Bead model hydrodynamics: an in-depth comparison between GRPY and ZENO

Comparing experimental and calculated hydrodynamic properties of (bio)-macromolecules, such as the translational diffusion coefficient $D_{t(20,w)}^0$ and the intrinsic viscosity [η], is a useful strategy for the validation of predicted and/or solved atomic-level structures. Bead modeling is a prominent methodology, with several computational tools available. The program GRPY (Generalized Rotne-Prager-Yamakawa) allows the hydrodynamic calculations to be performed at the one-atom one-bead scale, allowing overlaps, but it is computer intensive with CPU requirements depending on the number of beads N as ~ N³. The program ZENO, based on the electrostatics-hydrodynamics analogy and using a Monte Carlo numerical path integration, can compute $D_{t(20,w)}^0$ and [η] directly on bead models, and it is almost independent of the target size. Since bead models are a very efficient way to include the hydration effect when dealing with bio-macromolecules, we present here an in-depth comparison between GRPY and ZENO, both as implemented in the US-SOMO suite. Relatively low but systematic differences (0.2-2%, increasing with model size) appear when using bead models of proteins at the residue- or atomic-level scales. When comparing the results provided on a restricted set of bead models by two other computationally intensive methods having other drawbacks, the very accurate but not handling overlaps HYDROMULTIPOLE, and the boundary elements BEST requiring extrapolation, GRPY was found to fare better than ZENO. While efforts are in progress to directly improve the ZENO performance, a heuristic correction based on the results for a series of protein bead models is proposed, allowing for a better consistency with GRPY.