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S. Hoellrigl-Binder, B. Hischenhuber, W. Schreiner, B. Knapp:
"Characterisation of TCR Motions in Reaction to Immunogenic and Non-Immunogenic Peptides: A PCA Approach";
Talk: MATHMOD 2012 - 7th Vienna Conference on Mathematical Modelling, Wien; 02-14-2012 - 02-17-2012; in: "Preprints Mathmod 2012 Vienna - Full Paper Volume", F. Breitenecker, I. Troch (ed.); Argesim / Asim, 38 (2012), 405 - 406.

Introduction. The adaptive immune system differentiates between antigens which elicit an immune response and
antigens which do not - they are usually referred to as immunogenic and non-immunogenic peptides respectively.
These peptides are bound to major histocompatibility complex (MHC) molecules located on the cell surface which
present the peptides (p) to T-cell receptors (TCR) of T-cells (TC). If the peptide is considered immunogenic a
signalling cascade is triggered.
There are many theories concerning antigen recognition and the induction of this cascade [1]. The purpose of this
study is to find indications that the TCR undergoes subtle conformational changes if bound to an immunogenic
peptide/MHC complex.
Method. To find evidence in order to support this hypothesis molecular dynamics (MD) simulations are a
promising approach. MD simulations enable us to analyze atomic motions in detail and have proven to be a
powerful tool to study biomolecules [2]. A common approach to extract motions of biological significance is to
compute the correlated so-called collective motions. A well known method to extract this information is the
principle component analysis (PCA) [3].
We analysed 58 MD simulations of TCRpMHC complexes performed by B. Knapp. Although the considered
peptides only differ by one amino acid, this single mutation changes its immunogenicity severely. In order to
reduce the amount of data we only considered the C-alpha atoms of amino acids. Furthermore, we removed the
overall motions such as rotation and translation to obtain only internal motions. This is achieved by superimposing
a reference structure onto the trajectory. As reference structure we chose the crystal structure of the protein data
bank (PDB) accession code 1mi5 and superimposed it onto all 58 trajectories.
In the next step we concatenated the trajectories of all 58 simulations which consist of immunogenic as well as
non-immunogenic complexes and applied a PCA to this concatenated trajectory. A PCA requires the computation
of the covariance matrix of the atomic fluctuation and subsequently its eigenvectors and eigenvalues. The
eigenvectors corresponding to the biggest eigenvalues represent the direction of the strongest correlated motions.
This procedure was performed using Gromacs 4 which was already employed to realize the MD simulations.
The major hypothesis of this study is that there is a collective motion responsible for signal transduction. By
merging all 58 trajectories into one long trajectory and computing its correlated motions, we will be able to find at
least one eigenvector which represents the designated motion. By projecting the trajectories onto this eigenvector
we should be able to differentiate immunogenic and non-immunogenic TCRpMHC complexes.
The length of the projection is of special interest, since it gives insight how well the eigenvector covers the
direction of the molecule´s movement and most importantly leads to a considerable data reduction.
Results and Prospects. We obtained a considerable amount of 2d-plots each of which represents the projections
of the simulations onto two different eigenvectors. To date, the analysis of the data obtained is still in progress and
only preliminary results are available. However, on the basis of clustering we are confident to find the collective
motions which discriminate best between immunogenic and nonimmunogenic complexes.
Data of another 114 MD simulations of TCRpMHCs is available and will be processed once evidence supporting
our hypothesis is found.