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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.

Vienna, 22-05-2006                        6
Transition Matrix

Vienna, 22-05-2006                       7
Transition Matrix

Vienna, 22-05-2006                       8
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

Vienna, 22-05-2006                           10
Transition Matrix

Vienna, 22-05-2006                       11
Transition Matrix

Vienna, 22-05-2006                       12
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 

Vienna, 22-05-2006                 17
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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