Synchronization and enhanced catalysis of mechanically coupled enzymes*

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. Moreover, the effective enzyme-enzyme phase coupling we obtain is interesting from a theoretical perspective, as it arises from off-diagonal terms in the mobility matrix that connects forces to velocities, and thus leaves the equilibrium probability distribution of the system intact while introducing non-trivial effects in an out-of-equilibrium setting (in contrast to ad-hoc couplings, e.g. Kuramoto-like).