  We examine the stochastic dynamics of two enzymes that are mechanically
coupled to each other, e.g., through an elastic substrate or a fluid medium.
The enzymes undergo conformational changes during their catalytic cycle, which
itself is driven by stochastic steps along a biased chemical free energy
landscape. We find conditions under which the enzymes can synchronize their
catalytic steps, and discover that the coupling can lead to a significant
enhancement in their overall catalytic rate. Both effects can be understood as
arising from a global bifurcation in the underlying dynamical system at
sufficiently strong coupling. Our findings suggest that, despite their
molecular scale, enzymes can be cooperative and improve their performance in
metabolic clusters.
