Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by the non-Markovian version of the Langevin equation that includes an arbitrary memory function. When averaged over cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterized by Gaussian velocity distributions. Accordingly, the data are described by a linear memory model which includes different random walk models that were previously used to account for various aspects of cell motility such as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memory function is extracted from the trajectory data without restrictions or assumptions, thus making our approach truly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayed single-exponential negative friction, which clearly distinguishes cell motion from the simple persistent random walk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extracted memory function we formulate a generalized exactly solvable cell migration model which indicates that negative friction generates cell persistence over long timescales. The nonequilibrium character of cell motion is investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model that involves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process.

The dielectric constant and the viscosity of water at the interface of hydrophilic surfaces differ from their bulk values, and it has been proposed that the deviation is caused by the strong electric field and the high ion concentration in the interfacial layer. We calculate the dependence of the dielectric constant and the viscosity of bulk electrolytes on the electric field and the salt concentration. Incorporating the concentration and field-dependent dielectric constant and viscosity in the extended Poisson–Boltzmann and Stokes equations, we calculate the electro-osmotic mobility. We compare the results to literature experimental data and explicit molecular dynamics simulations of OH-terminated surfaces and show that it is necessary to additionally include the presence of a subnanometer wide interfacial water layer, the properties of which are drastically transformed by the sheer presence of the interface. We conclude that the origin of the anomalous behavior of aqueous interfacial layers cannot be found in electrostriction or electroviscous effects caused by the interfacial electric field and ion concentration. Instead, it is primarily caused by the intrinsic ordering and orientation of the interfacial water layer.

Abstract. We investigate the mean-square displacement (MSD) for random motion governed by the generalized Langevin equation for memory functions that contain two different time scales: In the first model, the memory kernel consists of a delta peak and a single-exponential and in the second model of the sum of two exponentials. In particular, we investigate the scenario where the long-time exponential kernel contribution is negative. The competition between positive and negative friction memory contributions produces an enhanced transient persistent regime in the MSD, which is relevant for biological motility and active matter systems. Graphical abstract