Swimming Escherichia coli Cells Explore the Environment by Lévy Walk

Run-and-tumble like motion of a camphor-infused Marangoni swimmer

'Run-and-tumble' (RT) motion has been a subject of intense research for several decades. Many organisms, such as bacteria, perform such motion in the presence or absence of local chemical concentration gradients and it is found to be advantageous in search processes. Although there are previous reports involving the successful design of non-living self-propelled particles exhibiting such motion in the presence of external stimuli (chemical/mechanical), RT motion with 'rest' has not yet been observed for autonomous non-living active particles. We have designed a swimmer that performs motion using a combination of 'run', 'tumble', and 'rest' states with stochastic transitions. In the present scenario, it arises solely due to self-generated local surface tension gradients. We quantify the residence time statistics by analyzing the swimmer trajectories from the experimental data, which suggests that the 'rest' and 'tumble' states are more frequent than 'run'. Then, we quantify the motion properties by computing the mean squared displacement, which shows that the swimmer performs ballistic motion on a short time scale and then slows down due to tumbling and resting. To validate the observed transport properties, we introduce a minimal model of a chiral active Brownian particle, stochastically switching between three internal states. The model parameters were extracted from the experiments, which rendered a good agreement between the experiments and simulations.

Biased Lévy Walk Enables Light Gradient Sensing in Euglena gracilis

We examine the navigation behavior of the photosensitive alga Euglena gracilis in confined environments. Under uniform lighting conditions, E. gracilis exhibits stochastic movements with nearly straight runs interrupted by abrupt directional changes. The lengths of these runs follow a long-tailed distribution typical of a Lévy walk, with scaling exponents that vary with light intensity. In gradient lighting conditions, the cells modulate their run durations-extending them upon detecting an increase in light intensity and shortening them when a decrease is detected. This adjustment effectively biases the Lévy walk, enabling the cells to ascend the spatial light gradient. This behavior mirrors well-known prokaryotic stochastic navigation strategies, such as bacterial chemotaxis, offering a eukaryotic parallel. The experimental observations under varied lighting conditions are consistently replicated through an agent-based model.

Enhanced chemotaxis efficiency of Escherichia coli in viscoelastic solutions

Bacteria inhabit complex environments rich in macromolecular polymers that exhibit viscoelastic properties. While the influence of viscoelasticity on bacterial swimming is recognized, its impact on chemotaxis-a critical behavior for bacterial survival and colonization-remains elusive. In this study, we employed a microfluidic device to establish attractant gradients and observed the chemotactic behavior of Escherichia coli in both viscoelastic solutions containing carboxymethyl cellulose (CMC) and Newtonian buffers. Our results reveal that E. coli demonstrates markedly enhanced chemotactic efficiency in viscoelastic media. Notably, bacteria achieved faster migration velocities and higher steady-state accumulation in areas with higher attractant concentrations compared to those in Newtonian conditions. Through 3D tracking, we determined that changes in bulk motility parameters alone do not account for the observed enhancements. Further investigations through theoretical analysis and stochastic simulations suggested that the main enhancement mechanisms are mitigation of surface hydrodynamic hindrance resulting from solid surfaces commonly present in bacterial habitats, and the induction of a lifting force in viscoelastic solutions. These findings highlight the significant role of the rheological properties of bacterial habitats in shaping their chemotactic strategies, offering deeper insights into bacterial adaptive mechanisms in both natural and clinical settings.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

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.

Anomalous diffusion of E. coli under microfluidic confinement and chemical gradient

We report a two-layer microfluidic device to study the combined effect of confinement and chemical gradient on the motility of wild-type E. coli. We track individual E. coli in 50 μm and 10 μm wide microchannels, with a channel height of 2 μm, to generate quasi-2D conditions. We find that contrary to expectations, bacterial trajectories are superdiffusive even in the absence of a chemical (glucose) gradient. The superdiffusive behaviour becomes more pronounced upon introducing a chemical gradient or strengthening the lateral confinement. Run length distributions for weak lateral confinement in the absence of chemical gradients follow an exponential distribution. Both confinement and chemoattraction induce deviations from this behaviour, with the run length distributions approaching a power-law form under these conditions. Both confinement and chemoattraction suppress large-angle tumbles as well. Our results suggest that wild-type E. coli modulates both its runs and tumbles in a similar manner under physical confinement and chemical gradient. Our findings have implications for understanding how bacteria modulate their motility behaviour in natural habitats.

The ecological roles of bacterial chemotaxis

How bacterial chemotaxis is performed is much better understood than why. Traditionally, chemotaxis has been understood as a foraging strategy by which bacteria enhance their uptake of nutrients and energy, yet it has remained puzzling why certain less nutritious compounds are strong chemoattractants and vice versa. Recently, we have gained increased understanding of alternative ecological roles of chemotaxis, such as navigational guidance in colony expansion, localization of hosts or symbiotic partners and contribution to microbial diversity by the generation of spatial segregation in bacterial communities. Although bacterial chemotaxis has been observed in a wide range of environmental settings, insights into the phenomenon are mostly based on laboratory studies of model organisms. In this Review, we highlight how observing individual and collective migratory behaviour of bacteria in different settings informs the quantification of trade-offs, including between chemotaxis and growth. We argue that systematically mapping when and where bacteria are motile, in particular by transgenerational bacterial tracking in dynamic environments and in situ approaches from guts to oceans, will open the door to understanding the rich interplay between metabolism and growth and the contribution of chemotaxis to microbial life.

Escherichia coli chemotaxis is information limited

Organisms acquire and use information from their environment to guide their behaviour. However, it is unclear whether this information quantitatively limits their behavioural performance. Here, we relate information to the ability of Escherichia coli to navigate up chemical gradients, the behaviour known as chemotaxis. First, we derive a theoretical limit on the speed with which cells climb gradients, given the rate at which they acquire information. Next, we measure cells' gradient-climbing speeds and the rate of information acquisition by their chemotaxis signaling pathway. We find that E. coli make behavioural decisions with much less than the one bit required to determine whether they are swimming up-gradient. Some of this information is irrelevant to gradient climbing, and some is lost in communication to behaviour. Despite these limitations, E. coli climb gradients at speeds within a factor of two of the theoretical bound. Thus, information can limit the performance of an organism, and sensory-motor pathways may have evolved to efficiently use information acquired from the environment.

Individual based models exhibiting Lévy-flight type movement induced by intracellular noise

We use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the intrinsic noise plays a central role. Compared with previous work in Perthame et al. (Z Angew Math Phys 69(3):1-15, 2018), in which the parametric assumptions are mainly targeted for mathematical convenience but not well-suited for numerical simulations or comparison with experimental results, our current paper makes use of biologically meaningful pathways and tumbling kernels. The main contribution of this current work is bridging the gap between the theoretical results and experimentally available data. Some particular forms of how the tumbling frequency depends on the internal variable are proposed. Moreover, we propose two individual-based models, one for the tumbling frequency and the other for the receptor activity, and perform numerical simulations. Power-law decay of the run length distribution, which corresponds to Lévy-type motions, is observed in our numerical results. The particular decay rate agrees quantitatively with the analytical result.

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.

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior

Non-genetic phenotypic diversity plays a significant role in the chemotactic behavior of bacteria, influencing how populations sense and respond to chemical stimuli. First, we review the molecular mechanisms that generate phenotypic diversity in bacterial chemotaxis. Next, we discuss the functional consequences of phenotypic diversity for the chemosensing and chemotactic performance of single cells and populations. Finally, we discuss mechanisms that modulate the amount of phenotypic diversity in chemosensory parameters in response to changes in the environment.