments that mimic properties of the host environment may advance the understanding of how motility contributes to infection.

Theoretical Constraints Imposed by Gradient Detection and Dispersal on Microbial Size in Astrobiological Environments

The capacity to sense gradients efficiently and acquire information about the ambient environment confers many advantages such as facilitating movement toward nutrient sources or away from toxic chemicals. The amplified dispersal evinced by organisms endowed with motility is possibly beneficial in related contexts. Hence, the connections between information acquisition, motility, and microbial size are explored from an explicitly astrobiological standpoint. By using prior theoretical models, the constraints on organism size imposed by gradient detection and motility are elucidated in the form of simple heuristic scaling relations. It is argued that environments such as alkaline hydrothermal vents, which are distinguished by the presence of steep gradients, might be conducive to the existence of "small" microbes (with radii of ≳0.1 μm) in principle, when only the above two factors are considered; other biological functions (e.g., metabolism and genetic exchange) could, however, regulate the lower bound on microbial size and elevate it. The derived expressions are potentially applicable to a diverse array of settings, including those entailing solvents other than water; for example, the lakes and seas of Titan. The article concludes with a brief exposition of how this formalism may be of practical and theoretical value to astrobiology.

High-speed, three-dimensional imaging reveals chemotactic behaviour specific to human-infective Leishmania parasites

Cellular motility is an ancient eukaryotic trait, ubiquitous across phyla with roles in predator avoidance, resource access, and competition. Flagellar motility is seen in various parasitic protozoans, and morphological changes in flagella during the parasite life cycle have been observed. We studied the impact of these changes on motility across life cycle stages, and how such changes might serve to facilitate human infection. We used holographic microscopy to image swimming cells of different Leishmania mexicana life cycle stages in three dimensions. We find that the human-infective (metacyclic promastigote) forms display ‘run and tumble’ behaviour in the absence of stimulus, reminiscent of bacterial motion, and that they specifically modify swimming direction and speed to target host immune cells in response to a macrophage-derived stimulus. Non-infective (procyclic promastigote) cells swim more slowly, along meandering helical paths. These findings demonstrate adaptation of swimming phenotype and chemotaxis towards human cells.

Microswimmers learning chemotaxis with genetic algorithms

Various microorganisms and some mammalian cells are able to swim in viscous fluids by performing nonreciprocal body deformations, such as rotating attached flagella or by distorting their entire body. In order to perform chemotaxis (i.e., to move toward and to stay at high concentrations of nutrients), they adapt their swimming gaits in a nontrivial manner. Here, we propose a computational model, which features autonomous shape adaptation of microswimmers moving in one dimension toward high field concentrations. As an internal decision-making machinery, we use artificial neural networks, which control the motion of the microswimmer. We present two methods to measure chemical gradients, spatial and temporal sensing, as known for swimming mammalian cells and bacteria, respectively. Using the genetic algorithm NeuroEvolution of Augmenting Topologies, surprisingly simple neural networks evolve. These networks control the shape deformations of the microswimmers and allow them to navigate in static and complex time-dependent chemical environments. By introducing noisy signal transmission in the neural network, the well-known biased run-and-tumble motion emerges. Our work demonstrates that the evolution of a simple and interpretable internal decision-making machinery coupled to the environment allows navigation in diverse chemical landscapes. These findings are of relevance for intracellular biochemical sensing mechanisms of single cells or for the simple nervous system of small multicellular organisms such as Caenorhabditis elegans.

Origins of eukaryotic excitability

All living cells interact dynamically with a constantly changing world. Eukaryotes, in particular, evolved radically new ways to sense and react to their environment. These advances enabled new and more complex forms of cellular behaviour in eukaryotes, including directional movement, active feeding, mating, and responses to predation. But what are the key events and innovations during eukaryogenesis that made all of this possible? Here we describe the ancestral repertoire of eukaryotic excitability and discuss five major cellular innovations that enabled its evolutionary origin. The innovations include a vastly expanded repertoire of ion channels, the emergence of cilia and pseudopodia, endomembranes as intracellular capacitors, a flexible plasma membrane and the relocation of chemiosmotic ATP synthesis to mitochondria, which liberated the plasma membrane for more complex electrical signalling involved in sensing and reacting. We conjecture that together with an increase in cell size, these new forms of excitability greatly amplified the degrees of freedom associated with cellular responses, allowing eukaryotes to vastly outperform prokaryotes in terms of both speed and accuracy. This comprehensive new perspective on the evolution of excitability enriches our view of eukaryogenesis and emphasizes behaviour and sensing as major contributors to the success of eukaryotes. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Impact of confined geometries on hopping and trapping of motile bacteria in porous media

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

Rhizobial Chemotaxis and Motility Systems at Work in the Soil

Bacteria navigate their way often as individual cells through their chemical and biological environment in aqueous medium or across solid surfaces. They swim when starved or in response to physical and chemical stimuli. Flagella-driven chemotaxis in bacteria has emerged as a paradigm for both signal transduction and cellular decision-making. By altering motility, bacteria swim toward nutrient-rich environments, movement modulated by their chemotaxis systems with the addition of pili for surface movement. The numbers and types of chemoreceptors reflect the bacterial niche and lifestyle, with those adapted to complex environments having diverse metabolic capabilities, encoding far more chemoreceptors in their genomes. The Alpha-proteobacteria typify the latter case, with soil bacteria such as rhizobia, endosymbionts of legume plants, where motility and chemotaxis are essential for competitive symbiosis initiation, among other processes. This review describes the current knowledge of motility and chemotaxis in six model soil bacteria: Sinorhizobium meliloti, Agrobacterium fabacearum, Rhizobium leguminosarum, Azorhizobium caulinodans, Azospirillum brasilense, and Bradyrhizobium diazoefficiens. Although motility and chemotaxis systems have a conserved core, rhizobia possess several modifications that optimize their movements in soil and root surface environments. The soil provides a unique challenge for microbial mobility, since water pathways through particles are not always continuous, especially in drier conditions. The effectiveness of symbiont inoculants in a field context relies on their mobility and dispersal through the soil, often assisted by water percolation or macroorganism movement or networks. Thus, this review summarizes the factors that make it essential to consider and test rhizobial motility and chemotaxis for any potential inoculant.

The ecology of plasmid-coded antibiotic resistance: a basic framework for experimental research and modeling

Many antibiotic resistance genes are associated with plasmids. The ecological success of these mobile genetic elements within microbial communities depends on varying mechanisms to secure their own propagation, not only on environmental selection. Among the most important are the cost of plasmids and their ability to be transferred to new hosts through mechanisms such as conjugation. These are regulated by dynamic control systems of the conjugation machinery and genetic adaptations that plasmid-host pairs can acquire in coevolution. However, in complex communities, these processes and mechanisms are subject to a variety of interactions with other bacterial species and other plasmid types. This article summarizes basic plasmid properties and ecological principles particularly important for understanding the persistence of plasmid-coded antibiotic resistance in aquatic environments. Through selected examples, it further introduces to the features of different types of simulation models such as systems of ordinary differential equations and individual-based models, which are considered to be important tools to understand these complex systems. This ecological perspective aims to improve the way we study and understand the dynamics, diversity and persistence of plasmids and associated antibiotic resistance genes.

Bacterial motility enhances adhesion to oil droplets

Adhesion of bacteria to liquid-liquid interfaces can play a role in the biodegradation of dispersed hydrocarbons and in biochemical and bioprocess engineering. Whereas thermodynamic factors underpinning adhesion are well studied, the role of bacterial activity on adhesion is less explored. Here, we show that bacterial motility enhances adhesion to surfactant-decorated oil droplets dispersed in artificial sea water. Motile Halomonas titanicae adhered to hexadecane droplets stabilized with dioctyl sodium sulfosuccinate (DOSS) more rapidly and at greater surface densities compared to nonmotile H. titanicae, whose flagellar motion was arrested through addition of a proton uncoupler. Increasing the concentration of DOSS reduced the surface density of both motile and nonmotile bacteria as a result of the reduced interfacial tension.

Haloarchaea swim slowly for optimal chemotactic efficiency in low nutrient environments

Archaea have evolved to survive in some of the most extreme environments on earth. Life in extreme, nutrient-poor conditions gives the opportunity to probe fundamental energy limitations on movement and response to stimuli, two essential markers of living systems. Here we use three-dimensional holographic microscopy and computer simulations to reveal that halophilic archaea achieve chemotaxis with power requirements one hundred-fold lower than common eubacterial model systems. Their swimming direction is stabilised by their flagella (archaella), enhancing directional persistence in a manner similar to that displayed by eubacteria, albeit with a different motility apparatus. Our experiments and simulations reveal that the cells are capable of slow but deterministic chemotaxis up a chemical gradient, in a biased random walk at the thermodynamic limit.

Phenotypic Parallelism during Experimental Adaptation of a Free-Living Bacterium to the Zebrafish Gut

Although animals encounter many bacterial species throughout their lives, only a subset colonize vertebrate digestive tracts, and these bacteria can profoundly influence the health and development of their animal hosts. We used experimental evolution to study a free-living bacterium as it adapts to a novel vertebrate host by serially passaging replicate populations of Shewanella oneidensis through the intestines of larval zebrafish (Danio rerio). Our results demonstrate that adaptation to the zebrafish gut is complex, with multiple evolutionary pathways capable of improving colonization, but that motility plays an important role during the onset of host association.

Although animals encounter a plethora of bacterial species throughout their lives, only a subset colonize vertebrate digestive tracts, and these bacteria can profoundly influence the health and development of their animal hosts. However, our understanding of how bacteria initiate symbioses with animal hosts remains underexplored, and this process is central to the assembly and function of gut bacterial communities. Therefore, we used experimental evolution to study a free-living bacterium as it adapts to a novel vertebrate host by serially passaging replicate populations of Shewanella oneidensis through the intestines of larval zebrafish (Danio rerio). After approximately 200 bacterial generations, isolates from evolved populations improved their ability to colonize larval zebrafish during competition against their unpassaged ancestor. Genome sequencing revealed unique sets of mutations in the two evolved isolates exhibiting the highest mean competitive fitness. One isolate exhibited increased swimming motility and decreased biofilm formation compared to the ancestor, and we identified a missense mutation in the mannose-sensitive hemagglutinin pilus operon that is sufficient to increase fitness and reproduce these phenotypes. The second isolate exhibited enhanced swimming motility but unchanged biofilm formation, and here the genetic basis for adaptation is less clear. These parallel enhancements in motility and fitness resemble the behavior of a closely related Shewanella strain previously isolated from larval zebrafish and suggest phenotypic convergence with this isolate. Our results demonstrate that adaptation to the zebrafish gut is complex, with multiple evolutionary pathways capable of improving colonization, but that motility plays an important role during the onset of host association.

Run-and-tumble bacteria slowly approaching the diffusive regime

The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: (i) the conventional RT model with complete reorientation after tumbling; (ii) the case of partial reorientation, characterized by a distribution of tumbling angles; (iii) a run-and-reverse model with rotational diffusion; and (iv) a RT particle where the tumbling rate depends on the stochastic concentration of an internal protein. By analyzing the associated kinetic equations for the probability density function and simulating the models, we find that for models (ii), (iii), and (iv) the relaxation to diffusion can take much longer than the mean time between tumble events, evidencing the existence of large tails in the particle displacements. Moreover, the excess kurtosis can assume large positive values. In model (ii) it is possible for some distributions of tumbling angles that the MSD reaches a linear time dependence but, still, the dynamics remains non-Gaussian for long times. This is also the case in model (iii) for small rotational diffusivity. For all models, the long-time diffusion coefficients are also obtained. The theoretical approach, which relies on eigenvalue and angular Fourier expansions of the van Hove function, is in excellent agreement with the simulations.

Chemotaxis strategies of bacteria with multiple run modes

Bacterial chemotaxis-a fundamental example of directional navigation in the living world-is key to many biological processes, including the spreading of bacterial infections. Many bacterial species were recently reported to exhibit several distinct swimming modes-the flagella may, for example, push the cell body or wrap around it. How do the different run modes shape the chemotaxis strategy of a multimode swimmer? Here, we investigate chemotactic motion of the soil bacterium Pseudomonas putida as a model organism. By simultaneously tracking the position of the cell body and the configuration of its flagella, we demonstrate that individual run modes show different chemotactic responses in nutrition gradients and, thus, constitute distinct behavioral states. On the basis of an active particle model, we demonstrate that switching between multiple run states that differ in their speed and responsiveness provides the basis for robust and efficient chemotaxis in complex natural habitats.

Two-dimensional active motion

The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

On Modeling Ensemble Transport of Metal Reducing Motile Bacteria

Many metal reducing bacteria are motile with their run-and-tumble behavior exhibiting series of flights and waiting-time spanning multiple orders of magnitude. While several models of bacterial processes do not consider their ensemble motion, some models treat motility using an advection diffusion equation (ADE). In this study, Geobacter and Pelosinus, two metal reducing species, are used in micromodel experiments for study of their motility characteristics. Trajectories of individual cells on the order of several seconds to few minutes in duration are analyzed to provide information on (1) the length of runs, and (2) time needed to complete a run (waiting or residence time). A Continuous Time Random Walk (CTRW) model to predict ensemble breakthrough plots is developed based on the motility statistics. The results of the CTRW model and an ADE model are compared with the real breakthrough plots obtained directly from the trajectories. The ADE model is shown to be insufficient, whereas a coupled CTRW model is found to be good at predicting breakthroughs at short distances and at early times, but not at late time and long distances. The inadequacies of the simple CTRW model can possibly be improved by accounting for correlation in run length and waiting time.

Generalized Ornstein-Uhlenbeck model for active motion

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E 90, 012111 (2014)10.1103/PhysRevE.90.012111]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.

Tunable bimodal explorations of space from memory-driven deterministic dynamics

We present a wave-memory-driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a pointlike particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wave-field gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes: linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity.

A Jump-Distance-Based Parameter Inference Scheme for Particulate Trajectories

This study presents an improved quantitative tool for the analysis of particulate trajectories. Particulate trajectory data appears in several different biological contexts, from the trajectory of chemotaxing bacteria to the nuclear mobility inferred from the trajectory of MS2 spots. Presently, the majority of analyses performed on particulate trajectory data have been limited to mean-squared displacement (MSD) analysis. Although simple, MSD analysis has several pitfalls, including difficulty in selecting between competing methods of motion, handling systems with multiple distinct subpopulations, and parameter extraction from limited time-series data. Here, we provide an alternative to MSD analysis using the jump distance distribution (JDD), which addresses the aforementioned issues. In particular, the method outperforms MSD analysis in the data-poor limit, thereby giving access to a larger range of temporal dynamics. In this work, we construct and validate a derivation of the JDD for different transportation modes and dimensions and implement a parameter estimation and model selection scheme. This scheme is validated, and direct improvements over MSD analysis are shown. Through an analysis of bacterial chemotaxis data, we highlight the JDD's ability to extract parameters at a variety of timescales, as well as extract underlying biological features of interest.

A stochastic model for bacteria-driven micro-swimmers

Experiments have recently shown the feasibility of utilising bacteria as micro-scale robotic devices, with special attention paid to the development of bacteria-driven micro-swimmers taking advantage of built-in actuation and sensing mechanisms of cells. Here we propose a stochastic fluid dynamic model to describe analytically and computationally the dynamics of microscopic particles driven by the motion of surface-attached bacteria undergoing run-and-tumble motion. We compute analytical expressions for the rotational diffusion coefficient, the swimming speed and the effective diffusion coefficient. At short times, the mean squared displacement (MSD) is proportional to the square of the swimming speed, which is independent of the particle size (for fixed density of attached bacteria) and scales linearly with the number of attached bacteria; in contrast, at long times the MSD scales quadratically with the size of the swimmer and is independent of the number of bacteria. We then extend our result to the situation where the surface-attached bacteria undergo chemotaxis within the linear response regime. We demonstrate that bacteria-driven particles are capable of performing artificial chemotaxis, with a chemotactic drift velocity linear in the chemical concentration gradient and independent of the size of the particle. Our results are validated against numerical simulations in the Brownian dynamics limit and will be relevant to the optimal design of micro-swimmers for biomedical applications.

Diffusion of active particles in a complex environment: Role of surface scattering

Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on run-and-tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations for pusherlike collisions. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how nonclassical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

Identifying the mechanism for superdiffusivity in mouse fibroblast motility

We seek to characterize the motility of mouse fibroblasts on 2D substrates. Utilizing automated tracking techniques, we find that cell trajectories are super-diffusive, where displacements scale faster than t1/2 in all directions. Two mechanisms have been proposed to explain such statistics in other cell types: run and tumble behavior with Lévy-distributed run times, and ensembles of cells with heterogeneous speed and rotational noise. We develop an automated toolkit that directly compares cell trajectories to the predictions of each model and demonstrate that ensemble-averaged quantities such as the mean-squared displacements and velocity autocorrelation functions are equally well-fit by either model. However, neither model correctly captures the short-timescale behavior quantified by the displacement probability distribution or the turning angle distribution. We develop a hybrid model that includes both run and tumble behavior and heterogeneous noise during the runs, which correctly matches the short-timescale behaviors and indicates that the run times are not Lévy distributed. The analysis tools developed here should be broadly useful for distinguishing between mechanisms for superdiffusivity in other cells types and environments.

Flagellar number governs bacterial spreading and transport efficiency

Peritrichous bacteria synchronize and bundle their flagella to actively swim, while disruption of the bundle leads to a slow motility phase with a weak propulsion. It is still not known whether the number of flagella represents an evolutionary adaptation toward optimizing bacterial navigation. We study the swimming dynamics of differentially flagellated Bacillus subtilis strains in a quasi-two-dimensional system. We find that decreasing the number of flagella N f reduces the average turning angle between two successive run phases and enhances the run time and the directional persistence of the run phase. As a result, having fewer flagella is beneficial for long-distance transport and fast spreading, while having a lot of flagella is advantageous for the processes that require a slower spreading, such as biofilm formation. We develop a two-state random walk model that incorporates spontaneous switchings between the states and yields exact analytical expressions for transport properties, in remarkable agreement with experiments. The results of numerical simulations based on our two-state model suggest that the efficiency of searching and exploring the environment is optimized at intermediate values of N f. The optimal choice of N f, for which the search time is minimized, decreases with increasing the size of the environment in which the bacteria swim.

Probing the Spatiotemporal Dynamics of Catalytic Janus Particles with Single-Particle Tracking and Differential Dynamic Microscopy

We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution for the ISF of the paradigmatic active Brownian particle model and find striking agreement with experimental results from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the largest ones, which probe effective diffusion due to rotational Brownian motion. At intermediate length scales, characteristic oscillations resolve the crossover between directed motion to orientational relaxation and allow us to discriminate active Brownian motion from other reorientation processes, e.g., run-and-tumble motion. A direct comparison to theoretical predictions reliably yields the rotational and translational diffusion coefficients of the particles, the mean and width of their speed distribution, and the temporal evolution of these parameters.

Biohybrid and Bioinspired Magnetic Microswimmers

Many motile microorganisms swim and navigate in chemically and mechanically complex environments. These organisms can be functionalized and directly used for applications (biohybrid approach), but also inspire designs for fully synthetic microbots. The most promising designs of biohybrids and bioinspired microswimmers include one or several magnetic components, which lead to sustainable propulsion mechanisms and external controllability. This Review addresses such magnetic microswimmers, which are often studied in view of certain applications, mostly in the biomedical area, but also in the environmental field. First, propulsion systems at the microscale are reviewed and the magnetism of microswimmers is introduced. The review of the magnetic biohybrids and bioinspired microswimmers is structured gradually from mostly biological systems toward purely synthetic approaches. Finally, currently less explored parts of this field ranging from in situ imaging to swarm control are discussed.

Langevin equations for the run-and-tumble of swimming bacteria

The run and tumble motions of a swimming bacterium are well characterized by two stochastic variables: the speed v(t) and the change of direction or deflection x(t) = cos φ(t), where φ(t) is the turning angle at time t. Recently, we have introduced [G. Fier, D. Hansmann and R. C. Buceta, A stochastic model for directional changes of swimming bacteria, Soft Matter, 2017, 13, 3385-3394.] a single stochastic model for the deflection x(t) of an E. coli bacterium performing both types of movement in isotropic media without taxis, based on available experimental data. In this work we introduce Langevin equations for the variables (v, x), which for particular values of a control parameter β correspond to run and tumble motions, respectively. These Langevin equations have analytical solutions, which make it possible to calculate the statistical properties of both movements in detail. Assuming that the stochastic processes x and v are not independent during the tumble, we show that there are small displacements of the center of mass along the normal direction to the axis of the bacterial body, a consequence of the flagellar unbundling during the run-to-tumble transition. Regarding the tumble we show, by means of the directional correlation, that the process is not stationary for tumble-times of the order of experimentally measured characteristic tumble-time. The mean square displacement is studied in detail for both movements even in the non-stationary regime. We determine the diffusion and ballistic coefficients for tumble- and run-times, establishing their properties and relationships.

Chemotactic drift speed for bacterial motility pattern with two alternating turning events

Bacterial chemotaxis is one of the most extensively studied adaptive responses in cells. Many bacteria are able to bias their apparently random motion to produce a drift in the direction of the increasing chemoattractant concentration. It has been recognized that the particular motility pattern employed by moving bacteria has a direct impact on the efficiency of chemotaxis. The linear theory of chemotaxis pioneered by de Gennes allows for calculation of the drift velocity in small gradients for bacteria with basic motility patterns. However, recent experimental data on several bacterial species highlighted the motility pattern where the almost straight runs of cells are interspersed with turning events leading to the reorientation of the cell swimming directions with two distinct angles following in strictly alternating order. In this manuscript we generalize the linear theory of chemotaxis to calculate the chemotactic drift speed for the motility pattern of bacteria with two turning angles. By using the experimental data on motility parameters of V. alginolyticus bacteria we can use our theory to relate the efficiency of chemotaxis and the size of bacterial cell body. The results of this work can have a straightforward extension to address most general motility patterns with alternating angles, speeds and durations of runs.

A polar bundle of flagella can drive bacterial swimming by pushing, pulling, or coiling around the cell body

Bacteria swim in sequences of straight runs that are interrupted by turning events. They drive their swimming locomotion with the help of rotating helical flagella. Depending on the number of flagella and their arrangement across the cell body, different run-and-turn patterns can be observed. Here, we present fluorescence microscopy recordings showing that cells of the soil bacterium Pseudomonas putida that are decorated with a polar tuft of helical flagella, can alternate between two distinct swimming patterns. On the one hand, they can undergo a classical push-pull-push cycle that is well known from monopolarly flagellated bacteria but has not been reported for species with a polar bundle of multiple flagella. Alternatively, upon leaving the pulling mode, they can enter a third slow swimming phase, where they propel themselves with their helical bundle wrapped around the cell body. A theoretical estimate based on a random-walk model shows that the spreading of a population of swimmers is strongly enhanced when cycling through a sequence of pushing, pulling, and wrapped flagellar configurations as compared to the simple push-pull-push pattern.

Generalized run-and-turn motions: From bacteria to Lévy walks

Swimming bacteria exhibit a repertoire of motility patterns, in which persistent motion is interrupted by turning events. What are the statistical properties of such random walks? If some particular instances have long been studied, the general case where turning times do not follow a Poisson process has remained unsolved. We present a generic extension of the continuous time random walks formalism relying on operators and noncommutative calculus. The approach is first applied to a unimodal model of bacterial motion. We examine the existence of a minimum in velocity correlation function and discuss the maximum of diffusivity at an optimal value of rotational diffusion. The model is then extended to bimodal patterns and includes as particular cases all swimming strategies: run-and-tumble, run-stop, run-reverse and run-reverse-flick. We characterize their velocity correlation functions and investigate how bimodality affects diffusivity. Finally, the wider applicability of the method is illustrated by considering curved trajectories and Lévy walks. Our results are relevant for intermittent motion of living beings, be they swimming micro-organisms or crawling cells.