Analytical ultracentrifugation (AU) is reemerging as a versatile tool for the study of proteins. Monitoring the sedimentation of macromolecules in the centrifugal field allows their hydrodynamic and thermodynamic characterization in solution, without interaction with any matrix or surface. The combination of new instrumentation and powerful computational software for data analysis has led to major advances in the characterization of proteins and protein complexes. The pace of new advancements makes it difficult for protein scientists to gain sufficient expertise to apply modern AU to their research problems. To address this problem, this review builds from the basic concepts to advanced approaches for the characterization of protein systems, and key computational and internet resources are provided. We will first explore the characterization of proteins by sedimentation velocity (SV). Determination of sedimentation coefficients allows for the modeling of the hydrodynamic shape of proteins and protein complexes. The computational treatment of SV data to resolve sedimenting components has been achieved. Hence, SV can be very useful in the identification of the oligomeric state and the stoichiometry of heterogeneous interactions. The second major part of the review covers sedimentation equilibrium (SE) of proteins, including membrane proteins and glycoproteins. This is the method of choice for molar mass determinations and the study of selfassociation and heterogeneous interactions, such as protein-protein, protein-nucleic acid, and protein-small molecule binding.Keywords: Sedimentation velocity; sedimentation equilibrium; protein interactions; reversible association; hydrodynamic shape; membrane proteins Although analytical ultracentrifugation (AU) played a notable role in the history of the characterization of proteins and protein complexes (Schachman 1992), this methodology has suffered a decline in use for many years, in considerable part because of a lack of new instrumentation capable of digital data acquisition. Fortunately, the capabilities of AU have been transformed by the combination of new instrumentation and major developments in computational software for data analysis. Very important new approaches for the determination of sedimentation coefficients and the deconvolution of sedimenting species have been introduced with respect to the analysis of boundary sedimentation velocity (SV) data. With regard to sedimentation equilibrium (SE) analysis, investigators now have the ability to determine association constants for many homogeneous and heterogeneous interacting systems from such measurements. Although there is an abundant literature using these new developments for characterizing protein systems, numerous investigators, and particularly new investigators, are unfamiliar with AU methodologies. The objective of this review is to assist protein scientists to gain a greater understanding of AU and the power of SV and SE for the characterization of proteins and protein complexes.

Retrovirus particle assembly is mediated by the Gag protein. Gag is a multi-domain protein containing discrete domains connected by flexible linkers. When recombinant HIV-1 Gag protein (lacking myristate at its N terminus and the p6 domain at its C terminus) is mixed with nucleic acid, it assembles into virus-like particles (VLPs) in a fully defined system in vitro. However, this assembly is defective in that the radius of curvature of the VLPs is far smaller than that of authentic immature virions. This defect can be corrected to varying degrees by addition of inositol phosphates to the assembly reaction. We have now explored the binding of inositol hexakisphosphate (IP6) to Gag and its effects upon the interactions between Gag protein molecules in solution. Our data indicate that basic regions at both ends of the protein contribute to IP6 binding. Gag is in monomer-dimer equilibrium in solution, and mutation of the previously described dimer interface within its capsid domain drastically reduces Gag dimerization. In contrast, when IP6 is added, Gag is in monomer-trimer rather than monomer-dimer equilibrium. The Gag protein with a mutation at the dimer interface also remains almost exclusively monomeric in IP6; thus the "dimer interface" is essential for the trimeric interaction in IP6. We discuss possible explanations for these results, including a change in conformation within the capsid domain induced by the binding of IP6 to other domains within the protein. The participation of both ends of Gag in IP6 interaction suggests that Gag is folded over in solution, with its ends near each other in three-dimensional space; direct support for this conclusion is provided in a companion manuscript. As Gag is an extended rod in immature virions, this apparent proximity of the ends in solution implies that it undergoes a major conformational change during particle assembly.

A single multi-domain viral protein, termed Gag, is sufficient for assembly of retrovirus-like particles in mammalian cells. We have purified the human immunodeficiency virus type 1 (HIV-1) Gag protein (lacking myristate at its N terminus and the p6 domain at its C terminus) from bacteria. This protein is capable of assembly into virus-like particles in a defined in vitro system. We have reported that it is in monomer-dimer equilibrium in solution, and have described a mutant Gag protein that remains monomeric at high concentrations in solution. We report that the mutant protein retains several properties of wild-type Gag. This mutant enabled us to analyze solutions of monomeric protein. Hydrodynamic studies on the mutant protein showed that it is highly asymmetric, with a frictional ratio of 1.66. Small-angle neutron scattering (SANS) experiments confirmed its asymmetry and yielded an R(g) value of 34 A. Atomic-level structures of individual domains within Gag have previously been determined, but these domains are connected in Gag by flexible linkers. We constructed a series of models of the mutant Gag protein based on these domain structures, and tested each model computationally for its agreement with the experimental hydrodynamic and SANS data. The only models consistent with the data were those in which Gag was folded over, with its N-terminal matrix domain near its C-terminal nucleocapsid domain in three-dimensional space. Since Gag is a rod-shaped molecule in the assembled immature virion, these findings imply that Gag undergoes a major conformational change upon virus assembly.