On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.

Structural and Biochemical Dissection of the Trehalose Biosynthetic Complex in Pathogenic Fungi

Trehalose is a non-reducing disaccharide essential for pathogenic fungal survival and virulence. The biosynthesis of trehalose requires the trehalose-6-phosphate synthase, Tps1, and trehalose-6-phosphate phosphatase, Tps2. More importantly, the trehalose biosynthetic pathway is absent in mammals, conferring this pathway as an ideal target for antifungal drug design. However, lack of germane biochemical and structural information hinders antifungal drug design against these targets.

In this dissertation, macromolecular X-ray crystallography and biochemical assays were employed to understand the structures and functions of proteins involved in the trehalose biosynthetic pathway. I report here the first eukaryotic Tps1 structures from Candida albicans (C. albicans) and Aspergillus fumigatus (A. fumigatus) with substrates or substrate analogs. These structures reveal the key residues involved in substrate binding and catalysis. Subsequent enzymatic assays and cellular assays highlight the significance of these key Tps1 residues in enzyme function and fungal stress response. The Tps1 structure captured in its transition-state with a non-hydrolysable inhibitor demonstrates that Tps1 adopts an “internal return like” mechanism for catalysis. Furthermore, disruption of the trehalose biosynthetic complex formation through abolishing Tps1 dimerization reveals that complex formation has regulatory function in addition to trehalose production, providing additional targets for antifungal drug intervention.

I also present here the structure of the Tps2 N-terminal domain (Tps2NTD) from C. albicans, which may be involved in the proper formation of the trehalose biosynthetic complex. Deletion of the Tps2NTD results in a temperature sensitive phenotype. Further, I describe in this dissertation the structures of the Tps2 phosphatase domain (Tps2PD) from C. albicans, A. fumigatus and Cryptococcus neoformans (C. neoformans) in multiple conformational states. The structures of the C. albicans Tps2PD -BeF3-trehalose complex and C. neoformans Tps2PD(D24N)-T6P complex reveal extensive interactions between both glucose moieties of the trehalose involving all eight hydroxyl groups and multiple residues of both the cap and core domains of Tps2PD. These structures also reveal that steric hindrance is a key underlying factor for the exquisite substrate specificity of Tps2PD. In addition, the structures of Tps2PD in the open conformation provide direct visualization of the conformational changes of this domain that are effected by substrate binding and product release.

Last, I present the structure of the C. albicans trehalose synthase regulatory protein (Tps3) pseudo-phosphatase domain (Tps3PPD) structure. Tps3PPD adopts a haloacid dehydrogenase superfamily (HADSF) phosphatase fold with a core Rossmann-fold domain and a α/β fold cap domain. Despite lack of phosphatase activity, the cleft between the Tps3PPD core domain and cap domain presents a binding pocket for a yet uncharacterized ligand. Identification of this ligand could reveal the cellular function of Tps3 and any interconnection of the trehalose biosynthetic pathway with other cellular metabolic pathways.

Combined, these structures together with significant biochemical analyses advance our understanding of the proteins responsible for trehalose biosynthesis. These structures are ready to be exploited to rationally design or optimize inhibitors of the trehalose biosynthetic pathway enzymes. Hence, the work described in this thesis has laid the groundwork for the design of Tps1 and Tps2 specific inhibitors, which ultimately could lead to novel therapeutics to treat fungal infections.

A Comparative Review of Computational Methods as Applied to Gold(I) Complexes and Mechanisms

In the last two decades, the field of homogeneous gold catalysis has been

extremely active, growing at a rapid pace. Another rapidly-growing field—that of

computational chemistry—has often been applied to the investigation of various gold-

catalyzed reaction mechanisms. Unfortunately, a number of recent mechanistic studies

have utilized computational methods that have been shown to be inappropriate and

inaccurate in their description of gold chemistry. This work presents an overview of

available computational methods with a focus on the approximations and limitations

inherent in each, and offers a review of experimentally-characterized gold(I) complexes

and proposed mechanisms as compared with their computationally-modeled

counterparts. No aim is made to identify a “recommended” computational method for

investigations of gold catalysis; rather, discrepancies between experimentally and

computationally obtained values are highlighted, and the systematic errors between

different computational methods are discussed.