Cell motility as random motion: A review

Abstract

Abstract. The historical co-evolution of biological motility models with models of Brownian motion is outlined. Recent results for how to derive cell-type-specific motility models from experimental cell trajectories are reviewed. Experimental work in progress, which tests the generality of this phenomenological model building is reported. So is theoretical work in progress, which explains the characteristic time scales and correlations of phenomenological models in terms of the dynamics of cytoskeleton, lamellipodia, and pseudopodia.1 The co-evolution of theories for Brownian and biological random motion Robert Brown did not discover Brownian motion.

Active Brownian particles

“…A prominent example is the work of Howard C. Berg [31], who made random walk theory an intrinsic part of modeling; new concepts along these lines are developed even nowadays [229,102]. From the huge literature, we would like to highlight here few examples, such as the work by H. Gruler and M. Schienbein [300], by H. Othmer and coworkers [252,160] or the recent integrated theoretical and experimental approach by H. Flyvberg and collaborators [314,313].…”

“…This active fluctuations are a pure far-from equilibrium phenomenon and are relevant in the motion of an biological agents or artificial self-propelled particles. The origin of these fluctuations can be for example variations in the propulsion of chemically powered colloids [260,164,295], complex intra-cellular processes in cell motility [313,41] or unresolved internal decision processes in animals [245,195,26]. For example, the motion of a macroscopic animal moving in a homogeneous environment, where the fluctuations due the environment can be assumed as negligible, may nevertheless appear random to an external observer.…”

“…The term "active" refers here to the ability of individual units to move actively by gaining kinetic energy from the environment. Examples of such systems range from the dynamical behavior of individual units such as Brownian motors [280], motile cells [123,313,41], macroscopic animals [182,195] or artificial self-propelled particles [260,164] to large ensembles of interacting active particles and their large scale collective dynamics [354,60,23]. A major driving force of the active matter research are the continuously improving experimental techniques such as for example automated digital tracking [321,313,17] or the realization of active granular and colloidal systems (see e.g.…”

Controlling uphill motion of an active Brownian particle driven by shot-noise energy pulses

“…A combined action of Brownian random forces and of the energy-powered propulsion mechanism is by now a well established model for motility of cells or microorganisms [1][2][3][4][5] and functioning of molecular biodevices [6][7][8][9]. Many molecular catalysts, motors, or pumps convert chemical energy into motion which can be illustrated as a (biased) random walk on a representative free energy landscape.…”

Relation between cooperative molecular motors and active Brownian particles

“…For an active Brownian particle (ABP), as considered in the following, the nonlinear dissipation term f (v) is negative for a range of velocities, which precludes thermodynamic equilibrium. Several authors have measured * Corresponding author: benji@pks.mpg.de the functions f (v) and g(v) (also in multidimensional setups) from experimental data of biological systems [6,[12][13][14].…”