Differential geometric analysis of alterations in MH α-helices

Authors

  • Birgit Hischenhuber,

    1. Center for Medical Statistics, Informatics, and Intelligent Systems, Section for Biosimulation and Bioinformatics, Medical University of Vienna, Vienna, Austria
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  • Hans Havlicek,

    1. Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, Research Group for Differential Geometry and Geometric Structures, Vienna University of Technology, Vienna, Austria
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  • Jelena Todoric,

    1. Laboratory of Gene Regulation and Signal Transduction, Departments of Pharmacology and Pathology, School of Medicine, University of California, California, San Diego
    2. Department of Laboratory Medicine, Medical University Vienna, Vienna, Austria
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  • Sonja Höllrigl-Binder,

    1. Center for Medical Statistics, Informatics, and Intelligent Systems, Section for Biosimulation and Bioinformatics, Medical University of Vienna, Vienna, Austria
    2. Faculty of Mathematics and Geoinformation, Institute of Analysis and Scientific Computing, Research Group for Mathematical Modelling and Simulation, Vienna University of Technology, Vienna, Austria
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  • Wolfgang Schreiner,

    1. Center for Medical Statistics, Informatics, and Intelligent Systems, Section for Biosimulation and Bioinformatics, Medical University of Vienna, Vienna, Austria
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  • Bernhard Knapp

    Corresponding author
    1. Center for Medical Statistics, Informatics, and Intelligent Systems, Section for Biosimulation and Bioinformatics, Medical University of Vienna, Vienna, Austria
    2. Department of Statistics, Protein Informatics Group, University of Oxford, Oxford, United Kingdom
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Errata

This article is corrected by:

  1. Errata: Corrigendum: Differential geometric analysis of alterations in MH α-helices Volume 34, Issue 32, 2834, Article first published online: 12 October 2013

  • The whole software for the description of MH α-helices based on differential geometric parameters and simple examples are available for free for academic researchers. The software package is implemented in Matlab version 7 and therefore available as platform independent source code from: http://www.meduniwien.ac.at/msi/md/sourceCodes/diffParams/diffParams.htm

Abstract

Antigen presenting cells present processed peptides via their major histocompatibility (MH) complex to the T cell receptors (TRs) of T cells. If a peptide is immunogenic, a signaling cascade can be triggered within the T cell. However, the binding of different peptides and/or different TRs to MH is also known to influence the spatial arrangement of the MH α-helices which could itself be an additional level of T cell regulation. In this study, we introduce a new methodology based on differential geometric parameters to describe MH deformations in a detailed and comparable way. For this purpose, we represent MH α-helices by curves. On the basis of these curves, we calculate in a first step the curvature and torsion to describe each α-helix independently. In a second step, we calculate the distribution parameter and the conical curvature of the ruled surface to describe the relative orientation of the two α-helices. On the basis of four different test sets, we show how these differential geometric parameters can be used to describe changes in the spatial arrangement of the MH α-helices for different biological challenges. In the first test set, we illustrate on the basis of all available crystal structures for (TR)/pMH complexes how the binding of TRs influences the MH helices. In the second test set, we show a cross evaluation of different MH alleles with the same peptide and the same MH allele with different peptides. In the third test set, we present the spatial effects of different TRs on the same peptide/MH complex. In the fourth test set, we illustrate how a severe conformational change in an α-helix can be described quantitatively. Taken together, we provide a novel structural methodology to numerically describe subtle and severe alterations in MH α-helices for a broad range of applications. © 2013 Wiley Periodicals, Inc.

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