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 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 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.

Energetics of Shuttle Runs: The Effects of Distance and Change of Direction

2014 ◽  
Vol 9 (6) ◽  
pp. 1033-1039 ◽  
Author(s):  
Paola Zamparo ◽  
Ivan Zadro ◽  
Stefano Lazzer ◽  
Marco Beato ◽  
Luigino Sepulcri
Keyword(s):  
Oxygen Uptake ◽  
Energy Cost ◽  
Physiological Responses ◽  
Minor Role ◽  
Basketball Players ◽  
Turning Angle ◽  
Change Of Direction ◽  
Maximal Speed ◽  
A Minor ◽  
The Relationship

Shuttle runs can be used to study the physiological responses in sports (such as basketball) characterized by sprints (accelerations/decelerations) and changes of direction.Purpose:To determine the energy cost (C) of shuttle runs with different turning angles and over different distances (with different acceleration/deceleration patterns).Methods:Nine basketball players were asked to complete 6 intermittent tests over different distances (5, 10, 25 m) and with different changes of direction (180° at 5 and 25 m; 0°, 45°, 90°, and 180° at 10 m) at maximal speed (v ≍ 4.5 m/s), each composed by 10 shuttle runs of 10-s duration and 30-s recovery; during these runs oxygen uptake (VO2), blood lactate (Lab), and C were determined.Results:For a given shuttle distance (10 m) no major differences where observed in VO2 (~33 mL · min−1 · kg−1), Lab (~3.75 mM), and C (~21.2 J · m−1 · kg−1) when the shuttle runs were performed with different turning angles. For a given turning angle (180°), VO2 and Lab were found to increase with the distance covered (VO2 from 26 to 35 mL · min−1 · kg−1; Lab from 0.7 to 7.6 mM) while C was found to decrease with it (from 29.9 to 10.6 J · m−1 · kg−1); the relationship between C and d (m) is well described by C = 92.99 × d0.656, R2 = .971.Conclusions:The metabolic demands of shuttle tests run at maximal speeds can be estimated based on the running distance, while the turning angle plays a minor role in determining C.

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.

Stochastic Models of Particle Trajectories in Turbulent Atmosphere Flows by Using the LANGEVIN Equations

Proceedings ◽  
2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Youssra El Qasemy ◽  
Abdelfatah Achahbar ◽  
Abdellatif Khamlichi
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Classical Method ◽  
Degradation Mechanism ◽  
Transformation Process ◽  
Langevin Equations ◽  
Turbulence Data ◽  
Power Curves ◽  
And Diffusion ◽  
Fluctuating Wind

The stochastic behavior of wind speed is a particular characteristic of wind energy production, which affects the degradation mechanism of the turbine, resulting in stochastic charging on the wind turbine. A model stochastic is used in this study to evaluate the efficiency of wind turbine power of whatever degree given fluctuating wind turbulence data. This model is based on the Langevin equations, which characterize, by two coefficients, drift and diffusion functions. These coefficients describe the behavior of the transformation process from the input wind speed to the output data that need to be determined. For this present work, the computation of drift and diffusion functions has been carried out by using the stochastic model to assess the output variables in terms of the torque and power curves as a function of time, and it is compared by the classical method. The results show that the model stochastic can define the efficiency of wind turbine generation more precisely.

scholarly journals Greater Power but Not Strength Gains Using Flywheel Versus Equivolumed Traditional Strength Training in Junior Basketball Players

2021 ◽  
Vol 18 (3) ◽  
pp. 1181
Author(s):  
Marko D. M. Stojanović ◽  
Mladen Mikić ◽  
Patrik Drid ◽  
Julio Calleja-González ◽  
Nebojša Maksimović ◽  
...  
Keyword(s):  
Strength Training ◽  
Training Group ◽  
T Test ◽  
Control Group ◽  
Basketball Players ◽  
Significant Group ◽  
Sprint Time ◽  
Change Of Direction ◽  
Time Interaction ◽  
And Control

The main aim of the present study was to compare the effects of flywheel strength training and traditional strength training on fitness attributes. Thirty-six well trained junior basketball players (n = 36; 17.58 ± 0.50 years) were recruited and randomly allocated into: Flywheel group (FST; n = 12), traditional strength training group (TST; n = 12) and control group (CON; n = 12). All groups attended 5 basketball practices and one official match a week during the study period. Experimental groups additionally participated in the eight-week, 1–2 d/w equivolume intervention conducted using a flywheel device (inertia = 0.075 kg·m−2) for FST or free weights (80%1 RM) for TST. Pre-to post changes in lower limb isometric strength (ISOMET), 5 and 20 m sprint time (SPR5m and SPR20m), countermovement jump height (CMJ) and change of direction ability (t-test) were assessed with analyses of variance (3 × 2 ANOVA). Significant group-by-time interaction was found for ISOMET (F = 6.40; p = 0.000), CMJ (F = 7.45; p = 0.001), SPR5m (F = 7.45; p = 0.010) and T test (F = 10.46; p = 0.000). The results showed a significantly higher improvement in CMJ (p = 0.006; 11.7% vs. 6.8%), SPR5m (p = 0.001; 10.3% vs. 5.9%) and t-test (p = 0.045; 2.4% vs. 1.5%) for FST compared to the TST group. Simultaneously, th FST group had higher improvement in ISOMET (p = 0.014; 18.7% vs. 2.9%), CMJ (p = 0.000; 11.7% vs. 0.3%), SPR5m (p = 0.000; 10.3% vs. 3.4%) and t-test (p = 0.000; 2.4% vs. 0.6%) compared to the CON group. Players from the TST group showed better results in CMJ (p = 0.006; 6.8% vs. 0.3%) and t-test (p = 0.018; 1.5% vs. 0.6%) compared to players from the CON group. No significant group-by-time interaction was found for sprint 20 m (F = 2.52; p = 0.088). Eight weeks of flywheel training (1–2 sessions per week) performed at maximum concentric intensity induces superior improvements in CMJ, 5 m sprint time and change of direction ability than equivolumed traditional weight training in well trained junior basketball players. Accordingly, coaches and trainers could be advised to use flywheel training for developing power related performance attributes in young basketball players.

scholarly journals Analyzing the Magnitude of Interlimb Asymmetries in Young Female Soccer Players: A Preliminary Study

2021 ◽  
Vol 18 (2) ◽  
pp. 475
Author(s):  
Javier Raya-González ◽  
Filipe Manuel Clemente ◽  
Daniel Castillo
Keyword(s):  
Range Of Motion ◽  
Muscle Mass ◽  
Injury Risk ◽  
Young Female ◽  
Asymmetry Index ◽  
Lower Limbs ◽  
Soccer Players ◽  
Countermovement Jump ◽  
Change Of Direction ◽  
Jump Ability

Although asymmetries in lower limbs have been linked with players’ performance in male soccer players, literature that has been published addressing female soccer is scarce. Thus, the aim of this study was twofold: (i) describe the asymmetries of women soccer players during jumping, change-of-direction and range-of-motion tests; and (ii) test possible relationships between asymmetries and injury risk in female soccer players. Sixteen female players (15.5 ± 1.5 years) performed a battery of fitness tests (i.e., jump ability, change-of-direction ability and passive range-of-motion) and muscle mass analysis via dual-energy X-ray absorptiometry, through which the specific asymmetry index and the related injury risk were calculated. Significant (p < 0.05) lower asymmetries in the change-of-direction test were observed in comparison to those observed in jumping and range-of-motion tests; significant (p < 0.05) lower asymmetries in muscle mass were also reported compared to those found in the change-of-direction and countermovement jump tests. Additionally, increased injury risk for countermovement jump and hip flexion with extended knee range-of-motion (relating to asymmetry values) and for ankle flexion with flexed knee range-of-motion in both legs (relating to reference range-of-motion values), as well as increased individual injury risk values, were observed across all tests. These findings suggest the necessity to implement individual approaches for asymmetry and injury risk analyses.

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