Optical Tweezers for Single Molecule Biology

Molecular machinery on the micro-scale, believed to be the fundamental building blocks of life, involve forces of 1-100 pN and movements of nanometers to micrometers. Micromechanical single-molecule experiments seek to understand the physics of nucleic acids, molecular motors, and other biological systems through direct measurement of forces and displacements. Optical tweezers are a popular choice among several complementary techniques for sensitive force-spectroscopy in the field of single molecule biology. The main objective of this thesis was to design and construct an optical tweezers instrument capable of investigating the physics of molecular motors and mechanisms of protein/nucleic-acid interactions on the single-molecule level. A double-trap optical tweezers instrument incorporating acousto-optic trap-steering, two independent detection channels, and a real-time digital controller was built. A numerical simulation and a theoretical study was performed to assess the signal-to-noise ratio in a constant-force molecular motor stepping experiment. Real-time feedback control of optical tweezers was explored in three studies. Position-clamping was implemented and compared to theoretical models using both proportional and predictive control. A force-clamp was implemented and tested with a DNA-tether in presence of the enzyme lambda exonuclease. The results of the study indicate that the presented models describing signal-to-noise ratio in constant-force experiments and feedback control experiments in optical tweezers agree well with experimental data. The effective trap stiffness can be increased by an order of magnitude using the presented position-clamping method. The force-clamp can be used for constant-force experiments, and the results from a proof-of-principle experiment, in which the enzyme lambda exonuclease converts double-stranded DNA to single-stranded DNA, agree with previous research. The main objective of the thesis was thus achieved. The developed instrument and presented results on feedback control serve as a stepping stone for future contributions to the growing field of single molecule biology.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.

Dual-trap optical tweezers with real-time force clamp control

Single molecule force clamp experiments are widely used to investigate how enzymes, molecular motors, and other molecular mechanisms work. We developed a dual-trap optical tweezers instrument with real-time (200 kHz update rate) force clamp control that can exert 0–100 pN forces on trapped beads. A model for force clamp experiments in the dumbbell-geometry is presented. We observe good agreement between predicted and observed power spectra of bead position and force fluctuations. The model can be used to predict and optimize the dynamics of real-time force clamp optical tweezers instruments. The results from a proof-of-principle experiment in which lambda exonuclease converts a double-stranded DNA tether, held at constant tension, into its single-stranded form, show that the developed instrument is suitable for experiments in single molecule biology.

Analysing local algorithms in location-aware quasi-unit-disk graphs

A local algorithm with local horizon r is a distributed algorithm that runs in r synchronous communication rounds; here r is a constant that does not depend on the size of the network. As a consequence, the output of a node in a local algorithm only depends on the input within r hops from the node. We give tight bounds on the local horizon for a class of local algorithms for combinatorial problems on unit-disk graphs (UDGs). Most of our bounds are due to a refined analysis of existing approaches, while others are obtained by suggesting new algorithms. The algorithms we consider are based on network decompositions guided by a rectangular tiling of the plane. The algorithms are applied to matching, independent set, graph colouring, vertex cover, and dominating set. We also study local algorithms on quasi-UDGs, which are a popular generalisation of UDGs, aimed at more realistic modelling of communication between the network nodes. Analysing the local algorithms on quasi-UDGs allows one to assume that the nodes know their coordinates only approximately, up to an additive error. Despite the localisation error, the quality of the solution to problems on quasi-UDGs remains the same as for the case of UDGs with perfect location awareness. We analyse the increase in the local horizon that comes along with moving from UDGs to quasi-UDGs.

Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.