The boom of nanoscience and nanotechnology has pushed the instrumentation forward. The experimental setups have been developed so intensively that the single-molecule experiments have now become standard techniques. Such experiments represent a new way to observe, measure and get information from nature. The control and measuring devices are more accurate and precise every day. This allows the scientists to observe, explore and quantify processes that some years ago were considered too complex. Thanks to the single-molecule techniques, biophysics has experienced a revolution. The traditional experiments performed in bulk have been repeated at the single-molecule level, which has revealed the extraordinary capabilities of the cellular machinery. All these advances have established biophysics as a scientific discipline, different from biology and physics; with its own topics, concerns and issues.

Optical tweezers were initially developed by physicists who were fascinated by the radiation pressure of light. Biophysicists soon foresaw the useful applications of optical tweezers to manipulate tiny objects. The range of forces measured and exerted by optical tweezers is suitable to carry out experiments with biomolecules. Optical tweezers is a clean and non-invasive technique which also allows to do experiments in vivo. The Minitweezers is an optical tweezers experimental setup characterized by its compactness, stability, accuracy and user-friendliness. The optical trap is generally formed with two counter propagating lasers and a micropipette is used as an anchor point. The force is measured by conservation of light momentum and the distances are measured with light-levers. The calibration is independent of most experimental parameters (e.g., laser power, bead size) so that it only has to be done once. The Minitweezers were designed to be easily customized. Therefore, new experimental pulling protocols can be easily implemented and the already existing ones can be modified and expanded.

The molecule of DNA has a central role in life: It stores the genetic information. The central dogma of molecular biology states the general flow of genetic information in life (replication and transcription of DNA, and translation of RNA). The double-helix structure of DNA preserves the base-pairs located in between, which are the physical carriers of genetic information. The cellular machinery needs to disrupt the hydrogen-bonds that hold the base-pairs together in order to read the sequence of bases. Similarly, mechanical unzipping of DNA consists in pulling on the two strands of DNA from the same end in order to split them apart. Unzipping can be performed with several single-molecule manipulation techniques (microneedles, AFM, magnetic tweezers). Optical tweezers can produce unzipping at controlled position or at controlled force, which give different experimental measurements. At controlled position the FDC exhibits a sawtooth pattern, whose slopes correspond to the stretching of ssDNA and the force rips correspond to the disruption of base-pairs. At controlled force, the base-pairs are disrupted in large groups and the FDC is a monotonically increasing function. In both cases, the FDC is sequence-dependent. The NN model describes the hybridization reaction of two strands that form a duplex of dsDNA. Such model can be completed with elastic models of polymers to describe the unzipping experiments. The so-called mesoscopic model provides a prediction of the FDC, an estimation of the free energy landscape and the number of open base-pairs as the DNA is unzipped.

From a physical point of view, the unzipping of DNA can be studied as a cracking phenomenon. Here, the details about the sequence of the molecule are less relevant. The attention is focused on the statistical properties of the metastable states observed during unzipping. A Bayesian approach has been developed in order to infer the number of open base-pairs of the intermediate states observed during unzipping. This allows us to calculate the size of the unzipping regions. The distribution of sizes depends on the experimental conditions (trap stiffness, NNBP free energies). The sizes range from 10-80 bp and the smaller ones are more frequent than larger ones. The experimental accuracy does not allow to observe all regions of sizes below 10 bp. On the other hand, the effective trap stiffness must be much higher to observe single bp openings of large unzipping regions. The toy model is capable of reproducing the statistical properties of unzipping with the minimal necessary elements. The model predicts and qualitatively reproduces the experimental distribution of sizes. The unzipping of one base-pair at a time can only be achieved by applying local force on the unzipping fork and by having a trap stiffness value higher than 100 pN/nm. The stiffness of a ssDNA nucleotide coincides with this value, which is a remarkable property of DNA that allows the cellular machinery to access the genetic information one base-pair at a time.

The NNBP free energies obtained from temperature melting experiments cannot quantitatively reproduce the FDC obtained from DNA unzipping experiments. The discrepancies are markedly significant at low salt concentration. The unzipping experiments performed on DNA can be used to extract the formation free energy of NNBP motifs. The experimental data can be fit to the mesoscopic model in order to determine the values of the NNBP energies. The model has to be completed with an accurate description of the elastic properties of the ssDNA, a shift function that corrects the instrumental drift and the specific free energy formation of the end loop. The fit is performed with a Monte Carlo optimization algorithm that provides the values of the fitting parameters rapidly and robustly. Differently from the UO rules, the resulting NNBP energies at all salt concentrations are well described by a heterogeneous salt correction. Such dependency can be attributed to the different solvation of the base-pairs, or to the sequence-dependent elastic response of the ssDNA. The unzipping experiments cannot provide the enthalpies and entropies of the NNBP motifs nor the initiation factors. However, the enthalpies and entropies can be inferred by fitting the melting temperatures of oligonucleotides. The results show that the new values of the NNBP energies correctly describe both the melting and unzipping experiments. Furthermore, the new NNBP energies predict the melting temperatures of oligos longer than 15 bp better than the UO NNBP energies. This methodology can be extended to other experimental conditions in which the melting experiments cannot be applied. For instance, in a melting experiment RNA is hydrolyzed by magnesium when the temperature increases. The unzipping of RNA would circumvent such problem. In the end, the NN model is capable of describing the disruption and hybridization of nucleic acids, no matter what external agent (temperature or force) triggers the reaction.

The Minitweezers experimental setup can also be used to perform unzipping experiments at controlled force using a force feedback. The bandwidth of the force feedback is not high enough to keep the force constant in the presence of thermal fluctuations. Nevertheless, the average force is kept constant while the DNA molecule undergoes the opening of base-pairs. The experimental FDC$ _x$ is significantly different from the FDC$ _f$ and the latter always exhibits hysteresis at the timescale of the measurements. The hysteresis is not suppressed at the lowest feasible loading rate and increases with the loading rate. The mesoscopic model cannot predict the experimental FDC$ _f$ well, because this is not a quasistatic measurement. The intermediate states observed at controlled force are different from the ones observed at controlled position. At controlled force, there are small openings of base-pairs in the beginning of the unzipping and large openings in the end. This is a consequence of the tilt of the free energy landscape induced by the force. An analysis of the intermediate states shows that the number of open base-pairs vs. force follow the theoretically predicted scaling properties.

This thesis has focused on the statistical and thermodynamic properties of DNA unzipping measured with optical tweezers. This study has answered some questions and has open new ones. The next step is to extend the work to comprehend the remarkable properties of DNA, and to find practical applications based on the achievements exposed here.

JM Huguet 2014-02-12