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Molecular biophysics is a rapidly evolving field aimed at the physics-based investigation of the biomolecular processes that enable life. In this thesis, we explore two such processes: the thermodynamics of DNA bending, and the mechanism of the RecQ DNA helicase. A computational approach using a coarse-grained model of DNA is employed for the former; an experimental approach relying heavily on single-molecule fluorescence for the latter. There is much interest in understanding the physics of DNA bending, due to both its biological role in genome regulation and its relevance to nanotechnology. Small DNA bending fluctuations are well described by existing models; however, there is less consensus on what happens at larger bending fluctuations. A coarse-grained simulation is used to fully characterize the thermodynamics and mechanics of duplex DNA bending. We then use this newfound insight to harmonize experimental results between four distinct experimental systems: a 'molecular vise', DNA cyclization, DNA minicircles and a 'strained duplex'. We find that a specific structural defect present at large bending fluctuations, a 'kink', is responsible for the deviation from existing theory at lengths below about 80 base pairs. The RecQ DNA helicase is also of much biological and clinical interest, owing to its essential role in genome integrity via replication, recombination and repair. In humans, heritable defects in the RecQ helicases manifest clinically as premature aging and a greatly elevated cancer risk, in disorders such as Werner and Bloom syndromes. Unfortunately, the mechanism by which the RecQ helicase processes DNA remains poorly understood. Although several models have been proposed to describe the mechanics of helicases based on biochemical and structural data, ensemble experiments have been unable to address some of the more nuanced questions of helicase function. We prepare novel substrates to probe the mechanism of the RecQ helicase via single-molecule fluorescence, exploring DNA binding, translocation and unwinding. Using this insight, we propose a model for RecQ helicase activity.

In this thesis, the response of DNA and RNA to linear and torsional mechanical stress is studied using coarse-grained models. Inspired by single-molecule assays developed over the last two decades, the end-to-end extension, buckling and torque response behaviour of the stressed molecules is probed under conditions similar to experimentally used setups. Direct comparison with experimental data yields excellent agreement for many conditions. Results from coarse-grained simulations are also compared to the predictions of continuum models of linear polymer elasticity. A state diagram for supercoiled DNA as a function of twist and tension is determined. A novel confomational state of mechanically stressed DNA is proposed, consisting of a plectonemic structure with a denaturation bubble localized in its end-loop. The interconversion between this novel state and other, known structural motifs of supercoiled DNA is studied in detail. In particular, the influence of sequence properties on the novel state is investigated. Several possible implications for supercoiled DNA structures in vivo are discussed. Furthermore, the dynamical consequences of coupled denaturation and writhing are studied, and used to explain observations from recent single molecule experiments of DNA strand dynamics. Finally, the denaturation behaviour, topology and dynamics of short DNA minicircles is studies using coarse-grained simulations. Long-range interactions in the denaturation behaviour of the system are observed. These are induced by the topology of the system, and are consistent with results from recent molecular imaging studies. The results from coarse-grained simulations are related to modelling of the same system in all-atom simulations and a local denaturation model of DNA, yielding insight into the applicability of these different modelling approaches to study different processes in nucleic acids.

The interaction between nucleic acids and small molecule ligands is continuously generating significant interest due to their widespread biological and bioanalytical applications. We investigated the mechanical property of the binding between aptamers and small molecules. Using an ATP binding aptamer as an example, we observed that the mechanical stability of the aptamers that are bound with ATP is higher than those without a ligand. Therefore, a force-based sensor can be developed to detect small molecules using aptamers as a platform. We determined the dissociation constant, Kd, for aptamer-ligand interactions at the single-molecule level by applying a Hess-like cycle. Our experiments allow the Kd determination from only one ligand concentration which was further validated by our capillary electrophoresis (CE) method. By using only one ligand concentration, such a method not only saves time and material, but also is less susceptible to reduced reproducibility due to run-to-run fluctuations. G-quadruplex forming sequences which are wide spread in the genome particularly in telomeres and promoter regions have been shown to be therapeutic targets. G-quadruplex structures have been extensively studied using mostly conventional methods. However, the mechanical stability, thermodynamics, kinetics properties of these interactions at the single-molecule level, remains to be fully understood. While the formation of these G-quadruplex structures is highly dynamic, they are mechanically stabilized upon ligand binding which may affect their biological functions. Small molecules which bind to nucleic acid structures may interfere with vital cellular processes such as transcription and protein translation during cell division by acting as energy barriers or mechanical blockage. Therefore, understanding stability of nucleic structures from a mechanical stability stand point is critical to fully explore their therapeutic potentials. We have investigated the human telomeric repeat containing RNA (TERRA) G-quadruplex structures. By using a TERRA sequence that hosts only one G-quadruplex at the single-molecule level in a laser-tweezers instrument, we are able to investigate intramolecular G-quadruplex without implications from high order structures due to the tendency of the TERRA sequence to self-associate. Using a mechanical unfolding and refolding method, we revealed multiple TERRA G-quadruplexes in a solution mixture. One of the structures is consistent with the parallel conformation determined by NMR/X-ray techniques. In addition, we identified a partially folded structure that serves as an intermediate to the unfolding and refolding of the TERRA G-quadruplex. By applying a force-jump approach, the refolding kinetics of the TERRA G-quadruplex and the intermediate were measured and compared with those of human telomeric DNA (hTelo) G-quadruplex. We have found that formation of the TERRA G-quadruplex is slower than that of hTelo G-quadruplex. Together with the higher thermodynamic and mechanical stability of the TERRA with respect to the hTelo G-quadruplex, these results suggest different regulatory capacities of RNA and DNA G-quadruplexes for processes associated with human telomeres.Lastly, a quantitative assay was developed to investigate sphingosine kinase 2 (SphK2) activity both in vitro and with cell lysates, using capillary electrophoresis with laser-induced fluorescence (CE-LIF) and sphingosine fluorescein as the substrate. Sphingosine and sphingosine-1-phosphate are found in very minute quantities in cells and therefore require highly sensitive techniques for quantitative analysis.

This thesis presents the development and application of nanoscale techniques to trap and

Studying the thermal fluctuations of DNA molecules reveals not only a wealth of interesting equilibrium and non-equilibrium statistical mechanics, but is also of importance for understanding the dynamics of DNA in vivo. An instance of the latter is in the context of regulatory functions that require collaborative interactions of distant operator sites on the DNA molecule. These thermal fluctuations are extremely sensitive to mechanical constraints, such as super-coiling or mechanical tension in the DNA. The natural force scale fc on which these fluctuations are sensitive to tension is related to the molecule's persistence length lp by fc = kBT/lp = 80 fN. We studied the dynamics of single DNA molecules subjected to tension under equilibrium and non-equilibrium conditions using a modified scanning-line laser trap. The studies of the hydrodynamic and entropic forces associated with DNA molecules in solution required the ability to study and manipulate single DNA molecules with unprecedented accuracy. Towards this end, we developed and calibrated an all-optical, scanning-line tweezer based apparatus, which allows us to generate constant forces between 20 fN and 3pN. We also developed a fast, high-resolution (50nm) particle position measurement scheme that is based on synchronous detection of forward-scattered laser light during a line scan of the beam. Using these techniques, we studied the behavior of lambda-DNA molecules that were relaxing to an equilibrium configuration as well as those already at equilibrium. In the non-equilibrium studies we found good general agreement with the predictions derived from the wormlike-chain (WLC) model for extended DNA molecules. Studying the energies involved in these experiments also revealed that the hydrodynamic drag of the DNA molecule contributes almost a third of the energy dissipated due to the viscous forces in the system. In the equilibrium studies we observed a decrease of the fundamental time constant with increasing extension of the molecule. This suggests that the change in spring constant dominates changes in the intra-chain hydrodynamic coupling between segments as the Gaussian coil unravels into an extended conformation.

The development of single molecule spectroscopy over the last two decades has made it possible to probe the conformational structure and dynamics of biomolecules with an unprecedented level of detail. Room-temperature Single-Molecule Fluorescence Resonance Energy Transfer (SM-FRET), in particular, provides the ability to probe intra- and inter-molecular distances as a function of time in a direct manner. These experiments also give rise to many new theoretical questions regarding the behavior of single molecules as apposed to averages over large ensembles. Previous theoretical work on SM-FRET has been based on relatively simple phenomenological stochastic models. In this thesis, we take the next step by attempting to provide a more molecular view of the conformational structure and dynamics underlying SM-FRET experiments. To this end, we use combination of Langevin Dynamics simulations of the biopolymer together with kinetic Monte Carlo simulations of the photon statistics. The analysis focuses on quantities which are particularly relevant to SM-FRET experiments, such as the distribution of donor-acceptor distance and its displacement. Emphasis is put on the unique ability of those experiments to provide information on the correlations between conformational structure and dynamics. We also explore the effect of immobilizing the biopolyiner on surface or trapping it in a pore. Our investigation focuses on two off-lattice models, one of a freely-joined homopolymer and another of a polyypeptide. In the homopolymer case, we consider the conformational structure and dynamics in good and poor solvents, as well as the effect of immobilization on attractive or repulsive surfaces. The polypeptide model is designed to mimic the two-stranded coiled-coil from the yeast transcription factor GCN4 that was studied in the pioneering SM-FILET experiment by Hochstrasser and co-workers[46, 47]. In this case, we consider itninobilizations on repulsive and attractive surfaces as well as encapsulation inside of a pore with varying sizes and shapes. We also consider two types of denaturated states that differ with respect to the amount of residual secondary structure. Finally, we propose a new way for extracting the dine scales of conformational dynamics from single-molecule single-photon fluorescence statistics. To this end, we derive a general relation between the autocorrelation function of the time-delay, between excitation and single photon emission and the autocorrelation function of the fluorescence life-time. We also examine the conditions under which there is a direct relation between the decay of the delay-time autocorrelation function and the time scale of conformational dynamics. We demonstrate how the time scales of conformational dynamics can be extracted from the time-delay autocorrelation function via applications to the above-mentioned homopolyner and polypeptide models.