Date of Award

2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mechanical Engineering & Applied Mechanics

First Advisor

Prashant K. Purohit

Abstract

This thesis discusses the development and applications of a double-stranded elastic rod model for DNA, henceforth called \textit{birod} model. The model highlights the role of DNA elasticity in allosteric interactions between two ligands bound to DNA (chapters 3 and 4) and--combined with statistical mechanics--provides insights into the micromechanics of DNA melting (chapter 5).

In chapters 3 and 4, the birod model for DNA is used to compute the allosteric interaction energy between two ligands on DNA. This interaction is quantified by measuring the change in free energy as a function of the distance between the binding sites for two ligands. The trends in this interaction energy can be explained using the birod model which accounts for the helical shape of DNA, elastic deformation of strands and base-pairs, and the stacking energy due to perturbations in position and orientation of the bases caused by the binding of ligands. The model predicts that the interaction energy between two ligands decays exponentially with the distance between them and oscillates with the periodicity of the double helix, which by appropriate parameter fitting is shown to quantitatively match with the experimental measurements. Furthermore, the decaying oscillatory trend in the perturbation of groove width in a protein-DNA complex predicted by the model is consistent with the results from molecular simulations.

In chapter 2, structural transitions in DNA are studied using ideas from the Zimm-Bragg helix-coil transition theory and the theory of fluctuating elastic rods. Experimental studies on single molecules of DNA have reported several cooperative structural transitions, including the coexistence of three phases, when tensile force or twisting moment is applied to the molecule. The interface energy between two phases of DNA imparts the cooperative character to the force-extension curve or torque-rotation curve observed experimentally. In chapter 5, we choose one such structural transition from dsDNA to single-stranded DNA--called DNA melting--and study it using the statistical mechanics and continuum mechanics of an elastic birod. The detailed microscopic description of the outer-strands and base-pairs admissible in the birod model enables us to decipher why the DNA oligomers with higher GC content are stiffer. Furthermore, a nonlinear asymmetric interaction between the outer strands leads to a sudden and highly cooperative melting transition. Furthermore, the model enables us to examine the effect of tensile force on the melting temperature.

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