We study the effect of an asymmetry on the transport properties of an active Brownian particle. We demonstrate the existence of a critical force or, more generally, of a critical asymmetry that separates parameter regimes of giant diffusion from those with reliable directed transport. We derive a condition for the critical asymmetry by means of an exact expression for the diffusion coefficient and by a simplified discrete picture. A critical asymmetry, as predicted by the simple model, is also found in a detailed model of coupled molecular motors displaying bidirectional motion.
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