Theoretical and Numerical Studies of Dynamics in Nucleic Acids based on Experimental NMR Data

Thesis (Ph.D.)--University of Washington, 2012The collection of work presented in this thesis is directed towards building an understanding of the dynamics of nucleic acid molecules and their components using data obtained from solid state and solution NMR experiments. The focus of these studies is to develop analytical and numerical methods of elucidating motional trajectories of residues in example molecules, by simulating the impact of specific choices of models on NMR observables. Specifically, the target molecules studied were the unbound HIV-1 TAR RNA, a 29 nucleotide RNA segment, and the unbound dodecamer HhaI methyltransferase-recognition DNA. The data available for various residues in these systems include solid state line shapes, longitudinal (T_1Z) and quadrupolar (T_1Q) relaxation times, as well as solution longitudinal (T₁) and rotating frame (T_1&rho) relaxation times and Nuclear Overhauser Effects (NOEs). The four projects discussed in this thesis form a cohesive whole, with each succeeding method either building upon previous work or adding a new means of analysis: firstly, a slow exchange theory is presented where discrete-jump motional models derived using solid state NMR data can be tested against solution relaxation times, by the inclusion of both overall molecular tumbling and exchange between conformers occurring at a time scale much slower than the tumbling time scale. The time scale separation allows for a particularly simple weighted summation over the spectral density contributions from the various conformers. The second project, discussed subsequently, removes this assumption of time scale separation, and allows for any rate of exchange between conformers. Both simulation protocols use the TAR RNA molecule as the test system. Parallel work on the HhaI-recognition DNA builds a framework for testing a discrete-jump trajectory constructed using pre-existing rotamers of the molecule against solid state relaxation times. This visualization of the dynamics of a residue is then carried over to the solution domain, where the properties of computationally energy-minimized structures of TAR RNA are used to define a solution trajectory. In this last case, data available for multiple sites on the molecule are used to test the model for the trajectory, as well as to fit the rates of motion