Biophysical and computational investigations into G-quadruplex structural polymorphism and interaction with small molecules.

In the cell, guanine-rich nucleic acids can self-assemble into unique four stranded tertiary structures known as G-quadruplexes. G-quadruplex formation in the telomere leads inhibits telomerase, an enzyme activated in cancer cells to maintain the telomere and allowing for cancer cells to achieve immortality. G-quadruplex formation in the promoters and 5’-untranslated regions regulates the expression of many oncogenes. Furthermore, G-quadruplex formation during cellular replication promotes genomic instability, a characteristic which enables tumor development. Because of their implication in cancer, G-quadruplex structures have emerged as attractive drug targets for anti-tumor therapeutics. In the current dissertation work, we present three experimental approaches to investigate G-quadruplex structures, biophysical properties, small molecule interaction, and the thermodynamics of G-quadruplex formation. Current approaches to study G-quadruplex structures often employ sequence modifications or changes to the experimental condition, as a way of resolving the structural polymorphism associated with many G-quadruplex-forming sequences, to select for a single conformation for high-resolution structural studies. Our strategy for resolving G-quadruplex structural polymorphism is superior in that the experimental approaches do not result in drastic perturbation of the system. In the first approach, we employed size exclusion chromatography to separate a mixture of G-quadruplex structures formed from a G-quadruplex-forming sequence. We demonstrated that it is possible to isolate distinct species of G-quadruplex structures for further biophysical studies. In the second approach, we employed hydrodynamic bead modeling to study the structural polymorphism of a G-quadruplex-forming sequence. We showed that properties calculated from models agreed with experimentally determined values and could be used to predict the folding of G-quadruplex-forming oligonucleotides whose high-resolution structures are ambiguous or not available. In our third approach, we presented a virtual screening platform that was successful in identifying a new Gquadruplex-interacting small molecule. The results of the virtual screen were validated with extensive biophysical testing. Our target for the virtual screen was a G-quadruplex structure generated in silico, which represents one approach to receptor-based drug discovery when high-resolution structures of the binding site are not available. Taken together, our three approaches represent a new paradigm for drug discovery from guaninerich sequence to anti-cancer drugs

Finite-region stability of 2-D singular Roesser systems with directional delays

In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds

ON THE SINGULAR INTEGRAL EQUATIONS WITH CARLEMAN SHIFT IN THE CASE OF THE VANISHING COEFFICIENT

Joint Research on Environmental Science and Technology for the Eart

On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the instability cause. Since the solution exhibits unstable dependence on the given data functions, we propose a new regularization method to stabilize the solution. then obtain the error estimate. A numerical example shows that the method is efficient and feasible. This work slightly extends to the earlier results in Zouyed et al. \cite{key-9} (2014).Comment: 19 pages, 4 figures, 1 tabl

Approximation of mild solutions of the linear and nonlinear elliptic equations

In this paper, we investigate the Cauchy problem for both linear and semi-linear elliptic equations. In general, the equations have the form $$\frac{\partial^{2}}{\partial t^{2}}u\left(t\right)=\mathcal{A}u\left(t\right)+f\left(t,u\left(t\right)\right),\quad t\in\left[0,T\right],$$ where $\mathcal{A}$ is a positive-definite, self-adjoint operator with compact inverse. As we know, these problems are well-known to be ill-posed. On account of the orthonormal eigenbasis and the corresponding eigenvalues related to the operator, the method of separation of variables is used to show the solution in series representation. Thereby, we propose a modified method and show error estimations in many accepted cases. For illustration, two numerical examples, a modified Helmholtz equation and an elliptic sine-Gordon equation, are constructed to demonstrate the feasibility and efficiency of the proposed method.Comment: 29 pages, 16 figures, July 201

A Status Data Transmitting System for Vessel Monitoring

This paper presents a status data transmitting system suitable for vessel monitoring. The system consists of four main parts, which are a status data module, a frequency synthesizer, a power amplifier and a horn antenna. The status data module packs information of the identification, longitude, latitude and state of the vessel into data frames. FSK/MSK/GMSK schemes were used to modulate the data. The frequency synthesizer was designed with very high stability over temperature and very low frequency tolerance. The power amplifier provides 130 W output power at S band. The impedance bandwidth of the horn antenna can be controlled using the beveling technique