Kernel Energy Method:  The Interaction Energy of the Collagen Triple Helix

There is a rapid growth in computational difficulty with the number of atoms when quantum mechanics is applied to the study of biological molecules. This difficulty may be alleviated in two different ways. One is the advance of parallel supercomputers. And the second is the use of a quantum crystallographic formalism based upon quantum kernels. The kernel methodology is well suited for parallel computation. Recently published articles have applied these advances to calculate the quantum mechanical ab initio molecular energy of peptides, protein (insulin), DNA, and RNA. The results were found to have high accuracy. This paper shows that it is possible to use the full power of ab initio quantum mechanics to calculate the interaction of long chain molecules of biological and medicinal interest. Such molecules may contain thousands or even tens of thousands of atoms. In the approach presented here the computational difficulty of representing a molecule increases only modestly with the number of atoms. The calculations are simplified by representing a full molecule by smaller "kernels" of atoms. The general case is illustrated by a specific example using an important protein, viz., a triple helix collagen molecule of known molecular structure. In order for such a molecule to be a stable helix, the overall interactions among the chains must be attractive. The results show that such interactions are accurately represented by application of the KEM to this triple helix.