Learning the space-time phase diagram of bacterial swarm expansion

Bacterial surface motility is modulated by colony-scale flow and granular jamming

Microbes routinely face the challenge of acquiring territory and resources on wet surfaces. Cells move in large groups inside thin, surface-bound water layers, often achieving speeds of 30 µm s^-1 within this environment, where viscous forces dominate over inertial forces (low Reynolds number). The canonical Gram-positive bacterium Bacillus subtilis is a model organism for the study of collective migration over surfaces with groups exhibiting motility on length-scales three orders of magnitude larger than themselves within a few doubling times. Genetic and chemical studies clearly show that the secretion of endogenous surfactants and availability of free surface water are required for this fast group motility. Here, we show that: (i) water availability is a sensitive control parameter modulating an abiotic jamming-like transition that determines whether the group remains fluidized and therefore collectively motile, (ii) groups self-organize into discrete layers as they travel, (iii) group motility does not require proliferation, rather groups are pulled from the front, and (iv) flow within expanding groups is capable of moving material from the parent colony into the expanding tip of a cellular dendrite with implications for expansion into regions of varying nutrient content. Together, these findings illuminate the physical structure of surface-motile groups and demonstrate that physical properties, like cellular packing fraction and flow, regulate motion from the scale of individual cells up to length scales of centimetres.

Emergent collective dynamics of bottom-heavy squirmers under gravity

We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.

One-dimensional model for chemotaxis with hard-core interactions

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based on the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.

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.

A compound isolated from Alpinia officinarum Hance. inhibits swarming motility of Pseudomonas aeruginosa and down regulates virulence genes

AIM

The study was aimed at purifying the active principle from Alpinia officinarum rhizomes responsible for inhibition of swarming motility of Pseudomonas aeruginosa and analysing the mechanism of action.

METHODS AND RESULTS

The active compound from methanol extract of A. officinarum was purified by silica gel column chromatography followed by elution from Amberlite resin. The compound 1-(3,5-dihydroxyphenyl)-2-(methylamino)ethan-1-one, inhibited swarming motility at 12·5 µg ml^-1 . This inhibition was independent of rhamnolipid production. Real-time PCR analysis showed significant down-regulation of virulence-associated genes including T3SS exoS, exoT and flagella master regulator fleQ.

CONCLUSIONS

The compound from A. officinarum inhibited swarming motility and significantly down-regulated the expression of type III secretory system effector genes exoS and exoT and flagellar master regulator fleQ genes.

SIGNIFICANCE AND IMPACT OF THE STUDY

The study identifies a potent swarming inhibitory compound from the common medicinal plant A. officinarum and reinstates the potential of plant-derived compounds in tackling virulence properties of pathogenic bacteria.

Using machine learning to predict extreme events in the Hénon map

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We analyze here the performance of one algorithm for the prediction of extreme events in the two-dimensional Hénon map at the classical parameters. The task is to determine whether a trajectory will exceed a threshold after a set number of time steps into the future. This task has a geometric interpretation within the dynamics of the Hénon map, which we use to gauge the performance of the neural networks that are used in this work. We analyze the dependence of the success rate of the ML models on the prediction time T, the number of training samples N_T, and the size of the network N_p. We observe that in order to maintain a certain accuracy, N_T∝exp⁡(2hT) and N_p∝exp⁡(hT), where h is the topological entropy. Similar relations between the intrinsic chaotic properties of the dynamics and ML parameters might be observable in other systems as well.

Spatial propagation of electrical signals in circular biofilms: A combined experimental and agent-based fire-diffuse-fire study

Bacterial biofilms are a risk to human health, playing critical roles in persistent infections. Recent studies have observed electrical signaling in biofilms and thus biofilms represent a new class of active excitable matter in which cell division is the active process and the spiking of the individual bacterial cells is the excitable process. Electrophysiological models have predominantly been developed to describe eukaryotic systems, but we demonstrate their use in understanding bacterial biofilms. Our agent-based fire-diffuse-fire (ABFDF) model successfully simulates the propagation of both centrifugal (away from the center) and centripetal (toward the center) electrical signals through biofilms of Bacillus subtilis. Furthermore, the ABFDF model allows realistic spatial positioning of the bacteria in two dimensions to be included in the fire-diffuse-fire model and this is the crucial factor that improves agreement with experiments. The speed of propagation is not constant and depends on the radius of the propagating electrical wave front. Centripetal waves are observed to move faster than centrifugal waves, which is a curvature driven effect and is correctly captured by our simulations.

Chemotactic behaviour of Escherichia coli at high cell density

At high cell density, swimming bacteria exhibit collective motility patterns, self-organized through physical interactions of a however still debated nature. Although high-density behaviours are frequent in natural situations, it remained unknown how collective motion affects chemotaxis, the main physiological function of motility, which enables bacteria to follow environmental gradients in their habitats. Here, we systematically investigate this question in the model organism Escherichia coli, varying cell density, cell length, and suspension confinement. The characteristics of the collective motion indicate that hydrodynamic interactions between swimmers made the primary contribution to its emergence. We observe that the chemotactic drift is moderately enhanced at intermediate cell densities, peaks, and is then strongly suppressed at higher densities. Numerical simulations reveal that this suppression occurs because the collective motion disturbs the choreography necessary for chemotactic sensing. We suggest that this physical hindrance imposes a fundamental constraint on high-density behaviours of motile bacteria, including swarming and the formation of multicellular aggregates and biofilms.

Cooperation in Microbial Populations: Theory and Experimental Model Systems

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities.

Surface-to-volume scaling and aspect ratio preservation in rod-shaped bacteria

Rod-shaped bacterial cells can readily adapt their lengths and widths in response to environmental changes. While many recent studies have focused on the mechanisms underlying bacterial cell size control, it remains largely unknown how the coupling between cell length and width results in robust control of rod-like bacterial shapes. In this study we uncover a conserved surface-to-volume scaling relation in Escherichia coli and other rod-shaped bacteria, resulting from the preservation of cell aspect ratio. To explain the mechanistic origin of aspect-ratio control, we propose a quantitative model for the coupling between bacterial cell elongation and the accumulation of an essential division protein, FtsZ. This model reveals a mechanism for why bacterial aspect ratio is independent of cell size and growth conditions, and predicts cell morphological changes in response to nutrient perturbations, antibiotics, MreB or FtsZ depletion, in quantitative agreement with experimental data.

Cell Shape and Population Migration Are Distinct Steps of Proteus mirabilis Swarming That Are Decoupled on High-Percentage Agar

Swarming on rigid surfaces requires movement of cells as individuals and as a group of cells. For the bacterium Proteus mirabilis, an individual cell can respond to a rigid surface by elongating and migrating over micrometer-scale distances. Cells can form groups of transiently aligned cells, and the collective population is capable of migrating over centimeter-scale distances. To address how P. mirabilis populations swarm on rigid surfaces, we asked whether cell elongation and single-cell motility are coupled to population migration. We first measured the relationship between agar concentration (a proxy for surface rigidity), single-cell phenotypes, and swarm colony phenotypes. We find that cell elongation and single-cell motility are coupled with population migration on low-percentage hard agar (1% to 2.5%) and become decoupled on high-percentage hard agar (>2.5%). Next, we evaluate how disruptions in lipopolysaccharide (LPS), specifically the O-antigen components, affect responses to hard agar. We find that LPS is not essential for elongation and motility of individual cells, as predicted, and instead functions to broaden the range of agar concentrations on which cell elongation and motility are coupled with population migration. These findings demonstrate that cell elongation and motility are coupled with population migration under a permissive range of surface conditions; increasing agar concentration is sufficient to decouple these behaviors. Since swarm colonies cover greater distances when these steps are coupled than when they are not, these findings suggest that collective interactions among P. mirabilis cells might be emerging as a colony expands outwards on rigid surfaces.IMPORTANCE How surfaces influence cell size, cell-cell interactions, and population migration for robust swarmers like P. mirabilis is not fully understood. Here, we have elucidated how cells change length along a spectrum of sizes that positively correlates with increases in agar concentration, regardless of population migration. Single-cell phenotypes can be decoupled from collective population migration simply by increasing agar concentration. A cell's lipopolysaccharides function to broaden the range of agar conditions under which cell elongation and single-cell motility remain coupled with population migration. In eukaryotes, the physical environment, such as a surface matrix, can impact cell development, shape, and migration. These findings support the idea that rigid surfaces similarly act on swarming bacteria to impact cell shape, single-cell motility, and collective population migration.

Common concepts for bacterial collectives

The expansion of bacterial swarms and the spreading of biofilms can be described by a unified biophysical theory that involves both active and passive processes.

A statistical physics view of swarming bacteria

Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.