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Dynamics

Dynamics. Time-scales. comparison of 2 static structures clustering of rotation vectors extraction of hinges, axes. Elastic Network Models. couple Ca’s together with springs (coarse-graining) connectivity based on side-chain contacts (<7A), not backbone

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Dynamics

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  1. Dynamics Time-scales • comparison of 2 static structures • clustering of rotation vectors • extraction of hinges, axes

  2. Elastic Network Models • couple Ca’s together with springs (coarse-graining) • connectivity based on side-chain contacts (<7A), not backbone • simulate dynamics, extract modes • from B-factors to local unfolding to domain rotations • Atilgan,A.R., Durell,S.R., Jernigan,R.L., Demirel,M.C., Keskin,O., and Bahar,I. (2001). Anisotropy of fluctuation dynamics of proteins with an elastic network model. • anisotropic motions • spatial clustering lk and uk: eigenvalues and eigenvectors of G wk=(glk)1/2 lysozyme

  3. a) first mode of vibration of RBP – note motion in loops b) loops are where transthyretin binds

  4. The conformational plasticity of protein kinases (Huse and Kruiyan, Cell, 2002)

  5. Normal modes analysis • Brooks and Karplus (1983) – BPTI • Bruccoleri, Karplus, McCammon (1986) - lysozyme • Dobbins Lesk, Sterberg (2008) – NMA analysis of induced-fit changes at protein-protein interfaces • approximate potential around minimum with harmonic • simulations: all-atom MD vs. elastic network among contacts • diagonalization rotates vibrations into orthogonal linear-combination dimensions (decoupled)

  6. Levitt Sander Stern (1985) –methodology (normalization condition) (from Lagrange’s equation) (solve equations of motion) ribonuclease

  7. Jianpeng Ma: F1-ATPase motions

  8. Relationship of Normal Modes Vibrations to Allostery • D. Ming and M. Wall (2005). Quantifying Allosteric Effects in Proteins. • ligand-binding often causes subtle changes that transmit to remote sites • hypothesis: dynamic effects, rather than conformational • use NMA to compare vibrations with and without ligand bound • can identify functional interaction sites; try different surface positions • CHARMM modules: VIBRAN, DIAG • define allosteric potential Dx • Kullback-Leibler divergence of conformational PDFs • must compute marginal distr of bound confs to unbound • simulate with harmonic vibrations around joint states equilibrium z0=(x0,y0) via MD • approximate potential with Hessian; diagonalize

  9. distribution of Dx(m) for 4859 atoms on surface of lysozyme, complex with NAG • fits extreme-value distribution

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