University of Macau / Faculty of Science and Technology. / Department of Computer and Information Science

Chemical pesticides have long been used to control insect populations on field crops, and their widespread availability and ease of manipulation present an ideal system for the exploration of the relationship between vital rates and population dynamics. Research has shown that models of population effects of insecticides are more accurate when time-varying parameters are used, but the scientific community has been slow to accept such models, which may involve complicated mathematics such as partial differential equations. Additionally, many of the pesticides now in use have both acute and sublethal effects, and these differing modes of action, along with concerns for the scientific community's understanding of the models, motivate a new approach to mathematical modeling of the effects of insecticides on population dynamics. We first consider an ordinary differential equation model, which, while simple, provides highly accurate fits to population data, though it accounts for only one generation at a time without explicitly considering reproductive effects. An evaluation of the effects of insecticides on insect fecundity is considered separately. We then develop, implement, and analyze a coupled time-delay differential equation model, which incorporates information for multiple generations and is an intermediate model in terms of ease of understanding for non-mathematicians. Sensitivity results for the time delay kernel are also presented.

Free and/or moving boundary problems occur in a wide range of applications. These boundaries can obey either local or global conditions. In this dissertation, new numerical techniques for solving some of these problems are developed, analyzed, implemented and tested. The new techniques for free and moving boundary problems are 1) a second order method for solving moving boundary problems and 2) a hybrid level set/boundary element method for solving some free boundary problems. The main tool used in both is the Fast Marching method, a fast algorithm for solving the eikonal equation. An application using Fast Marching to solve a model for sand pile formation in domains with obstacles is shown. A new, second order Fast Marching scheme for domains with obstacles is introduced. We look at the stability and accuracy of discretizations commonly used with Fast Marching. The performance of Fast Marching is compared that of Fast Sweeping, another eikonal solver. The second order method for solving moving boundary problems is applied to some simple examples. Finally, a globally defined free boundary problem inspired by fluid dynamics, the Bernoulli problem, is solved using the hybrid method.

Various models are developed to describe several different aspects of the dynamics of polymers. First, a model is developed which describes the dynamics of a single polymer chain, residing in a viscous fluid, in response to various stimuli. Next, constitutive models leading to reptation are developed, which determine the stress-strain relations for a system of physically constrained (PC) molecules residing within a chemically cross-linked (CC) system of molecules acting as a constraining tube for the PC system. These reptation models treat relaxation within the context of both intra-molecular and inter-molecular variability. Finally, a model is developed which combines the Rouse model of relaxing polymers and the stick-slip reptation model. This stick-slip/Rouse hybrid model incorporates parameters which were ignored in models developed in the earlier parts of the dissertation.

Thesis (Ph. D.)--University of Texas at Dallas, 2006. / Includes vita. Includes bibliographical references (leaves 95-99).

This thesis further developments strain smoothing techniques in finite element methods for structural analysis. Two methods are investigated and analyzed both theoretically and numerically. The first is a smoothed finite element method (SFEM) where an assumed strain field is derived from a smoothed operator of the compatible strain field via smoothing cells in the element. The second is a nodally smoothed finite element method (N-SFEM),where an assumed strain field is evaluated using the strain smoothing in neighbouring domains connected with nodes. For the SFEM, 2D, 3D, plate and shell problems are studied in details. Two issues based on a selective integration and a stabilization approach for volumetric locking are considered. It is also shown that the SFEM in 2D with a single smoothing cell is equivalent to a quasi-equilibrium model. For the N-SFEM, a priori error estimation is established and the convergence is confirmed numerically by benchmark problems. In addition, a quasi-equilibrium model is obtained and as a result a dual analysis is very promising to estimate an upper bound of the global error in finite elements. It is also expected that two present approaches are being incorporated with the extended finite element methods to improve the discontinuous solution of fracture mechanics.

The conformational flexibility of target proteins is a major challenge in understanding and modeling protein-drug interactions. A fundamental issue, yet to be clarified, is whether the observed conformational changes are controlled by the protein, or induced by the inhibitor. While the concept of induced fit has been widely adopted for describing the structural changes that accompany ligand binding, there is growing evidence in support of the dominance of proteins intrinsic dynamics, which has been evolutionarily optimized to accommodate its functional interactions. The wealth of structural data for target proteins in the presence of different ligands now permits us to make a critical assessment of the balance between these two effects in selecting the bound forms. We focused on three widely studied drug targets, HIV-1 reverse transcriptase, p38 MAP kinase, and cyclin-dependent kinase 2. A total of 292 structures determined for these enzymes in the presence of different inhibitors as well as unbound form permitted us to perform an extensive comparative analysis of the conformational space accessed upon ligand binding, and its relation to the intrinsic dynamics prior to ligand binding as predicted by elastic network model analysis. Further, we analyzed NMR ensembles of ubiquitin and calmodulin representing their microseconds range solution dynamics. Our results show that the ligand selects the conformer that best matches its structural and dynamic properties amongst the conformers intrinsically accessible to the protein in the unliganded form. The results suggest that simple but robust rules encoded in the protein structure play a dominant role in pre-defining the mechanisms of ligand binding, which may be advantageously exploited in designing inhibitors. We apply these lessons to the study of MAP kinase phosphatases (MKPs), which are therapeutically relevant but challenging signaling enzymes. Our study provides insights into the interactions and selectivity of MKP inhibitors and shows how an allosteric inhibition mechanism holds for a recently discovered inhibitor of MKP-3. We also provide evidence for the functional significance of the structure-encoded dynamics of rhodopsin and nicotinic acetylcholine receptor, members of two membrane proteins classes serving as targets for more than 40% of all current FDA approved drugs.

This thesis focuses on applying meta-analysis methods for combining genomic studies on biomarker detection and pathway enrichment analysis. DNA microarray technology has been maturely developed in the past decade and led to an explosion on publicly available microarray data sets. However, the noisy nature of DNA microarray technology results in low reproducibility across microarray studies. Therefore, it is of interest to apply meta-analysis to microarray data to increase the reliability and robustness of results from individual studies. Currently most meta-analysis methods for combining genomic studies focus on biomarker detection, and meta-analysis for pathway analysis has not been systematically pursued. We investigated two natural approaches of meta-analysis for pathway enrichment (MAPE) by combining statistical significance across studies at the gene level (MAPE_G) or at the pathway level (MAPE_P). Simulation results showed increased statistical power of both approaches and their complementary advantages under different scenarios. We also developed an integrated method (MAPE_I) that incorporates advantages of both approaches. Applications to real data on drug response of a breast cancer cell line, lung and prostate cancer tissues were evaluated to compare the performance of the different methods. MAPE_P has the general advantage of not requiring gene matching across studies. When MAPE_G and MAPE_P show complementary advantages, the integrated version MAPE_I is recommended. A software package named MetaPath, was implemented to perform the MAPE analysis. In addition to developing MAPE methods, we also applied meta-analysis approach to chemotherapy research to discover robust biomarkers and multi-drug response genes, which have prognostic value and the potential of identifying new therapeutic targets.

Protein-protein interactions (PPIs) constitute an emerging class of targets for pharmaceutical intervention pursued by both industry and academia. Despite their fundamental role in many biological processes and diseases such as cancer, PPIs are still largely underrepresented in todays drug discovery. This dissertation describes novel computational approaches developed to facilitate the discovery/design of small-molecule inhibitors of PPIs, using the oncogenic c-Myc/Max interaction as a case study. First, we critically review current approaches and limitations to the discovery of small-molecule inhibitors of PPIs and we provide examples from the literature. Second, we examine the role of protein flexibility in molecular recognition and binding, and we review recent advances in the application of Elastic Network Models (ENMs) to modeling the global conformational changes of proteins observed upon ligand binding. The agreement between predicted soft modes of motions and structural changes experimentally observed upon ligand binding supports the view that ligand binding is facilitated, if not enabled, by the intrinsic (pre-existing) motions thermally accessible to the protein in the unliganded form. Third, we develop a new method for generating models of the bioactive conformations of molecules in the absence of protein structure, by identifying a set of conformations (from different molecules) that are most mutually similar in terms of both their shape and chemical features. We show how to solve the problem using an Integer Linear Programming formulation of the maximum-edge weight clique problem. In addition, we present the application of the method to known c-Myc/Max inhibitors. Fourth, we propose an innovative methodology for molecular mimicry design. We show how the structure of the c-Myc/Max complex was exploited to designing compounds that mimic the binding interactions that Max makes with the leucine zipper domain of c-Myc. In summary, the approaches described in this dissertation constitute important contributions to the fields of computational biology and computer-aided drug discovery, which combine biophysical insights and computational methods to expedite the discovery of novel inhibitors of PPIs.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 74-79). Also available in electronic version. Access restricted to campus users.