Generative Topographic Mapping of Conformational Space

Abstract

Herein, Generative Topographic Mapping (GTM) was challenged to produce planar projections of the highdimensional conformational space of complex molecules (the 1LE1 peptide). GTM is a probability-based mapping strategy, and its capacity to support property prediction models serves to objectively assess map quality (in terms of regression statistics). The properties to predict were total, non-bonded and contact energies, surface area and fingerprint darkness. Map building and selection was controlled by a previously introduced evolutionary strategy allowed to choose the best-suited conformational descriptors, options including classical terms and novel atom-centric autocorrellograms. The latter condensate interatomic distance patterns into descriptors of rather low dimensionality, yet precise enough to differentiate between close favorable contacts and atom clashes. A subset of 20 K conformers of the 1LE1 peptide, randomly selected from a pool of 2 M geometries (generated by the S4MPLE tool) was employed for map building and cross-validation of property regression models. The GTM build-up challenge reached robust three-fold cross-validated determination coefficients of Q 2 = 0.7…0.8, for all modeled properties. Mapping of the full 2 M conformer set produced intuitive and information-rich property landscapes. Functional and folding subspaces appear as well-separated zones, even though RMSD with respect to the PDB structure was never used as a selection criterion of the maps.

Monitoring of the Conformational Space of Dipeptides by Generative Topographic Mapping

“…This work describes a generic procedure to build optimal generative topographic maps as 2D representation of the conformational space of dipeptides. Following the first attempt to use GTM technology for CS mapping, the therein developed Atom Property Autocorrellograms (APA) were shown to be competent descriptors for these essential building blocks of proteins, and lead to GTMs with excellent propensities to support highly predictive landscapes of various conformational properties (energy, accessible area, intramolecular contact counts, etc ). The GTM construction approach was successful for almost a dozen of various dipeptides, three of which were chosen for specific investigation in this paper: AA, KE and KR: the simplest representative of the family, a zwitterionic species and the most flexible family member (in terms of side chain length), respectively.…”

“…Another key parameter encoded by the chromosome is the type of descriptors to use – here, the four distinct sets of Atom‐Centric Property Autocorrellograms APA: APO (occurrence‐based), APD (distance‐based), APQ (charge‐based) and APQ2 (squared‐charge‐based) formed the pool of possible choices. Please refer to the cited paper for the formal definitions of APA conformational descriptors and their four subtypes.…”

“…In a recent publication, we have considered the non‐linear dimension reduction procedure called Generative Topographic Mapping (GTM) to produce two‐dimensional maps of the Conformational Space (CS) of molecules, herewith proposing a both meaningful and intuitive way to visualize and analyze this abstract, high‐dimensional space. A system with N atoms requires 3N‐6 coordinates to be fully defined, i. e. each geometry can be represented as a point (vector) of a (3N‐6)‐dimensional Conformational Space (CS).…”

Generative Topographic Mapping of the Docking Conformational Space

“…It has been shown that generative topographic maps of CS are not only intuitive, supporting the visualization of key features and intramolecular interactions, but actually support construction of quantitative, predictive landscapes of conformational properties (energy, RMSD versus the native fold, etc.). This is a key advantage of the approach over “classical” state-of-the-art methods for CS analysis, as discussed previously [1,2].…”

“…In two recent publications [1,2], the non-linear dimension reduction procedure called Generative Topographic Mapping (GTM) [3,4,5,6] has been adapted to visualize and analyze the abstract, (3 N -6)-dimensional Conformational Space (CS) of arbitrary N-atomic molecules up to the size of polypeptides with more than 10 residues. It has been shown that generative topographic maps of CS are not only intuitive, supporting the visualization of key features and intramolecular interactions, but actually support construction of quantitative, predictive landscapes of conformational properties (energy, RMSD versus the native fold, etc.).…”