Molecular motors play key roles URLanizing the interior of cells. An efficient motor in cargo transport would travel with a high speed and a minimal error in transport time (or distance ) while consuming  minimal amount of energy. The travel distance  and its variance of motor are, however, physically constrained by energy consumption, the principle of which has recently been formulated into the thermodynamic uncertainty relation , the product between the heat dissipated from a motor and the squared relative error in the displacement, has a minimal theoretical bound (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} . Here, we reinterpret the uncertainty measure (\mathcal{Q) defined in the thermodynamic uncertainty relation such that a motor efficient in cargo transport is characterized with a small \mathcal{Q} . } Analyses on the motility data from several types of molecular motors show that \mathcal{Q} is a nonmonotic function of ATP concentration and load (f). For kinesin-1, \mathcal{Q} \muM  is locally minimized at [ATP] \approx 200 \muM and f\approx 4 pN. Remarkably, for the mutant with a longer neck-linker this local minimum vanishes , and the energetic cost to achieve the same precision as the wild-type increases significantly , which underscores the importance of molecular structure in transport properties. For the biological motors studied here , their value of \mathcal{Q semi-optimized under the cellular condition ([ATP] \approx 1 mM, f=0-1 pN). We find that among the motors, kinesin-1 at single molecule level is the most efficient in cargo transport .
Molecular motors play pivotal roles URLanizing 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 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 (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} . ) defined in the thermodynamic uncertainty relation such that a motor efficient in cargo transport is characterized with a small \mathcal{Q} . } 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\muM - 10 mM), and is locally minimized at [ATP] \approx 200 \muM . In stark contrast, this local minimum vanishes for a mutant that has a longer neck-linker , and the value of \mathcal{Q , 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 .
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