The solution properties, including hydrodynamic quantities and the radius of gyration, of globular proteins are calculated from their detailed, atomic-level structure, using bead-modeling methodologies described in our previous article (, Biophys. J. 76:3044-3057). We review how this goal has been pursued by other authors in the past. Our procedure starts from a list of atomic coordinates, from which we build a primary hydrodynamic model by replacing nonhydrogen atoms with spherical elements of some fixed radius. The resulting particle, consisting of overlapping spheres, is in turn represented by a shell model treated as described in our previous work. We have applied this procedure to a set of 13 proteins. For each protein, the atomic element radius is adjusted, to fit all of the hydrodynamic properties, taking values close to 3 A, with deviations that fall within the error of experimental data. Some differences are found in the atomic element radius found for each protein, which can be explained in terms of protein hydration. A computational shortcut makes the procedure feasible, even in personal computers. All of the model-building and calculations are carried out with a HYDROPRO public-domain computer program.

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The hydrodynamic properties of rigid particles are calculated from models composed of spherical elements (beads) using theories developed by Kirkwood, Bloomfield, and their coworkers. Bead models have usually been built in such a way that the beads fill the volume occupied by the particles. Sometimes the beads are few and of varying sizes (bead models in the strict sense), and other times there are many small beads (filling models). Because hydrodynamic friction takes place at the molecular surface, another possibility is to use shell models, as originally proposed by Bloomfield. In this work, we have developed procedures to build models of the various kinds, and we describe the theory and methods for calculating their hydrodynamic properties, including approximate methods that may be needed to treat models with a very large number of elements. By combining the various possibilities of model building and hydrodynamic calculation, several strategies can be designed. We have made a quantitative comparison of the performance of the various strategies by applying them to some test cases, for which the properties are known a priori. We provide guidelines and computational tools for bead modeling.

There is a striking disparity between the heart-shaped structure of human serum albumin (HSA) observed in single crystals and the elongated ellipsoid model used for decades to interpret the protein solution hydrodynamics at neutral pH. These two contrasting views could be reconciled if the protein were flexible enough to change its conformation in solution from that found in the crystal. To investigate this possibility we recorded the rotational motions in real time of an erythrosin-bovine serum albumin complex (Er-BSA) over an extended time range, using phosphorescence depolarization techniques. These measurements are consistent with the absence of independent motions of large protein segments in solution, in the time range from nanoseconds to fractions of milliseconds, and give a single rotational correlation time phi(BSA, 1 cP, 20 degrees C) = 40 +/- 2 ns. In addition, we report a detailed analysis of the protein hydrodynamics based on two bead-modeling methods. In the first, BSA was modeled as a triangular prismatic shell with optimized dimensions of 84 x 84 x 84 x 31.5 A, whereas in the second, the atomic-level structure of HSA obtained from crystallographic data was used to build a much more refined rough-shell model. In both cases, the predicted and experimental rotational diffusion rate and other hydrodynamic parameters were in good agreement. Therefore, the overall conformation in neutral solution of BSA, as of HSA, should be rigid, in the sense indicated above, and very similar to the heart-shaped structure observed in HSA crystals.

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