Identification of Domains using Structural Data Niranjan Nagarajan Department of Computer Science Cornell University

Assorted Definitions of Domains Subsequences that can fold independently into a stable structure. Structurally compact substructures. Functionally well-defined building blocks. Evolutionarily conserved and reused fragments.

Protein Structural Domain Identification William R. Taylor

Basic Algorithm Initial Assignment of Labels –Sequential residue numbering Update of Labels Termination Condition –Mean squared deviation of average between successive cycles (length of protein)/2

Update Formula S i t+1 = S i t + step(t+1)*sign(   j f(S i t, S j t ))  i. sign(x) = 1 if x > 0, -1 if x < 0, 0 if x = 0. f(S i t, S j t ) = –r/d ij if S j t > S i t and d ij < r. –-r/d ij if S j t < S i t and d ij < r. –0 otherwise. Step(x) = –1 if x < N/2. –2(N-x)/N if N/2 <= x < N. –0 otherwise.

Example Full lines indicate protein backbone. Neighboring residues within radius r are connected by dashed lines. Connections between i and i + 2 have been omitted for clarity. Label evolution is done without inverse distance weighting.

Refinements Median based smoothing with a window size of 21 to reclaim short loops of 10 or less residues. Small domains reassigned by using the weighted mean values of its neighbors (weights are given using f.) Domain recalculation repeated for at most five times.

Preserving  -sheets Matrix B of possible  -sheet interactions between residues generated based on distance data and heuristics. Weighted mean heuristic used to generate initial assignment of labels with the averaging being iterated to convergence. Post-processing also done to badly broken  -sheets.

Self-testing with fake homologs Fake homologs generated by smoothing –Replacing central atom of triple by average. –Process repeated five times. Domain assignments compared and similarity evaluated based on overlap score. r optimized for best overlap score.

Extension to Multiple Structures Algorithm is simultaneously run on structures corresponding to a multiple sequence alignment. Labels are synchronized to the average of the labels at a position after each iteration.