Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding III

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Bioinformatics Practical Application of
Simulation and Data MiningProtein Folding III

• Prof. Corey OHern
• Department of Mechanical Engineering
• Department of Physics
• Yale University

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Conservation of Total Energy
Newtons equations of motion

• Newtons equations of motion conserve energy, not
  T

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Velocity Verlet Integration Scheme
?Eltv2gtO(?t2)
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Numerical Error
?E(?t)2
Why not use higher-order methods?
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Boltzmann Distribution
(2D)
Boltzmann
Boltzmann

• Temperature is given by rms velocity of heat bath
• In atomic simulations at constant NVE, atoms
  provide
• heat bath

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Temperature Fluctuations
T0.01
NVE
(?T)2/ltTgt2 1/N
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Implicit Solvent No solvent atoms

• Alter equations of motion for atoms in molecule
• to approximate motion at fixed T

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Thermostats I Gaussian constraint on velocities
Instantaneous kinetic energy
choose
at each step
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Thermostats II Langevin Equation
4.0
2.0
1.0
T0.1
(1)
Choose ? randomly from Gaussian distribution
Integrate (1) using modified Velocity Verlet
algorithm derived in HW
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Metastability/Misfolding
slow cooling
Tf
fast cooling
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Gap in Timescales
secondary structure formation
MD timestep
long MD trajectories
bond stretching
Fastest folding proteins
Log time
0.1 ?s
1-10?s
1fs
10 ns
How do we bridge gap from ns to ?s?
1000 trajectories ns/trajectory ?s
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Folding_at_home

• http//folding.stanford.edu/
• Distributed computing environment set
• up by Prof. Vijay Pande, Stanford Univ.
• In2000
• Hundreds of thousands of CPUs around
• the world running processes in background
• Mac OSX, Windows, Linux, PS3
• Automatic upload of finished task,
• download of new task, and restart when
• shut off
• Tinker/Gromacs molecular simulation
• packages

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23-residue mini-protein BBA5
?-hairpin
?-helix
YRVpSYDFSRSDELAKLLRQHAG-NH2
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RMSDC?2.2Å
RMSDC?2.4Å
RMSDC?2.6Å
RMSDC?3.0Å
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Comparison of extended and folded ensembles
unfolded
folded
folded
Folding is a statistical process!
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Secondary Structure
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Folding and Unfolding Kinetics
BLN model
folding
unfolding
lt?Fgt 7.5?3.5?s at 298K (experiments)
lt?Fgt 6?5?s at 298K (simulations)
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What if ?MD/?fold ltlt 10-6?
Markov modeling