Graph models for the conformations of ion channel proteins
by
Robin Sue Sanders
Buffalo State College
Coauthors: Fred Sachs (Department of Physiology and Biophysics at the University at Buffalo)

The conformations of an ion channel protein may be modeled by the vertices of a graph, the conformational changes by edges between those vertices (labeled with kinetic constants), and observable conductance levels by a nonstandard graph coloring. The model for a particular ion channel protein is not known a priori, but the Channel Group in the Department of Physiology and Biophysics at the University at Buffalo has developed methods for determining how well a particular model matches the data. We have developed methods that use nauty to list (not merely enumerate) the distinct colored graphs on small numbers of vertices so that further testing can be done to determine the suitable models. As in many combinatorial problems, the number of objects grows quite rapidly: There are 105, 764 two-colored graphs on 8 vertices with maximum degree 4 and no more than 10 edges. Due to the large number of graphs involved, the Channel Group cannot hope to test all possible graphs on a given number of vertices with a given color partition. Future work must be done so that additional information can be used to create only those graphs with the greatest likelyhood of conforming to the channel's behavior.

Date received: April 20, 2001