Optimization Algorithms for Macromolecular Modeling

Global optimization techniques are central to the solution of macromolecular modeling and simulation problems, The aim of this project is to develop a high-performance environment for the Center for Computational Science and Technology at Argonne that supports large scale global optimization. We have done work on the determination of protein structures, ionic systems and molecular clusters. Current work focuses on distance geometry optimization for protein structures.

Gaussian Smoothing

An appealing idea for finding the global minimizer of a function is to transform the function into a smoother function with fewer local minimizers, apply an optimization algorithm to the transformed function, and trace the minimizers back to the original function.

A transformed function is a coarse approximation to the original function, with small and narrow minimizers being removed while the overall structure of the function is maintained. This property allows a local minimization procedure to skip less interesting local minimizers and to concentrate on regions with low function values, where a global minimizer is most likely to be located.

The smoothing transform, called the Gaussian transform, depends on a parameter that controls the degree of smoothing. The original function is obtained if the parameter is zero, while smoother functions are obtained as the parameter increases.

Further information on Gaussian smoothing can be found in the following papers:

 


Macromolecular Conformation

We have developed DGSOL, a software package for for the solution of distance geometry problems with lower and upper bounds on the distance data. These problems arise in the interpretation of NMR data and in the determination of protein structures. DGSOL has been developed for both sequential and parallel architectures.

Solutions have been obtained for a set of model problems with up to 1500 variables, with excellent performance on the IBM SP. We have also used the algorithms to determine the structure of protein fragments, such as the the active fragment of E. Coli STh enterotoxin shown here, or the DNA-binding protein shown above.


Configurations of Ionic Systems

We have also developed algorithms for finding stable configurations of ionic systems. The stable configuration for an ionic system can be found by minimizing the energy function for the system over configuration space.

Stable configurations for a set of small systems have been obtained by using Gaussian smoothing algorithms on the IBM Quad. We are now working on larger ionic systems. An important goal of this work is to find the stable configurations for very large systems, say, systems of 200,000 ions. The optimal structure with 200 ions is shown here.

This work is joint with John Schiffer and Steve Pieper of Argonne's Physics division.


Argonne National Laboratory / more@mcs.anl.gov