By: Z. S. Rezaei

Structural comparison  Structural alignment  spectrum of structural alignment methods  The properties of output  Types of comparison  Algorithmic complexity  Representation of structures  Distance matrix  Methods  Alignment of large RNA molecules  The classes of scoring

Structural alignment  homology between two or more polymer (2)  a window into the distant past of protein evolution(1)  identification homologous(1)  imply evolutionary relationships between proteins that share very little common sequence(2)  prediction of the functions and the family of the query protein(2)

 rely on information about conformations.( from X-ray crystallography or NMR spectroscopy or structure prediction methods)  for evaluating prediction methods

spectrum of structural alignment methods(1)

The properties of out put  a superposition of the atomic coordinate sets and a minimal RMSD.  existence of multiple protein domains complicates the Structural alignment  a set of superposed three-dimensional coordinates for each input structure(2)

the root mean square (RMS) (3)

A geometrical system Determination uniquely a spatial element

Coordinate system  Spatial coordinate  Planar coordinate

Types of comparisons  Structural superposition used to compare multiple conformations of the same protein uses a simple least-squares fitting algorithm(2)  Alignment Algorithms based on multidimensional rotations and modified quaternions (2)

Definition of quaternion  a number system In mathematics  a quaternion as the quotient of two directed lines in a three-dimensional  represented as the sum of a scalar and a vector (6)

Algorithmic complexity  Optimal solution  Approximate solution(2)

Optimal solution  The optimal "threading" shown to be NP-complete  Strictly speaking, an optimal solution is only known for certain protein structure similarity measures  the algorithm for optimal solution is not practical (2)

Approximate solution Approximate polynomial-time algorithms for structural alignment theoretically classify the approximate protein structure alignment(2)

Representation of structures Protein structurrepresented in some coordinate-independent space by constructing series of matrices (2)

distance matrix a two-dimensional matrix distances between some subset of the atoms (such as the alpha carbons) Reducing the protein to a coarse metric such as secondary structure elements (SSEs)(2)

Methods(2)  DALI  Combinatorial extension(CE)  GANGSTA+  MAMMOTH  ProBiS  RAPIDO  SABERTOOTH  SSAP  Spalign  TOPOFIT  SSM

DALI  distance alignment matrix method  breaks the input structures into hexapeptide fragments and calculates a distance matrix  Distance matrix has two diagonals  conducted via a series of overlapping submatrices of size 6x6  Submatrix matches are reassembled into a final alignment

DALI  The original version used a Monte Carlo simulation  The DALI method has also been used to construct a database known as FSSP (Fold classification based on Structure-Structure alignment of Proteins, or Families of Structurally Similar Proteins)  There is an searchable database based on DALI as well as a downloadable program and web search based on a standalone version known as DaliLite.

Montecarlo method a class of computational algorithms relies on repeated random sampling to compute their results especially useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (4)

Combinatorial extension(CE) is similar to DALI uses AFPs to define a similarity matrix A number of similarity metrics are possible

Combinatorial extension(CE)  initial AFP pair that nucleates the alignment  proceed with the next AFP  The RCSB PDB has recently released an updated version of CE and FATCAT as part of the RCSB PDB Protein Comparison Tool  provides a new variation of CE that can detect circular permutations in protein structures

Circular permutations  A circular permutation is a relationship between proteins whereby the proteins have a changed order of amino acids in their peptide sequence. The result is a protein structure with different connectivity, but overall similar three- dimensional (3D) shape(7)

GANGSTA+  A combinatorial algorithm for non-sequential structural alignment of proteins  searching for similarity in databases (  evaluates based on contact maps and secondry structure

MAMMOTH  MAtching Molecular Models Obtained from Theory  For comparing models coming from structure prediction  decompose the protein structure into heptapeptides  The similarity score between two heptapeptides is calculated using a unit-vector RMS (URMS) method  These scores are stored in a similarity matrix  Derived from the likelihood of obtaining a given structural alignment by chance

MAMMOTH-mult  extension of the MAMMOTH algorithm  is very fast  produces consistent and high quality structural alignments  produces structurally implied sequence alignments that can be further used for multiple-template homology modeling

ProBiS  Protein Binding Sites. ProBiS  detects structurally similar sites on protein surfaces  compares the query protein to members of a database of protein 3D structures  Using an efficient maximum clique algorithm  Structural similarity scores are calculated for the query protein’s surface residues, and are expressed as different colors  used successfully for the detection of protein– protein, protein–small ligand and protein–DNA binding sites

RAPIDO  Rapid Alignment of Proteins In terms of Domains  a web server for the 3D alignment of crystal  using an approach based on difference distance matrices  The Matching Fragment Pairs (MFPs) are then represented as nodes in a graph  nodes in graph are chained together to form an alignment by means of an algorithm for the identification of the longest path on a DAG (Directed Acyclic Graph).  The final step: improve the quality of the alignment

SABERTOOTH  structural profiles to perform structural alignments  has favourable scaling of computation time with chain length  SABERTOOTH can be used online at

SSAP  Sequential Structure Alignment Program  uses double dynamic programming  constructs its vectors from the beta carbons for all residues except glycine  A series of matrices are constructed  Dynamic programming applied to each resulting matrix  matrices are then summed into a "summary" matrix to  Final dynamic programming is applied again to determine the overall structural alignment

SSAP  originally produced only pairwise alignments  but has since been extended to multiple alignments as well  applied in an all-to-all fashion to produce a hierarchical fold classification scheme known as CATH (Class, Architecture, Topology, Homology)  construct the CATH Protein Structure Classification database

SPalign  Based on a new size-independent score called SPscore for  The source code for SPalign and the server are available at server/SPalign/

TOPOFIT  Based on Delaunay tessellation (DT)  identifies a feature point on the RMSD/Ne curve  topomax point  to detect conformational changes, topological differences in variable parts

SSM  Secondary Structure Matching (SSM), or PDBeFold at the Protein Data Bank in Europe  uses graph matching followed by c- alpha alignment to compute alignments

Recent Developments Tmalign uses a novel method for weighting its distance matrix correct for effects arising from alignment lengths

RNA structural alignment  large RNA molecules also form characteristic tertiary structures  A recent method for pairwise structural alignment of RNA sequences implemented in the program FOLDALIGN  In low sequence identity cases

(1)

References 1. Hitomi Hasegawa and Liisa Holm: Advances and pitfalls of protein structural alignment, Current Opinion in Structural Biology 2009, 19:341– en.wikipedia.org/wiki/structural_alignment software 3. Cartwright, Kenneth V (Fall 2007). "Determining the Effective or RMS Voltage of Various Waveforms without Calculus". Technology Interface 8 (1): 20 pages 4. Anderson, H.L. (1986). "Metropolis, Monte Carlo and the MANIAC". Los Alamos Science 14: 96– Weisstein, Eric W., "Coordinate System" from MathWorld 6. Boris Abramovich Rozenfel ʹ d (1988). The history of non-euclidean geometry: evolution of the concept of a geometric space. Springer. p Cunningham, B. A.; Hemperly, J. J.; Hopp, T. P.; Edelman, G. M. (1979). "Favin versus concanavalin A: Circularly permuted amino acid sequences". Proceedings of the National Academy of Sciences of the United States of America 76 (7): 3218–3222

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