Parabolic section and distance excess of space curves applied to protein structure classification

Røgen, Peter; Karlsson, Per W.

doi:10.1007/s10711-008-9247-z

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…Not all descriptor-based methods are directly sensitive to topology. Examples are the method with the most accurate re-classification of protein structures reported, FragBag [ 23 ], and the distance excess-based descriptors [ 24 ]. The later method however presents an elegant solution to the problem of detecting (plastic) deformation as caused by mutations.…”

Section: Introductionmentioning

confidence: 99%

Quantifying steric hindrance and topological obstruction to protein structure superposition

Røgen

2021

Algorithms Mol Biol

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Background In computational structural biology, structure comparison is fundamental for our understanding of proteins. Structure comparison is, e.g., algorithmically the starting point for computational studies of structural evolution and it guides our efforts to predict protein structures from their amino acid sequences. Most methods for structural alignment of protein structures optimize the distances between aligned and superimposed residue pairs, i.e., the distances traveled by the aligned and superimposed residues during linear interpolation. Considering such a linear interpolation, these methods do not differentiate if there is room for the interpolation, if it causes steric clashes, or more severely, if it changes the topology of the compared protein backbone curves. Results To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. To determine if the self-intersections alter the protein’s backbone curve significantly or not, we present a path-finding algorithm that checks if there exists a self-avoiding path in a neighborhood of the linear interpolation. A new path is constructed by altering the linear interpolation using a novel interpretation of Reidemeister moves from knot theory working on three-dimensional curves rather than on knot diagrams. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. Each of these indicates a significant difference between the folds of the aligned protein structures. As expected, we find at least one essential self-intersection separating most unknotted structures from a knotted structure, and we find even larger motions in proteins connected by obstruction free linear interpolations. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. TM-align is one of the most restrictive alignment programs. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts. Conclusions Based on the data we conclude that our program provides significant additional information to alignment scores based solely on distances between aligned and superimposed residue pairs.

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Section: Introductionmentioning

confidence: 99%

Quantifying steric hindrance and topological obstruction to protein structure superposition

Røgen

2021

Algorithms Mol Biol

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Extracting knowledge from protein structure geometry

Røgen

Koehl

2013

Proteins

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Protein structure prediction techniques proceed in two steps, namely the generation of many structural models for the protein of interest, followed by an evaluation of all these models to identify those that are native-like. In theory, the second step is easy, as native structures correspond to minima of their free energy surfaces. It is well known however that the situation is more complicated as the current force fields used for molecular simulations fail to recognize native states from misfolded structures. In an attempt to solve this problem we follow an alternate approach and derive a new potential from geometric knowledge extracted from native and misfolded conformers of protein structures. This new potential, MPP, has two main features that are key to its success. Firstly, it is composite in that it includes local and non local geometric information on proteins. At the short range level it captures and quantifies the mapping between the sequences and structures of short (7-mer) fragments of protein backbones through the introduction of a new local energy term. The local energy term is then augmented with a non local residue-based pairwise potential, and a solvent potential. Secondly, it is optimized to yield a maximized correlation between the energy of a structural model and its RMS to the native structure of the corresponding protein. We have shown that MPP yields high correlation values between RMS and energy and that it is able to retrieve the native structure of a protein from a set of high-resolution decoys.

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An Algebro-Topological Description of Protein Domain Structure

et al. 2011

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The space of possible protein structures appears vast and continuous, and the relationship between primary, secondary and tertiary structure levels is complex. Protein structure comparison and classification is therefore a difficult but important task since structure is a determinant for molecular interaction and function. We introduce a novel mathematical abstraction based on geometric topology to describe protein domain structure. Using the locations of the backbone atoms and the hydrogen bonds, we build a combinatorial object – a so-called fatgraph. The description is discrete yet gives rise to a 2-dimensional mathematical surface. Thus, each protein domain corresponds to a particular mathematical surface with characteristic topological invariants, such as the genus (number of holes) and the number of boundary components. Both invariants are global fatgraph features reflecting the interconnectivity of the domain by hydrogen bonds. We introduce the notion of robust variables, that is variables that are robust towards minor changes in the structure/fatgraph, and show that the genus and the number of boundary components are robust. Further, we invesigate the distribution of different fatgraph variables and show how only four variables are capable of distinguishing different folds. We use local (secondary) and global (tertiary) fatgraph features to describe domain structures and illustrate that they are useful for classification of domains in CATH. In addition, we combine our method with two other methods thereby using primary, secondary, and tertiary structure information, and show that we can identify a large percentage of new and unclassified structures in CATH.

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Parabolic section and distance excess of space curves applied to protein structure classification

Cited by 3 publications

References 25 publications

Quantifying steric hindrance and topological obstruction to protein structure superposition

Quantifying steric hindrance and topological obstruction to protein structure superposition

Extracting knowledge from protein structure geometry

An Algebro-Topological Description of Protein Domain Structure

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