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Differential geometric analysis of alterations in MH ?-helices.

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 ?-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 ?-helices by curves. On the basis of these curves, we calculate in a first step the curvature and torsion to describe each ?-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 ?-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 ?-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 ?-helix can be described quantitatively. Taken together, we provide a novel structural methodology to numerically describe subtle and severe alterations in MH ?-helices for a broad range of applications.

SUBMITTER: Hischenhuber B

PROVIDER: S-EPMC3739936 | biostudies-literature | 2013 Aug

REPOSITORIES: biostudies-literature

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Differential geometric analysis of alterations in MH α-helices.

Hischenhuber Birgit B Havlicek Hans H Todoric Jelena J Höllrigl-Binder Sonja S Schreiner Wolfgang W Knapp Bernhard B

Journal of computational chemistry 20130524 21

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 ...[more]

PMID: 23703160

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Project description:Major histocompatibility proteins share a common overall structure or peptide binding groove. Two binding groove domains, on the same chain for major histocompatibility class I or on two different chains for major histocompatibility class II, contribute to that structure that consists of two α-helices ("wall") and a sheet of eight anti-parallel beta strands ("floor"). Apart from the peptide presented in the groove, the major histocompatibility α-helices play a central role for the interaction with the T cell receptor. This study presents a generalized mathematical approach for the characterization of these helices. We employed polynomials of degree 1 to 7 and splines with 1 to 2 nodes based on polynomials of degree 1 to 7 on the α-helices projected on their principal components. We evaluated all models with a corrected Akaike Information Criterion to determine which model represents the α-helices in the best way without overfitting the data. This method is applicable for both the stationary and the dynamic characterization of α-helices. By deriving differential geometric parameters from these models one obtains a reliable method to characterize and compare α-helices for a broad range of applications.Program summaryProgram title: MH2c (MH helix curves) Catalogue identifier: AELX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELX_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 327 565 No. of bytes in distributed program, including test data, etc.: 17 433 656 Distribution format: tar.gz Programming language: Matlab Computer: Personal computer architectures Operating system: Windows, Linux, Mac (all systems on which Matlab can be installed) RAM: Depends on the trajectory size, min. 1 GB (Matlab) Classification: 2.1, 4.9, 4.14 External routines: Curve Fitting Toolbox and Statistic Toolbox of Matlab Nature of problem: Major histocompatibility (MH) proteins share a similar overall structure. However, identical MH alleles which present different peptides differ by subtle conformational alterations. One hypothesis is that such conformational differences could be another level of T cell regulation. By this software package we present a reliable and systematic way to compare different MH structures to each other. Solution method: We tested several fitting approaches on all available experimental crystal structures of MH to obtain an overall picture of how to describe MH helices. For this purpose we transformed all complexes into the same space and applied splines and polynomials of several degrees to them. To draw a general conclusion which method fits them best we employed the "corrected Akaike Information Criterion". The software is applicable for all kinds of helices of biomolecules. Running time: Depends on the data, for a single stationary structure the runtime should not exceed a few seconds.

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Differential geometric analysis of alterations in MH ?-helices.

Publications

Differential geometric analysis of alterations in MH α-helices.

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