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					        Simulating Protein Folding
                       - Some Ideas

                     Christian Hedegaard Jensen
                     Dmitry Nerukh




Vienna, 22-05-2006                                1
                     Outline
• Introduction
• Transition Matrix
• Wang-Landau




Vienna, 22-05-2006             2
                     Outline
• Introduction
• Transition Matrix
• Wang-Landau




Vienna, 22-05-2006             3
                     Introduction
• We are simulation protein folding using
  Molecular Dynamics, and understanding
  using complexity analysis.
• Try to do statistics on trajectories, to see
  if there are any patterns in where they
  go. (Transition Matrix)
• Try and look at the paths that a protein
  can take when it folds. (Wang-Landau)
Vienna, 22-05-2006                           4
                     Outline
• Introduction
• Transition Matrix
• Wang-Landau




Vienna, 22-05-2006             5
                     Transition Matrix
• Find states in trajectory
• Find transitions between states in
  trajectory
• Write up transition matrix for system
• Possibly include some memory into the
  system.



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                     Transition Matrix




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                     Transition Matrix




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                     Transition Matrix
• We have a molecular dynamics simulation
  of a tripeptide.
• Trianaline
• 300 K, 1 atm
• 12 ps (2fs)
• OPLSAA-2001 force field
• GROMACS

Vienna, 22-05-2006                       9
                     Transition Matrix
                         Ramachandran Plot




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                     Transition Matrix




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                     Transition Matrix




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                     Transition Matrix
• Gives useful information about what is
  going on in the system.
• Find out where we end and with what
  probabilities.
• Look at transitions between clusters of
  states.



Vienna, 22-05-2006                          13
                     Outline
• Introduction
• Transition Matrix
• Wang-Landau




Vienna, 22-05-2006             14
                     Wang-Landau
• Wang-Landau simulations, using a
  combination of Molecular Dynamics and
  Monte Carlo.




Vienna, 22-05-2006                        15
                     Wang-Landau
• Wang-Landau gives the (relative) density of
  states.
• The dos of a simple protein was obtained,
  d(E).
• Try to calculate d(,E) or d(, ,E) .




Vienna, 22-05-2006                              16
                     Wang-Landau

   dos                        




                                   
         0             2p 




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                       Wang-Landau
• Define reaction coordinates
               
    R  R  ,  ,  ,  ,                              
                                       S  S  ,  ,  ,  ,


• Sample as function of these coordinates
                                         
   d ( R, R, S , S , , E )  d ( R, R, S , S , , T )


• Method does not say what the system does,
  but is says what is possible.

Vienna, 22-05-2006                                              18
                     Wang-Landau
• Matlab




Vienna, 22-05-2006                 19
                     Thank you!




Vienna, 22-05-2006                20

				
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