# Stall force of a cargo driven by N interacting motor proteins

## TL;DR

This paper presents a model showing that the stall force of a cargo driven by N motor proteins is always equal to the sum of individual stall forces, regardless of interactions, based on a thermodynamic equilibrium analogy.

## Contribution

It provides an exact analytical result that the stall force is independent of motor interactions, supported by numerical simulations.

## Key findings

- Stall force equals the sum of individual motor stall forces.
- The stall state is analogous to thermodynamic equilibrium.
- Numerical simulations confirm the analytical predictions.

## 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 motor-motor 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.