Quantifying Structure–Function Uncertainty: A Graph Theoretical Exploration into the Origins and Limitations of Protein Annotation

Since the advent of investigations into structural genomics, research has focused on correctly identifying domain boundaries, as well as domain similarities and differences in the context of their evolutionary relationships. As the science of structural genomics ramps up adding more and more information into the databanks, questions about the accuracy and completeness of our classification and annotation systems appear on the forefront of this research. A central question of paramount importance is how structural similarity relates to functional similarity. Here, we begin to rigorously and quantitatively answer these questions by first exploring the consensus between the most common protein domain structure annotation databases CATH, SCOP and FSSP. Each of these databases explores the evolutionary relationships between protein domains using a combination of automatic and manual, structural and functional, continuous and discrete similarity measures. In order to examine the issue of consensus thoroughly, we build a generalized graph out of each of these databases and hierarchically cluster these graphs at interval thresholds. We then employ a distance measure to find regions of greatest overlap. Using this procedure we were able not only to enumerate the level of consensus between the different annotation systems, but also to define the graph-theoretical origins behind the annotation schema of class, family and superfamily by observing that the same thresholds that define the best consensus regions between FSSP, SCOP and CATH correspond to distinct, non-random phase-transitions in the structure comparison graph itself. To investigate the correspondence in divergence between structure and function further, we introduce a measure of functional entropy that calculates divergence in function space. First, we use this measure to calculate the general correlation between structural homology and functional proximity. We extend this analysis further by quantitatively calculating the average amount of functional information gained from our understanding of structural distance and the corollary inherent uncertainty that represents the theoretical limit of our ability to infer function from structural similarity. Finally we show how our measure of functional “entropy” translates into a more intuitive concept of functional annotation into similarity EC classes.