Relation between cooperative molecular motors and active Brownian particles

Abstract

Active Brownian particles (ABPs), obeying a nonlinear Langevin equation with speed-dependent drift and noise amplitude, are well-known models used to describe self-propelled motion in biology. In this paper we study a model describing the stochastic dynamics of a group of coupled molecular motors (CMMs). Using two independent numerical methods, one based on the stationary velocity distribution of the motors and the other one on the local increments (also known as the Kramers-Moyal coefficients) of the velocity, we establish a connection between the CMM and the ABP models. The parameters extracted for the ABP via the two methods show good agreement for both symmetric and asymmetric cases and are independent of N, the number of motors, provided that N is not too small. This indicates that one can indeed describe the CMM problem with a simpler ABP model. However, the power spectrum of velocity fluctuations in the CMM model reveals a peak at a finite frequency, a peak which is absent in the velocity spectrum of the ABP model. This implies richer dynamic features of the CMM model which cannot be captured by an ABP model.

Active Brownian particles

“…5c). It has been suggested [14,218,344] that the velocity of a large motor assembly (N ≫ 1) can be well described byẋ…”

“…(74) is a reasonable approximation of the CMM model and suppose, a long time series of the assembly's velocity is given, how could we determine the functions f (v) and g(v)? There are two methods to determine these functions [370,344]. First, we could measure how the velocity changes on a short time-scale.…”

“…In either limits the spectrum is well described by Lorentzian spectra, which correspond to those of a two state process of velocity reversals (range of low frequencies) and an approximate Ornstein-Uhlenbeck process for small-scale fluctuations around the two metastable velocities. For the ABP model, summing up these two contributions [344] …”

Effects of cross-correlated noises on the transport of active Brownian particles

“…Recently, the transport properties of active Brownian particles (ABP) have attracted much attention since it can explain the origin of the self-propelled motion, and the active (self-propelled) motion is one of the obvious signatures of many living systems and can be observed on different levels, ranging from the motion of motor proteins within cells to the motility of cells and bacteria [13][14][15][16][17][18][19]. Our system is closely related to the one investigated in Ref.…”

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

“…Models of passive long molecules translocation driven by motors have been also recently studied [10][11][12][13]. Collective effects of such groups of motors have been also addressed and existing literature points to a possible mapping of the stochastic dynamics of coupled molecular motors to models of active Brownian motion (ABM) [1,14,15].…”