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. We 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 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. This allows fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds. Applying GISA to sets of several thousand high resolution structures, we first show how the most basic Gauss integral, the writhe, enables swift identification of pre-defined 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, an application of the basic scan method in GISA’s tool-box revealed 10 known cases of knots as the top positive writhe cases, while placing at the top of the negative writhe 14 cases in cis-trans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed. Possible general applications of GISA are fold classification and structural alignment based on local Gauss integrals. Others 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. GISA 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).

Topoly: Python package to analyze topology of polymers

“…The user may analyze either two parts of the same chain (specified by the indices) or two separate chains. The GLN was already used to study the conformation and entanglement of proteins [ 7 , 8 , 13 , 27 , 46 , 47 ] and chromosomes [ 60 ].…”

Novel topological methods for identifying surprising protein tertiary structure relationships

“…The measures introduced in [54,55] were recently developed further in [58] where the Gaussian-integral approach was applied to subsets (fragments) of the protein, via a fingerprinting technique, using the entanglement of sub chains to identify rare conformations in proteins, essentially pairs of subsections of protein which are mutually entangled in some manner which is relatively rare. By contrast, in our case we aim to demonstrate there are tertiary structure motifs which are both common and similar across proteins, but which are not classed as similar in the standard classifications.…”

The SKMT Algorithm: A method for assessing and comparing underlying protein entanglement

“…In [31] a more rapid metric was created from the same Gaussian integrals as in the other two studies, once again shown to compare favourably to the SCOP benchmark set. The measures introduced in [29] were recently developed further in [32] where the Gaussian-integral approach was applied to subsections (fragments) of the protein, via a fingerprinting technique, using the entanglement of sub-chains to identify rare conformations in proteins. We highlight two aspects of these works that motivate developing our own approach.…”