Mark Tuckerman of New York University is supported by an award from the Theory Models and Computational Method program of the Chemistry Division to carry out research, development, and application of novel methods for enhanced conformational sampling, free energy prediction, and hybrid QM/MM calculations. The aim of this project is to address directly measurable structural and dynamical quantities of complex chemical processes in the condensed phase in novel ways based on modeling and simulation. To that end, a novel approach to conformational sampling based on the introduction of specialized variable transformations in the classical canonical partition function is being developed. This approach reduces the effect of energy barriers without altering thermodynamic and equilibrium properties of the system. Applications include systems with increasing complexity, from peptides to fast-folding proteins. Hence, there are potential benefits to fields ranging from human health (simulations of protein folding and miss-folding) to the rational design of novel materials. A second component of the project addresses chemical reactivity in large biomolecules such as enzymes via the quantum mechanical/molecular mechanical (QM/MM) method. A rigorous theory of molecular pseudo-potentials is developed for describing the interaction between the QM and MM subsystems. The new pseudo-potentials are to be gathered in a database made available to the community on the awardee's Web site.
Methodology development and its incorporation into user-friendly open-source software that is freely available to the community are components of the project that strongly impact computational chemistry and biology, leading to new approaches for solving complex problems in silico. Tuckerman's undergraduate and graduate students and postdoctoral researchers are a diverse and gender-balanced group. Notes of the graduate Statistical Mechanics course, currently available through the Web, are supplemented with advances in this project. Outreach seminars at the Mathematics Speakers Bureau (MSB) of the New York section of the Mathematical Association of America enrich the background of students and faculty of regional middle schools, high schools, colleges and universities on topics reaching beyond the traditional math curriculum.
Predicting the preferred arrangements of the chemical units and/or subunits that comprise a complex system remains one of the grand challenges in the computational molecular sciences. This problem, known as the "structure prediction problem", has a profound impact in nearly all branches of materials science, including pharmaceuticals, clean energy technologies, and biomaterials, to name just a few. The development of novel computational algorithms capable of elucidating these preferred arrangements and ranking them according to the rules of thermodynamics would constitute a significant advance in materials science, as well as in chemistry and physics. Indeed, the need for the theoretical and computational molecular sciences to play a key role in the development of new materials and processes was highlighed in the White House's recent white paper on the Materials Genome Initiative. Over the lifetime of this project, my research group has undertaken the challenge of creating computational tools -- algorithms and software -- capable of tacking the structure prediction problem. Pharmaceuticals constitute a $500 billion dollar market worldwide with roughly half concentrated in the United States alone. Many common medications are packaged and sold as compacted crystalline particles of small, active molecules. In many instances, such molecules could have more than one preferred crystalline form, a phenomenon known as "polymorphism", and when this happens, one or more of these structures might be so stable as to be incapable of dissolving in the stomache, which would render the drug ineffective. It is, therefore, critical to determine the existence of such structures before going to market with a new compound, and computational techniques can potentially achieve this more efficiently and inexpensively than can be done at the bench in a lab. One of the goals of our project, therefore, has been to initiate the development of a computational algorithm for searching and ranking the polymorphs of small-molecule crystals at any desired temperature and pressure using an approach known as "enhanced sampling". We have implemented this approach in a suite of software tools we have been developing, and we illustrate the discovery of two polymorphs of a simple crystal, here crystalline benzene, in the first accompanying graphic. Crystalline benzene has six stable polymorphs at the conditions studied, and our approach was able to identify and rank them in just a few hours on an ordinary desktop computer. We have tested our approach on three other compounds with similar success, and we are now turning our attention to compounds of potential use in anti-cancer therapies. A second goal of our project concerns the prediction of the conformational preferences of another class of pharmaceutically relevant compounds, specifically, short peptide sequences. Being composed of the same chemical units (the amino acids) that compose the naturally occurring proteins in the body, these compounds can potentially offer the same therapeutic function as small molecule drugs with much lower toxicity. Although these peptide sequences are rather flexible, they often need to assume a particular conformation when they bind to their biochemical target. Discovering the active conformation and/or the possibility of other active conformations is another problem in which computational approaches can play an important role, again due to their efficiency and relatively low cost. We have advanced a new set of algorithms for efficiently scanning and ranking the conformational preferences of such molecules in any environment, including the binding site of the therapeutic target. This approach targets a small subset of the variables that characterize the conformations of the molecule and subjects them to enhanced sampling. As a test of our approach to discover the preferred conformations of short peptide sequences, we have chosen a melanoma antigen, called melan-A, which is readily recognized by the body's T-cells. A naturally occuring peptide consisting of nine amino acids binds to melan-A in a structure that contains a prominent bulge in the middle (see top panel of second graphic). Recently, it was observed that this peptide could also bind in an extended, active conformation (see lower panel of accompanying graphic), making this the only immunogenic melan-A peptide that binds in this configuration. Understanding why multiple binding configurations are possible can aid in the design of engineered peptides that can enhance T-cell recognition. Our calculations of the system shown in the graphic suggest that the energy needed to change the conformation of the bound peptide shown in the accompanying figure is actually quite low, thus answering the question of why multiple binding configurations are possible. This mechanism provides important clues as to potentially useful compositions of engineered peptides for use in melanoma therapies.
