Advances in modelling solution properties of macromolecules and particles.

Introduction to bead modelling The size and detailed shape of rigid macromolecules or particles can be inferred from the properties of their solutions or suspensions. Some of these are hydrodynamic properties, such as the sedimentation coefficient, s, the translational diffusion coefficient, D,, rotational diffusion coefficients, D,, and relaxation times, z, and the intrinsic viscosity [q]. There are also equilibrium solution properties, including the angular dependence of radiation scattering, P (O), the radius of gyration, R, and the covolume, u. Theoretical formalisms, implemented in adequate computer procedures, are required to correlate global structure (size and shape) with solution properties. In some instances, the overall shape can be conveniently described by revolution or triaxial ellipsoids, for which theory and simple procedures are available [1,2], but in many other cases the ellipsoidal shape is clearly inadequate to model the very specific shape of biological macromolecules. For such cases, Bloomfield et al. [3,4] designed the so-called bead models, in which the shape of a rigid particle is represented by an array of spherical elements. By using a sufficient number of beads of (possibly) varying size, the intricate details of macromolecular shape can be deduced. Two illustrative examples are displayed in Figure 1. The theory on which bead modelling is based comes from the pioneering works on macromolecular hydrodynamics by Kirkwood and Riseman [5,6], of which Bloomfield et al. adopted an approximate, simplified form. Garcia de la Torre, Bloomfield and co-workers improved the theoretical treatment and took advantage of the increasing availability of computing power, developing methods for efficient and accurate calculation of hydrodynamic properties of bead models of arbitrary complexity [7-131. A few years ago the computer program HYDRO was published [14] as a useful tool to calculate some hydrodynamic properties of bead models. It was soon evident that the utility of bead modelling could be pushed further in various directions. (1) Prediction of complex, more involved solution properties, usually related to rotational brownian diffusion of the rigid solute particles, that are monitored in some electrooptical and spectroscopic techniques. (2) Calculation of compound quantities involving two solution properties in such a way that the combination depends on the shape but not on the size of the particles. Such quantities had been