Photodynamic Therapy: Agents and Mechanisms

Despite enormous efforts, cancer remains a leading cause of morbidity and mortality world-wide. The main challenges currently facing cancer therapy include lack of adequate tumor targeting, failure to treat hypoxic tumor cells, and induction therapy resistant tumors. A solution to these limitations can be found in photodynamic therapy (PDT) which combines light and light activatable compounds, photosensitizers (PSs), to produce cytotoxic reactive oxygen species (ROS) to damage tumor tissue. This creates a spatiotemporal therapeutic effect, where cell damage only occurs at the intersection of the PS and light. PDT can treat tumors through unique mechanisms which reduce induction of tumor resistance. Although PDT has had clinical success in treating skin cancer and macular degeneration, it has yet to be a widely adopted or accepted therapy. In this dissertation, we lay the groundwork for a new PDT strategy which systematically addresses and optimizes each aspect of PDT. To overcome the limitation of PDT to treat hypoxic tumors, we developed a novel nano-photosensitizer, TiO2-N3, that produces cytotoxic ROS even under hypoxic conditions. Next, to determine the optimal intracellular target for TiO2-N3, we compared the therapeutic outcome of ROS generated in endosomes, lysosomes, mitochondria, and ER. We identified the ER as the organelle most sensitive to ROS damage and therefore the optimal intracellular target for TiO2-N3. Finally, to deliver TiO2-N3 to tumors in vivo, we developed two tumor targeting agents, both of which are equipped with near-infrared fluorophores for whole body imaging. This work has laid the foundation for a novel PDT strategy by overcoming issues that have limited the clinical adoption of PDT

Darboux dressing and undressing for the ultradiscrete KdV equation

We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over $\mathbb R$ for any potential with compact (finite) support, by explicitly constructing bound state and non-bound state eigenfunctions. We then show how to reconstruct the potential in the scattering problem at any time, using an ultradiscrete analogue of a Darboux transformation. This is achieved by obtaining data uniquely characterising the soliton content and the `background' from the initial potential by Darboux transformation.Comment: 41 pages, 5 figures // Full, unabridged version, including two appendice

Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations

We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard

Maximum fidelity retransmission of mirror symmetric qubit states

In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set. A suitable figure of merit for this process is the fidelity, which is the probability that the state we construct on the basis of the measurement result is found by a subsequent test to match the original state. We consider the maximisation of the fidelity for a set of three mirror symmetric qubit states. In contrast to previous examples, we find that the strategy which minimises the probability of erroneously identifying the state does not generally maximise the fidelity

Entanglement and Collective Quantum Operations

We show how shared entanglement, together with classical communication and local quantum operations, can be used to perform an arbitrary collective quantum operation upon N spatially-separated qubits. A simple teleportation-based protocol for achieving this, which requires 2(N-1) ebits of shared, bipartite entanglement and 4(N-1) classical bits, is proposed. In terms of the total required entanglement, this protocol is shown to be optimal for even N in both the asymptotic limit and for `one-shot' applications

The azimuthal component of Poynting's vector and the angular momentum of light

The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms

Matrix-valued θ\theta-deformed bi-orthogonal polynomials, Non-commutative Toda theory and B\"acklund transformation

This paper is devoted to revealing the relationship between matrix-valued $\theta$-deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wronski quasi-determinants are widely used and play the role of non-commutative $\tau$-functions. At the same time, B\"acklund transformations are realized by using a moment modification method and non-commutative $\theta$-deformed Volterra hierarchies are obtained, which contain the known examples of the Itoh-Narita-Bogoyavlensky lattices and the fractional Volterra hierarchy.Comment: 30 pages. Comments are welcom

B\"acklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations

We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants. We also explain the origins of all of the ingredients of the Backlund transformations within the framework of noncommutative twistor theory. In particular we show that the generated solutions belong to a noncommutative version of the Atiyah-Ward ansatz.Comment: v2: 21 pages, published versio

Maximum Confidence Quantum Measurements

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.Comment: 4 pages, 2 figure

Cloning, Purification, and Partial Characterization of the Halobacterium sp. NRC-1 Minichromosome Maintenance (MCM) Helicase

The MCM gene from the archaeon Halobacterium, with and without its intein, was cloned into an Escherichia coli expression vector, overexpressed and the protein was purified and antibodies were generated. The antibodies were used to demonstrate that in vivo only the processed enzyme, without the intein, could be detected