Clustering the Temporal Sequences of 3D Protein Structure

1. Clustering the Temporal Sequences of 3D Protein Structure Mayumi Kamada+*, Sachi Kimura, Mikito Toda‡, Masami Takata+, Kazuki Joe+ +：Graduate School of Humanities and Science, Information and Computer Sciences, Nara Women’s University ‡：Departments of physics, Nara Women’s University

2. Outline • Motivation • Flexibility Docking • Feature Extraction using Motion • Analysis • Conclusions and Future Work

3. Motivation • Protein in biological molecules “Docking” • Transform oneself and Combinewith other materials • Prediction of Docking 　 Prediction of resultant functions

4. Existing Docking Simulation Rigid structures PDB* structure A structure B Fluctuating in living cells  Low prediction accuracy Docking simulation Predicted structures from docking Docking simulation Considering fluctuations * Protein Data Bank

5. Flexibility Docking • Considering fluctuation of proteins in living cells Extraction of fluctuated structures PDB structure A structure B Flexibility handling Docking simulation Predicted structures from docking Consideration of structural fluctuation of proteins

6. Create filters by using RMSD Flexibility Handling Flexibility handling • Molecular dynamic simulation(MD) • Simulation of motion of • molecules in a polyatomic system MD output file output file output file output file output file ・・・ ・・・ • Filtering • Selection of representative structures • from similar structures Filter Representative structure Representative structure ・・・ ・・・

7. Filters using RMSD • RMSD(Root Mean Square Deviation) • Comparison of the similarity of two structures • Propose two filtering algorithms <Filter-1> Maximum RMSD selection filter <Filter-2> Below RMSD 1Å deletion filter • Result • Useful for the heat fluctuation condition • RMSD Unification of topology information Lapse of information Feature extraction focusing on Protein Motion not Structure

8. Capture Protein Motion The frequency may change momentarily! MD ・・・ ・・・ Wavelet transform ・・・ ・・・ Feature extraction Continuous wavelet transform: Morlet wavelet ・・・ ・・・ Clustering Clustering algorithm: Affinity Propagation Selection of representative motions

9. Target Protein • 1TIB • Residue length: 269 • MD simulation • Software: AMBER • Simulation run time: 2 nsec • Resultdata files: 200 • Space coordinates of Cα atoms

10. Matrix A: • At time step i (ti) • Components column ： Cα • row ： Frequency Singular Value Decomposition • SVD(Singular value decomposition) • Definition: • Unitary matrix U: • Left-singular vectors • Spatial motion • Unitary matrix V: • Right-singular vectors • Frequency fluctuation ★matrix-size of A: 807×199

11. Matrix A: • At time step i (ti) • Components column ： Cα • row ： Frequency Singular Value Decomposition • SVD(Singular value decomposition) • Definition: • Unitary matrix U: • Left-singular vectors • Spatial motion • Unitary matrix V: • Right-singular vectors • Frequency fluctuation ★matrix-size of A: 807×199

12. M=1 • N=1 • M=4 • N=4 • M=6 • M=8 • N=6 • N=8 Verification of Reproducibility • Singular values and principal components Left Singular Vectors (Spatial motion) Right Singular Vectors (Frequency fluctuation)

13. Reproducibility Using the eight principal components, the motion expressed by 199 components can be reproduced ! Almost adjusted !

14. Examination (1) Each of singular values (2)The first singular value • Accounted for about 30% over 　Expression of the original motion  Possible by the six singular values The first singular value is useful

15. Clustering Analysis • Focus on the first principal component • Definition • Similarities and Preference  Clustering by using the above values

16. 1 0 Kij :Value Same direction Differential direction Similarities (1) • For left singular vectors • Difference of spatial directs  Inner products • Similarity : Cα

17. Similarities (2) • For right singular vectors • Difference between distributions of spectrum  Hellinger Distance • Similarity:

18. Clustering Method • Affinity propagation(AP) • Brendan J. Frey and Delbert Dueck • “Clustering by Passing Messages Between Data Points”. Science315, 972–976.2007 • Obtain “Exemplars”: cluster centers • Preference • Left singular vectors • Average of similarities • Right singular vectors • minimum of similarities－（maximum of similarities－minimum）

19. Similarities between Left Singular Vectors

20. Clustering　of Left Singular Vectors

21. Similarities between Right Singular Vectors

22. Clustering of Right Singular Vectors

23. Discussions • Each of motions • Spatial motion • Repetition of several similar spatial motions in time variation • Frequency fluctuation • Repetition of similar frequency patterns in time variation • Relationship 　　　Characteristic Frequency fluctuation 　　　Group transition on spatial motion

24. Conclusionsand Future Work • Flexibility docking • Flexibility handling: MD and Filter • Feature extraction based motion • Wavelet analysis • Analysis of motions • Clustering • Future work • Collective motion • Relationship • Perform the docking simulation

25. Conclusionsand Future Work • Flexibility docking • Flexibility handling: MD and Filter • Feature extraction based motion • Wavelet analysis • Analysis of motions • Clustering • Future work • Collective motion • Relationship • Perform the docking simulation