Energetic costs, precision, and efficiency of a biological motor in cargo transport

TL;DR

This study applies thermodynamic uncertainty relations to analyze the energy efficiency and precision of molecular motors in cargo transport, revealing how their performance depends on biochemical and mechanical factors.

Contribution

It introduces a quantitative framework using the thermodynamic uncertainty relation to evaluate biological motor efficiency and demonstrates how molecular structure influences transport performance.

Findings

$ ext{Q}$ approaches the theoretical bound at specific load and ATP levels for kinesin-1.

Transport efficiency is semi-optimized under typical cellular conditions.

Molecular structure, such as neck-linker length, affects energy-accuracy trade-offs.

Abstract

Molecular motors play pivotal roles in organizing the interior of cells. A motor efficient in cargo transport would move along cytoskeletal filaments with a high speed and a minimal error in transport distance (or time) while consuming a minimal amount of energy. The travel distance of the motor and its variance are, however, physically constrained by the free energy being consumed. A recently formulated \emph{thermodynamic uncertainty relation} offers a theoretical framework for the energy-accuracy trade-off relation ubiquitous in biological processes. According to the relation, a measure $\mathcal{Q}$, the product between the heat dissipated from a motor and the squared relative error in the displacement, has a minimal theoretical bound ($\mathcal{Q} \geq 2 k_B T$), which is approached when the time trajectory of the motor is maximally regular for a given amount of free energy input. Here, we use $\mathcal{Q}$ to quantify the transport efficiency of biological motors. Analyses on the motility data from several types of molecular motors reveal that $\mathcal{Q}$ is a complex function of ATP concentration and load ($f$). For kinesin-1, $\mathcal{Q}$ approaches the theoretical bound at $f\approx 4$ pN and over a broad range of ATP concentration (1 $\mu$M - 10 mM), and is locally minimized at [ATP] $\approx$ 200 $\mu$M. In stark contrast, this local minimum vanishes for a mutant that has a longer neck-linker, and the value of $\mathcal{Q}$ is significantly greater, which underscores the importance of molecular structure. Transport efficiencies of the biological motors studied here are semi-optimized under the cellular condition ([ATP] $\approx 1$ mM, $f=0-1$ pN). Our study indicates that among many possible directions of optimization, cytoskeletal motors are designed to operate at a high speed with a minimal error while leveraging their energy resources.