Bacterial Motion Research Articles

Continuous solutions for a two-dimensional cross-diffusion problem involving doubly degenerate diffusion and logistic proliferation

Emerging from the modeling of intricate structures formed by bacterial motion in nutrient-deficient environments, the doubly degenerate nutrient taxis system [Formula: see text] is considered in smoothly bounded domains [Formula: see text]. In contrast to frameworks devoid of logistic growth where only small-data global solutions have so far been found in the literature, quadratic degradation in the logistic growth is shown to markedly amplify the overall dissipative effects to the extent that, for arbitrary smooth initial data, an associated no-flux type initial-boundary problem possesses global continuous weak solutions. Central to our findings is the identification of an advantageous dissipative structure subtly embedded in the system, the exploitation of which leads to the establishment of a positive lower bound for nutrients levels within any finite time interval, thereby ruling out the appearance of cross-degeneracies within such timeframes.

Motile bacteria crossing liquid-liquid interfaces of an aqueous isotropic-nematic coexistence phase.

In nature, bacteria often swim in complex fluids, but our understanding of the interactions between bacteria and complex surroundings is still evolving. In this work, rod-like Bacillus subtilis swims in a quasi-2D environment with aqueous liquid-liquid interfaces, i.e., the isotropic-nematic coexistence phase of an aqueous chromonic liquid crystal. Focusing on the bacteria motion near and at the liquid-liquid interfaces, we collect and quantify bacterial trajectories ranging across the isotropic to the nematic phase. Despite its small magnitude, the interfacial tension of the order of 10 μN m-1 at the isotropic-nematic interface justifies our observations that bacteria swimming more perpendicular to the interface have a higher probability of crossing the interface. Our force-balance model, considering the interfacial tension, further predicts how the length and speed of the bacteria affect their crossing behaviors. Investigating how a phase change affects bacterial motion, we also find, as soon as the bacteria cross the interface and enter the nematic phase, they wiggle less, but faster, and that this occurs as the flagellar bundles aggregate within the nematic phase. Given the ubiquity of multi-phases in biological environments, our findings will help to understand active transport across various phases.

High shear flow prevents bundling of bacterial flagella and induces lateral migration away from a wall

Since the discovery of bacteria in the 17th century, bacterial motion has been the focus of great research interest. As an example of bacterial chemotaxis, Escherichia coli exhibits run-and-tumble motion by bundling and unbundling flagella, propelling the cells along a concentration gradient. However, the behavior of bacteria in high-shear flow environments remains poorly understood. In this study, we showed experimentally that E. coli swimming is severely inhibited at shear rates above a few hundred per second. Our simulations revealed that E. coli flagellar bundling cannot occur in a high-shear regime, because the background shear flow is stronger than the flagellar-generated flow required to form a bundle. Bacteria under strong shear behave like deformable objects and exhibit lateral migration away from a wall. These results suggest that bacteria that are unable to bundle their flagella in strong shear near a wall alter their locomotion strategy to passively escape from the wall.

Viscoelasticity enhances collective motion of bacteria.

Bacteria form human and animal microbiota. They are the leading causes of many infections and constitute an important class of active matter. Concentrated bacterial suspensions exhibit large-scale turbulent-like locomotion and swarming. While the collective behavior of bacteria in Newtonian fluids is relatively well understood, many fundamental questions remain open for complex fluids. Here, we report on the collective bacterial motion in a representative biological non-Newtonian viscoelastic environment exemplified by mucus. Experiments are performed with synthetic porcine gastric mucus, natural cow cervical mucus, and a Newtonian-like polymer solution. We have found that an increase in mucin concentration and, correspondingly, an increase in the suspension's elasticity monotonously increases the length scale of collective bacterial locomotion. On the contrary, this length remains practically unchanged in Newtonian polymer solution in a wide range of concentrations. The experimental observations are supported by computational modeling. Our results provide insight into how viscoelasticity affects the spatiotemporal organization of bacterial active matter. They also expand our understanding of bacterial colonization of mucosal surfaces and the onset of antibiotic resistance due to swarming.

Dynamic mode structure of active turbulence

The collective motion of dense suspensions of swimming bacteria is typical of a broad class of active materials, which serve an array of important biological and ecological functions. This work combines microfluidic experiments with modal analysis, typically reserved for inertial turbulence, to quantify the active turbulence of bacterial suspensions. Our results unveil the underlying constituent flow structures responsible for the interactions of chaotic bacterial motion with solid boundaries and external flows, and establish an analysis framework to facilitate new experimental and modeling approaches in active matter systems.

Chip for dielectrophoretic microbial capture, separation and detection II: experimental study

In our previous paper we have modelled a dielectrophoretic force (DEP) and cell particle behavior in a microfluidic channel (Weber MU et al 2023 Chip for dielectrophoretic microbial capture, separation and detection I: theoretical basis of electrode design Nanotechnology this issue). Here we test and confirm the results of our modeling work by experimentally validating the theoretical design constraints of the ring electrode architecture. We have compared and tested the geometry and particle capture and separation performance of the two separate electrode designs (the ring and dot electrode structures) by investigating bacterial motion in response to the applied electric field. We have quantitatively evaluated the electroosmosis (EO) to positive DEP (PDEP) transition in both electrode designs and explained the differences in capture efficiency of the ring and dot electrode systems. The ring structure shows 99% efficiency of bacterial capture both for PDEP and for EO. Moreover, the ring structure shows an over 200 faster bacterial response to the electric field. We have also established that the ring electrode architecture, with appropriate structure periodicity and spacing, results in efficient capture and separation of microbial cells. We have identified several critical design constraints that are required to achieve high efficiency bacterial capture. We have established that the spacing between consecutive DEP traps smaller than the length of the depletion zone will ensure that the DEP force dominates bacterial motion over motility and Brownian motion.

Impact of viscoelastic ooze slime on complex wavy gliders near a solid boundary

• Fluid mechanics of bacterial motion is discussed numerically. • Glider is approximated as a 2D complex wavy sheet. • To capture the viscoelastic properties of slime FENE-P fluid model is utilized. • The gliding motion is highly dependent on slime rheology and wave amplitudes. Prokaryote propulsion is bewilderingly diverse. Many bacteria swim through the fluid medium via rotating a long helical flagellum driven by a rotary motor, some possesses helical shaped bodies and use mechanochemical filaments. Rod-shaped Bacteria (present near the solid wall) practice another mechanism of locomotion, generally called gliding motility. It is hypothesized that rod-shaped bacteria propel it selves by producing waves in their body and leave an adhesive slime trail. Based on these observations, we use a mathematical model (of complex undulating sheet) to examine the gliding motility of bacteria on a layer of non-Newtonian slime. FENE-P fluid model is approximated as a layer of non-Newtonian slime. Navier-Stokes equation is simplified using the lubrication assumption which results in a second-order differential equation. The speed of organism, flow rate and energy loss at larger values of the involved parameters are simulated using a blended numerical technique. The streamlines pattern and velocity of the slime are also drawn for the realistic pairs of speed and flow rate and are thoroughly explained.

Bacterial mobility and motility in porous media mimicked by microspheres

Bacterial motion in porous media is essential for their survival, proper functioning, and various applications. Here we investigated the motion of Escherichia coli bacteria in microsphere-mimicked porous media. We observed reduced bacterial velocity and enhanced directional changes of bacteria as the density of microspheres increased, while such changes happened mostly around the microspheres and due to the collisions with the microspheres. More importantly, we established and quantified the correlation between the bacterial trapping in porous media and the geometric confinement imposed by the microspheres. In addition, numerical simulations showed that the active Brownian motion model in the presence of microspheres resulted in bacterial motion that are consistent with the experimental observations. Our study suggested that it is important to distinguish the ability of bacteria to move easily – bacterial mobility – from the ability of bacteria to move independently – bacteria motility. Our results showed that bacterial motility remains similar in porous media, but bacterial mobility was significantly affected by the pore-scale confinement.

Biomechanics of bacterial gliding motion with Oldroyd-4 constant slime

Biomechanics of bacterial gliding motion with Oldroyd-4 constant slime

Frustrated 'run and tumble' of swimming Escherichia coli bacteria in nematic liquid crystals.

In many situations, bacteria move in complex environments, as soils, oceans or the human gut-track, where carrier fluids show complex structures associated with non-Newtonian rheology. Many fundamental questions concerning the ability to navigate in such environments remain unsolved. Recently, it has been shown that the kinetics of bacterial motion in structured fluids as liquid crystals (LCs) is constrained by the orientational molecular order (or director field) and that novel spatio-temporal patterns arise. A question unaddressed so far is how bacteria change swimming direction in such an environment. In this work, we study the swimming mechanism of a single bacterium, Esherichia coli, constrained to move along the director field of a lyotropic chromonic liquid crystal confined to a planar cell. Here, the spontaneous 'run and tumble' motion of the bacterium gets frustrated: the elasticity of the LC prevents flagella from unbundling. Interestingly, to change direction, bacteria execute a reversal motion along the director field, driven by the relocation of a single flagellum, a 'frustrated tumble'. We characterize this phenomenon in detail experimentally, exploiting exceptional spatial and temporal resolution of bacterial and flagellar dynamics, using a two colour Lagrangian tracking technique. We suggest a possible mechanism accounting for these observations.

Swimming faster despite obstacles: a universal mechanism behind bacterial speed enhancement in complex fluids.

Bacteria constitute about 15% of global biomass and their natural environments often contain polymers and colloids, which show complex flow behaviors. It is crucial to study their motion in such environments to understand their growth and spreading as well as to design synthetic microswimmers for biomedical applications. Bacterial motion in complex viscous environments, although extensively studied over the past six decades, still remains poorly understood. In our recent study combining experimental data and theoretical analysis, we found a surprising similarity between bacterial motion in dilute colloidal suspensions and polymer solutions, which challenged the established view on the role of polymer dynamics on bacterial speed enhancement. We subsequently developed a physical model that provides a universal mechanism explaining bacterial speed enhancement in complex fluids.

Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar

A no-flux initial-boundary value problem for the doubly degenrate parabolic system ut=∇·(uv∇u)+ℓuv,vt=Δv-uv,(⋆)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\left\\{ \\begin{array}{l} u_t = \ abla \\cdot \\big ( uv\ abla u\\big ) + \\ell uv, \\\\ v_t = \\Delta v - uv, \\end{array} \\right. \\qquad \\qquad (\\star ) \\end{aligned}$$\\end{document}is considered in a smoothly bounded convex domain Omega subset mathbb {R}^n, with nge 1 and ell ge 0. The first of the main results asserts that for nonnegative initial data (u_0,v_0)in (L^infty (Omega ))^2 with u_0not equiv 0, v_0not equiv 0 and sqrt{v_0}in W^{1,2}(Omega ), there exists a global weak solution (u, v) which, inter alia, belongs to C^0(overline{Omega }times (0,infty )) times C^{2,1}(overline{Omega }times (0,infty )) and satisfies sup _{t>0} Vert u(cdot ,t)Vert _{L^p(Omega )}<infty for all pin [1,p_0) with p_0:=frac{n}{(n-2)_+}. It is next seen that for each of these solutions one can find u_infty in bigcap _{pin [1,p_0)} L^p(Omega ) such that, within an appropriate topological setting, (u(cdot ,t),v(cdot ,t)) approaches the equilibrium (u_infty ,0) in the large time limit. Finally, in the case nle 5 a result ensuring a certain stability property of any member in the uncountably large family of steady states (u_0,0), with arbitrary and suitably regular u_0:Omega rightarrow [0,infty ), is derived. This provides some rigorous evidence for the appropriateness of (star ) to model the emergence of a strikingly large variety of stable structures observed in experiments on bacterial motion in nutrient-poor environments. Essential parts of the analysis rely on the use of an apparently novel class of functional inequalities to suitably cope with the doubly degenerate diffusion mechanism in (star ).

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 minireview highlights (i) aspects of swarming motility that differentiate it from other methods of bacterial locomotion, (ii) facilitatory mechanisms deployed by diverse bacteria to overcome different surface challenges, (iii) the (often difficult) approaches required to cultivate genuine swarmers, (iv) the methods available to observe and assess the various facets of this collective motion, and (v) the features exhibited by the population as a whole.

Biocorrosion on Nanofilms Induces Rapid Bacterial Motions via Iron Dissolution.

Stability and reactivity of solid metal or mineral surfaces in contact with bacteria are critical properties for development of biocorrosion protection and for understanding bacteria–solid environmental interactions. Here, we opted to work with nanosheets of iron nanolayers offering arbitrarily large and stable areas of contact that can be simply monitored by optical means. We focused our study on the sediments’ bacteria, the strain Shewanella oneidensis WT MR-1, that served as models for previous research on electroactivity and iron-reduction effects. Data show that a sudden uniform corrosion appeared after an early electroactive period without specific affinities and that iron dissolution induced rapid bacterial motions. By extending the approach to mutant strains and three bacterial species, we established a correlation between corrosion onset and oxygen-depletion combined with iron reduction and demonstrated bacteria’s extraordinary ability to transform their solid environments.

Using Experimentally Calibrated Regularized Stokeslets to Assess Bacterial Flagellar Motility Near a Surface

The presence of a nearby boundary is likely to be important in the life cycle and evolution of motile flagellate bacteria. This has led many authors to employ numerical simulations to model near-surface bacterial motion and compute hydrodynamic boundary effects. A common choice has been the method of images for regularized Stokeslets (MIRS); however, the method requires discretization sizes and regularization parameters that are not specified by any theory. To determine appropriate regularization parameters for given discretization choices in MIRS, we conducted dynamically similar macroscopic experiments and fit the simulations to the data. In the experiments, we measured the torque on cylinders and helices of different wavelengths as they rotated in a viscous fluid at various distances to a boundary. We found that differences between experiments and optimized simulations were less than 5% when using surface discretizations for cylinders and centerline discretizations for helices. Having determined optimal regularization parameters, we used MIRS to simulate an idealized free-swimming bacterium constructed of a cylindrical cell body and a helical flagellum moving near a boundary. We assessed the swimming performance of many bacterial morphologies by computing swimming speed, motor rotation rate, Purcell’s propulsive efficiency, energy cost per swimming distance, and a new metabolic energy cost defined to be the energy cost per body mass per swimming distance. All five measures predicted that the optimal flagellar wavelength is eight times the helical radius independently of body size and surface proximity. Although the measures disagreed on the optimal body size, they all predicted that body size is an important factor in the energy cost of bacterial motility near and far from a surface.

(Invited) Biosensors and Bioanalytical Platforms for in Situ Monitoring of Bacterial Phenotypes

: Bacterial cells are found everywhere and can be both beneficial or harmful to our diverse ecosystem, from plants to animals and humans. As such, studying them to better understand their interactions with the surrounding environment is important from both fundamental and applied perspectives. The existing analytical methods for studying bacterial cells require bulky readout equipment and complex sample preparation, are cell-destructive, or involve excessive sample preparation (1–3) which make real-time and in situ analysis hardly possible. In addition, probing bacterial growth has been traditionally done using colony counting, which is an end-point method and takes at least 24 hours for results.In situ monitoring of bacterial phenotypes (e.g. motion, respiration, adhesion, virulence factors) and how they change in response to environmental perturbation will have a broad impact in food safety, microbial fuels, studying gut-brain interaction, and fighting antibiotic resistance. This talk presents our recent works on developing novel biosensing tools for in situ and non-destructive probing and monitoring of bacterial phenotypes – from electrochemical sensors for reagent-free monitoring of metabolic activity or measuring biofilm virulence factors, to impedimetric sensors to decipher the mechanism of action of new antibiotics or activation of osmoregulatory transporters (4–7), to machine learning-enabled dynamic laser speckle imaging for monitoring bacterial motion (8), and others.

Interpolation Methods Applied on Biomolecules and Condensed Matter Brownian Motion

Biophysical and condensed matter systems connection is of great importance nowadays due to the need for a new approach in microelectronic biodevices, biocomputers or biochips advanced development. Considering that the living and nonliving systems’ submicroparticles are identical, we can establish the biunivocally correspondent relation between these two particle systems, as a biomimetic correlation based on Brownian motion fractal nature similarities, as the integrative property. In our research, we used the experimental results of bacterial motion under the influence of energetic impulses, like music, and also some biomolecule motion data. Our goal is to define the relation between biophysical and physical particle systems, by introducing mathematical analytical forms and applying Brownian motion fractal nature characterization and fractal interpolation. This work is an advanced research in the field of new solutions for high-level microelectronic integrations, which include submicrobiosystems like part of even organic microelectronic considerations, together with some physical systems of particles in solid-state solutions as a nonorganic part. Our research is based on Brownian motion minimal joint properties within the integrated biophysical systems in the wholeness of nature.

Wall-induced translation of a rotating particle in a shear-thinning fluid

Particle–wall interactions have broad biological and technological applications. In particular, some artificial microswimmers capitalize on their translation–rotation coupling near a wall to generate directed propulsion. Emerging biomedical applications of these microswimmers in complex biological fluids prompt questions on the impact of non-Newtonian rheology on their propulsion. In this work, we report some intriguing effects of shear-thinning rheology, a ubiquitous non-Newtonian behaviour of biological fluids, on the translation–rotation coupling of a particle near a wall. One particularly interesting feature revealed here is that the wall-induced translation by rotation can occur in a direction opposite to what might be intuitively expected for an object rolling on a solid substrate. We elucidate the underlying physical mechanism and discuss its implications on the design of micromachines and bacterial motion near walls in complex fluids.

Traveling wave solutions to the density-suppressed motility model

To understand the “self-trapping” mechanism inducing spatio-temporal pattern formations observed in the experiment of [21] for bacterial motion, the following density-suppressed motility model{ut=Δ(γ(v)u)+u(a−bu),vt=Δv+u−v, was proposed in [6,21], where u(x,t) and v(x,t) represent the densities of bacteria and the chemical emitted by the bacteria, respectively; γ(v) is called the motility function satisfying γ′(v)<0 and a,b>0 are positive constants accounting for the growth and death rates of bacterial cells. The analysis of the above system is highly non-trivial due to the cross-diffusion and possible degeneracy resulting from the nonlinear motility function γ(v) and mathematical progresses on the global well-posedness and asymptotics of solutions were just made recently. Among other things, the purpose of this paper is to consider the above system with motility function γ(v)=1(1+v)m(m>0) and investigate the traveling wave solutions which are genuine patterns observed in the experiment of [21]. By introducing an auxiliary parabolic problem to which the comparison principle applies and constructing relaxed super- and sub-solutions with spatially inhomogeneous decay rates, we show that there exist two constants b⁎(m,a) and K(m,a), for b>b⁎(m,a) and K(m,a)<1, the above density-suppressed motility model admits traveling wave solutions (u,v)(x,t)=:(U,V)(x⋅ξ−ct) in RN along the direction ξ∈SN−1 for all wave speed c≥2a connecting the equilibrium (a/b,a/b) to (0,0), while positive traveling wave solutions will not exist if c<2a. As m→0, we have b⁎(m,a)→0 and K(m,a)→0, our results are well consistent with the relevant results for the well-known Fisher-KPP equation (i.e. the first equation of the above system with γ(v)=1). The main novel idea in the analysis of this paper is the construction of super- and sub-solutions with spatially inhomogeneous (i.e. non-constant) decay rates, in contrast to the constant decay rates used in the literature for reaction-diffusion equations, which was developed to cope with the difficulty caused by the density-dependent nonlinear diffusion in the system. We further discuss the selection of wave patterns and wave speeds for given initial value and use numerical simulations to illustrate that both monotone and non-monotone traveling wavefronts exist depending on whether the motility function γ(v) changes its convexity at v=a/b. Two-dimensional simulations demonstrate that the system can generate outward expanding ring (strip) pattern as observed in the experiment.

Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in nutrient-poor environments

The doubly degenerate nutrient taxis model ut=∇⋅(uv∇u)−∇⋅(u2v∇v)+ℓuv,x∈Ω,t>0,vt=Δv−uv,x∈Ω,t>0,is considered in smoothly bounded convex subdomains of the plane, with ℓ≥0. It is shown that for any p>2 and each fixed nonnegative u0∈W1,∞(Ω), a smallness condition exclusively involving v0 can be identified as sufficient to ensure that an associated no-flux type initial–boundary value problem with (u,v)|t=0=(u0,v0) admits a global weak solution satisfying esssupt>0‖u(⋅,t)‖Lp(Ω)<∞. The proof relies on the use of an apparently novel class of functional inequalities which provide estimates from below for certain Dirichlet integrals involving possibly degenerate weight functions.