Data analysis and modeling of small-angle neutron scattering data with contrast variation from bio-macromolecular complexes

Small-angle neutron scattering (SANS) with contrast variation (CV) is a valuable technique in the structural biology toolchest. Accurate structural parameters-e.g., radii of gyration, volumes, dimensions, and distance distribution(s)-can be derived from the SANS-CV data to yield the shape and disposition of the individual components within stable complexes. Contrast variation is achieved through the substitution of hydrogen isotopes (¹H for ²H) in molecules and solvents to alter the neutron scattering properties of each component of a complex. While SANS-CV can be used a stand-alone technique for interrogating the overall structure of biomacromolecules in solution, it also complements other methods such as small-angle X-ray scattering, crystallography, nuclear magnetic resonance, and cryo-electron microscopy. Undertaking a SANS-CV experiment is challenging, due in part to the preparation of significant quantities of monodisperse samples that may require deuterium (²H) labeling. Nevertheless, SANS-CV can be used to study a diverse range biomacromolecular complexes including protein-protein and protein-nucleic acid systems, membrane proteins, and flexible systems resistant to crystallization. This chapter describes how to approach the data analysis and modeling of SANS data, including: (1) Analysis of the forward scattering (I(0)) and calculation of theoretical estimates of contrast; (2) Analysis of the contrast dependence of the radius of gyration using the Stuhrmann plot and parallel axis theorem; (3) Calculation of composite scattering functions to evaluate the size, shape, and dispositions of individual components within a complex, and; (4) Development of real-space models to fit the SANS-CV data using volume-element bead modeling or atomistic rigid body modeling.

Capillary electrophoretic reactor for estimation of spontaneous dissociation rate of Trypsin-Aprotinin complex

A capillary electrophoretic reactor was used to analyze the dissociation kinetics of an enzyme-inhibitor complex in a homogeneous solution without immobilization. The complex consisting of trypsin (Try) and aprotinin (Apr) was used as the model. Capillary electrophoresis provided a reaction field for Try-Apr complex to dissociate through the steady removal of free Try and Apr from the Try-Apr zone. By analyzing the dependence of peak height of Try-Apr on separation time, the dissociation rate k_d^H was obtained as 2.73 × 10^-4 s^-1 (298 K) at pH 2.46. The dependence of k_d^H on the proton concentration (pH = 2.09-3.12) revealed a first-order dependence of k_d^H on [H⁺]; k_d^H = k_d + k₁[H⁺], where k_d is the spontaneous dissociation rate and was 5.65 × 10^-5 s^-1, and k₁ is the second-order rate constant and was 5.07 × 10^-2 M^-1 s^-1. From the k_d value, the half-life of the Try-Apr complex at physiological pH was determined as 3.4 h. The presence of the proton-assisted dissociation can be explained by the protonation of -COO^- of the Asp residue in Try, which breaks the salt bridge with the -NH₃⁺ group of Lys in Apr.