EMBIO Meeting Vienna, 2006

1. EMBIO Meeting Vienna, 2006 Heidelberg Group IWR, Computational Molecular Biophysics, University of Heidelberg Kei Moritsugu • MD simulation analysis of interprotein vibrations and boson peak • Kinetic characterization of temperature-dependent protein internal motion by essential dynamics • Langevin model of protein dynamics 22/5/2006 EMBIO Meeting

2. Langevin Model of Protein Dynamics • Introduction • Dynamical model for understanding protein dynamics • Langevin equation • Direct application of Langevin dynamics: • Velocity autocorrelation function model • Extension of the Langevin model: • Coordinate autocorrelation function model EMBIO Meeting Vienna, May 22, 2006 IWR, University of Heidelberg Kei Moritsugu and Jeremy C. Smith

3. Physical interest: - multi-body (> ~1000 atoms) - inhomogeneous system Anharmonic motion on rough potential energy surface Biological/chemical interest: - expression and regulation of function - mediated by anharmonic protein dynamics conformational transition Why Protein Dynamics? Understand a “molecular machine” from physical point of view 22/5/2006 EMBIO Meeting

4. Data Analysis Dynamical Model • harmonic approximation • two-state jump model • Langevin model Settles et.al., Faraday Discussion 193, 269 (1996) Simplification …. Model Parameters Protein Dynamics Protein Dynamics: How to Analyze? Neutron Scattering Experiment • - low resolution • large, complex system with • surrounding environments Molecular Dynamics Simulation • - atomic motions with fs-ns timescales • limited time < ms, system size < ~100 Å 22/5/2006 EMBIO Meeting

5. Harmonic Approximation of Potential Energy Langevin Equation Friction Random force Dynamical Model PES roughness=Friction curvature= Frequency 22/5/2006 EMBIO Meeting

6. Mode Analysis Simplifying Protein Dynamics Normal Mode/Principal Component collective motion high frequency vibration Apply Dynamical Model for Each Mode 22/5/2006 EMBIO Meeting

7. Calculations of Langevin Parameters MD Simulations Normal Mode Analysis 120 K in vacuum 300 K in solution Velocity Autocorrelation Function (VACF) Model Langevin Parameters wn , gnn by each normal mode, n Temperature dependence Solvent effects 22/5/2006 EMBIO Meeting

8. Computations 1 Molecular Dynamics Simulations • myoglobin(1A6G, 2512 atoms, 153 residues) • equilibrium conditions at 120K and 300K • 1-ns MD simulation with CHARMM vacuum: microcanonical MD • solution: rectangular box with 3090 TIP3P waters, NPT, PME Normal Mode Analysis • vacuum force field • minimization of 1-ns average structure in vacuum • calculate the Hessian matrix and its diagonalization independent atomic motion, with vibrational frequency, wn 22/5/2006 EMBIO Meeting

9. Langevin Friction 300K water 300K vacuum 120K water 120K vacuum • in water > in vacuum • 300K > 120 K 22/5/2006 EMBIO Meeting

10. Langevin Frequency Dw(anharmonicity) < 0 : low w >high w 300 K > 120 K Dw(solvation) > 0 : low w >high w 300 K = 120 K 22/5/2006 EMBIO Meeting

11. Normal Mode Vacuum MD Water MD intra-protein interaction solvation: collisions with waters suppress protein vibrations g : roughness Dw(anharmonicity) < 0 increase of g : increased roughness Dw(solvation) > 0, independent of T NMA vacuum solution Potential Energy Surface via Langevin Model 22/5/2006 EMBIO Meeting

12. Dynamic Structure Factors q = 2Å-1 MD Trajectory 120K water 120K vacuum 300K water 300K vacuum Langevin Model Langevin Model + Diffusion 22/5/2006 EMBIO Meeting

13. Conclusion 1 • Langevin model via VACF Protein vibrational dynamics Friction: - anharmonicity low w > high w high T > low T increase via solvation Frequency shift: Dw (anharmonicity) < 0 • Dw (solvation) > 0 Svib(q,w) 22/5/2006 EMBIO Meeting

14. 300K water diffusion PCA mode 1 PCA mode 100 vibration PCA mode 1 PCA mode 100 x(t) v(t) t Modified Model for Diffusion Extended Langevin model 1) CACF model 2) Adddiffusional contribution 22/5/2006 EMBIO Meeting

15. PCA mode 1 PCA mode 100 diffusion 1-k MD model MD model k Langevin vibration Probabilistic Vibration/Diffusion Model Coordinate Autocorrelation Function (CACF) Model 22/5/2006 EMBIO Meeting

16. Computations 2 Molecular Dynamics Simulations • myoglobin(1A6G, 2512 atoms, 153 residues) • in solution: rectangular box with 3090 TIP3P waters • equilibrium conditions under NPT ensemble • T = 120, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 280, 300 K • 1-ns MD simulation with CHARMM • PME Principal Component Analysis independent atomic motion, with square fluctuation, ln variance-covariance matrix: diagonalization Fitting: Calculation of model parameters least square fit to model function MD trajectories t = 0 ~ 5, 10, 20 ps 22/5/2006 EMBIO Meeting

17. Mean Square Fluctuations: Decomposition ln: eigenvalue of PCA k : model parameter 22/5/2006 EMBIO Meeting

18. Temperature Dependence: Dynamical Transition Vibrational Frequency Vibrational Friction Ratio of Vibration 22/5/2006 EMBIO Meeting

19. 230 K 250 K 280 K 300 K Height of Vibrational Potential Wells via Model for k < 1 22/5/2006 EMBIO Meeting

20. : diffusion on 1D lattice ~ ~ MD Kramers theory k k k Diffusion Constant via Model k Kramers Rate Theory 22/5/2006 EMBIO Meeting

21. S(q,w) 300 K in water MD CACF model VACF model q = 2Å-1 22/5/2006 EMBIO Meeting

22. Conclusion 2 • Langevin-vibration&diffusion model via CACF Protein dynamics Simulation-based probabilistic description Vibration: linear scheme with T- , gv Diffusion: nonlinear scheme with T- , wv , k Diffusion constant via the present model using Kramers theory S(q,w) 22/5/2006 EMBIO Meeting

23. Acknowledgement Vandana Kurkal-Siebert Fellowship by JSPS Thanks for your attention! 22/5/2006 EMBIO Meeting