Macromolecular Structure Computation Based on Energy Function Approximation by Wavelets
We outline an approach using domain decomposition and wavelet techniques to analyze the geometry of macromolecules and to investigate important physical properties by means of simulations. The classical method of force field calculations requires minimizing of the energy as a function of the Cartesian coordinates of all atoms. Presently this method is limited to relatively small molecules due to the large number of degrees of freedom, which leads to severe problems in the minimization procedure. In our approach, we reduce the number of free variables by assembling certain groups of atoms into configurational structures with considerably less degrees of freedom. In this way, a whole hierarchy of coordinate spaces with decreasing dimensions is defined. Furthermore, approximations to the energy function with respect to these variables are constructed using methods from the theory of splines and wavelets. The problem of global approximation on the parameter manifolds leads to a unified approach to constructing wavelets on SO(3), S 3, and S 2. Therefore we also address another subject related to biological and medical applications, namely, the representation of surfaces, for example in tomography.