Enzymes have been recently proposed to have mechanical activity associated with their chemical activity. In a number of recent studies, it has been reported that enzymes undergo enhanced diffusion in the presence of their corresponding substrate, when this substrate is uniformly distributed in solution. Moreover, if the concentration of the substrate is non-uniform, enzymes and other small molecules have been reported to show chemotaxis -- biased stochastic movement in the direction of the substrate gradient -- typically towards higher concentrations of this substrate, with a few exceptions. The underlying physical mechanisms responsible for enhanced diffusion and chemotaxis at the nanoscale, however, are still not well understood. Understanding these processes is important both for fundamental biological research, e.g. in the context of spatial organization of enzymes in metabolic pathways (metabolon formation), as well as for engineering applications, such as in the design of new vehicles for targeted drug delivery. In this Account, we will review the available experimental observations of both enhanced diffusion and chemotaxis, and we will discuss critically the different theories that have been proposed to explain the two. We first focus on enhanced diffusion, beginning with an overview of the experimental results. We then discuss the two main types of mechanisms that have been proposed, namely active mechanisms relying on the catalytic step of the enzymatic reaction, and equilibrium mechanisms which consider the reversible binding and unbinding of the substrate to the enzyme. We put particular emphasis on an equilibrium model recently introduced by us, which describes how the diffusion of dumbbell-like modular enzymes can be enhanced in the presence of substrate, thanks to a binding-induced reduction of the internal fluctuations of the enzyme. We then turn to chemotaxis, [...]
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