5 November 2008
Manoj Gopalkrishnan
Adleman Group
Department of Computer Science, USC
I shall describe two contributions, one theoretical and one experimental, that have been prompted by a quest to better understand self-assembly.
Our theoretical contribution takes the form of a mathematical investigation of the law of mass action in chemistry. This is joint work with Len Adleman, Ming-Deh Huang, Pablo Moisset and Dustin Reishus. The law of mass action was formulated by Waage and Guldberg in 1864. Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the mathematical foundations of mass action chemistry: to provide precise definitions, elucidate what can now be proved, and indicate what is only conjectured. In addition, we believe that the law of mass action is of intrinsic mathematical interest and should be made available in a form that might allow it to transcend its application to chemistry alone. We are led to a dynamical theory of sets of binomials over the complex numbers.
My second contribution is to the emerging field of DNA self-assembly. It has been suggested that DNA self-assembly may lead to the manufacture of novel materials and computational devices. In 2004, Chelyapov, Brun, Reishus, Shaw, Adleman and I reported DNA complexes in the shape of triangles and in the pattern of hexagonal, planar tilings. More recently, Nikhil Gopalkrishnan, Adleman and I have reported DNA complexes in the shape of cylinders and Mobius strips which were formed using Rothemund's method of DNA origami.