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      Differential Geometric Analysis of Alterations in MH α-Helices

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          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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          Most cited references61

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          How TCRs bind MHCs, peptides, and coreceptors.

          Since the first crystal structure determinations of alphabeta T cell receptors (TCRs) bound to class I MHC-peptide (pMHC) antigens in 1996, a sizable database of 24 class I and class II TCR/pMHC complexes has been accumulated that now defines a substantial degree of structural variability in TCR/pMHC recognition. Recent determination of free and bound gammadelta TCR structures has enabled comparisons of the modes of antigen recognition by alphabeta and gammadelta T cells and antibodies. Crystal structures of TCR accessory (CD4, CD8) and coreceptor molecules (CD3epsilondelta, CD3epsilongamma) have further advanced our structural understanding of most of the components that constitute the TCR signaling complex. Despite all these efforts, the structural basis for MHC restriction and signaling remains elusive as no structural features that define a common binding mode or signaling mechanism have yet been gleaned from the current set of TCR/pMHC complexes. Notwithstanding, the impressive array of self, foreign (microbial), and autoimmune TCR complexes have uncovered the diverse ways in which antigens can be specifically recognized by TCRs.
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            MHC-dependent antigen processing and peptide presentation: providing ligands for T lymphocyte activation.

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              Evolutionarily conserved amino acids that control TCR-MHC interaction.

              The rules for the conserved reaction of alphabeta T cell receptors (TCRs) with major histocompatibility complex (MHC) proteins plus peptides are poorly understood, probably because thymocytes bearing TCRs with the strongest MHC reactivity are lost by negative selection. Thus, only TCRs with an attenuated ability to react with MHC appear on mature T cells. Also, the interaction sites between TCRs and MHC may be inherently flexible and hence difficult to spot. We reevaluated contacts between TCRs and MHC in the solved structures of their complexes with these points in mind. Relatively conserved amino acids in the TCR complementarity-determining regions (CDR) 1 and CDR2 are often used to bind exposed areas of the MHC alpha-helices. These areas are exposed because of small amino acids that allow somewhat flexible binding of the TCRs. The TCR amino acids involved are specific to families of variable (V) regions and to some extent different rules may govern the recognition of MHCI versus MHCII.
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                Author and article information

                Journal
                J Comput Chem
                J Comput Chem
                jcc
                Journal of Computational Chemistry
                Blackwell Publishing Ltd
                0192-8651
                1096-987X
                05 August 2013
                24 May 2013
                : 34
                : 21
                : 1862-1879
                Affiliations
                [[a] ]Center for Medical Statistics, Informatics, and Intelligent Systems, Section for Biosimulation and Bioinformatics, Medical University of Vienna Vienna, Austria
                [[b] ]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
                [[c] ]Laboratory of Gene Regulation and Signal Transduction, Departments of Pharmacology and Pathology, School of Medicine, University of California California, San Diego
                [[d] ]Department of Laboratory Medicine, Medical University Vienna Vienna, Austria
                [[e] ]Faculty of Mathematics and Geoinformation, Institute of Analysis and Scientific Computing, Research Group for Mathematical Modelling and Simulation, Vienna University of Technology Vienna, Austria
                [[f] ]Department of Statistics, Protein Informatics Group, University of Oxford Oxford, United Kingdom E-mail: bernhard.knapp@ 123456stats.ox.ac.uk
                Author notes
                [*]

                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

                Contract/grant sponsor: Austrian Science Fund; contract/grant number: FWF P22258-B12

                Contract/grant sponsor: 2020 Science Programme (EPSRC Cross-Discipline Interface Programme); contract/grant number: EP/I017909/1

                Article
                10.1002/jcc.23328
                3739936
                23703160
                e9930d70-e848-4111-a914-9dc190597e74
                Copyright © 2013 Wiley Periodicals, Inc.

                Re-use of this article is permitted in accordance with the Creative Commons Deed, Attribution 2.5, which does not permit commercial exploitation.

                History
                : 23 January 2013
                : 12 April 2013
                : 13 April 2013
                Categories
                Software News and Updates

                Computational chemistry & Modeling
                characterization of structural alterations,differential geometric parameters,major histocompatibility com- plex,alpha-helices,immunoinformatics

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