Structural alignment methods Like in sequence alignment, try to find best correspondence: –Look at atoms –A 3-dimensional problem –No a priori knowledge of equivalent positions

Alignment Structures are known for query sequences –X-ray crystallography –NMR spectroscopy –Structure prediction methods pair wise multiple sequence

Alignment Output –Superposition of atomic coordinate sets root mean square distance (RMSD) discrete Frechet distance –Multiple protein domains possible (additional difficulty)

Alignment Output: –Correspondence implies sequence allignment –Superposed 3-dimensional coordinates Used to compute –RMSD –PSI (percent of structural identity) –Other scores

Alignment Usually ignore side chains –Align backbones Use backbone atoms in the peptide bond –Often only alpha carbons are used (why?) For highly similar structures –Align side-chain atoms –RMSD accounts for rotameric states

Algorithmic complexity Optimal threading: sequence → structure –NP-complete (threading: best alignment to members of a library of candidate structures) Optimal multiple sequence alignment –NP-complete Structural alignment: –Not known

Algorithmic complexity Due to noise –optimal solution may not be necessary Find approximate solutions –heuristics –guaranteed bounds Polynomial time approximation within a given error є from optimal is possible –O(n 10 /є 6 ) possible