  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, [...]
