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Title: Kinetics of Brownian transport
Author: Gladrow, Jannes
ISNI:       0000 0004 8500 3672
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2019
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The rate of progress of Brownian processes is not easily quantifiable. An importantmeasure of the "speed" of Brownian motion is themean first-passage time (FPT) to a given distance. FPTs exist in various flavours including exit- and transition-path times, which, for instance, can be used to quantify the length of reaction paths in folding transitions inmolecules such as DNA. Due to their inherently stochastic nature, measurements of any FPTs require repeated experiments under controlled conditions. In my thesis, I systematically explore FPTs in various contexts using a custom-built automated holographic optical tweezers (HOT) setup. More precisely, I investigate transition- and exit-path-time symmetries in equilibrium systems and demonstrate the breakdown of the symmetry in out-of-equilibriumsystems. Experimental data from folding DNA-hairpins show that the principles established on the mesoscale extend well into the molecular regime. In Kramers escape problem, the reciprocal of the escape rate corresponds to the time of first-passage to leave the initial state. A lower bound for the achievable FPT, e.g. of the reaction coordinate of a folding molecule, therefore corresponds to a speed-limit of the ensemble reaction rate. Using my setup, I show that certain barrier shapes can substantially lower the escape time across the barrier without changing the overall energy balance. This result has deep implications for reaction kinetics, e.g. in protein folding. Furthermore, I investigate the role of entropic forces in Brownian transport, show that hydrodynamic drag plays a crucial role in Brownian motion in confined systems, and give an experimental realisation of Fick-Jacobs theory. The thermodynamic applications of HOTs considered here necessitate the creation of fine-tuned optical landscapes, which requires precise phase-retrieval to compute the necessary holograms. In order to address this problem, I explore novel algorithms based on deep conditional generative models and test whether such models can assist in finding holograms for a given desired light distribution. I compare several differentmodels, including conditional generative-adversarial networks and conditional variational autoencoders, which are trained on data sets sampled on the HOT setup. Furthermore, I propose a novel forward-loss-minimising architecture and demonstrate its excellent performance on both validation and artificially-created test data sets.
Supervisor: Keyser, Ulrich F. Sponsor: European Training Network (ETN)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: Brownian Motion ; Optical Tweezers ; Thermodynamics ; Machine Learning