Turning Angle Distribution Research Articles

Simple model of cytoskeletal fluctuations

The spontaneous motion of microbeads bound to the cytoskeleton of living cells is not an ordinary random walk. Unlike Brownian motion, the mean-square displacement undergoes a transition from subdiffusive to superdiffusive behavior with time. This transition is associated with characteristic changes of the turning angle distribution. Recent experimental data demonstrated that force fluctuations measured in an elastic hydrogel matrix beneath the cell correlate with the bead motion [C. Raupach, Phys. Rev. E 76, 011918 (2007)]. These data indicate that the bead trajectory is driven by motor forces originating from the actomyosin network and that cytoskeletal remodeling processes with short- and long-time dynamics are mainly responsible for the non-Brownian behavior. We show that the essential statistical properties of the spontaneous bead motion can be reproduced by a particle diffusing in a potential well with a slowly drifting minimum position. Based on this simple model, which can be solved analytically, we develop a biologically plausible numerical model of a tensed and continuously remodeling actomyosin network that accounts quantitatively for the measured data.

Advantages of hopping on a zig-zag course

We investigate self-moving particles which prefer to hop with a certain turning angle equally distributed to the right or left. We assume this turning angle distribution to be given by a double Gaussian distribution. Based on the model of Active Brownian particles and we calculate the diffusion coefficient in dependence on the mean and the dispersion of the turning angles. It is shown that bounded distribution of food in patches will be optimally consumed by the objects if they hop preferably with a given angle and not straight forwardly.

A model of animal movements in a bounded space

Most studies describing animal movements have been developed in the framework of population dispersion or population dynamics, and have mainly focused on movements in open spaces. During their trips, however, animals are likely to encounter physical heterogeneities that guide their movements and, as a result, influence their spatial distribution. In this paper, we develop a statistical model of individual movement in a bounded space. We introduced cockroaches in a circular arena and quantified accurately the behaviors underlying their movement in a finite space. Close to the edges, we considered that the animals exhibit a linear movement mode with a constant probability per unit time to leave the edge and enter the central zone of the arena. Far from the walls cockroaches were assumed to move according to a diffusive random walk which enabled us to overcome the inherent problem of the quantification of the turning angle distribution. A numerical model implementing the behavioral rules derived from our experiments, confirms that the pattern of the spatial distribution of animals observed can be reliably accounted for by wall-following behaviors combined with a diffusive random walk. The approach developed in this study can be applied to model the movements of animals in various environment under consideration of spatial structure.

Chaos and fractals in fish school motion, II

It is shown that the turning angle distribution of a modelled moving fish school affects the fractal properties of the school trajectories. The multifractal spectrum is shifted to higher Hölder exponents.

Modelling animal movement as a persistent random walk in two dimensions: expected magnitude of net displacement

We present semi-empirical model of persistent random walk for studying animal movements in two-dimensions. The model incorporates an arbitrary distribution for the angles between successive steps in the tracks. Inclusion of a turning angle distribution enables explicit computation of the effect of persistence in the direction of travel on the expected magnitude of net displacement of the animal over time. We employed a form-analogous approach to obtain expressions for the expected net displacement and derived root mean square of the expected displacement of an animal at the end of a multi-step random walk in which turning angles were drawn from the Lemicon of Pascal, the elliptical, the von Mises, and the wrapped Cauchy distributions. The accuracy of these expressions for the expected magnitude of net displacement was tested by comparison with simulated results of persistent random walks where turning angles were drawn form the wrapped Cauchy distribution. Our results should be useful in predicting two-dimensional distribution of moving animals for which frequency distributions of the turning angles can be measured.

Temperature-sensitive motility of Sulfolobus acidocaldarius influences population distribution in extreme environments.

A three-dimensional tracking microscope was used to quantify the effects of temperature (50 to 80 degrees C) and pH (2 to 4) on the motility of Sulfolobus acidocaldarius, a thermoacidophilic archaeon. Swimming speed and run time increased with temperature but remained relatively unchanged with increasing pH. These results were consistent with reported changes in the rate of respiration of S. acidocaldarius as a function of temperature and pH. Cells exhibited a forward-biased turn angle distribution with a mean of 54 degrees. Cell trajectories during a run were in the shape of right-handed helices. A cellular dynamics simulation was used to test the hypothesis that a population of S. acidocaldarius cells could distribute preferentially in a spatial temperature gradient due to variation in swimming speed. Simulation results showed that a population of cells could migrate from a higher to a lower temperature in the presence of sharp temperature gradients. This simulation result was achieved without incorporating the ability of cells to sense a temporal thermal gradient; thus, the response was not thermotactic. We postulate that this temperature-sensitive motility is one survival mechanism of S. acidocaldarius that allows this organism to move away from lethal hot spots in its hydrothermal environment.

Turn angle and run time distributions characterize swimming behavior for Pseudomonas putida.

The swimming behavior of Pseudomonas putida was analyzed with a tracking microscope to quantify its run time and turn angle distributions. Monte Carlo computer simulations illustrated that the bimodal turn angle distribution of P. putida reduced collisions with obstacles in porous media in comparison to the unimodal distribution of Escherichia coli.

Scaling relationships for anisotropic random walks

Aspects of transport in a highly multiple-scattering environment are investigated by examining random walkers moving in media having anisotropic angular scattering cross sections (turn-angle distributions). A general expression is obtained for the mean square displacement 〈x2〉 of a random walker executing ann-step walk in an infinite homogeneous material, and results are used to predict scaling relations for the probabilityγ(ρ) that a walker returns to the planar surface of a semi-infinite medium at a distanceρ from the point of its insertion.

A numerical study of incompressible Navier-Stokes flow through rectilinear and radial cascade of turbine blades

A numerical study is conducted to analyse the two-dimensional incompressible Navier-Stokes flows through the rectilinear and radial cascade of turbine blades. The flows are turbulent and their characteristics are relevant to those of the hydraulic turbines. For the rectilinear cascade, calculations have been made for a NACA 80 series turbine blade with various angles of attack. The outflow turning angle, force coefficients and static pressure distribution have been compared between the prediction and measurement with satisfactory agreements being obtained. The implications of flow turning angles on the total pressure loss are also discussed. The effects of grid distribution on the numerical predictions are also observed.

Biased random walk models for chemotaxis and related diffusion approximations.

Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distribution are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.

Chemotropism indices for polymorphonuclear leukocytes

Trajectories of polymorphonuclear leukocytes which are responding to a chemical gradient are analyzed in order to deduce probability distributions of the angles between successive path segments. The turn angle probability distributions thus obtained are seen to be strongly dependent on the direction of locomotion prior to a turn, in that cells usually turn to maintain alignment along an axis directed towards the chemoattractant source. A mathematical model based on these observations is developed in order to understand the relationship between net chemotactic response and parameters characterizing stochastic movements of individual cells. In particular, the manner in which the chemotropism index depends on details of the turn-angle distributions is examined. When bias in the direction of turn is induced by a chemotactic field, transition from random motion to directed response occurs most abruptly if the turn-angle distribution is narrow. "Accommodation," viz., a dependence of the mean angle of turn upon prior orientation, is found to have relatively little effect on the magnitude of the response.

A generalized Pearson random walk allowing for bias

We calculate asymptotic values of the first two moments of a planar walk in which the step lengths depend on the direction of motion. The model is suggested by experiments on the locomotion of biological cells. Internally induced persistence due to nonuniform turn angle distributions is also accounted for.