Randomly curved runs interrupted by tumbling: A model for bacterial motion

Abstract

Small bacteria are strongly buffeted by Brownian forces that make completely straight runs impossible. A model for bacterial motion is formulated in which the effects of fluctuational forces and torques on the run phase are taken into account by using coupled Langevin equations. An integrated description of the motion, including runs and tumbles, is then obtained by the use of convolution and Laplace transforms. The properties of the velocity-velocity correlation function, of the mean displacement, and of the two relevant diffusion coefficients are examined in terms of the bacterial sizes and of the magnitude of the propelling forces. For bacteria smaller than E. coli, the integrated diffusion coefficient crosses over from a jump-dominated to a rotational-diffusion-dominated form.

Active Brownian particles

“…(65). We note that D ϕ is not necessarily small: For the RayleighHelmholtz model (42) with α 2 /β ≫ D the value of v 0 is of the order α/β and D ϕ ≃ Dβ/α can be rather large for moderate values of α.…”

“…As a consequence the first variant of the friction function is symmetric with respect to v = 0 (apolar): there is no front or back for an active particle -the particle moves always to the "front". Related equations of motion with constant propulsion and linear friction have been used for example in the description of bacterial motion [72,65].…”

Influence of swimming strategy on microorganism separation by asymmetric obstacles

“…During the run mode, the flagella rotate counterclockwise and the microorganism moves in a forward, relatively straight direction, whereas during the tumble mode, one or more flagella rotate clockwise and the bacterium is reoriented towards a new direction [19,20]. In the case of the paradigmatic bacterium Escherichia coli, the dynamics of its wild type and two mutants has been previously studied by Berg and Brown [21] using a three-dimensional tracking microscope.…”

Quantifying the sorting efficiency of self-propelled run-and-tumble swimmers by geometrical ratchets

“…[14,15]. Various aspects of the microorganism dynamics have been the subject of recent studies [16][17][18][19][20][21][22][23].…”