Spatiotemporal multistage consensus clustering in molecular dynamics studies of large proteins.

The aim of this work is to find semi-rigid domains within large proteins as reference structures for fitting molecular dynamics trajectories. We propose an algorithm, multistage consensus clustering, MCC, based on minimum variation of distances between pairs of Cα-atoms as target function. The whole dataset (trajectory) is split into sub-segments. For a given sub-segment, spatial clustering is repeatedly started from different random seeds, and we adopt the specific spatial clustering with minimum target function: the process described so far is stage 1 of MCC. Then, in stage 2, the results of spatial clustering are consolidated, to arrive at domains stable over the whole dataset. We found that MCC is robust regarding the choice of parameters and yields relevant information on functional domains of the major histocompatibility complex (MHC) studied in this paper: the α-helices and ß-floor of the protein (MHC) proved to be most flexible and did not contribute to clusters of significant size. Three alleles of the MHC, each in complex with ABCD3 peptide and LC13 T-cell receptor (TCR), yielded different patterns of motion. Those alleles causing immunological allo-reactions showed distinct correlations of motion between parts of the peptide, the binding cleft and the complementary determining regions (CDR)-loops of the TCR. Multistage consensus clustering reflected functional differences between MHC alleles and yields a methodological basis to increase sensitivity of functional analyses of bio-molecules. Due to the generality of approach, MCC is prone to lend itself as a potent tool also for the analysis of other kinds of big data.

Geometry Dynamics of α -Helices in Different Class I Major Histocompatibility Complexes.

MHC α-helices form the antigen-binding cleft and are of particular interest for immunological reactions. To monitor these helices in molecular dynamics simulations, we applied a parsimonious fragment-fitting method to trace the axes of the α-helices. Each resulting axis was fitted by polynomials in a least-squares sense and the curvature integral was computed. To find the appropriate polynomial degree, the method was tested on two artificially modelled helices, one performing a bending movement and another a hinge movement. We found that second-order polynomials retrieve predefined parameters of helical motion with minimal relative error. From MD simulations we selected those parts of α-helices that were stable and also close to the TCR/MHC interface. We monitored the curvature integral, generated a ruled surface between the two MHC α-helices, and computed interhelical area and surface torsion, as they changed over time. We found that MHC α-helices undergo rapid but small changes in conformation. The curvature integral of helices proved to be a sensitive measure, which was closely related to changes in shape over time as confirmed by RMSD analysis. We speculate that small changes in the conformation of individual MHC α-helices are part of the intrinsic dynamics induced by engagement with the TCR.

Relative Movements of Domains in Large Molecules of the Immune System.

Molecular dynamics was used to simulate large molecules of the immune system (major histocompatibility complex class I, presented epitope, T-cell receptor, and a CD8 coreceptor.) To characterize the relative orientation and movements of domains local coordinate systems (based on principal component analysis) were generated and directional cosines and Euler angles were computed. As a most interesting result, we found that the presence of the coreceptor seems to influence the dynamics within the protein complex, in particular the relative movements of the two α-helices, Gα1 and Gα2.

Geometric analysis of alloreactive HLA α-helices.

Molecular dynamics (MD) is a valuable tool for the investigation of functional elements in biomolecules, providing information on dynamic properties and processes. Previous work by our group has characterized static geometric properties of the two MHC α-helices comprising the peptide binding region recognized by T cells. We build upon this work and used several spline models to approximate the overall shape of MHC α-helices. We applied this technique to a series of MD simulations of alloreactive MHC molecules that allowed us to capture the dynamics of MHC α-helices' steric configurations. Here, we discuss the variability of spline models underlying the geometric analysis with varying polynomial degrees of the splines.

Finding semirigid domains in biomolecules by clustering pair-distance variations.

Dynamic variations in the distances between pairs of atoms are used for clustering subdomains of biomolecules. We draw on a well-known target function for clustering and first show mathematically that the assignment of atoms to clusters has to be crisp, not fuzzy, as hitherto assumed. This reduces the computational load of clustering drastically, and we demonstrate results for several biomolecules relevant in immunoinformatics. Results are evaluated regarding the number of clusters, cluster size, cluster stability, and the evolution of clusters over time. Crisp clustering lends itself as an efficient tool to locate semirigid domains in the simulation of biomolecules. Such domains seem crucial for an optimum performance of subsequent statistical analyses, aiming at detecting minute motional patterns related to antigen recognition and signal transduction.

PeptX: using genetic algorithms to optimize peptides for MHC binding.

BACKGROUND: The binding between the major histocompatibility complex and the presented peptide is an indispensable prerequisite for the adaptive immune response. There is a plethora of different in silico techniques for the prediction of the peptide binding affinity to major histocompatibility complexes. Most studies screen a set of peptides for promising candidates to predict possible T cell epitopes. In this study we ask the question vice versa: Which peptides do have highest binding affinities to a given major histocompatibility complex according to certain in silico scoring functions? RESULTS: Since a full screening of all possible peptides is not feasible in reasonable runtime, we introduce a heuristic approach. We developed a framework for Genetic Algorithms to optimize peptides for the binding to major histocompatibility complexes. In an extensive benchmark we tested various operator combinations. We found that (1) selection operators have a strong influence on the convergence of the population while recombination operators have minor influence and (2) that five different binding prediction methods lead to five different sets of "optimal" peptides for the same major histocompatibility complex. The consensus peptides were experimentally verified as high affinity binders. CONCLUSION: We provide a generalized framework to calculate sets of high affinity binders based on different previously published scoring functions in reasonable runtime. Furthermore we give insight into the different behaviours of operators and scoring functions of the Genetic Algorithm.