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

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.