Supplementary Materialsjcc0034-1862-SD1. to spell it out each -helix separately. In another stage, we calculate the distribution parameter as well as the conical curvature from the ruled surface area to spell it out the comparative orientation of both -helices. Based on four different check sets, we present how these differential geometric variables can be used to describe changes in the spatial set up of the MH -helices for different biological difficulties. In the 1st test arranged, we illustrate on the basis of all available crystal constructions for (TR)/pMH complexes how the binding of TRs influences the MH helices. In the second test arranged, we display a mix evaluation of different MH alleles with the same peptide and the same MH allele with different peptides. In the third test arranged, we present the spatial effects of different TRs on the same peptide/MH complex. In the fourth test arranged, we illustrate how a severe conformational switch in an -helix can be explained quantitatively. Taken collectively, we provide a novel structural strategy to numerically describe subtle and severe alterations in MH -helices for a broad range of applications. ? 2013 Wiley Periodicals, Inc. on the basis of I-Au in complex with modified peptide ligands from myelin fundamental protein.6 The structural basis how a single TR signaling cascade is activated remains still an unsolved query. Several different models for this process were proposed7 and in most of them at least delicate structural deformations of the TR/pMH interface are expected. Therefore, the appropriate structural description of this interface is a crucial challenge. To characterize such deformations, several generic protein characterization methods are available from your literature: They include solvent accessible surface area, the number and KPT-330 enzyme inhibitor position of hydrogen bonds and connection energies, radius of gyration, bond-angle mixtures, and secondary structure task. Also, structural alphabets based on the relationship and torsion angle of four-residue long protein fragments are available.8 Via combination of this alphabet and principal component analysis, the motions of proteins have been described.9 However, structural KPT-330 enzyme inhibitor methods specific for MH -helix characterization are sparse and most of the time standard methods are used to describe MH -helices in the stationary10 and dynamic case.11,12 Hence, in this study we propose novel methods originating from differential geometry to investigate the spatial orientation of MH -helices based on curve models previously published by our group.13 Such differential geometric methods have been applied before for several aspects of structural bioinformatics: Goldman and Wipke14 described the molecular surface complementarity in ligand docking. Marathe et al.15 used the radius of curvature and the torsion angle to compare free DNA complexes against protein-bound DNA. Shazman et al.16 investigated the geometry and shape of the binding interfaces of DNA and RNA complexes. Schmidt et al.17 investigated the relation between Gaussian KPT-330 enzyme inhibitor curvature of membranes and bactericidal activity via membrane destabilization. Hausrath and Goriely18 used curvature profiles to construct atomically detailed protein models. The calculations of the curvature and torsion relating to characterize a curve is a common method: Lewiner et al.19 presented a method to estimate the curvature and torsion from sampled curves. However, the application of differential geometric parameters for the description of MH -helices is still lacking. In the current study, we show how such differential geometric parameters can be used to describe the -helices of both MH class 1 (MH1) and MH class 2 (MH2). We present methods to FJX1 describe the MH -helices independently as well as in their relative arrangement. Subsequently, we show how our methodology sheds light on several aspects of TR/pMH interaction: First, on the geometric differences between single MH complexes and MH complexes binding a TR; second, on different MH alleles with the KPT-330 enzyme inhibitor same peptide and the same MH alleles with different peptides; third, on spatial deformation in the same pMH by binding two different TRs; and fourth, on helical disruption arising during a Molecular Dynamics (MD) simulation. Methods Differential geometric parameters for MH -helices We have shown in a previous study,13 how MH -helices can be fitted by polynomials and curves in an appropriate way by application of the corrected Akaike-criterion.20 In the following, we present several different differential geometric methods of how these curves can be compared and described to each other. The following strategies are implemented based on the.