Sufficient conditions for the additivity of stall forces generated by multiple filaments or motors

TL;DR

This paper investigates the conditions under which the collective stall force of multiple cytoskeletal filaments or molecular motors is additive, revealing that additivity holds at equilibrium but not necessarily out of equilibrium, and introduces a predictive measure for this deviation.

Contribution

The paper provides a unified theoretical framework explaining when and why the stall force additivity fails in non-equilibrium systems of filaments and motors, and proposes a new predictive quantity.

Findings

Additivity of stall force holds at equilibrium.

Non-additivity occurs when systems are out of equilibrium.

A new measure predicts deviation from additivity.

Abstract

Molecular motors and cytoskeletal filaments work collectively most of the time under opposing forces. This opposing force may be due to cargo carried by motors or resistance coming from the cell membrane pressing against the cytoskeletal filaments. Some recent studies have shown that the collective maximum force (stall force) generated by multiple cytoskeletal filaments or molecular motors may not always be just a simple sum of the stall forces of the individual filaments or motors. To understand this excess or deficit in the collective force, we study a broad class of models of both cytoskeletal filaments and molecular motors. We argue that the stall force generated by a group of filaments or motors is additive, that is, the stall force of $N$ number of filaments (motors) is $N$ times the stall force of one filament (motor), when the system is in equilibrium at stall. Conversely, we show that this additive property typically does not hold true when the system is not at equilibrium at stall. We thus present a novel and unified understanding of the existing models exhibiting such non-addivity, and generalise our arguments by developing new models that demonstrate this phenomena. We also propose a quantity similar to thermodynamic efficiency to easily predict this deviation from stall-force additivity for filament and motor collectives.