Logarithmic sensing in Bacillus subtilis aerotaxis

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. However, in contrast to inertial turbulence, the microscopic dynamics underlying bacterial turbulence is only beginning to be understood. Here, we report experiments revealing correlations between microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our results demonstrate the existence of three microscopic dynamical regimes: initial ballistic dynamics followed by an intermittent Lévy walk before the intriguing decay to random Gaussian fluctuations. Our experiments capture that the fluid correlation time earmarks the transition from Lévy to Gaussian fluctuations demonstrating the microscopic reason underlying the observation. By harnessing the flow activity via bacterial concentration, we reveal systematic control over the flow correlation timescales, which, in turn, allows controlling the duration of the Lévy walk.

Microfluidic approaches in microbial ecology

Microbial life is at the heart of many diverse environments and regulates most natural processes, from the functioning of animal organs to the cycling of global carbon. Yet, the study of microbial ecology is often limited by challenges in visualizing microbial processes and replicating the environmental conditions under which they unfold. Microfluidics operates at the characteristic scale at which microorganisms live and perform their functions, thus allowing for the observation and quantification of behaviors such as growth, motility, and responses to external cues, often with greater detail than classical techniques. By enabling a high degree of control in space and time of environmental conditions such as nutrient gradients, pH levels, and fluid flow patterns, microfluidics further provides the opportunity to study microbial processes in conditions that mimic the natural settings harboring microbial life. In this review, we describe how recent applications of microfluidic systems to microbial ecology have enriched our understanding of microbial life and microbial communities. We highlight discoveries enabled by microfluidic approaches ranging from single-cell behaviors to the functioning of multi-cellular communities, and we indicate potential future opportunities to use microfluidics to further advance our understanding of microbial processes and their implications.

Chemical Approaches for the Preparation of Bacteria - Nano/Microparticle Hybrid Systems

Bacteria represent a class of living cells that are very attractive carriers for the transport and delivery of nano- and microsized particles. The use of cell-based carriers, such as for example bacteria, may allow to precisely direct nano- or microsized cargo to a desired site, which would greatly enhance the selectivity of drug delivery and allow to mitigate side effects. One key step towards the use of such nano-/microparticle - bacteria hybrids is the immobilization of the cargo on the bacterial cell surface. To fabricate bacteria - nano-/microparticle biohybrid microsystems, a wide range of chemical approaches are available that can be used to immobilize the particle payload on the bacterial cell surface. This article presents an overview of the various covalent and noncovalent chemistries that are available for the preparation of bacteria - nano-/microparticle hybrids. For each of the different chemical approaches, an overview will be presented that lists the bacterial strains that have been modified, the type and size of nanoparticles that have been immobilized, as well as the methods that have been used to characterize the nanoparticle-modified bacteria.

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 dopamine circuit as a reward-taxis navigation system

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

Simultaneous visualization of flow fields and oxygen concentrations to unravel transport and metabolic processes in biological systems

From individual cells to whole organisms, O2 transport unfolds across micrometer- to millimeter-length scales and can change within milliseconds in response to fluid flows and organismal behavior. The spatiotemporal complexity of these processes makes the accurate assessment of O2 dynamics via currently available methods difficult or unreliable. Here, we present "sensPIV," a method to simultaneously measure O2 concentrations and flow fields. By tracking O2-sensitive microparticles in flow using imaging technologies that allow for instantaneous referencing, we measured O2 transport within (1) microfluidic devices, (2) sinking model aggregates, and (3) complex colony-forming corals. Through the use of sensPIV, we find that corals use ciliary movement to link zones of photosynthetic O2 production to zones of O2 consumption. SensPIV can potentially be extendable to study flow-organism interactions across many life-science and engineering applications.

Chemotactic smoothing of collective migration

Collective migration-the directed, coordinated motion of many self-propelled agents-is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient-revealing a population-scale consequence of the manner in which individual cells transduce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.

pH-taxis drives aerobic bacteria in duodenum to migrate into the pancreas with tumors

As oral or intestinal bacteria have been found in pancreatic cystic fluid and tumors, understanding bacterial migration from the duodenum into the pancreas via hepato-pancreatic duct is critical. Mathematical models of migration of aerobic bacteria from the duodenum to the pancreas with tumors were developed. Additionally, the bacterial distributions under the pH gradient and those under flow were measured in double-layer flow based microfluidic device and T-shaped cylinders. Migration of aerobic bacteria from the duodenum into pancreas is counteracted by bile and pancreatic juice flow but facilitated by pH-taxis from acidic duodenum fluid toward more favorable slightly alkaline pH in pancreatic juice. Additionally, the reduced flow velocity in cancer patients, due to compressed pancreatic duct by solid tumor, facilitates migration. Moreover, measured distribution of GFP E. coli under the pH gradient in a microfluidic device validated pH-tactic behaviors. Furthermore, Pseudomonas fluorescens in hydrochloride solution, but not in bicarbonate solution, migrated upstream against bicarbonate flow of > 20 μm/s, with an advancement at approximately 50 μm/s.

Microfluidic devices for studying bacterial taxis, drug testing and biofilm formation

Some bacteria have coevolved to establish symbiotic or pathogenic relationships with plants, animals or humans. With human association, the bacteria can cause a variety of diseases. Thus, understanding bacterial phenotypes at the single-cell level is essential to develop beneficial applications. Traditional microbiological techniques have provided great knowledge about these organisms; however, they have also shown limitations, such as difficulties in culturing some bacteria, the heterogeneity of bacterial populations or difficulties in recreating some physical or biological conditions. Microfluidics is an emerging technique that complements current biological assays. Since microfluidics works with micrometric volumes, it allows fine-tuning control of the test conditions. Moreover, it allows the recruitment of three-dimensional (3D) conditions, in which several processes can be integrated and gradients can be generated, thus imitating physiological 3D environments. Here, we review some key microfluidic-based studies describing the effects of different microenvironmental conditions on bacterial response, biofilm formation and antimicrobial resistance. For this aim, we present different studies classified into six groups according to the design of the microfluidic device: (i) linear channels, (ii) mixing channels, (iii) multiple floors, (iv) porous devices, (v) topographic devices and (vi) droplet microfluidics. Hence, we highlight the potential and possibilities of using microfluidic-based technology to study bacterial phenotypes in comparison with traditional methodologies.

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

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.

Temporal fluctuations in chemotaxis gain implement a simulated-tempering strategy for efficient navigation in complex environments

Bacterial chemotaxis is a major testing ground for systems biology, including the role of fluctuations and individual variation. Individual bacteria vary in their tumbling frequency and adaptation time. Recently, large cell-cell variation was also discovered in chemotaxis gain, which determines the sensitivity of the tumbling rate to attractant gradients. Variation in gain is puzzling, because low gain impairs chemotactic velocity. Here, we provide a functional explanation for gain variation by establishing a formal analogy between chemotaxis and algorithms for sampling probability distributions. We show that temporal fluctuations in gain implement simulated tempering, which allows sampling of attractant distributions with many local peaks. Periods of high gain allow bacteria to detect and climb gradients quickly, and periods of low gain allow them to move to new peaks. Gain fluctuations thus allow bacteria to thrive in complex environments, and more generally they may play an important functional role for organism navigation.

Chemotactic migration of bacteria in porous media

Chemotactic migration of bacteria-their ability to direct multicellular motion along chemical gradients-is central to processes in agriculture, the environment, and medicine. However, current understanding of migration is based on studies performed in bulk liquid, despite the fact that many bacteria inhabit tight porous media such as soils, sediments, and biological gels. Here, we directly visualize the chemotactic migration of Escherichia coli populations in well-defined 3D porous media in the absence of any other imposed external forcing (e.g., flow). We find that pore-scale confinement is a strong regulator of migration. Strikingly, cells use a different primary mechanism to direct their motion in confinement than in bulk liquid. Furthermore, confinement markedly alters the dynamics and morphology of the migrating population-features that can be described by a continuum model, but only when standard motility parameters are substantially altered from their bulk liquid values to reflect the influence of pore-scale confinement. Our work thus provides a framework to predict and control the migration of bacteria, and active matter in general, in complex environments.

Photo-bioconvection: towards light control of flows in active suspensions

The persistent motility of individual constituents in microbial suspensions represents a prime example of the so-called active matter systems. Cells consume energy, exert forces and move, overall releasing the constraints of equilibrium statistical mechanics of passive elements and allowing for complex spatio-temporal patterns to emerge. Moreover, when subject to physico-chemical stimuli their collective behaviour often drives large-scale instabilities of a hydrodynamic nature, with implications for biomixing in natural environments and incipient industrial applications. In turn, our ability to exert external control of these driving stimuli could be used to govern the emerging patterns. Light, being easily manipulable and, at the same time, an important stimulus for a wide variety of microorganisms, is particularly well suited to this end. In this paper, we will discuss the current state, developments and some of the emerging advances in the fundamentals and applications of light-induced bioconvection with a focus on recent experimental realizations and modelling efforts. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Biofilms at interfaces: microbial distribution in floating films

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

Microfluidic techniques for separation of bacterial cells via taxis

The microbial environment is typically within a fluid and the key processes happen at the microscopic scale where viscosity dominates over inertial forces. Microfluidic tools are thus well suited to study microbial motility because they offer precise control of spatial structures and are ideal for the generation of laminar fluid flows with low Reynolds numbers at microbial lengthscales. These tools have been used in combination with microscopy platforms to visualise and study various microbial taxes. These include establishing concentration and temperature gradients to influence motility via chemotaxis and thermotaxis, or controlling the surrounding microenvironment to influence rheotaxis, magnetotaxis, and phototaxis. Improvements in microfluidic technology have allowed fine separation of cells based on subtle differences in motility traits and have applications in synthetic biology, directed evolution, and applied medical microbiology.

Bacterial chemotaxis in a microfluidic T-maze reveals strong phenotypic heterogeneity in chemotactic sensitivity

Many microorganisms have evolved chemotactic strategies to exploit the microscale heterogeneity that frequently characterizes microbial habitats. Chemotaxis has been primarily studied as an average characteristic of a population, with little regard for variability among individuals. Here, we adopt a classic tool from animal ecology - the T-maze - and implement it at the microscale by using microfluidics to expose bacteria to a sequence of decisions, each consisting of migration up or down a chemical gradient. Single-cell observations of clonal Escherichia coli in the maze, coupled with a mathematical model, reveal that strong heterogeneity in the chemotactic sensitivity coefficient exists even within clonal populations of bacteria. A comparison of different potential sources of heterogeneity reveals that heterogeneity in the T-maze originates primarily from the chemotactic sensitivity coefficient, arising from a distribution of pathway gains. This heterogeneity may have a functional role, for example in the context of migratory bet-hedging strategies.

Derivation of a bacterial nutrient-taxis system with doubly degenerate cross-diffusion as the parabolic limit of a velocity-jump process

This paper is devoted to the justification of the macroscopic, mean-field nutrient taxis system with doubly degenerate cross-diffusion proposed by Leyva et al. (Phys A 392:5644-5662, 2013) to model the complex spatio-temporal dynamics exhibited by the bacterium Bacillus subtilis during experiments run in vitro. This justification is based on a microscopic description of the movement of individual cells whose changes in velocity (in both speed and orientation) obey a velocity jump process governed by a transport equation of Boltzmann type. For that purpose, the asymptotic method introduced by Hillen and Othmer (SIAM J Appl Math 61:751-775, 2000; SIAM J Appl Math 62:1222-1250, 2002) is applied, which consists of the computation of the leading order term in a regular Hilbert expansion for the solution to the transport equation, under an appropriate parabolic scaling and a first order perturbation of the turning rate of Schnitzer type (Schnitzer in Phys Rev E 48:2553-2568, 1993). The resulting parabolic limit equation at leading order for the bacterial cell density recovers the degenerate nonlinear cross diffusion term and the associated chemotactic drift appearing in the original system of equations. Although the bacterium B. subtilis is used as a prototype, the method and results apply in more generality.

Emergent properties of bacterial chemotaxis pathway

The chemotaxis pathway of Escherichia coli is the most studied sensory system in prokaryotes. The highly conserved general architecture of this pathway consists of two modules which mediate signal transduction and adaptation. The signal transduction module detects and amplifies changes in environmental conditions and rapidly transmits these signals to control bacterial swimming behavior. The adaptation module gradually resets the activity and sensitivity of the first module after initial stimulation and thereby enables the temporal comparisons necessary for bacterial chemotaxis. Recent experimental and theoretical work has unraveled multiple quantitative features emerging from the interplay between these two modules. This has laid the groundwork for rationalization of these emerging properties in the context of the evolutionary optimization of the chemotactic behavior.