  Several enzymes exhibit enhanced diffusion in the presence of a substrate.
One explanation of this enhancement arises from fluctuating dimer models, which
suggest that enzymes have a higher diffusion constant when interacting with
substrates compared to when they are free. Another possible mechanism,
suggested in both experimental and theoretical studies, is that enzymes act as
nanoswimmers. However, existing nanoswimmer models have struggled to account
for the exceptionally high self-propulsion speeds observed in experiments, with
estimated increases in diffusion due to self-propulsion found to be minimal. In
this study, we model enzymes as dimers with fluctuating mobility. We show that
even dimers can exhibit run-and-tumble motion when transitioning between states
of varying mobility within the enzymatic cycle. By exploring a three-state
enzymatic cycle, we identify the conditions under which self-propulsion speeds
and increases in diffusion rate consistent with experimental observations can
be achieved.
