Machine Recognition of Protein-Like Features in Crystallographic Electron Density Maps. Erik Nelson and Lynn TenEyck, San Diego Supercomputer Center, P.O. Box 85608, La Jolla, CA 92186

Machine recognition of protein crystal structure requires the ability to identify and connect local topographic features in the electron probability density map [rho](x, y, z). Individual atoms, or clusters of atoms appear as maxima in the probability distribution, and ideally because of the exchange of electrons between bonded atoms, the maxima are connected by density ''tubes'' or saddles. To specify the signature of a particlar map a statistical approach can be taken in which the allowed configurations of the system are spanning graphs, the distance l_ij between maxima i and j is identified with the energy E_ij in the Boltzmann factor exp(-E_ij/kT), and the ground state is identified with the minimal spanning graph.

To construct the minimal spanning graph we nucleate it at all N maxima. In the first iteration of the algorithm every point is connected to its nearest neighbor, producing n <= N/2 disconnected minimal subgraphs g(j). In the next iteration, each g(j) is connected to its nearest neighbor g(k). After O(log(N)) iterations, this process generates the minimal spanning graph as a sequence of minimal spanning subgraphs. The method is appropriate for studying fluctuations about the ground state in the statistical approach and makes it possible to apply a neural network model to recognize protein-like patterns. We discuss these methods, and their assimilation into the Xtalview analysis platform.