I am involved in a few related projects at present. One is theoretical research in computational biophysics; another is a software development project related to that research. The third project is related to a long-range research goal.
In the fall of 2007, I made a decision to change research tracks. As I describe in greater detail in Research History, my original research area was in software testing. After much consideration though, I decided that I wanted to do research in computational biology. The problems there had appeal to me, and in particular I became interested in the problem of protein structure prediction from sequences. This was not going to be easy, because I knew very little biology, very little about genetics, and barely remembered high school chemistry. I decided thatit was finally time to take my long overdue sabbatical and use that time to retrain myself.
During the spring of 2008, I started learning those topics in genetics most closely related to the problem of protein structure and synthesis. I narrowed down my interest to ab initio methods of protein structure prediction. Among the different protein structure prediction strategies, only ab initio (also known as de novo) methods use physical principles alone rather than relying on previously solved structures. These physical principles are all based on the Thermodynamic Hypothesis (also known as Anfinsen's Dogma), which asserts that the three-dimensional structure of a protein in its "normal physiological milieu" is the one in which the Gibbs free energy of the entire system is at a global minimum. Gibbs free energy is a thermodynamic property, depending upon the properties of the molecule's environment such as temperate, pressure, and so on. Under suitable conditions, Anfinsen's Dogma can essentially be interpreted to mean that the native folded protein's conformation is at the global minimum of the potential energy surface of the molecule. Finding the global minimum of the potential energy surface of even the smallest of molecules was pretty much impossible, and ab initio methods were considered to be infeasible. However, they are becoming more feasible as computers have grown in power and as research has led to improved global minimization algorithms. Therefore, I decided that it made sense to pursue this line of research and that in order to do so, I needed to know the underlying mathematics and physics of the potential energy functions of macromolecules.
I spent the summer of 2008 brushing up on classical physics and special relativity, just to make sure I understood whether or not the problem required a relativistic solution. Then I took a class in quantum chemistry. Most approaches to the problem of molecular modeling use classical molecular mechanics, even though quantum mechanics yields more accurate answers. The argument against using quantum mechanics is that it is still infeasible to use it, and that for practical purposes, it does not provide higher quality information than classical mechanics. The jury is still out on this question though -- there are voices on each side of the argument -- and quantum mechanics is at the heart of the problem.
My taking the class in quantum chemistry was fortuitous because I started having discussions with Lou Massa about the research that he, Lulu Huang, and Jerome Karle had been doing in applying quantum chemical methods to proteins and nucleic acids. They had developed a method of approximating the total energy of a molecule from crystallographic data, called the kernel energy method (KEM). In this approach, the molecule was decomposed into smaller fragments called kernels, and quantum mechanical methods were used to compute the total energy of each kernel as well as the interaction energies of various combined kernels. Because application of the method was painstaking and tedious, I proposed to them to design a software tool to facilitate the application of the method. From about January 2009 through the spring of 2009, we prepared a software requirements specification that we will use to seek funding for it.
In the course of studying the application of the kernel energy method, I discovered a way to extend and generalize it, and have completed a first draft of a manuscript for journal submission. The work that I have been doing recently applies ideas from graph theory and algorithmic analysis to improve the efficiency and applicability of the KEM. With this extension to their work, it makes it possible to analyze larger molecules and to get more accurate estimates of molecular energy and interaction energies with not much more computational effort than in the original method. I hope to incorporate these ideas into a much more powerful software tool.
My most recent activity is in the application of parallel algorithms to other computational chemistry problems. For this purpose I have been using the resources of CUNY's High Performance Computing Center, and the Gaussian software package. One problem that I have yet to solve is related to modeling the formation of gel-like substances when impurities are injected into superfluid helium, a collaboration with German Kolmakov, a physicist at New York City Technical College.