Mechanics and biological function of nucleic acids are intimately coupled. The DNA double helix must be opened to allow base pairing of RNA during transcription; RNA must bend and fold in its many cellular functions. Presented in this dissertation are two investigations of mechanical deformations of nucleic acids, conducted with optical tweezers.

In the introduction, the mechanical properties of DNA and RNA and their relevance to their cellular functions are introduced, to give the reader context for the results presented in the Chapters 2 and 3. This is followed by an introduction to the theory of semiflexible polymer elasticity. The optical tweezers instruments used in conducting these investigations are then presented, along with calibration procedures and a short introduction to optical trapping physics.

Chapter 2 presents an investigation of the effect of downstream DNA tension on initiation by T7 RNA polymerase. A hidden Markov model is fit to force-dependent lifetimes obtained from optical tweezers experiments, allowing us to identify which steps in initiation are force-dependent and estimate rates and transition state distances. We find that 1-2 pN of tension is sufficient to turn off gene expression by causing transcription bubble collapse and destabilizing the bound state. Our force-dependence scheme and estimated transition distances provide independent support for the "scrunching" model of initiation.

The effects of cation binding and screening on single-stranded helix formation in poly(A) RNA are presented in Chapter 3. Magnesium and calcium bind to poly(A), stabilize the helix, and change its mechanical properties. A new model of helix-coil transitions is presented and used to estimate energetics and mechanical properties.

Chapter 4 presents the first fully objective algorithm for use in analyzing the noisy staircaselike data that is often produced by single-molecule fluorescence experiments. A test based on the SIC (BIC) statistic is used in conjunction with a progressive step-placement scheme to locate changepoints (steps) in noisy data. Its performance is compared to other step detection algorithms in use by biophysicists by repeating tests performed in a recent review.

Experimental protocols and computer codes used in these investigations are presented in detail in the appendices.