Stall force of a cargo driven by N interacting motor proteins

Abstract

We study a generic one-dimensional model for an intracellular cargo driven by N motor proteins against an external applied force. The model includes motor-cargo and motormotor interactions. The cargo motion is described by an over-damped Langevin equation, while motor dynamics is specified by hopping rates which follow a local detailed balance condition with respect to change in energy per hopping event. Based on this model, we show that the stall force, the mean external force corresponding to zero mean cargo velocity, is completely independent of the details of the interactions and is, therefore, always equal to the sum of the stall forces of the individual motors. This exact result is arrived on the basis of a simple assumption: the (macroscopic) state of stall of the cargo is analogous to a state of thermodynamic equilibrium, and is characterized by vanishing net probability current between any two microstates, with the latter specified by motor positions relative to the cargo. The corresponding probability distribution of the microstates under stall is also determined. These predictions are in complete agreement with numerical simulations, carried out using specific forms of interaction potentials. p-2

Performance scaling and trade-offs for collective motor-driven transport

“…Using models similar to ours, but with discrete steps rather than continuous motor dynamics [25,28], found a similar monotonic and concave functional dependence of the mean velocity v on motor number N, although their findings are restricted to relatively small N. Likewise, [28] also found D eff ∝ 1/N for the greatest N they investigated. Another recent study [29] found that the total load capacity, or effective stall force, is N times the stall force for a single motor. We can easily incorporate into our model a constant external force f ext pulling the cargo in the opposite direction of the chemical force driving the motors.…”

“…However, analysis of transport by single motors has shown that pulling a diffusing cargo and pulling against a constant force lead to qualitatively different transport behavior [23,24]. Researchers have proposed and explored several dynamical models for transport of diffusive cargo by multiple motors [25][26][27][28][29][30]. These approaches rely primarily on numerical simulation, and as such are limited by computational resources to exploring systems with relatively small numbers of motors.…”

Performance scaling and trade-offs for collective motor-driven transport

“…Using models similar to ours, but with discrete steps rather than continuous motor dynamics, [24] and [27] found a similar monotonic and concave functional dependence of the mean velocity v on motor number N , although their findings are restricted to relatively small N . Another recent study [28] found that the total load capacity, or effective stall force, is N times the stall force for a single motor. We can easily incorporate into our model a constant external force f ext pulling the cargo in the opposite direction of the chemical force driving the motors.…”

“…However, analysis of transport by single motors has shown that pulling a diffusing cargo and pulling against a constant force lead to qualitatively different transport behavior [23]. Researchers have proposed and explored several dynamical models for transport of diffusive cargo by multiple motors [24][25][26][27][28][29]. These approaches rely primarily on numerical simulation, and as such are limited by computational resources to exploring systems with relatively small numbers of motors.…”

Dynamic and thermodynamic bounds for collective motor-driven transport

“…Many specific models of transport systems have been explored, including deterministic phenomenological models [7,9,10], discrete stochastic models [11][12][13], and continuous stochastic models [14,15]. A common goal of these investigations has been to determine how various parameters (such as coupling strength, stall force, diffusivity, and number of motors) tune the performance of these systems.…”