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EMBIO Meeting Vienna, 2006

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

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EMBIO Meeting Vienna, 2006

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  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

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