Quasi-steady-state analysis of coupled flashing ratchets

Abstract

We perform a quasi-steady-state (QSS) reduction of a flashing ratchet to obtain a Brownian particle in an effective potential. The resulting system is analytically tractable and yet preserves essential dynamical features of the full model. We first use the QSS reduction to derive an explicit expression for the velocity of a simple two-state flashing ratchet. In particular, we determine the relationship between perturbations from detailed balance, which are encoded in the transitions rates of the flashing ratchet, and a tilted-periodic potential. We then perform a QSS analysis of a pair of elastically coupled flashing ratchets, which reduces to a Brownian particle moving in a two-dimensional vector field. We suggest that the fixed points of this vector field accurately approximate the metastable spatial locations of the coupled ratchets, which are, in general, impossible to identify from the full system.

Breaking time-reversal symmetry for ratchet models of molecular machines

“…We have investigated the trade-offs of time asymmetry and dissipation for driven systems diffusing in sawtooth potentials, which are frequently used as simple ratchet models for molecular machines [17][18][19][20][21][22][23][24][25][26][27][28][29]. Accordingly, we explored the effect of sawtooth potential (height and asymmetry) and protocol (speed and driving strength) characteristics on time asymmetry.…”

“…The second component E r (x) is a time-independent periodic sawtooth (ratchet) potential (Fig. 1) that enables directional motion for simple models of molecular machines [17][18][19][20][21][22][23][24][25][26][27][28][29], 3). When the sawtooth is asymmetric, the gradual ( i > 0.5) and steep ( i < 0.5) sides of the sawtooth are indicated.…”

“…We investigate the trade-off between time asymmetry and dissipation in the context of molecular machines, using a sawtooth potential that is frequently used to represent a ratchet model of a molecular machine [17][18][19][20][21][22][23][24][25][26][27][28][29]. 'Flashing' ratchet models, which switch between multiple potential energy landscapes, have been used to generate autonomous directed motion [23].…”

Collective transient ratchet transport induced by many elastically interacting particles

“…The time evolution of the relevant physical quantities is obtained by considering N elastically coupled Ratchet Maps (RMs) 44 , 58 in the form where the first neighbor coupling between the ratchets follows 59 , 60 with K being the nonlinearity parameter and the effective coupling strength between the ratchets. Usually, we write , where is the coupling strength between the ratchets and the limit of infinite size is obtained using , which implies that .…”

On balance relations for irreversible chemical reaction networks

“…In practice, the problem of obtaining information about the density of the thermodynamic limit is usually much more manageable than attempting to study the full stochastic model. In particular, the PDMP is much less costly to simulate [26]. As a specific example, let us return to the network (4.1).…”