Applying mesh conformation on shape analysis with missing data

A mesh conformation approach that makes use of deformable generic meshes has been applied to establishing correspondences between 3D shapes with missing data. Given a group of shapes with correspondences, we can build up a statistical shape model by applying principal component analysis (PCA). The conformation at first globally maps the generic mesh to the 3D shape based on manually located corresponding landmarks, and then locally deforms the generic mesh to clone the 3D shape. The local deformation is constrained by minimizing the energy of an elastic model. An algorithm was also embedded in the conformation process to fill missing surface data of the shapes. Using synthetic data, we demonstrate that the conformation preserves the configuration of the generic mesh and hence it helps to establish good correspondences for shape analysis. Case studies of the principal component analysis of shapes were presented to illustrate the successes and advantages of our approach

Molecular flexibility of citrus pectins by combined sedimentation and viscosity analysis

The flexibility/rigidity of pectins plays an important part in their structure-function relationship and therefore on their commercial applications in the food and biomedical industries. Earlier studies based on sedimentation analysis in the ultracentrifuge have focused on molecular weight distributions and qualitative and semi-quantitative descriptions based on power law and Wales-van Holde treatments of conformation in terms of "extended" conformations [Harding, S. E., Berth, G., Ball, A., Mitchell, J.R., & Garcìa de la Torre, J. (1991). The molecular weight distribution and conformation of citrus pectins in solution studied by hydrodynamics. Carbohydrate Polymers, 168, 1-15; Morris, G. A., Foster, T. J., & Harding, S.E. (2000). The effect of degree of esterification on the hydrodynamic properties of citrus pectin. Food Hydrocolloids, 14, 227-235]. In the present study, four pectins of low degree of esterification 17-27% and one of high degree of esterification (70%) were characterised in aqueous solution (0.1 M NaCl) in terms of intrinsic viscosity [η], sedimentation coefficient (s°20,w) and weight average molar mass (Mw). Solution conformation/flexibility was estimated qualitatively using the conformation zoning method [Pavlov, G.M., Rowe, A.J., & Harding, S.E. (1997). Conformation zoning of large molecules using the analytical ultracentrifuge. Trends in Analytical Chemistry, 16, 401-405] and quantitatively (persistence length Lp) using the traditional Bohdanecky and Yamakawa-Fujii relations combined together by minimisation of a target function. Sedimentation conformation zoning showed an extended coil (Type C) conformation and persistence lengths all within the range Lp=10-13 nm (for a fixed mass per unit length)

p97 Disease Mutations Modulate Nucleotide-Induced Conformation to Alter Protein-Protein Interactions.

The AAA+ ATPase p97/VCP adopts at least three conformations that depend on the binding of ADP and ATP and alter the orientation of the N-terminal protein-protein interaction (PPI) domain into up and down conformations. Point mutations that cause multisystem proteinopathy 1 (MSP1) are found at the interface of the N domain and D1-ATPase domain and potentially alter the conformational preferences of p97. Additionally, binding of adaptor proteins to the N-domain regulates p97s catalytic activity. We propose that p97/adaptor PPIs are coupled to p97 conformational states. We evaluated the binding of nucleotides and the adaptor proteins p37 and p47 to wild-type p97 and MSP1 mutants. Notably, p47 and p37 bind 8-fold more weakly to the ADP-bound conformation of wild-type p97 compared to the ATP-bound conformation. However, MSP1 mutants lose this nucleotide-induced conformational coupling because they destabilize the ADP-bound, down conformation of the N-domain. Loss in conformation coupling to PPIs could contribute to the mechanism of MSP1

Coil-helix transition of polypeptide at water-lipid interface

We present the exact solution of a microscopic statistical mechanical model for the transformation of a long polypeptide between an unstructured coil conformation and an $\alpha$-helix conformation. The polypeptide is assumed to be adsorbed to the interface between a polar and a non-polar environment such as realized by water and the lipid bilayer of a membrane. The interfacial coil-helix transformation is the first stage in the folding process of helical membrane proteins. Depending on the values of model parameters, the conformation changes as a crossover, a discontinuous transition, or a continuous transition with helicity in the role of order parameter. Our model is constructed as a system of statistically interacting quasiparticles that are activated from the helix pseudo-vacuum. The particles represent links between adjacent residues in coil conformation that form a self-avoiding random walk in two dimensions. Explicit results are presented for helicity, entropy, heat capacity, and the average numbers and sizes of both coil and helix segments.Comment: 22 pages, 12 figures, accepted for publication by JSTA

Accuracy of generic mesh conformation: the future of facial morphological analysis

Three-dimensional (3D) analysis of the face is required for the assessment of changes following surgery, to monitor the progress of pathological conditions and for the evaluation of facial growth. Sophisticated methods have been applied for the evaluation of facial morphology, the most common being dense surface correspondence. The method depends on the application of a mathematical facial mask known as the generic facial mesh for the evaluation of the characteristics of facial morphology. This study evaluated the accuracy of the conformation of generic mesh to the underlying facial morphology. The study was conducted on 10 non-patient volunteers. Thirty-four 2-mm-diameter self-adhesive, non-reflective markers were placed on each face. These were readily identifiable on the captured 3D facial image, which was captured by Di3D stereophotogrammetry. The markers helped in minimising digitisation errors during the conformation process. For each case, the face was captured six times: at rest and at the maximum movements of four facial expressions. The 3D facial image of each facial expression was analysed. Euclidean distances between the 19 corresponding landmarks on the conformed mesh and on the original 3D facial model provided a measure of the accuracy of the conformation process. For all facial expressions and all corresponding landmarks, these distances were between 0.7 and 1.7 mm. The absolute mean distances ranged from 0.73 to 1.74 mm. The mean absolute error of the conformation process was 1.13 ± 0.26 mm. The conformation of the generic facial mesh is accurate enough for clinical trial proved to be accurate enough for the analysis of the captured 3D facial images

Engineering of Cyclodextrin Product Specificity and pH Optima of the Thermostable Cyclodextrin Glycosyltransferase from Thermoanaerobacterium thermosulfurigenes EM1

The product specificity and pH optimum of the thermostable cyclodextrin glycosyltransferase (CGTase) from Thermoanaerobacterium thermosulfurigenes EM1 was engineered using a combination of x-ray crystallography and site-directed mutagenesis. Previously, a crystal soaking experiment with the Bacillus circulans strain 251 β-CGTase had revealed a maltononaose inhibitor bound to the enzyme in an extended conformation. An identical experiment with the CGTase from T. thermosulfurigenes EM1 resulted in a 2.6-Å resolution x-ray structure of a complex with a maltohexaose inhibitor, bound in a different conformation. We hypothesize that the new maltohexaose conformation is related to the enhanced α-cyclodextrin production of the CGTase. The detailed structural information subsequently allowed engineering of the cyclodextrin product specificity of the CGTase from T. thermosulfurigenes EM1 by site-directed mutagenesis. Mutation D371R was aimed at hindering the maltohexaose conformation and resulted in enhanced production of larger size cyclodextrins (β- and γ-CD). Mutation D197H was aimed at stabilization of the new maltohexaose conformation and resulted in increased production of α-CD. Glu258 is involved in catalysis in CGTases as well as α-amylases, and is the proton donor in the first step of the cyclization reaction. Amino acids close to Glu258 in the CGTase from T. thermosulfurigenes EM1 were changed. Phe284 was replaced by Lys and Asn327 by Asp. The mutants showed changes in both the high and low pH slopes of the optimum curve for cyclization and hydrolysis when compared with the wild-type enzyme. This suggests that the pH optimum curve of CGTase is determined only by residue Glu258.

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure