Wu Li - US grants

9973218

The proposer's main objective is to resolve some theoretical and computational issues in developing innovative and efficient numerical methods for solving constrained minimization problems that can be reformulated as unconstrained minimization of piecewise quadratic functions. More specifically, the proposer's objectives are the following: (i) identifying constrained minimization problems that can be converted to the unconstrained minimization of convex piecewise quadratic functions; (ii) designing numerical algorithms for solving the unconstrained reformulation problem that take advantage of the structure of the original problem; (iii) developing matrix factorization and matrix updating techniques for solving symmetric (but possibly singular) systems of linear equations; and (iv) establishing error bounds that are useful for convergence analysis of numerical algorithms for solving certain minimax problems for convex quadratic functions. The potential impact of the project is an innovation on how quadratic programming problems should be solved in sequential quadratic programming methods as well as in trust region methods for solving constrained minimization problems. The theory on new merit functions will provide a completely new perspective on how constraints should be handled in solving constrained minimization problems. The new penalty function theory also serves as a theoretical basis for developing new methods for solving constrained minimization problems. New techniques for finding a descent Newton direction when the Hessian of an objective function is only positive semidefinite will significantly advance the theory on Newton methods and allow people to use Newton methods to find a minimizer of a convex piecewise quadratic function in finitely many iterations, even though the set of all minimizers might be unbounded. New error bounds will provide new ways to establish convergence results for some numerical algorithms.

Quadratic programming is the key for solving constrained minimization problems that have significant applications in many areas such as bio-engineering, chemical engineering, aircraft design, etc. For example, a faster and more accurate way of solving certain constrained minimization problems means a shorter and more efficient design cycle in developing new aircraft for Boeing. This project aims at using an innovative approach for solving large-scale quadratic programming problems that can be used to obtain accurate solutions of constrained minimization problems efficiently. This will lead to better software tools for solving many engineering application problems.

DESCRIPTION: The functional transformation of a predominantly organic matrix into a 95 percent inorganic tissue of high structural organization and mechanical integrity (e.g., enamel, requires a spatial and timely accurate cleavage and degradation of matrix proteins). The metalloproteinase 20 (enamelysin) hydrolyses amelogenin proteins, the major protein component of the developing enamel matrix, at the C-terminal and N-terminal resulting in protein fragments including a 20 kDa amelogenin (Amg20), a tyrosine rich amelogenin peptide (TRAP) and a leucine rich amelogenin peptide (LRAP). Enamel maturation and the formation of the unique enamel microstructure must be a result of the involvement of these protein fragments by presumably controlling growth rate, orientation and morphology of apatite crystals. All MMP-20 cleavage sites in amelogenin contain an upstream proline residue that may be important for optimal enzyme function. A mutation of the proline near the TRAP cleavage site, resulted in reduced amelogenin hydrolysis in vitro, and has been linked to amelogenesis imperfecta in vivo. In this proposal, we aim to alter hydrolysis of amelogenin by MMP-20 at the N- and C-terminal hydrolysis sites in vivo and in vitro, to identify the role Amg20, TRAP and LRAP fragments in enamel biomineralization. We hypothesize that the proline residues nearby the MMP-20 cleavage sites in amelogenin, are critical for MMP-20 binding to amelogenin to form Amg20, TRAP and LRAP and that these cleavage products have unique functional roles in enamel biomineralization. The hypotheses will be tested by following specific aims: 1). To determine the role of proline residues near the MMP-20 proteinase cleavage sites, on the kinetics of amelogenin degradation by MMP-20 in vitro. 2). To determine the role of N- and C-terminal amelogenin hydrolysis by MMP-20 in enamel biomineralization in vivo by creating transgenic mouse models. 3). To determine the role of N- and C- terminal amelogenins created by MMP-20 and altered hydrolysis by mutations, on hydroxyapatite crystal growth in vitro. This proposal is designed to clarify mechanisms of enamel development, especially regarding the formation and function of Amg20, TRAP and LRAP during enamel maturation. This project will gain insights in the interactions between MMP-20 and amelogenin proteins at the molecular level as well as their interactions with forming apatite mineral. Furthermore the proposed studies will help us to gain knowledge in the pathogenesis of amelogenesis imperfecta.

DESCRIPTION: The functional transformation of a predominantly organic matrix into a 95 percent inorganic tissue of high structural organization and mechanical integrity (e.g., enamel, requires a spatial and timely accurate cleavage and degradation of matrix proteins). The metalloproteinase 20 (enamelysin) hydrolyses amelogenin proteins, the major protein component of the developing enamel matrix, at the C-terminal and N-terminal resulting in protein fragments including a 20 kDa amelogenin (Amg20), a tyrosine rich amelogenin peptide (TRAP) and a leucine rich amelogenin peptide (LRAP). Enamel maturation and the formation of the unique enamel microstructure must be a result of the involvement of these protein fragments by presumably controlling growth rate, orientation and morphology of apatite crystals. All MMP-20 cleavage sites in amelogenin contain an upstream proline residue that may be important for optimal enzyme function. A mutation of the proline near the TRAP cleavage site, resulted in reduced amelogenin hydrolysis in vitro, and has been linked to amelogenesis imperfecta in vivo. In this proposal, we aim to alter hydrolysis of amelogenin by MMP-20 at the N- and C-terminal hydrolysis sites in vivo and in vitro, to identify the role Amg20, TRAP and LRAP fragments in enamel biomineralization. We hypothesize that the proline residues nearby the MMP-20 cleavage sites in amelogenin, are critical for MMP-20 binding to amelogenin to form Amg20, TRAP and LRAP and that these cleavage products have unique functional roles in enamel biomineralization. The hypotheses will be tested by following specific aims: 1). To determine the role of proline residues near the MMP-20 proteinase cleavage sites, on the kinetics of amelogenin degradation by MMP-20 in vitro. 2). To determine the role of N- and C-terminal amelogenin hydrolysis by MMP-20 in enamel biomineralization in vivo by creating transgenic mouse models. 3). To determine the role of N- and C- terminal amelogenins created by MMP-20 and altered hydrolysis by mutations, on hydroxyapatite crystal growth in vitro. This proposal is designed to clarify mechanisms of enamel development, especially regarding the formation and function of Amg20, TRAP and LRAP during enamel maturation. This project will gain insights in the interactions between MMP-20 and amelogenin proteins at the molecular level as well as their interactions with forming apatite mineral. Furthermore the proposed studies will help us to gain knowledge in the pathogenesis of amelogenesis imperfecta.

DESCRIPTION: The functional transformation of a predominantly organic matrix into a 95 percent inorganic tissue of high structural organization and mechanical integrity (e.g., enamel, requires a spatial and timely accurate cleavage and degradation of matrix proteins). The metalloproteinase 20 (enamelysin) hydrolyses amelogenin proteins, the major protein component of the developing enamel matrix, at the C-terminal and N-terminal resulting in protein fragments including a 20 kDa amelogenin (Amg20), a tyrosine rich amelogenin peptide (TRAP) and a leucine rich amelogenin peptide (LRAP). Enamel maturation and the formation of the unique enamel microstructure must be a result of the involvement of these protein fragments by presumably controlling growth rate, orientation and morphology of apatite crystals. All MMP-20 cleavage sites in amelogenin contain an upstream proline residue that may be important for optimal enzyme function. A mutation of the proline near the TRAP cleavage site, resulted in reduced amelogenin hydrolysis in vitro, and has been linked to amelogenesis imperfecta in vivo. In this proposal, we aim to alter hydrolysis of amelogenin by MMP-20 at the N- and C-terminal hydrolysis sites in vivo and in vitro, to identify the role Amg20, TRAP and LRAP fragments in enamel biomineralization. We hypothesize that the proline residues nearby the MMP-20 cleavage sites in amelogenin, are critical for MMP-20 binding to amelogenin to form Amg20, TRAP and LRAP and that these cleavage products have unique functional roles in enamel biomineralization. The hypotheses will be tested by following specific aims: 1). To determine the role of proline residues near the MMP-20 proteinase cleavage sites, on the kinetics of amelogenin degradation by MMP-20 in vitro. 2). To determine the role of N- and C-terminal amelogenin hydrolysis by MMP-20 in enamel biomineralization in vivo by creating transgenic mouse models. 3). To determine the role of N- and C- terminal amelogenins created by MMP-20 and altered hydrolysis by mutations, on hydroxyapatite crystal growth in vitro. This proposal is designed to clarify mechanisms of enamel development, especially regarding the formation and function of Amg20, TRAP and LRAP during enamel maturation. This project will gain insights in the interactions between MMP-20 and amelogenin proteins at the molecular level as well as their interactions with forming apatite mineral. Furthermore the proposed studies will help us to gain knowledge in the pathogenesis of amelogenesis imperfecta.

DESCRIPTION (provided by applicant): Tooth enamel is a highly mineralized hard tissue, uniquely comprised of millions of hexagonal carbonated hydroxyapatite (HAP) crystals. These crystals are very thin and extremely long, which determine excellent mechanical properties of tooth enamel. Mineralized enamel crystals develop from a layer of enamel protein matrix that is predominated by amelogenins (>90%), which forms special nanostructures to modulate crystal formation. Amelogenins are gradually and completely removed by enamel proteinases MMP20 and KLK4 to form highly mineralized enamel at the end of maturation stage. The interactions between crystal, amelogenin and proteinase dynamically and delicately controlled the growth rate, direction and morphology of enamel crystals. We hypothesize that the binding of amelogenin to apatite crystal changes the conformation of amelogenin adsorbed on crystals and results in preferential degradation of amelogenin from crystal surface by proteinases. The amelogenin adsorption and degradation are also specific on different crystal planes, which drive the crystal to elongate primarily along the c axis and widen/thicken along a and b axes in different developmental stages of amelogenesis. In addition, the N-terminal proline 70 is involved in the plane-specific adsorption and degradation of amelogenin. The mutation of the proline (P70T, linked to a type of amelogenesis imperfect) interferes with crystal- amelogenin-proteinase interactions, resulting in abnormal enamel mineralization and morphology. Three specific aims are proposed to evaluate the hypothesis: Specific Aim 1, to characterize and compare (001) and (hk0) planes of oriented HAP crystals;Specific Aim 2, to determine amelogenin-crystal interactions by identifying the binding domains, analyzing binding affinities and kinetics, and investigating the binding patterns of amelogenins on (001) and (hk0) planes of HAP crystals;Specific Aim 3, To investigate amelogenin-proteinases interactions before and after amelogenin binding to apatite crystals and determine how the interactions affect the growth of crystal. The amelogenin carrying P70T mutation will be also used to test the effects of the mutation on crystal- amelogenin-proteinase interactions. The proposed studies will integrate the roles of HAP, amelogenin and proteinase into an interactive unity, and study how the interactions modulate the enamel crystal growth and morphology. The findings collected in this study will build new concepts to advance our knowledge of the unique principle of amelogenin-mediated crystal growth and help us to better understand the fundamental mechanism of AI. The new concepts may be also useful for future acellular tooth enamel repair and regeneration. PUBLIC HEALTH RELEVANCE: This project will use state of the art techniques to study the mechanism of tooth enamel formation. The proposed studies focus on the enamel crystal growth modulated by interactions between apatite crystals, amelogenin and proteinases during different development stages and the defective growth of crystals in a type of amelogenesis imperfecta.