scholarly journals Stochastic Model for Direction Changes of Swimming Bacteria

2016 ◽  
Author(s):  
G. Fier ◽  
D. Hansmann ◽  
R. C. Buceta
Keyword(s):  
Stochastic Model ◽  
Control Parameter ◽  
Rotational Diffusion ◽  
Steady State Solution ◽  
E Coli ◽  
Isotropic Media ◽  
Swimming Bacteria ◽  
Run And Tumble ◽  
The Green Function ◽  
Centers Of Mass

AbstractIn this work we introduce a stochastic model to describe directional changes in the movement of swimming bacteria. We use the probability density function (PDF) of turn angles, measured on tumbling E. coli wild-type, to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media. We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter. We conclude that the tumble motion, which is manifested as abrupt turns, is primarily caused by the rotational boost generated by the flagellar motor and complementarily by the rotational diffusion introduced by noise. We show that, in the tumble motion, the deflection is a non-stationary stochastic processes during times where the tumble occurs. By tuning the control parameter our model is able to explain small turns of the bacteria around their centers of mass along the run. We show that the deflection during the run is an Ornstein-Uhlenbeck process, which for typical run times is stationary. We conclude that, along the run, the rotational boosts do not exist or are neglectable and that only the rotational diffusion remains. Thus we have a single model to explain the turns of the bacterium during the run or tumble movements, through a control parameter that can be tuned through a critical value that can explain the transition between the two turn behaviours. This model is also able to explain very satisfactory all available statistical experimental data, such as PDFs and average values of turning angles and times, of both run and tumble motions.

scholarly journals New Insights into the Dynamics of Swarming Bacteria: A Theoretical Study

2016 ◽  
Author(s):  
David Hansmann ◽  
Guido Fier ◽  
Rubén C. Buceta
Keyword(s):  
Inelastic Collision ◽  
Theoretical Study ◽  
Rotational Diffusion ◽  
Agar Plate ◽  
Soft Agar ◽  
E Coli ◽  
Swimming Bacteria ◽  
Run And Tumble ◽  
K 12 ◽  
Swarming Behaviour

In the present work we simulate the basic two-dimensional dynamics of swarmingE. colibacteria on the surface of a moderately soft agar plate. Individual bacteria are modelled by self-propelled ridged bodies (agents), which interact with each other only through inelastic collision and with the highly viscous environment through damping forces. The motion of single agents is modelled closely corresponding to the behaviour of swimming bacteria. The dynamics of the model were adjusted to reproduce the experimental measurements of swimmingE. coliK-12. Accordingly, simulations with loosely packed agents (ρ≈0) show typical run-and-tumble statistics. In contrast, simulations with densely packed agents (ρ≈0.3-0.7) are dominated by interactions (collisions) between agents which lead to the emergence of swarming behaviour. In addition, we model the motion of single agents on the base of modified run-and-tumble dynamics, where the bacteria do not turn actively during the tumble. We show that simulations with densely packed modified agents lead as well the emergence of swarming behaviour, if rotational diffusion is considered.

scholarly journals Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

2014 ◽  
Vol 11 (97) ◽  
pp. 20140320 ◽  
Author(s):  
Gabriel Rosser ◽  
Ruth E. Baker ◽  
Judith P. Armitage ◽  
Alexander G. Fletcher
Keyword(s):  
Rhodobacter Sphaeroides ◽  
Computational Algorithm ◽  
Rotational Diffusion ◽  
Particle Model ◽  
Cell Geometry ◽  
Brownian Rotation ◽  
Swimming Bacteria ◽  
Run And Tumble ◽  
Open Question ◽  
Straight Lines

Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly understood reorientation mechanism in the monoflagellate species Rhodobacter sphaeroides . The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. Two further models incorporate stochastic reorientations, describing ‘run-and-tumble’ motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events in R. sphaeroides . This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation.

scholarly journals Modelling and analysis of bacterial tracks suggest an active reorientation mechanism inRhodobacter sphaeroides

2014 ◽  
Author(s):  
Gabriel Rosser ◽  
Ruth E. Baker ◽  
Judith P. Armitage ◽  
Alexander George Fletcher
Keyword(s):  
Computational Algorithm ◽  
Rotational Diffusion ◽  
Particle Model ◽  
Summary Statistics ◽  
Cell Geometry ◽  
Brownian Rotation ◽  
Swimming Bacteria ◽  
Run And Tumble ◽  
Open Question ◽  
Straight Lines

Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly-understood reorientation mechanism in the monoflagellate speciesRhodobacter sphaeroides. The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. A further two models also include stochastic reorientations, describing 'run-and-tumble' motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events inR. sphaeroides. This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation.

scholarly journals Blue light is a universal tactic signal forEscherichia coli

2017 ◽  
Author(s):  
Tatyana Perlova ◽  
Martin Gruebele ◽  
Yann R. Chemla
Keyword(s):  
Blue Light ◽  
Light Exposure ◽  
Biological Significance ◽  
Proton Motive Force ◽  
Motive Force ◽  
Swimming Velocity ◽  
Bacterial Strains ◽  
E Coli ◽  
Before And After ◽  
Swimming Bacteria

AbstractBlue light has been shown to elicit a tumbling response inE. coli, a non-phototrophic bacterium. The exact mechanism of this phototactic response is still unknown, and its biological significance remains unclear. Here, we quantify phototaxis inE. coliby analyzing single-cell trajectories in populations of free-swimming bacteria before and after light exposure. Bacterial strains expressing only one type of chemoreceptor reveal that all fiveE. colireceptors - Aer, Tar, Tsr, Tap and Trg - are capable of mediating a response to light. In particular, light exposure elicits a running response in Tap-only strain, the opposite of the tumbling response observed for all other strains. Light therefore emerges as a universal stimulus for allE. colichemoreceptors. We also show that blue light exposure causes a reversible decrease in swimming velocity, a proxy for proton motive force. We hypothesize that rather than sensing light directly, chemoreceptors sense light-induced perturbations in proton motive force.ImportanceOur findings provide new insights on the mechanism ofE. coliphototaxis, showing that all five chemoreceptor types respond to light and that their interactions play an important role in cell behavior. Our results also open up new avenues for examining and manipulatingE. colitaxis. Since light is a universal stimulus, it may provide a way to quantify interactions between different types of receptors. Since light is easier to control spatially and temporally than chemicals, it may be used to study swimming behavior in complex environments. Since phototaxis can cause migration ofE. colibacteria in light gradients, light may be used to control bacterial density for studying density-dependent processes in bacteria.

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

Soft Matter ◽  
2018 ◽  
Vol 14 (19) ◽  
pp. 3945-3954 ◽  
Author(s):  
G. Fier ◽  
D. Hansmann ◽  
R. C. Buceta
Keyword(s):  
Langevin Equations ◽  
Turning Angle ◽  
Change Of Direction ◽  
Swimming Bacteria ◽  
Run And Tumble

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.

scholarly journals Blue Light Is a Universal Signal forEscherichia coliChemoreceptors

2019 ◽  
Vol 201 (11) ◽  
Author(s):  
Tatyana Perlova ◽  
Martin Gruebele ◽  
Yann R. Chemla
Keyword(s):  
Blue Light ◽  
Light Exposure ◽  
Proton Motive Force ◽  
Motive Force ◽  
Swimming Velocity ◽  
Bacterial Strains ◽  
Content Type ◽  
E Coli ◽  
Before And After ◽  
Swimming Bacteria

ABSTRACTBlue light has been shown to elicit a tumbling response inEscherichia coli, a nonphototrophic bacterium. The exact mechanism of this phototactic response is still unknown. Here, we quantify phototaxis inE. coliby analyzing single-cell trajectories in populations of free-swimming bacteria before and after light exposure. Bacterial strains expressing only one type of chemoreceptor reveal that all fiveE. colireceptors (Aer, Tar, Tsr, Tap, and Trg) are capable of mediating responses to light. In particular, light exposure elicits a running response in the Tap-only strain, the opposite of the tumbling responses observed for all other strains. Therefore, light emerges as a universal stimulus for allE. colichemoreceptors. We also show that blue light exposure causes a reversible decrease in swimming velocity, a proxy for proton motive force. This result is consistent with a previously proposed hypothesis that, rather than sensing light directly, chemoreceptors sense light-induced perturbations in proton motive force, although other factors are also likely to contribute.IMPORTANCEOur findings provide new insights into the mechanism ofE. coliphototaxis, showing that all five chemoreceptor types respond to light and their interactions play an important role in cell behavior. Our results also open up new avenues for examining and manipulatingE. colitaxis. Since light is a universal stimulus, it may provide a way to quantify interactions among different types of receptors. Because light is easier to control spatially and temporally than chemicals, it may be used to study swimming behavior in complex environments. Since phototaxis can cause migration ofE. colibacteria in light gradients, light may be used to control bacterial density for studying density-dependent processes in bacteria.

scholarly journals Silver Ions Affect the Motility of E. coli by Disrupting the Markovian Run-and-tumble Process

2020 ◽  
Vol 118 (3) ◽  
pp. 126a
Author(s):  
Benjamin P. Russell ◽  
Yong Wang
Keyword(s):  
Silver Ions ◽  
E Coli ◽  
Run And Tumble

scholarly journals Stabiizing The Steady State Solution of Lasser Fever: Problems and Prospect

2022 ◽  
Vol 05 (01) ◽  
Author(s):  
Innocent C. Eli ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Control Parameter ◽  
Steady State Solution ◽  
Lassa Fever ◽  
Sexual Contact ◽  
Opposite Sex ◽  
The Stability ◽  
And Control ◽  
Disease Free

The study of mathematical modeling of the stability analysis of Lassa fever was examined. A mathematical model for the spread and control of Lassa fever was formulated and analyzed. The model incorporates a control parameter, the use of condom to control human to human transmission through sexual contact with opposite sex. The disease free and endemic equilibrium states were analyzed.

Critical bacterial concentration for the onset of collective swimming

2009 ◽  
Vol 632 ◽  
pp. 359-400 ◽  
Author(s):  
GANESH SUBRAMANIAN ◽  
DONALD L. KOCH
Keyword(s):  
Stability Analysis ◽  
Threshold Concentration ◽  
Swimming Velocity ◽  
Bacterial Number ◽  
Bacterial Concentration ◽  
E Coli ◽  
Weakly Interacting ◽  
Swimming Bacteria ◽  
Dilute Suspension ◽  
The Stability

We examine the stability of a suspension of swimming bacteria in a Newtonian medium. The bacteria execute a run-and-tumble motion, runs being periods when a bacterium on average swims in a given direction; runs are interrupted by tumbles, leading to an abrupt, albeit correlated, change in the swimming direction. An instability is predicted to occur in a suspension of ‘pushers’ (e.g.E. Coli,Bacillus subtilis, etc.), and owes its origin to the intrinsic force dipoles of such bacteria. Unlike the dipole induced in an inextensible fibre subject to an axial straining flow, the forces constituting the dipole of a pusher are directed outward along its axis. As a result, the anisotropy in the orientation distribution of bacteria due to an imposed velocity perturbation drives a disturbance velocity field that acts to reinforce the perturbation. For long wavelengths, the resulting destabilizing bacterial stress is Newtonian but with a negative viscosity. The suspension becomes unstable when the total viscosity becomes negative. In the dilute limit (nL3≪ 1), a linear stability analysis gives the threshold concentration for instability as (nL3)crit= ((30/Cℱ(r))(DrL/U)(1 + 1/(6τDr)))/(1−(15𝒢(r)/Cℱ(r))(DrL/U)(1 + 1/(6τDr))) for perfectly random tumbles; here,LandUare the length and swimming velocity of a bacterium,nis the bacterial number density,Drcharacterizes the rotary diffusion during a run and τ−1is the average tumbling frequency. The function ℱ(r) characterizes the rotation of a bacterium of aspect ratiorin an imposed linear flow; ℱ(r) = (r2−1)/(r2+ 1) for a spheroid, and ℱ(r) ≈ 1 for a slender bacterium (r≫ 1). The function 𝒢(r) characterizes the stabilizing viscous response arising from the resistance of a bacterium to a deforming ambient flow; 𝒢(r) = 5π/6 for a rigid spherical bacterium, and 𝒢(r)≈ π/45(lnr) for a slender bacterium. Finally, the constantCdenotes the dimensionless strength of the bacterial force dipole in units of μU L2; forE. Coli,C≈ 0.57. The threshold concentration diverges in the limit ((15𝒢(r)/Cℱ(r)) (DrL/U)(1 + 1/(6τDr))) → 1. This limit defines a critical swimming speed,Ucrit= (DrL)(15𝒢(r)/Cℱ(r))(1 + 1/(6τDr)). For speeds smaller than this critical value, the destabilizing bacterial stress remains subdominant and a dilute suspension of these swimmers therefore responds to long-wavelength perturbations in a manner similar to a suspension of passive rigid particles, that is, with a net enhancement in viscosity proportional to the bacterial concentration.On the other hand, the stability analysis predicts that the above threshold concentration reduces to zero in the limitDr→ 0, τ → ∞, and a suspension of non-interacting straight swimmers is therefore always unstable. It is then argued that the dominant effect of hydrodynamic interactions in a dilute suspension of such swimmers is via an interaction-driven orientation decorrelation mechanism. The latter arises from uncorrelated pair interactions in the limitnL3≪ 1, and for slender bacteria in particular, it takes the form of a hydrodynamic rotary diffusivity (Dhr); forE. Coli, we findDhr= 9.4 × 10−5(nUL2). From the above expression for the threshold concentration, it may be shown that even a weakly interacting suspension of slender smooth-swimming bacteria (r≫ 1, ℱ(r) ≈ 1, τ → ∞) will be stable providedDhr> (C/30)(nUL2) in the limitnL3≪ 1. The hydrodynamic rotary diffusivity ofE. Coliis, however, too small to stabilize a dilute suspension of these swimmers, and a weakly interacting suspension ofE. Coliremains unstable.

scholarly journals Self-regulating genes. Exact steady state solution by using Poisson representation

Open Physics ◽  
2014 ◽  
Vol 12 (9) ◽  
Author(s):  
István Sugár ◽  
István Simon
Keyword(s):  
Steady State ◽  
Cell Biology ◽  
Regulatory Networks ◽  
Steady State Solution ◽  
E Coli ◽  
Feedback Model ◽  
Quantitative Understanding ◽  
Poisson Representation ◽  
And Behavior ◽  
Steady State Solutions

AbstractSystems biology studies the structure and behavior of complex gene regulatory networks. One of its aims is to develop a quantitative understanding of the modular components that constitute such networks. The self-regulating gene is a type of auto regulatory genetic modules which appears in over 40% of known transcription factors in E. coli. In this work, using the technique of Poisson Representation, we are able to provide exact steady state solutions for this feedback model. By using the methods of synthetic biology (P.E.M. Purnick and Weiss, R., Nature Reviews, Molecular Cell Biology, 2009, 10: 410–422) one can build the system itself from modules like this.

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