Theoretical Studies of Single Molecule Biophysical Systems and Photochemical Ensembles

• Main Author: Ayalasomayajula, Meher Kiran Prakash
• Format: Thesis
• Language: English
• Published: California Institute of Technology 2008
• Subjects: catalysis; autocorrelation; bell's escape; jarzynski's equality; singl molecule; fluctuations; reflection principle; photodissociation; fluctuation theorem; Applied Physics; enzymes; nitrous oxide; fractionation; crooks theorem; spectral diffusion; Antarc*; Antarctica
• Online Access: https://dx.doi.org/10.7907/5d2k-7h81; https://resolver.caltech.edu/CaltechETD:etd-09062007-233423

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The focus of the present thesis is on theoretical analysis to understand the experimental results from three quite different systems - enzymes, RNA hairpins and nitrous oxide (N2O). Some experiments on single enzymes showed very unusual data: in separate experiments the fluctuations in catalysis rate ([...]) and fluorescence lifetime ([...]) of chromophore in single enzymes showed long-lasting autocorrelations, represented by a stretched exponential and power-law, respectively. With the aim of interpreting the origin of these fluctuations, we proposed a formulation based on fluctuations in electrostatic interaction energy ([...]) at the active site in the enzyme leading to the fluctuations in the various observables. We developed relations between the autocorrelation functions of [...], [...], spectral diffusion ([...]) and the radiative component of fluorescence lifetime ([...]). It was pointed out that the relation between [...] and [...], seen experimentally and modeled theoretically by using the relation noted above, is a dynamic analog of the solvatochromism concept used in the catalysis of organic reactions by solvent. The estimation of fluctuations in electrostatic interactions on the milliseconds to seconds time scale by computational methods is not possible, which are typically limited to tens of nanoseconds. To calculate the autocorrelation of electrostatic interactions and to compare them with experiments, we used the frequency dependent dielectric response of proteins and related it to the autocorrelation of [...]. Based on this formulation, we find a good agreement between the single molecule data on the enzyme candida antarctica lipase B and the calculation using dielectric response data on the enzyme. In single molecule data from other enzymes for which [...] is not yet available, we have predictions based on a commonly observed functional form of [...] for other proteins. Single molecule experiments on RNA hairpins were used to test a nonequilibrium statistical physics result - Crooks' theorem. Crooks' theorem is about an exact equality relating the probability distributions of work done (W) on a system by varying an external parameter in the forward and reverse directions in a predetermined way. Usually in the single molecule experiments this predetermined variation is a constant rate ([...]) of increase or decrease of the external force for all runs of the experiment. Our study focuses on the relevance of the RNA hairpin unfolding experiments to the theorem. The unfolding of the molecule leads to a drop in the externally controlled force on the molecule, a condition which is not suited to the existing derivations of Crooks' theorem. An alternative interpretation of the experimental unfolding and refolding data using a phenomenological force-dependent distortion of activation barriers is provided to gain insight into the data on the probability distribution of work done during unfolding, refolding corresponding to different rates of change of force. This interpretation shows that the crossing of the unfolding and refolding work distributions which happens at the same value of W for all [... is a necessary but not sufficient condition to verify the theorem. The experimental data on UV photodissociation of the greenhouse gas N2O and the associated isotope effects are important from the perspective of atmospheric interest. The calculations in the literature to model the photodissociation observations are of two kinds - some are computationally intensive quantum mechanical methods using wave packet propagation and the others are based on empirical calculations. The two different calculations we present, based on two different variants of the 'multidimensional reflection principle' maintain the simplicity of computation, while using the available ab initio data on the molecule for the potential energy surfaces and the transition dipole moments. In one of the calculations, the absorption cross section was broadened empirically to get agreement with the absorption data and the results were then used to make calculations of isotopologue fractionation. This broadening was also needed in a wave packet propagation calculation. In a later calculation, without introducing the broadening factor, the results were compared only on one side of the absorption cross section, where the isotopic fractionation measurements are available. Using these two methods, the fractionation of heavier isotopologues of N2O with respect to the most abundant isotopologue [...] were calculated and compared with the experiments. A simple relation between the fractionations of [...] and [...] was observed in the results from our calculations. A perturbation theoretical result was used to derive this relationship, which is independent of the detailed calculations required for each of the isotopologues individually.