The actin cytoskeleton plays a vital role in various biological processes such as cell migration, morphogenesis, and intracellular trafficking. The polymerization of actin filaments at membranes provides the force for generating dynamic actin structures such as protrusions and invaginations that drive these processes. In filopodia, which are finger-like protrusions comprised of bundled actin filaments, actin regulatory proteins are believed to assemble a distal 'tip complex' which stimulates actin nucleation at the membrane. However how these regulators collectively behave in a macromolecular complex still remains poorly understood. To understand the macromolecular nature of these complexes, I investigated the dynamic properties and spatial organization of actin regulatory factors, using an in vitro reconstitution assay for filopodia-like structures (FLS) utilizing artificial lipid bilayers and Xenopus laevis egg extracts. FRAP analysis of seven actin regulatory factors (Toca-1, N-WASP, GTPase-binding domain, Ena, VASP, Diaph3, Fascin) revealed that the FLS tip complex has both dynamic and stable properties, with different proteins displaying distinct dynamics. Further analyses on the membrane-binding protein Toca-1 showed that its dynamic turnover is controlled by interactions with actin and exchange of molecules with solution. Single-molecule localization microscopy resolved the nanoscale organization of Toca-1, showing its arrangement into flat plaque-like and narrowly elevated tubular substructures. Plaque-like structures showed similarities to phase-transition patterns, while tubule-like structures closely resembled those previously found to decorate membrane tubules in vitro, which are thought to be involved in endocytic membrane remodeling. Endocytic accessory proteins such as SNX9 and Dynamin2 were also found to localize to FLS tips. This work provides new insights into the dynamics and organization of protein ensembles at actin nucleation sites, and proposes a novel link between endocytosis and filopodia formation, which is relevant to understanding how cells decide when and where to assemble actin at the membrane.

Synapses are the communication junctions of the nervous system and contain protein machinery necessary for cognitive functions such as learning and memory. Postsynaptic density protein-95 (PSD-95) is a key scaffolding molecule at the PSD of synapses, yet its sub-synaptic organisation in the mammalian brain remains poorly understood. This thesis presents the use of genetically labelled PSD-95 with super-resolution imaging to resolve its nano-architecture in the mouse brain. To visualize PSD-95, two knock-in mouse lines were generated where the fluorescent proteins eGFP or mEos2 was fused to the carboxyl terminus of the endogenous PSD- 95 protein (PSD-95-eGFP or PSD-95-mEos2). Methods were developed by which fixed tissue sections of PSD-95-eGFP mice were examined using gated-stimulated emission depletion (g-STED) microscopy and PSD-95-mEos2 sections were examined with photoactivatable localisation microscopy (PALM) and quantitative image analysis was developed for both methods. From these platforms it was demonstrated that PSD-95 has a two tiered organisation: it is assembled into nanoclusters (NCs) approximately 140 nm diameter, which form part of the greater envelope of the PSD within synapses. Synapse subtypes were observed as characterised by the number of NCs per PSD. Using double colour g- STED microscopy. It was then asked whether PSD-95 nano-architecture remained the same across different sub-regions of the brain. A survey of PSD-95 was performed from seven different sub-regions of the hippocampus, quantifying ~110,000 NCs within ~70,000 PSDs from across the two super-resolution platforms. It was found that synapses displayed structural diversity both within and between different brain subregions as a function of the number of NCs per PSD. PSD-95 NCs were structurally conserved across the hippocampus, but showed molecular diversity in the abundance of PSD-95 molecules within. The findings of this thesis are: 1) genetic labelling of endogenous proteins combined with super-resolution microscopy is a powerful tool to study synaptic protein organisation in tissue. 2) Synaptic structural diversity in the brain is underlined by the number of PSD-95 NC units per synapse 3) PSD-95 NCs are structurally conserved but molecularly diverse synaptic units of synapses throughout the brain. These findings suggest that cognitive processing at the synapse is based upon a conserved, fundamental, molecular architecture.

In recent years, microlenses (ML), which are micro-scale spheres, have been used to overcome physical diffraction limit of optical microscopy (~200 nm). Although the use of such ML has provided highly resolved images of objects beyond the Abbe optical diffraction limit, the process needs to be refined before it can be applied widespread in materials, biological and clinical research. In this research work, we have implemented experiments on super-resolution imaging utilizing MLs of different refractive indices (n) and diameters to provide the scientific and engineering communities with practical guidelines for obtaining high resolution images with ease. With the support from experimental imaging data as well as FDTD simulations, we have shown that optimal super-resolution imaging with microspheres was accomplished under specific parameter range. We have identified ML with n=1.51 as a preferable choice over those MLs with n=1.4, 1.93, and 2.2, because of high reliability and high magnification for ML with n=1.51. With n=1.51 in mind, we have identified a diameter range from 15 μm to 50 μm provides high resolution and magnification for practical purposes. We show that other ML diameters provided high resolution as well; we believe that ML diameters between 15 μm and 50 μm are practically preferred. We were able to achieve <150 nm resolution and further refinement of this tool can potentially yield higher quality imaging results. Ideally, MLs will eventually be directly incorporated as a modular device in an optical microscope providing the researchers an effective, noninvasive, and economical alternative to complex super resolution microscopy techniques. To improve scanning efficiency, we also proposed microtubule (MT) based imaging. With the demonstration of theoretical optics, we conclude, at present time, that there are some practical concerns for MT-based imaging technique that may limit its application as super-resolution imaging technique. For example, MT-based imaging appears to possess a lower contrast than ML-based technique. Thus, although the concept of MT-based imaging is theoretically possible, we think that more work is needed to utilization of this tool for practical applications.

All far-field optical imaging is limited by diffraction from optical elements, a phenomenon called Rayleigh's curse. It has been shown that through the use of the spatial mode demultiplexing technique (SPADE), an arbitrarily small separation between two point sources can be resolved, given a sufficiently large total number of photons N. This quantum metrology approach to super-resolution has since then been demonstrated and generalized to more complex situations. We propose a variant of SPADE, that we call biphoton SPADE, applied to imaging systems with spatially entangled photon pairs generated through spontaneous parametric downconversion. Our method can achieve a higher precision than SPADE, given any non-zero level of entanglement. We furthermore demonstrate our technique in a coincidence imaging setup and show super-resolution while only projecting on a select few of the total optimal modes in the 2D joint basis. Since the method uses quantum light and provides even further sensitivity to SPADE, it can potentially be used in the future for various light-sensitive imaging applications and in combination with neural networks. In nature, one often finds structures that have only been replicated by humans through years of precise, state-of-the-art engineering. Polymer spherulites, naturally occurring birefringent crystals that grow around defects in a radial pattern, are an example of this. We show through the example of ascorbic acid, commonly referred to as Vitamin C, that spherulites are capable of creating beams with orbital angular momentum (OAM) through a process called spin-to-orbit coupling. This action of the ascorbic acid crystals is analogous to the one of spatially structured waveplates called q-plates, which are built to have an azimuthally dependant optic axis. This opens the door for potentially cheaper fabrication of q-plates, and possibilities of tuning the growth of the molecules for arbitrary wavefront shaping with natural crystals. Finally, because of the wide range of crystals in the spherulite class, further investigation into different spherulites could shed light on the relationship between crystal symmetry and structure, and the shaping of light.

The development of single-molecule and super-resolution fluorescence techniques has revolutionised biological imaging. Nano-scale cellular structures and heterogeneous dynamic processes are now able to be visualised with unprecedented resolution in both time and space. The achievable localisation precision and therefore the resolution is fundamentally limited by the number of photons a single-fluorophore can emit. The ideal super-resolution dye would emit a large number of photons over a short period of time. On the contrary, an optimal single-molecule tracking probe would be highly photostable and undergo no transient dark-state transitions. Single-molecule instrument development is beginning to reach technological saturation and as the frontiers of bioimaging expand, exorbitant demands are placed on the gamut of available probes that often cannot be met. Thus, the next key challenge in the field is the development of the better fluorophores that underlie these techniques; this includes both the synthesis of new chemical derivatives and alternative novel strategies to augment existing technologies. The results of this thesis are divided into two distinct parts; Project One details the development of new synthetic fluorescent probes for the study of amyloid protein aggregates implicated in neurodegenerative diseases. This includes a study of the photophysical and binding properties of a novel fluorophore library based on the amyloid dye Thioflavin-T. Following on from this, is the presentation of novel bifunctional dyes capable of simultaneously identifying hydrogen peroxide and amyloid aggregates by combining existing tools for the independent detection of these species. The sensing capabilities of these dyes are explored at the bulk and single-molecule levels. Project Two describes a new photo-modulatable fluorescent-protein fusion construct that can undergo Förster resonance energy transfer (FRET) to an organic dye molecule. This FRET cassette is comprised of a photoconvertible fluorescent protein donor, mEos3.2 and acceptor fluorophore, JF646. This strategy imparts a strong photostabilising effect on the fluorescent protein and a resistance to photobleaching. The functionality of this approach is demonstrated with in vitro single-molecule fluorescence studies and its biological applicability shown by tracking single proteins in the nuclei of live embryonic stem cells. Furthermore, initial characterisations of the excited state dynamics in effect are presented through the systematic modification of parameters.

Human Natural Killer (NK) cells are regulated by a variety of germ-line encoded activating and inhibitory receptors. Broadly, activating receptors detect ligands that are expressed or up-regulated on cancerous or infected cells, while inhibitory receptors bind self-molecules to induce tolerance against healthy cells. Highly homologous pairs of activating and inhibitory receptors are also expressed on NK cells, including Killer Ig-like Receptors KIR2DL1 and KIR2DS1, which bind the same ligands, class I MHC proteins from the C2 group. Here, two super-resolution microscopy techniques, stimulated emission depletion (STED) and ground state depletion microscopy followed by individual molecule return (GSDIM) were used to examine the nanometre-scale organization of KIR2DL1 and KIR2DS1, as well as molecules engaged in their signalling. Both receptors were observed to constitutively assemble in nanometre-scale clusters at the surface of NK cells but displayed differential patterns of clustering - the activating receptor KIR2DS1 formed nanoclusters 2.3-fold larger than its inhibitory counterpart KIR2DL1. Site-directed mutagenesis established that the size of nanoclusters was controlled by transmembrane amino-acid 233, a lysine in KIR2DS1. Mutated variant of KIR2DS1 in which lysine 233 was substituted with alanine formed significantly smaller clusters than the wild-type KIR2DS1. Reciprocally, substitution of isoleucine found at position 233 in KIR2DL1 sequence with lysine resulted in the receptor assembling into larger clusters. Super-resolution microscopy also revealed two ways in which KIR nanoclusters impact signalling. First, KIR2DS1 and DAP12 nanoclusters were juxtaposed in the resting-cell state but coalesced upon receptor ligation. Second, quantitative super-resolution microscopy revealed that membrane-proximal clusters of the kinase ZAP-70 or phosphatase SHP-1, as well as their phosphorylated active forms, were more often found in contact with larger KIR nanoclusters. Together, this work has established that size of KIR nanoclusters depends on the transmembrane sequence and impacts downstream signalling.

Video super-resolution (VSR) aims to give a satisfying estimation of a high-resolution (HR) image from multiple similar low-resolution (LR) images by exploiting their hidden redundancy. The rapid development of convolutional neural network (CNN) techniques provide numerous new possibilities to solve the VSR problem. Recent VSR methods combine CNN with motion compensation to cancel the inconsistencies among the LR images and merge them to an HR images. To compensate the motion, pixels in input frames are warped according to optical-flow-like information. In this procedure, trade-off has to be made between the distraction caused by spatio-temporal inconsistencies and the pixel-wise detail damage caused by the compensation. We proposed a novel VSR method with the name, Video Super-Resolution via Dynamic Local Filter Network, and its upgraded edition, Video Super-Resolution with Compensation in Feature Extraction. Both methods perform motion compensation via a dynamic local filter network, which processes the input images with dynamically generated filter kernels. These kernels are sample-specific and position-specific. Therefore, our proposed methods can eliminate the inter-frame differences during feature extractions without explicitly manipulating pixels. The experimental results demonstrate that our methods outperform the state-of-the-art VSR algorithms in terms of PSNR and SSIM and recover more details with superior visual quality.

Image super-resolution technique mainly aims at restoring high-resolution image with satisfactory novel details. In recent years, leaning-based single-image super-resolution has been developed and proved to produce satisfactory results. With one or some dictionaries trained from a training set, learning-based super-resolution is able to establish a mapping relationship between low-resolution images and their corresponding high-resolution ones. Among all these algorithms, sparsity-based super-resolution has been proved with outstanding performance from extensive experiments. By utilizing compact dictionaries, this class of super-resolution algorithms can be efficient with lower computation complexity and has shown great potential for the practical applications. Our proposed model, which is known as Joint Dictionary-based Super-Resolution (JDSR) algorithm, is a new sparsity-based super-resolution approach. Based on the observation that the initial values of Non-locally Centralized Sparse Representation (NCSR) model will affect the final reconstruction, we change its initial values by using results of Zeyde's model. Besides, with the purpose of further improvement, we also add a gradient histogram preservation term in the sparse model of NCSR, and modify the reference histogram estimation by a simple edge detection based enhancement so that the estimated histogram will be closer to the ground truth. The experimental results illustrate that our method outperforms the state-of-the-art methods in terms of sharper edges, clearer textures and better novel details.

In this thesis, we discuss several phenomena exhibiting `limiting behaviour' in physics. This includes the duality principle, delegated quantum computation, and super-resolution. The duality principle places a limit on the coexistence of wave and particle behaviours. We develop a framework that explains apparent violations of this principle while staying within the scope of quantum mechanics. In addition, we relate the duality principle to the sub-fidelity and weak-values. We also show that the maximum recoverable coherence of a qubit has a sharp transition from 0 to 1 when we have access to half of the environment to which the qubit is correlated. Delegated quantum computation consists of a computational weak client who wishes to delegate a complex quantum computation to a powerful quantum server. We develop a new protocol for delegated quantum computation requiring less quantum power than its predecessor. Finally, we develop and test a new theory for eigenmode super-resolution.

The diffraction limit restricts conventional light microscopes to approximately 250 nm laterally and 500 nm axially, these limits being first proposed by Abbe in 1873. Despite this, optical microscopes have found many applications in biological research and single cells that are 10 - 100 um in size. Furthermore by coupling the non-invasive nature of a light microscope with highly sensitive fluorescent probes, fluorescence microscopy has also become a standard imaging technique. Recent advances in fluorescence microscopy now provide a number of methods to circumvent the Abbe diffraction limit, with many techniques becoming prevalent over the last 10 years including direct Stochastic Optical Reconstruction Microscopy (dSTORM). A dSTORM system has been constructed and calibrated using a commercially available inverted florescence microscope and total internal reflection florescence (TIRF) imaging. dSTORM relies on the ability to switch sparse subsets of fluorophores and temporally separate them. Provided the spatial separation is sufficient between any member of a subset, the average error with which the emission can be localized is much less than size of the emission profile itself. The underlying mechanism for this switching is detailed based on the principle of photoinduced electron transfer (PET). The switching characteristics of the common florescent dye Alexa Fluor 568 are investigated and shown to be controlled by a number of factors including the excitation intensity and concentration of the primary thiol cysteamine beta-MEA. A number of parameters are defined, including the dye switching rate, for a given set of physical parameters. U2OS cells are labelled for the microtubule protein Tubulin using immunofluorescent labelling strategies. A direct comparison is made between diffraction limited TIRF images and dSTORM reconstructed images, with an average width for microtubules determined to (58.2 ± 8.1) nm. Further measurements are made by labelling the Rab5 effector Early Endosome Antigen 1 (EEA1). From this the aspect ratio for early endosomes is determined to be 1.68 ± 0.7 with an average radius of (45.8 ± 18.8) nm. The point spatial distribution of EEA1 is investigated by using the linearised form of Ripley's K-function H(r) and the null hypothesis of complete spatial randomness tested. EEA1 is shown to cluster at radius of 58.7 nm on individual endosomes, thought to be due to the well defined binding domains present on early endosomes for EEA1. Further evidence suggests that clustering is also exhibited at another maximum of approximately 500 nm when looking at an ensemble of EEA1 and early endosomes.