GISA: Using Gauss Integrals to identify rare conformations in protein structures

Abstract

The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few methods are sensitive to topologic-geometric features, the examples being knots, slipknots, lassos, links, and pokes, and with each method aimed only for a specific set of such configurations.\n\nWe here propose a general method which transforms a structure into a \"fingerprint of topological-geometric values\" consisting in a series of real-valued descriptors from mathematical Knot Theory. The extent to which a structure contains unusual configurations can then be judged from this fingerprint. The method is therefore not confined to a particular pre-defined topology or geometry (like a knot or a poke), and so, unlike existing methods, it is general. To achieve this our new algorithm, GISA, as a key novelty produces the descriptors, so called Gauss integrals, not only for the full chains of a protein but for all its sub-chains, thereby allowing fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds.\n\nApplying GISA to a set of about 8000 high resolution structures (top8000), we first show how it enables swift identification of predefined geometries such as pokes and links. We then apply GISA with no restrictions on geometry, to show how it allows identifying rare conformations by finding rare invariant values only. In this unrestricted search, pokes and links are still found, but also knotted conformations, as well as more highly entangled configurations not previously described. Thus, applying the basic scan method in GISAs tool-box to the top8000 set, 10 known cases of knots are ranked as the top positive Gauss number cases, while placing at the top of the negative Gauss numbers 14 cases in cis-trans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed.\n\nPotential applications of the GISA tools include finding errors in protein models and identifying unusual conformations that might be important for protein folding and function. By its broad potential, we believe that GISA will be of general benefit to the structural bioinformatics community.\n\nGISA is coded in C and comes as a command line tool. Source and compiled code for GISA plus read-me and examples are publicly available at GitHub (https://github.com).