Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles

Abstract

Many single molecule experiments for molecular motors comprise not only the motor but also large probe particles coupled to it. The theoretical analysis of these assays, however, often takes into account only the degrees of freedom representing the motor. We present a coarse-graining method that maps a model comprising two coupled degrees of freedom which represent motor and probe particle to such an effective one-particle model by eliminating the dynamics of the probe particle in a thermodynamically and dynamically consistent way. The coarse-grained rates obey a local detailed balance condition and reproduce the net currents. Moreover, the average entropy production as well as the thermodynamic efficiency is invariant under this coarse-graining procedure. Our analysis reveals that only by assuming unrealistically fast probe particles, the coarse-grained transition rates coincide with the transition rates of the traditionally used one-particle motor models. Additionally, we find that for multicyclic motors the stall force can depend on the probe size. We apply this coarse-graining method to specific case studies of the F1-ATPase and the kinesin motor.

Transport of organelles by elastically coupled motor proteins

“…This model has been studied extensively in the literature [28,33,34,35,36]. In some of these studies [33,34], in the exponent, θ n is accompanied by the external force exerted on the motor, whereas in our model (also in [35,36]) it is accompanied by the energy difference ε ± .…”

“…If ∆ n = x n − x 0 is the instantaneous separation between n'th motor and the cargo, then the instantaneous elastic force on the n'th motor is f n = −ℓκ n ∆ n and so the elastic force on the cargo due to all the motors at different locations on the filament is f c = ℓ N i=1 κ i ∆ i . For a cargo bound to N motor proteins and acted on by an external force f , the over-damped Langevin equation is written as [22,28] …”

“…Several studies have appeared in the last few years, based (mostly) on Hookean spring-like interaction between motor and the cargo [19,20,21,22,23,24,25,26,27,28,29]. In Kunwar et al [20], along with elastic interaction among the motors, non-linear force-velocity relations are assigned to different motors.…”

“…Some of the formalisms developed in the above mentioned analytical studies were applied to simple cases with at most two motor proteins driving a cargo [24,25,26,28], while many other studies are by and large computational in nature [19,20,22,23,29]. A general theoretical framework to study the motion of a cargo driven by arbitrary number of elastically bound motors has not been developed.…”

“…In a more recent study, Berger et al [25] identified four distinct transport regimes in a system of two elastically coupled motor proteins. In [28], the dynamics of the cargo coupled to a single motor protein was studied using a novel coarse-graining approach based on separation of time-scales between the cargo and motor. A very recent study by Bouzat [29] showed that a model in which motors experience history-dependent forces captures some of the experimental observations better than the previously studied models.…”