We first highlight the role of sedimentation velocity and sedimentation equilibrium in addressing receptor assembly state, and present a comparative analysis across the receptor family. We then use these results for understanding how receptors assemble at multisite regulatory elements, and hypothesize how these findings might play a role in receptor-specific gene regulation. Finally, we examine receptor behavior in a cellular context, with a view toward linking our in vitro studies with in vivo function.Sedimentation velocity experiments measure the transport of molecules in solution under centrifugal force. Here, we describe a method for monitoring the sedimentation of very large biological molecular assemblies using the interference optical systems of the analytical ultracentrifuge. The mass, partial-specific volume, and shape of macromolecules in solution affect their sedimentation rates as reflected in the sedimentation coefficient. The sedimentation coefficient is obtained by measuring the solute concentration as a function of radial distance during centrifugation. Monitoring the concentration can be accomplished using interference optics, absorbance optics, or the fluorescence detection system, each with inherent advantages. The interference optical system captures data much faster than these other optical systems, allowing for sedimentation velocity analysis of extremely large macromolecular complexes that sediment rapidly at very low rotor speeds. Supramolecular oligomeric complexes produced by self-association of 12-mer chromatin fibers are used to illustrate the advantages of the interference optics. Using interference optics, we show that chromatin fibers self-associate at physiological divalent salt concentrations to form structures that sediment between 10,000 and 350,000S. The method for characterizing chromatin oligomers described in this chapter will be generally useful for characterization of any biological structures that are too large to be studied by the absorbance optical system.Strong, positively cooperative binding can lead to the clustering of proteins on DNA. Here, we describe one approach to the analysis of such clusters. Our example is based on recent studies of the interactions of O(6)-alkylguanine DNA alkyltransferase (AGT) with high-molecular-weight DNAs (Adams et al., 2009; Tessmer, Melikishvili, & Fried, 2012). Cooperative cluster size distributions are predicted using the simplest homogeneous binding and cooperativity (HBC) model, together with data obtained by sedimentation equilibrium analysis. These predictions are tested using atomic force microscopy imaging; for AGT, measured cluster sizes are found to be significantly smaller than those predicted by the HBC model. A mechanism that may account for cluster size limitation is briefly discussed.Analytical ultracentrifugation (AUC) is a powerful tool that can provide thermodynamic information on associating systems. Here, we discuss how to use the two fundamental AUC applications, sedimentation velocity (SV), and sedimentation equilibrium (SE), to study nonspecific protein-nucleic acid interactions, with a special emphasis on how to analyze the experimental data to extract thermodynamic information. We discuss three specific applications of this approach (i) determination of nonspecific binding stoichiometry of E. coli integration host factor protein to dsDNA, (ii) characterization of nonspecific binding properties of Adenoviral IVa2 protein to dsDNA using SE-AUC, and (iii) analysis of the competition between specific and nonspecific DNA-binding interactions observed for E. coli integration host factor protein assembly on dsDNA. These approaches provide powerful tools that allow thermodynamic interrogation and thus a mechanistic understanding of how proteins bind nucleic acids by both specific and nonspecific interactions.G-quadruplexes are noncannonical four-stranded DNA or RNA structures formed by guanine-rich repeating sequences. Guanine nucleotides can hydrogen bond to form a planar tetrad structure. Such tetrads can stack to form quadruplexes of various molecularities with a variety of types of single-stranded loops joining the tetrads. High-resolution structures may be obtained by X-ray crystallography or NMR spectroscopy for quadruplexes formed by short (≈25 nt) sequences but these methods have yet to succeed in characterizing higher order quadruplex structures formed by longer sequences. An integrated computational and experimental approach was implemented in our laboratory to obtain structural models for higher order quadruplexes that might form in longer telomeric or promoter sequences. In our approach, atomic-level models are built using folding principles gleaned from available high-resolution structures and then optimized by molecular dynamics. The program HYDROPRO is then used to construct bead models of these structures to predict experimentally testable hydrodynamic properties. Models are validated by comparison of these properties with measured experimental values obtained by analytical ultracentrifugation or other biophysical tools. This chapter describes our approach and practical procedures.Analytical ultracentrifugation is a key tool to assess homogeneity of membrane protein samples, to determine protein association state and detergent concentration, and to characterize protein-protein equilibrium. Combining absorbance and interference detections gives information on the amount of the detergent and lipid bound to proteins. Changing the solvent density affects specifically the buoyancy of each of the different components, and can also be used to gain information on particle composition and interaction. We will present the related tools, recently implemented in the softwares Sedphat (sedfitsedphat.nibib.nih.gov/software) and Gussi (http//biophysics.swmed.edu/MBR/software.html), which help to measure the amount of detergent bound to the protein, and ascertain the protein association state within the protein-detergent complex. In addition, fluorescence detection allows focusing specifically on a labeled component within a complex mixture. We present two examples of sedimentation velocity experiments, allowing on one hand to evidence complex formation between an unpurified GFP-labeled protein and a membrane protein, and on the other hand to characterize fluorescent lipid vesicles. Small-angle X-ray and neutron scattering are techniques that give insights into the structure and conformation of macromolecules in solution. However, the detergents used to purify membrane protein are often imperfectly masked due to their amphipathic character. Particular strategies addressing membrane proteins were recently proposed, which are shortly presented.Amyloid fibrils result from the self-assembly of proteins into large aggregates with fibrillar morphology and common structural features. These fibrils form the major component of amyloid plaques that are associated with a number of common and debilitating diseases, including Alzheimer’s disease. Methylation inhibitor While a range of unrelated proteins and peptides are known to form amyloid fibrils, a common feature is the formation of aggregates of various sizes, including mature fibrils of differing length and/or structural morphology, small oligomeric precursors, and other less well-understood forms such as amorphous aggregates. These various species can possess distinct biochemical, biophysical, and pathological properties. Sedimentation velocity analysis can characterize amyloid fibril formation in exceptional detail, providing a particularly useful method for resolving the complex heterogeneity present in amyloid systems. In this chapter, we describe analytical methods for accurate quantification of both total amyloid fibril formation and the formation of distinct amyloid structures based on differential sedimentation properties. We also detail modern analytical ultracentrifugation methods to determine the size distribution of amyloid aggregates. We illustrate examples of the use of these techniques to provide biophysical and structural information on amyloid systems that would otherwise be difficult to obtain.Intrinsically disordered proteins have traditionally been largely neglected by structural biologists because a lack of rigid structure precludes their study by X-ray crystallography. Structural information must therefore be inferred from physicochemical studies of their solution behavior. Analytical ultracentrifugation yields important information about the gross conformation of an intrinsically disordered protein. Sedimentation velocity studies provide estimates of the weight-average sedimentation and diffusion coefficients of a given macromolecular state of the protein.Here, we review recent studies aimed at defining the importance of quaternary structure to a model oligomeric enzyme, dihydrodipicolinate synthase. This will illustrate the complementary and synergistic outcomes of coupling the techniques of analytical ultracentrifugation with enzyme kinetics, in vitro mutagenesis, macromolecular crystallography, small angle X-ray scattering, and molecular dynamics simulations, to demonstrate the role of subunit self-association in facilitating protein dynamics and enzyme function. This multitechnique approach has yielded new insights into the molecular evolution of protein quaternary structure.Sedimentation velocity analytical ultracentrifugation (SV-AUC) has seen a resurgence in popularity as a technique for characterizing macromolecules and complexes in solution. SV-AUC is a particularly powerful tool for studying protein conformation, complex stoichiometry, and interacting systems in general. Deconvoluting velocity data to determine a sedimentation coefficient distribution c(s) allows for the study of either individual proteins or multicomponent mixtures. The standard c(s) approach estimates molar masses of the sedimenting species based on determination of the frictional ratio (f/f0) from boundary shapes. The frictional ratio in this case is a weight-averaged parameter, which can lead to distortion of mass estimates and loss of information when attempting to analyze mixtures of macromolecules with different shapes. A two-dimensional extension of the c(s) analysis approach provides size-and-shape distributions that describe the data in terms of a sedimentation coefficient and frictional ratio grid. This allows for better resolution of species with very distinct shapes that may co-sediment and provides better molar mass determinations for multicomponent mixtures. An example case is illustrated using globular and nonglobular proteins of different masses with nearly identical sedimentation coefficients that could only be resolved using the size-and-shape distribution. Other applications of this analytical approach to complex biological systems are presented, focusing on proteins involved in the innate immune response to cytosolic microbial DNA.The ATPases associated with diverse cellular activities (AAA+) is a large superfamily of proteins involved in a broad array of biological processes. Many members of this family require nucleotide binding to assemble into their final active hexameric form. We have been studying two example members, Escherichia coli ClpA and ClpB. These two enzymes are active as hexameric rings that both require nucleotide binding for assembly. Our studies have shown that they both reside in a monomer, dimer, tetramer, and hexamer equilibrium, and this equilibrium is thermodynamically linked to nucleotide binding. Moreover, we are finding that the kinetics of the assembly reaction are very different for the two enzymes. Here, we present our strategy for determining the self-association constants in the absence of nucleotide to set the stage for the analysis of nucleotide binding from other experimental approaches including analytical ultracentrifugation.