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We recently introduced a model of an asymmetric dumbbell made of two hydrodynamically coupled subunits as a minimal model for a macromolecular complex, in order to explain the observation of enhanced diffusion of catalytically active enzymes. It was shown that internal fluctuations lead to a negative contribution to the overall diffusion coefficient and that the fluctuation-induced contribution is controlled by the strength of the interactions between the subunits and their asymmetry. We develop the model by studying the effect of anisotropy on the diffusion properties of a modular structure. Using a moment expansion method we derive an analytic form for the long-time diffusion coefficient of an asymmetric, anisotropic dumbbell and show systematically its dependence on internal and external symmetry. The method provides a tractable, analytical route for studying the stochastic dynamics of dumbbell models. The present work opens the way to more detailed descriptions of the effect of hydrodynamic interactions on the diffusion and transport properties of biomolecules with complex structures.

Fluctuation-induced hydrodynamic coupling in an asymmetric, anisotropic dumbbell