Browsing by Subject "Scientific Computation"
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Item Advanced computational methods in multi-view medical imaging(2012-09) Yatziv, LironItem Assessment and Improvement of Computational Models to Study Biological Catalysis(2014-08) Huang, MingA detailed understanding of the molecular mechanisms whereby molecules of RNA can catalyze important reactions such as phosphoryl transfer is fundamental to biology, and of high significance in the development of new biomedical technology. This thesis describes the testing, application and development of quantum models that advance our understanding of the mechanisms of RNA catalysis. Molecular simulations of catalytic mechanisms of RNA require the use of fast, accurate approximate quantum mechanical (QM) models. These models, however, were not necessarily designed and parameterized for biocatalysis. In order to assess the degree to which commonly used approximate QM models are appropriate for biocatalysis applications, a series of models has been tested against a wide range of data sets, including new datasets particularly relevant for RNA catalysis, and compared with high-level benchmark calculations. Results provide new insight into the strengths and weaknesses of these methods, and help to guide next generation model development. We note that both NDDO and SCC-DFTB based QM models fail dramatically in their ability to adequately describe the conformational landscape of DNA and RNA sugar rings. In order to overcome this problem, an empirical sugar pucker energy term has been introduced via multi-dimensional B-spline interpolation of a potential energy surface correction. The corrected semiempirical models closely reproduce the ab initio puckering profiles as well as the barrier of an RNA transesterification model reaction. In addition, a series of RNA transesterification model reactions with various leaving groups have been studied with density-functional calculations in solution to investigate linear free energy relationships (LFERs) and their connection to transition state structure and bonding. These relations can be used to aid in the interpretation of experimental data for non-catalytic and catalytic mechanisms. A driving force in this research has been the development of software infrastructure for scientific computation, including new interfaces to other computational chemistry software, libraries to retrieve information, convert format and apply potentials, and tools for data analysis and visualization.Item Hybridizable discontinuous Galerkin method for curved domains(2012-01) Solano Palma, Manuel EstebanIn this work we present a technique to numerically solve partial differential equations (PDE’s) defined in general domains . It basically consists in approximating the domain by polyhedral subdomains Dh and suitably defining extensions of the solution from Dh to . More precisely, we solve the PDE in Dh by using a numerical method for polyhedral domains. In order to do that, the boundary condition is transferred from ¡ := ∂ to ¡h, the boundary of Dh, by integrating the gradient of the scalar variable along a path. That is why, in principle, any numerical method that provides an accurate approximation of the gradient can be used. In this work we consider a hybridizable discontinuous Galerkin (HDG) method. This technique has two main advantages over other methods in the literature. First of all, it only requires the distance between ¡ and ¡h to be of the order of the meshsize. This allows us to easily mesh the computational domain. Moreover, high degree polynomial approximations can be used and still obtain optimal orders of convergence even though ¡h is “far” from ¡. We numerically explore this approach by considering three types of steady-state equations. As starting point, we deal with Dirichlet boundary problems for second order elliptic equations. For this problem we fully explain how to properly transfer the boundary condition and how to define the paths, as well. We then apply this technique to exterior diffusion problems. Herein, the HDG method is used for solving the so-called interior problem on a bounded region whereas a boundary element method (BEM) is used for solving the problem exterior to that region. Both methods are coupled at the smooth interface that divides the two regions. Finally, we consider convectiondiffusion problems where we explore how the magnitude of the convective field affects the performance of our method.Item Robust preconditioning for indefnite and Ill-conditioned sparse linear systems(2011-12) Osei-Kuffuor, DanieLinear systems originating from certain applications in the physical sciences can be challenging to solve by iterative methods. In the past, direct methods like Gaussian elimination have been often used to solve these systems, due to their robust nature. However, as problems are now often formulated in 3-D geometries, the use of direct solvers is becoming prohibitive. Moreover, unlike iterative solvers, direct solvers cannot be easily parallelized. Two classes of methods have attracted the interest of researchers in recent years. First, is the class of multigrid methods, which have been shown to be very efficient for elliptic-type problems, and for which various adaptations have been brought. Second, is the class of preconditioned Krylov subspace methods. Here, work has focused mainly on improving the preconditioning. The underlying challenge is to develop or identify techniques that are robust and efficient in terms of accuracy, stability, and scalability. As problems in computational science continue to evolve, so do preconditioning techniques, as new ideas are incorporated to develop solver technologies that are well adapted to solve novel and challenging problems. To further contribute to this endeavor, my research uses ideas from numerical linear algebra to address algorithmic and computational issues in the numerical solution of application problems. The ideas presented in this thesis will focus on improving the stability and effectiveness of ILU-based preconditioners to better handle challenging problems characterized by indefinite and poorly conditioned linear systems. First, we present various strategies designed to improve the quality of the ILU factorization in order to safeguard stability without compromising the accuracy of the resulting factors. These strategies introduce new contributions to the areas of shifted ILU methods, modified ILU and compensation-based techniques, and reordering techniques for ILU. The resulting factors yield good and more robust preconditioners that are effective on highly indefinite and ill-conditioned linear systems. Next, we demonstrate the effectiveness of combining ILU factorizations with multilevel methods. Multilevel ILU methods have become a popular area of research, as researchers seek to take advantage of the superior robustness of ILU, coupled with the efficiency and scalability of multilevel methods. We discuss issues related to constructing the next-level matrices in the multilevel hierarchy and present ideas from multilevel graph coarsening and reordering strategies to construct an algebraic multilevel ILU-based preconditioner. Finally, we discuss key concepts necessary for an efficient adaptation of the ILU-based preconditioner into a parallel framework. We discuss the parallel implementation within the structure of the parallel algebraic multilevel solver (pARMS) framework. We demonstrate how different preconditioning techniques may be incorporated into this framework, and discuss issues relating to scalability.Item Simulating biochemical physics with computers(2010-08) Lin, Pinsker Yen-linThis dissertation is composed of three parts. The first part is to argue the solvent effects on the solvatochromic shift of the n ! !* excitation of acetone in ambient and supercritical water fluid using a hybrid QM!CI/MM potential in MC simulations. The solute is described by the AM1 approach and water molecules are treated classically. Specially, the spontaneous polarization of the solvent due to the excitation of the solute was considered. The solvent effects on the blue shift of acetone in water fluids at various temperatures and solvent densities are examined. The second part is to investigate the role of dopa decarboxylase (DDC) in the catalysis of converting anti-Parkinson drug L-dopa into dopamine. By means of combined QM/MM potentials in MD simulations, we first analyze the factors contributing to the tautomeric equilibrium of an intramolecular proton transfer in the external PLP!L-dopa aldimine (the Michaelis complex). How the intrinsic properties, solvent effects as well as the enzyme environment control the shift of the equilibrium is discussed. Afterward, the free energy profiles for the decarboxylations of the external aldimines both in water and in DDC are calculated. The contributions of DDC to the rate enhancement of the reaction are elucidated. The reaction mechanism of L-dopa decarboxylation in DDC is proposed. The third part is to study the structural dynamics of lysine-specific demethylase (LSD1) in complex with CoREST and protein-substrate interactions of LSD1 with histone H3 tail. MD simulations of LSD1•CoREST complex bound to a 16 a.a. of the Nterminal H3-tail peptide (H3-p16) were carried out using NAMD to study the conformational flexibility of the protein complex, especially the substantial oscillation of the TOWER domain. In addition, the simulations reveal some important protein-peptide and peptide-peptide interactions between LSD1 and H3-p16 that are absent in the crystal structure.Item Theoretical study of biological phosphoryl transfer reactions.(2008-08) Liu, YunThe most prominent mechanism for cell signaling, energy conversion, and the synthesis and breakdown of nucleic acids involves the transfer of phosphoryl groups. The present work applies density-functional electronic structure methods to study the model phosphoryl transfer reactions. These reactions represent reaction models for RNA catalysis (including transesterification, migration, and hydrolysis), and GTP hydrolysis in Ras and RasGAP. The effect of solvent is treated with both explicit water molecules, and self-consistently with an implicit (continuum) solvation model. Aqueous free energy barriers are calculated, and the structures and bond orders of the rate-controlling transition states are characterized. The calculated kinetic isotope effects and thio effects are consistent with available experimental data, and provide useful information for the interpretation of measured isotope and thio effects used to probe mechanism in phosphoryl transfer reactions catalyzed by enzymes and ribozymes.