Derivation of persistent time for anisotropic migration of cells

Abstract

Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in which two different and independent persistent times are assumed for cell migrations in the xand y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function (VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.

Glycopolymer Engineering of the Cell Surface Changes the Single Cell Migratory Direction and Inhibits the Collective Migration of Cancer Cells

“…A value of β > 1 suggests that the cells undergo directional diffusion to some extent. 27 As seen in Figure 2g, the diffusive exponent β decreased from ∼1.35 to ∼1.1 for modified cells compared to unmodified cells, clearly indicating a lesser extent of directional diffusion of the modified cells. In summary, the migratory direction of the cells was changed after modification, and the capacity of the modified cells for directional diffusion motion was reduced.…”

“…Power law fits of these data, where MSD ∼ t β , were performed and the diffusive exponents, β, were estimated. A value of β > 1 suggests that the cells undergo directional diffusion to some extent . As seen in Figure g, the diffusive exponent β decreased from ∼1.35 to ∼1.1 for modified cells compared to unmodified cells, clearly indicating a lesser extent of directional diffusion of the modified cells.…”

Influence of matrix-metalloproteinase inhibitor on the interaction between cancer cells and matrigel*

“…The variation of MSD with time is usually presented in log-log plots: a line with the slope equal to one indicates the migration of cells is random; the larger the slope is, the more persistent the migration is. [24,25] 3.1. Influences of MMP inhibitor and DMSO in the presence of matrigel…”

Shannon entropy for time-varying persistence of cell migration

“…In studying cell behaviors in complex microenvironment, how to efficiently and accurately quantify cell migration capability has become a crucial issue. Thus, a number of works have been implemented to derive some estimators that can characterize cell migration capability [30,31]. For instance, the diffusion coefficient of one cell can be obtained from a time-lapse recorded trajectory by developing optimal methods [32,33].…”