Shape modeling and matching in identifying protein structure from low-resolution images

In this paper, we describe a novel, shape-modeling approach to recovering 3D protein structures from volumetric images. The input to our method is a sequence of α-helices that make up a protein, and a low-resolution volumetric image of the protein where possible locations of α-helices have been detected. Our task is to identify the correspondence between the two sets of helices, which will shed light on how the protein folds in space. The central theme of our approach is to cast the correspondence problem as that of shape matching between the 3D volume and the 1D sequence. We model both the shapes as attributed relational graphs, and formulate a constrained inexact graph matching problem. To compute the matching, we developed an optimal algorithm based on the A*-search with several choices of heuristic functions. As demonstrated in a suite of real protein data, the shape-modeling approach is capable of correctly identifying helix correspondences in noise-abundant volumes with minimal or no user intervention.

[1]  Giovanni Soda,et al.  Exploiting the past and the future in protein secondary structure prediction , 1999, Bioinform..

[2]  Manfred J. Sippl,et al.  Boltzmann's principle, knowledge-based mean fields and protein folding. An approach to the computational determination of protein structures , 1993, J. Comput. Aided Mol. Des..

[3]  Thomas A. Funkhouser,et al.  Partial matching of 3D shapes with priority-driven search , 2006, SGP '06.

[4]  Jianpeng Ma,et al.  Determining protein topology from skeletons of secondary structures. , 2005, Journal of molecular biology.

[5]  Gilles Bertrand,et al.  A parallel thinning algorithm for medial surfaces , 1995, Pattern Recognit. Lett..

[6]  Andrew K. C. Wong,et al.  An algorithm for graph optimal monomorphism , 1990, IEEE Trans. Syst. Man Cybern..

[7]  Sven J. Dickinson,et al.  Skeleton based shape matching and retrieval , 2003, 2003 Shape Modeling International..

[8]  Radu Horaud,et al.  Stereo Correspondence Through Feature Grouping and Maximal Cliques , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  King-Sun Fu,et al.  A distance measure between attributed relational graphs for pattern recognition , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Attila Kuba,et al.  A Parallel 3D 12-Subiteration Thinning Algorithm , 1999, Graph. Model. Image Process..

[11]  Gabriella Sanniti di Baja,et al.  Curve skeletonization of surface-like objects in 3D images guided by voxel classification , 2002, Pattern Recognit. Lett..

[12]  A. Sali,et al.  Statistical potential for assessment and prediction of protein structures , 2006, Protein science : a publication of the Protein Society.

[13]  Julian R. Ullmann,et al.  An Algorithm for Subgraph Isomorphism , 1976, J. ACM.

[14]  Nils J. Nilsson,et al.  Principles of Artificial Intelligence , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  John P. Overington,et al.  Derivation of rules for comparative protein modeling from a database of protein structure alignments , 1994, Protein science : a publication of the Protein Society.

[16]  M. Dhome,et al.  Inexact matching using neural networks , 1994 .

[17]  Yang Zhang,et al.  The protein structure prediction problem could be solved using the current PDB library. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Baker,et al.  Electron cryomicroscopy of biological machines at subnanometer resolution. , 2005, Structure.

[19]  Robert M. Haralick,et al.  Structural Descriptions and Inexact Matching , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Horst Bunke,et al.  Recent Advances in Graph Matching , 1997, Int. J. Pattern Recognit. Artif. Intell..

[21]  Kuo-Chin Fan,et al.  Genetic-based search for error-correcting graph isomorphism , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[22]  A. Sali.  100,000 protein structures for the biologist , 1998, Nature Structural Biology.

[23]  Ali Shokoufandeh,et al.  Retrieving Articulated 3-D Models Using Medial Surfaces and Their Graph Spectra , 2005, EMMCVPR.

[24]  Horst Bunke,et al.  Error Correcting Graph Matching: On the Influence of the Underlying Cost Function , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[25]  J. Frank,et al.  The ribosome at improved resolution: new techniques for merging and orientation refinement in 3D cryo-electron microscopy of biological particles. , 1994, Ultramicroscopy.

[26]  M. Baker,et al.  Identification of secondary structure elements in intermediate-resolution density maps. , 2007, Structure.

[27]  Matthew L. Baker,et al.  Computing a Family of Skeletons of Volumetric Models for Shape Description , 2006, GMP.

[28]  Michael Garland,et al.  Curvature maps for local shape comparison , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[29]  Horst Bunke,et al.  Inexact graph matching for structural pattern recognition , 1983, Pattern Recognit. Lett..

[30]  John Moult,et al.  A decade of CASP: progress, bottlenecks and prognosis in protein structure prediction. , 2005, Current opinion in structural biology.

[31]  Horst Bunke,et al.  A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[32]  M J Sippl,et al.  Who solved the protein folding problem? , 1999, Structure.

[33]  Helen M Berman,et al.  Large macromolecular complexes in the Protein Data Bank: a status report. , 2005, Structure.

[34]  William J. Christmas,et al.  Structural Matching in Computer Vision Using Probabilistic Relaxation , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  P. Foggia,et al.  Performance evaluation of the VF graph matching algorithm , 1999, Proceedings 10th International Conference on Image Analysis and Processing.

[36]  Radu Horaud,et al.  Symbolic image matching by simulated annealing , 1990, BMVC.

[37]  King-Sun Fu,et al.  Error-Correcting Isomorphisms of Attributed Relational Graphs for Pattern Analysis , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[38]  Ming Ouhyoung,et al.  On Visual Similarity Based 3D Model Retrieval , 2003, Comput. Graph. Forum.

[39]  Mario Vento,et al.  Thirty Years Of Graph Matching In Pattern Recognition , 2004, Int. J. Pattern Recognit. Artif. Intell..

[40]  Č. Venclovas,et al.  Comparative modeling in CASP6 using consensus approach to template selection, sequence‐structure alignment, and structure assessment , 2005, Proteins.

[41]  Daniel Cohen-Or,et al.  Salient geometric features for partial shape matching and similarity , 2006, TOGS.

[42]  M. Baker,et al.  Bridging the information gap: computational tools for intermediate resolution structure interpretation. , 2001, Journal of molecular biology.

[43]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[44]  Thomas A. Funkhouser,et al.  The Princeton Shape Benchmark , 2004, Proceedings Shape Modeling Applications, 2004..

[45]  David Baker,et al.  Protein Structure Prediction Using Rosetta , 2004, Numerical Computer Methods, Part D.

[46]  Gabriella Sanniti di Baja,et al.  Computing skeletons in three dimensions , 1999, Pattern Recognit..