Determination of Biomolecular Interdomain Motions using Nuclear Magnetic Resonance

Biological macromolecules can rearrange interdomain orientations when binding to various partners. Interdomain dynamics serve as a molecular mechanism to guide the transitions between orientations. However, our understanding of interdomain dynamics is limited because a useful description of interdomain motions requires an estimate of the probabilities of interdomain conformations, increasing complexity of the problem.

Staphylococcal protein A (SpA) has five tandem protein-binding domains and four interdomain linkers. The domains enable Staphylococcus aureus to evade the host immune system by binding to multiple host proteins including antibodies. Here, I present a study of the interdomain motions of two adjacent domains in SpA. NMR spin relaxation experiments identified a 6-residue flexible interdomain linker and interdomain motions. To quantify the anisotropy of the distribution of interdomain orientations, we measured residual dipolar couplings (RDCs) from the two domains with multiple alignments. The N-terminal domain was directly aligned by a lanthanide ion and not influenced by interdomain motions, so it acted as a reference frame to achieve motional decoupling. We also applied {\it de novo} methods to extract spatial dynamic information from RDCs and represent interdomain motions as a continuous distribution on the 3D rotational space. Significant anisotropy was observed in the distribution, indicating the motion populates some interdomain orientations more than others. Statistical thermodynamic analysis of the observed orientational distribution suggests that it is among the energetically most favorable orientational distributions for binding to antibodies. Thus, the affinity is enhanced by a pre-posed distribution of interdomain orientations while maintaining the flexibility required for function.

The protocol described above can be applied to other biological systems in general. Protein molecule calmodulin and RNA molecule trans-activation response element (TAR) also have intensive interdomain motions with relative small intradomain dynamics. Their interdomain motions were studied using our method based on published RDC data. Our results were consistent with literature results in general. The differences could be due to previous studies' use of physical models, which contain assumptions about potential energy and thus introduced non-experimental information into the interpretations.

Seismic Response Analysis of a Full-Scale Base-Isolated Structure via Measurements and Modeling

The full-scale base-isolated structure studied in this dissertation is the only base-isolated building in South Island of New Zealand. It sustained hundreds of earthquake ground motions from September 2010 and well into 2012. Several large earthquake responses were recorded in December 2011 by NEES@UCLA and by GeoNet recording station nearby Christchurch Women's Hospital. The primary focus of this dissertation is to advance the state-of-the art of the methods to evaluate performance of seismic-isolated structures and the effects of soil-structure interaction by developing new data processing methodologies to overcome current limitations and by implementing advanced numerical modeling in OpenSees for direct analysis of soil-structure interaction.

This dissertation presents a novel method for recovering force-displacement relations within the isolators of building structures with unknown nonlinearities from sparse seismic-response measurements of floor accelerations. The method requires only direct matrix calculations (factorizations and multiplications); no iterative trial-and-error methods are required. The method requires a mass matrix, or at least an estimate of the floor masses. A stiffness matrix may be used, but is not necessary. Essentially, the method operates on a matrix of incomplete measurements of floor accelerations. In the special case of complete floor measurements of systems with linear dynamics, real modes, and equal floor masses, the principal components of this matrix are the modal responses. In the more general case of partial measurements and nonlinear dynamics, the method extracts a number of linearly-dependent components from Hankel matrices of measured horizontal response accelerations, assembles these components row-wise and extracts principal components from the singular value decomposition of this large matrix of linearly-dependent components. These principal components are then interpolated between floors in a way that minimizes the curvature energy of the interpolation. This interpolation step can make use of a reduced-order stiffness matrix, a backward difference matrix or a central difference matrix. The measured and interpolated floor acceleration components at all floors are then assembled and multiplied by a mass matrix. The recovered in-service force-displacement relations are then incorporated into the OpenSees soil structure interaction model.

Numerical simulations of soil-structure interaction involving non-uniform soil behavior are conducted following the development of the complete soil-structure interaction model of Christchurch Women's Hospital in OpenSees. In these 2D OpenSees models, the superstructure is modeled as two-dimensional frames in short span and long span respectively. The lead rubber bearings are modeled as elastomeric bearing (Bouc Wen) elements. The soil underlying the concrete raft foundation is modeled with linear elastic plane strain quadrilateral element. The non-uniformity of the soil profile is incorporated by extraction and interpolation of shear wave velocity profile from the Canterbury Geotechnical Database. The validity of the complete two-dimensional soil-structure interaction OpenSees model for the hospital is checked by comparing the results of peak floor responses and force-displacement relations within the isolation system achieved from OpenSees simulations to the recorded measurements. General explanations and implications, supported by displacement drifts, floor acceleration and displacement responses, force-displacement relations are described to address the effects of soil-structure interaction.