Solvable model of a many-filament Brownian ratchet

Abstract

We construct and exactly solve a model of an extended Brownian ratchet. The model comprises an arbitrary number of heterogeneous, growing and shrinking filaments which together move a rigid membrane by a ratchet mechanism. The model draws parallels with the dynamics of actin filament networks at the leading edge of the cell. In the model, the filaments grow and contract stochastically. The model also includes forces which derive from a potential dependent on the separation between the filaments and the membrane. These forces serve to attract the filaments to the membrane or generate a surface tension that prevents the filaments from dispersing. We derive an N -dimensional diffusion equation for the N filament-membrane separations, which allows the steady-state probability distribution function to be calculated exactly under certain conditions. These conditions are fulfilled by the physically relevant cases of linear and quadratic interaction potentials. The exact solution of the diffusion equation furnishes expressions for the average velocity of the membrane and critical system parameters for which the system stalls and has zero net velocity. In the case of a restoring force, the membrane velocity grows as the square root of the force constant, whereas it decreases once a surface tension is introduced.

Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement

“…In this article, we demonstrate how even in a static, structureless environment, particles can themselves be the source of inter-particle ratcheting when they have heterogeneous properties and interact via volume exclusion. This inter-particle ratchet effect underlies correlation-phenomena found in a range of models including lattice exclusion processes with particle-wise disorder [10][11][12] or driven tracers [13,14], continuous-space single-file diffusion with random diffusivities [15][16][17] or friction [18], and a recent many-filament ratchet model [19].…”

“…Lastly, we describe how the many-filament ratchet of Ref. [19] relates to the previous cases through a simple mapping.…”

Undulation of a moving fluid membrane pushed by filament growth

“…However, membrane fluctuations have not yet been studied. In most studies reported in the literature [16][17][18][19][20][21][22][23], the membrane is modeled as a flat rigid surface; thus, no fluctuations are accounted for. Although the membrane fluctuations are assumed to be a Gaussian distribution of the membrane height in Ref.…”

“…For example, actin filaments grow at the front side of crawling cells and push the membrane forward. This membrane motion has been intensively studied by Brownian ratchet theories and simulations [15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Conversion of heat to work: An efficient inchworm

“…Two paradigmatic ratchet models, namely flashing and rocking ratchet [3,[13][14][15][16][17] models always involve an intermittent forcing to drive the system (modeled as a single particle) out of equilibrium. The work done by the system in this case is an amount of work extracted mostly from the source of directionless forcing.…”