oGNM: online computation of structural dynamics using the Gaussian Network Model

1. oGNM: online computation of structural dynamics using the Gaussian Network Model Lee-Wei Yang, A.J. Rader, Xiong Liu, Cristopher Jon Jursa, Shann Ching Chen, Hassan A. Karimi and Ivet Bahar Nucleic Acids Research, V34, 2006. Presented by Lidio Meireles at the Pitt-CMU Journal Club

2. Motivation • Biomolecular function is defined by its intrinsic structural dynamics. • Elastic Network (EN) models are useful tools to study the dynamics of biomolecules. • Here we’ll briefly see the Gaussian Network Model.

3. Outline • Introduction to GNM • Experiments • for protein complexes • for oligonucleotide/protein complexes • Conclusion

4. Gaussian Network Model • GNM is an EN model used to study atoms fluctuations and their correlated motions. • Protein dynamics is defined by the topology of the network.

5. Gaussian Network Model • Ri position of residue i • Ri0 equilibrium position of i • ∆Ri = Ri – Ri0 • Rij distance between i and j • ∆Rij distance fluctuation

6. Gaussian Network Model Mean-square (ms) fluctuation of a residue Correlation of fluctuations of two residues

7. Gaussian Network Model Assumptions: fluctuations are isotropic and Gaussian. Probability distribution of all fluctuations KB is the Boltzmann constant T is temperature γ is the spring constant What happen if T increases?

8. Gaussian Network Model It can be shown that: <∆Ri2> may be directly compared to the corresponding X-ray crystallography B-factor

9. Gaussian Network Model • The determinant of Г is zero, Г-1cannot be computed directly. • Instead, Г-1 is found by eigenvalue decomposition of Г.

10. Experiments • Proteins • Accuracy and efficiency • Effect of cutoff distance • Nucleotides • Evaluate the 3 GNM for oligonucleotide/protein complexes

11. GNM for Proteins: Accuracy and Efficiency Accuracy: PowerB approximation identically reproduces the results found by SVD. N3.3 For a 5748 residue structure, SVD required 15.6h as opposed to 6.6 min + 4.76s required by PowerB and BLZPACK. N2.04 N0.49

12. GNM for Proteins: Effect of Cutoff Distance Cutoff distance over the range 7.3 Å ~15 Å has little effect on GNM dynamics of proteins.

13. GNM for Oligonucleotide/Protein Complexes • 3 GNM’s • M1: one node per nt centered at the P-atom • M2: two nodes per nt at P and sugar O4’-atoms • M3: three node per nt at P, sugar C4’ and base C2-atoms

14. GNM for Oligonucleotide/Protein Complexes rc – cutoff dist. for residues rp – cutoff dist. for nt 1/2(rc+rp) – cutoff dist. for residue-nt Dashed line: rc= 7.3 Å Solid line: rc = 15 Å Nt cutoff distance rp

15. Conclusion • The running time of GNM was substantially reduced without compromising accuracy. • Cutoff distance 7.3 Å ~15 Å has little effect on GNM dynamics of proteins. Higher correlation with experimental data for higher temperature. • Evaluation of 3 models for oligonucleotide containing structures suggests model M3 with same cutoff distance as the one for protein residues, i.e., rc=rp=7 Å.