Run and Tumble Chemotaxis in a Shear Flow: The Effect of Temporal Comparisons, Persistence, Rotational Diffusion, and Cell Shape

2009 ◽  
Vol 71 (5) ◽  
pp. 1089-1116 ◽  
Author(s):  
J. T. Locsei ◽  
T. J. Pedley
Keyword(s):  
Shear Flow ◽  
Cell Shape ◽  
Rotational Diffusion ◽  
Run And Tumble

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.

Modelling Run-and-Tumble Chemotaxis in a Shear Flow

2000 ◽  
Vol 62 (4) ◽  
pp. 775-791 ◽  
Author(s):  
R Bearon
Keyword(s):  
Shear Flow ◽  
Run And Tumble

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.

Orientational Ordering of Rigid Rod Polymers in Shear Flow

1992 ◽  
Vol 289 ◽  
Author(s):  
B.E. Vugmeister ◽  
C. Wang ◽  
H.D. Ou-Yang
Keyword(s):  
Shear Flow ◽  
Order Parameter ◽  
Theoretical Study ◽  
Volume Fraction ◽  
Rotational Diffusion ◽  
Effective Interaction ◽  
Orientational Order ◽  
Flow Shear ◽  
Rigid Rod ◽  
Orientational Ordering

AbstractWe present the results of experimental and theoretical study of the orientational ordering of rigid rod like polymers in the presence of shear flow. Shear induced birefringence was measured to determine the dependence of orientational order parameter S=<3cos2θ−l>/2 on the shear rate at different values of the volume fraction. Experimental results are discussed in terms of an approximate solution of the rotational diffusion equation in the presence of shear flow based on the construction of the effective interaction energy.

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 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.

The effect of shear flow on the rotational diffusion of a single axisymmetric particle

2015 ◽  
Vol 772 ◽  
pp. 42-79 ◽  
Author(s):  
Brian D. Leahy ◽  
Donald L. Koch ◽  
Itai Cohen
Keyword(s):  
Aspect Ratio ◽  
Shear Flow ◽  
Intrinsic Viscosity ◽  
Strain Amplitude ◽  
Rotational Diffusion ◽  
Oscillatory Shear ◽  
Time Dependent ◽  
Continuous Shear ◽  
Orientation Distributions ◽  
Particle Aspect Ratio

Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion: $D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$, where $p$ is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio $p$, as $1/D_{0}^{r}p^{4}$ and as $1/D_{0}^{r}p^{2}$ for $p\gg 1$. For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of ${\approx}2$ and the rotational diffusion by a factor of ${\approx}40$.

Effect of rotational diffusion of anisotropic particles on the stability of a suspension shear flow

2019 ◽  
Vol 51 (3) ◽  
pp. 035507
Author(s):  
Zhanhong Wan ◽  
Kun Zhou ◽  
Wei Yang ◽  
Zhenjiang You ◽  
Ke Sun
Keyword(s):  
Shear Flow ◽  
Rotational Diffusion ◽  
Anisotropic Particles ◽  
The Stability

Deformation of liquid capsules with incompressible interfaces in simple shear flow

1995 ◽  
Vol 283 ◽  
pp. 175-200 ◽  
Author(s):  
Hua Zhou ◽  
C. Pozrikidis
Keyword(s):  
Shear Flow ◽  
Blood Cell ◽  
Simple Shear ◽  
Red Blood Cell ◽  
Cell Shape ◽  
Maximum Shear Stress ◽  
Three Dimensional ◽  
Spectral Projection ◽  
Simple Shear Flow ◽  
Membrane Tension

The transient deformation of liquid capsules enclosed by incompressible membranes whose mechanical properties are dominated by isotropic tension is studied as a model of red blood cell deformation in simple shear flow. The problem is formulated in terms of an integral equation for the distribution of the tension over the cell membrane which is solved using a point-wise collocation and a spectral-projection method. The computations illustrate the dependence of the deformed steady cell shape, membrane tank-treading frequency, membrane tension, and rheological properties of a dilute suspension, on the undeformed cell shape. The general features of the evolution of two-dimensional cells are found to be similar to those of three-dimensional cells, and the corresponding membrane tank-treading frequency and maximum tension are seen to attain comparable values. The numerical results are compared with previous asymptotic analyses for small deformations and available experimental observations, with satisfactory agreement. An estimate of the maximum shear stress for membrane breakup and red blood cell hemolysis is deduced on the basis of the computed maximum membrane tension at steady state.

Modulated polarization microscopy displays the dynamics of cytoskeletal structures in living, motile cells

1995 ◽  
Vol 53 ◽  
pp. 902-903
Author(s):  
J. R. Kuhn ◽  
M. Poenie
Keyword(s):  
Mitotic Spindle ◽  
Actin Filaments ◽  
Cell Shape ◽  
Dynamic Structure ◽  
Living Cells ◽  
Cytoskeletal Proteins ◽  
Polarization Microscopy ◽  
Video Enhancement ◽  
Ultrastructural Studies ◽  
Motile Cells

Cell shape and movement are controlled by elements of the cytoskeleton including actin filaments an microtubules. Unfortunately, it is difficult to visualize the cytoskeleton in living cells and hence follow it dynamics. Immunofluorescence and ultrastructural studies of fixed cells while providing clear images of the cytoskeleton, give only a static picture of this dynamic structure. Microinjection of fluorescently Is beled cytoskeletal proteins has proved useful as a way to follow some cytoskeletal events, but long terry studies are generally limited by the bleaching of fluorophores and presence of unassembled monomers.Polarization microscopy has the potential for visualizing the cytoskeleton. Although at present, it ha mainly been used for visualizing the mitotic spindle. Polarization microscopy is attractive in that it pro vides a way to selectively image structures such as cytoskeletal filaments that are birefringent. By combing ing standard polarization microscopy with video enhancement techniques it has been possible to image single filaments. In this case, however, filament intensity depends on the orientation of the polarizer and analyzer with respect to the specimen.

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