Diffusion coefficients for rigid macromolecules with irregular shapes that allow rotational-translational coupling

We consider six-dimensional diffusion and frictional tensors for a rigid macromolecule immersed in a viscous fluid at low Reynolds number. Our treatment allows for screwlike properties which couple rotational and translational movements. We show that the center of diffusion of a screwlike body can be distinct from its hydrodynamic center of reaction. Symmetry conditions which ensure coincidence are examined. The center of diffusion is found to be the point of a body with the slowest diffusive movements, while rotations about the center of reaction encounter the least average resistance. The macroscopic translational diffusion coefficient is evaluated from a perturbation analysis of the six-dimensional diffusion equation. We show that methodologies which ignore translational-rotational coupling will necessarily underestimate the diffusion rate of screwlike particles. A procedural framework is presented to calculate diffusion coefficients of complicated bodies. As an example we treat a long bent rod.