Hydrodynamic Models

BPJ_114_4.c1.inddDoes the quaternary structure implied by crystal packing of a macromolecule exist in solution? Which one(s) of the variable loop positions suggested by NMR data exist? What conformations constitute the ensemble of structures in a solution of intrinsically disordered proteins or flexible nucleic acids? To answer these questions one requires a hydrodynamic model that connects the solution behavior to the structural coordinates.

The cover image for the February 27 issue of the Biophysical Journal shows a progression of such models used over the last century to interpret solution studies of proteins and nucleic acids. On the left is a familiar atomic sphere representation of a protein crystal structure. The earliest hydrodynamic models were ellipsoids of revolution, as shown in the image to the right of the atomic model. From these simple geometric objects, the famous Perrin shape parameter equations were derived. The next revolution was modeling macromolecules as a collection of beads, which developed into mini-bead, shell models. An example is depicted in the third image. This and other bead models capture the shape of a protein and provide a theoretically rigorous path to calculation of hydrodynamic molecular properties. The final image on the right is a convex hull model, a mathematical construct that is the smallest convex envelope to contain a set of points. Representing proteins and nucleic acids and their complexes as their convex hulls permits surprisingly accurate calculations of molecular hydrodynamic properties. The convex hull captures not only the shape and volume of the molecule itself, but also the volume of cavity-entrained solvent influencing molecular diffusion. The advantage of the convex hull hydrodynamic method is speed of calculation: it may be used to quickly predict properties of large ensembles of molecular structures or to encode real-time target restraints during molecular simulations.

The code is freely available, and the convex hull method of hydrodynamic property prediction has also been implemented as a web service. A link can be found at hullrad.wordpress.com.

– Patrick Fleming, Karen Fleming