Dynamics

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Dynamics
Time-scales
Event Time
Bond stretch   1 to 20 fs  
Elastic domain modes   100 fs to several ps  
Water reorientation   4 ps  
Inter-domain bending   10 ps to 100 ns  
Globular protein tumbling   1 to 10 ns  
Aromatic ring flipping   100 µs to several sec  
Allosteric shifts   2 µs to several sec  
Local denaturation   1 ms to several sec  

• comparison of 2 static structures
• clustering of rotation vectors
• extraction of hinges, axes

2
Elastic Network Models

• couple Cas together with springs
  (coarse-graining)
• connectivity based on side-chain contacts (lt7A),
  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)

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• Levitt Sander Stern (1985) methodology

(normalization condition)
(from Lagranges equation)
(solve equations of motion)
ribonuclease
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Jianpeng Ma F1-ATPase motions
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(No Transcript)
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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

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