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Molecular motors play pivotal roles in organizing the interior of cells. Amotor efficient in cargo transport would move along cytoskeletal filaments witha high speed and a minimal error in transport distance (or time) whileconsuming a minimal amount of energy. The travel distance of the motor and itsvariance are, however, physically constrained by the free energy beingconsumed. A recently formulated \emph{thermodynamic uncertainty relation}offers a theoretical framework for the energy-accuracy trade-off relationubiquitous in biological processes. According to the relation, a measure$\mathcal{Q}$, the product between the heat dissipated from a motor and thesquared relative error in the displacement, has a minimal theoretical bound($\mathcal{Q} \geq 2 k_B T$), which is approached when the time trajectory ofthe 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 revealthat $\mathcal{Q}$ 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 islocally minimized at [ATP] $\approx$ 200 $\mu$M. In stark contrast, this localminimum vanishes for a mutant that has a longer neck-linker, and the value of$\mathcal{Q}$ is significantly greater, which underscores the importance ofmolecular structure. Transport efficiencies of the biological motors studiedhere are semi-optimized under the cellular condition ([ATP] $\approx 1$ mM,$f=0-1$ pN). Our study indicates that among many possible directions ofoptimization, cytoskeletal motors are designed to operate at a high speed witha minimal error while leveraging their energy resources.

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