Hydrodynamic resistance and diffusion coefficients of segmentally flexible macromolecules with two subunits

Abstract

We present an algorithm for the calculation of the resistance coefficients and diffusion coefficients for the translational and rotational motions of a particle composed of two rigid subunits joined at a single point of articulation. By modeling each subunit as a collection of hydrodynamic resistance elements or beads, the method allows the full inclusion of all hydrodynamic interactions. The generalized coordinates have been chosen in such a way that it is easy to treat cases with seven, eight, or nine degrees of freedom (the subunits being joined at a hinge, a universal joint, or a swivel), as well as the intermediate cases where the internal motions are opposed by restoring forces, and analytic expressions are given for the resistance and diffusion coefficients for these cases. The examination of the dependence of the various coefficients on the choice of the origin of the coordinate system reveals that the rotational diffusion coefficients are independent of the location of the origin, so any convenient point (such as the point of articulation) can be used for the analysis of rotational diffusion. On the other hand, the calculated translational diffusion coefficient does depend on the choice of origin, and we discuss the still unresolved problem of how to find the origin that will give a value corresponding to the experimentally observed translational diffusion coefficient. One specific application of the method is examined in detail, that of a particle made up of three identical spheres with one sphere for each arm and the central sphere serving as the joint. The various rotational diffusion coefficients of the model particle are given, and it is seen that ignoring hydrodynamic interactions produces large effects in the calculated values. Calculations on this same model also demonstrate the sensitivity of the calculated translational diffusion coefficient both to the effects of ignoring hydrodynamic interactions and to the choice of coordinate system.