Molecular computations for reactions and phase transitions: applications to protein stabilization, hydrates and catalysis

In this work we have made significant contributions in three different areas of interest: therapeutic protein stabilization, thermodynamics of natural gas clathrate-hydrates, and zeolite catalysis. In all three fields, using our various computational techniques, we have been able to elucidate phenomena that are difficult or impossible to explain experimentally. More specifically, in mixed solvent systems for proteins we developed a statistical-mechanical method to model the thermodynamic effects of additives in molecular-level detail. It was the first method demonstrated to have truly predictive (no adjustable parameters) capability for real protein systems. We also describe a novel mechanism that slows protein association reactions, called the “gap effect.” We developed a comprehensive picture of methioine oxidation by hydrogen peroxide that allows for accurate prediction of protein oxidation and provides a rationale for developing strategies to control oxidation. The method of solvent accessible area (SAA) was shown not to correlate well with oxidation rates. A new property, averaged two-shell water coordination number (2SWCN) was identified and shown to correlate well with oxidation rates. Reference parameters for the van der Waals Platteeuw model of clathrate-hydrates were found for structure I and structure II. These reference parameters are independent of the potential form (unlike the commonly used parameters) and have been validated by calculating phase behavior and structural transitions for mixed hydrate systems. These calculations are validated with experimental data for both structures and for systems that undergo transitions from one structure to another. This is the first method of calculating hydrate thermodynamics to demonstrate predictive capability for phase equilibria, structural changes, and occupancy in pure and mixed hydrate systems. We have computed a new mechanism for the methanol coupling reaction to form ethanol and water in the zeolite chabazite. The mechanism at 400°C proceeds via stable intermediates of water, methane, and protonated formaldehyde.

Vectorizing Face Images by Interpreting Shape and Texture Computations

The correspondence problem in computer vision is basically a matching task between two or more sets of features. In this paper, we introduce a vectorized image representation, which is a feature-based representation where correspondence has been established with respect to a reference image. This representation has two components: (1) shape, or (x, y) feature locations, and (2) texture, defined as the image grey levels mapped onto the standard reference image. This paper explores an automatic technique for "vectorizing" face images. Our face vectorizer alternates back and forth between computation steps for shape and texture, and a key idea is to structure the two computations so that each one uses the output of the other. A hierarchical coarse-to-fine implementation is discussed, and applications are presented to the problems of facial feature detection and registration of two arbitrary faces.

Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.