Optimization in Molecular Conformation

This work is supported by the National Science Foundation under the award 
Novel approaches to empirical force field models in molecular modeling via multidimensional scaling,

DMS 0713812.

What is Project Squid?

Squid is short for Squared Interatomic Distance parameterization of empirical force fields. We are investigating an approach to the determination of protein structure based on energy minimization. Rather than parameterize the energy functional in terms of the Cartesian coordinates of the atoms, we parameterize the energy functional in terms of interatomic distances. By vastly expanding the dimension of the space in which we search, we may be able to avoid the prodigious number of local minimizers of no physical interest that frequently bedevil energy minimization.

Topic description: One way to determine protein structure is to minimize the energy in the molecule due to the stretching of bonds, distortion of bond angles, van der Waal's forces, &c. Unfortunately, standard energy force field models lead to optimization problems with huge numbers of local minimizers that are not of physical interest, but which can trap optimization algorithms. This project focuses on a new approach to force field models based on distance geometry that leads to more tractable optimization problems.

Research opportunities: Development of the large-scale constrained optimization algorithm; numerical experimentation on real proteins; improved modeling of force field components; investigation of alternative methods of treating constraints; analysis, implementation, and experimentation with alternative problem formulations based on nonconvex duality.

Suggested prerequisites: Math 413, Math 414, experience with Matlab, C

Contact: R. M. Lewis