ITERATIVE TECHNIQUES FOR INVERSION OF THE NONLINEAR PERRIN EQUATIONS FOR DIFFUSION OF SPHEROIDS

Abstract

This chapter discusses iterative techniques for the inversion of the nonlinear Perrin equations for the diffusion of spheroids. Experimental studies on the size and shape of macromolecules in solution are often based on hydrodynamic procedures that yield information on the translational and/or rotational diffusion tensor. The methods associated with observation of the translation diffusion tensor are most often expressed as the trace of the tensor that corresponds to the arithmetic mean of three principal translational diffusion coefficients, denoted as D. On the other hand, methods associated with observation of the rotational diffusion tensor yield estimates of the individual principal rotational diffusion coefficients, which are denoted as R1, R2, and R3. Because each of the diffusion coefficients is a function of the size and shape of the macromolecule in question, any combination of these four coefficients taken three at a time may in principle be used to solve for three independent shape and size parameters. This chapter discusses the ellipsoids of revolution, referred to as spheroids. It also discusses the inversion procedures for two pairs of coefficients R1 and R3 and R1 and D.