Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding

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The objective of the proposed research is the study of the design, analysis, and implementation of algorithms for computing the global minima of a class of nonconvex energy functions. One of the most significant and challenging problems in molecular biophysics and biochemistry is that of computing the native 3-dimensional conformation (folded state) of a globular protein given its amino acid sequence, possibly in the presence of additional agents (e.g. drugs). The minimization of potential energy functions plays an important role in the determination of ground states or stable states of certain classes of molecular clusters and proteins. Since, in almost all the cases, the potential energy function is nonconvex and therefore has been made; the primary impediment is the lack of adequate global minimization methods for these large-dimensionality problems. Our research will focus on: (a) determination of suitable energy functions that can reliably model protein behaviour and (b) global optimization methods that can find global minima of nonconvex energy functions given the many degrees of freedom available to protein structures.