Computational Chemistry Molecular Mechanics/Dynamics F = Ma Quantum Chemistry Schr Ö dinger Equation H  = E 

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Presentation transcript:

Computational Chemistry Molecular Mechanics/Dynamics F = Ma Quantum Chemistry Schr Ö dinger Equation H  = E 

Simulation of a pair of polypeptides Duration: 100 ps. Time step: 1 ps (Ng, Yokojima & Chen, 2000)

Large Gear Drives Small Gear G. Hong et. al., 1999

Molecular Mechanics Force Field Bond Stretching Term Bond Angle Term Torsional Term Non-Bonding Terms: Electrostatic Interaction & van der Waals Interaction

Bond Stretching Potential E b = 1/2 k b (  l) 2 where, k b : stretch force constant  l : difference between equilibrium & actual bond length Two-body interaction

Bond Angle Deformation Potential E a = 1/2 k a (  ) 2 where, k a : angle force constant   : difference between equilibrium & actual bond angle  Three-body interaction

Periodic Torsional Barrier Potential E t = (V/2) (1+ cosn  ) where, V : rotational barrier  : torsion angle n : rotational degeneracy Four-body interaction

Non-bonding interaction van der Waals interaction for pairs of non-bonded atoms Coulomb potential for all pairs of charged atoms

VDW potential of CHARMM ε i and ε j are constants characteristic of the strengths of the van der Waals interactions of the two atoms, R min,i and R min,j are constants characteristic of the radii of the two atoms

MM Force Field Types MM2Small molecules AMBERPolymers CHAMMPolymers BIOPolymers OPLSSolvent Effects

CHAMM FORCE FIELD FILE

atom 1 1 HA "Nonpolar Hydrogen" atom 2 2 HP "Aromatic Hydrogen" atom 3 3 H "Peptide Amide HN" atom 4 4 HB "Peptide HCA" atom 5 4 HB "N-Terminal HCA" atom 6 5 HC "N-Terminal Hydrogen" atom 7 5 HC "N-Terminal PRO HN" atom 8 3 H "Hydroxyl Hydrogen" atom 9 3 H "TRP Indole HE1" atom 10 3 H "HIS+ Ring NH" atom 11 3 H "HISDE Ring NH" atom 12 6 HR1 "HIS+ HD2/HISDE HE1" atom 13 7 HR2 "HIS+ HE1" H-HH-CH2-CH3 H H H H H HO- H + H + H H H H

atom C "Peptide Carbonyl" atom CA "Aromatic Carbon" atom CC "C-Term Carboxylate" atom CT1 "Peptide Alpha Carbon" atom CT1 "N-Term Alpha Carbon" atom CT1 "Methine Carbon" atom CT2 "Methylene Carbon" atom CT3 "Methyl Carbon" atom CT2 "GLY Alpha Carbon" atom CT2 "N-Terminal GLY CA" atom CP1 "PRO CA Carbon"

/A o /(kcal/mol)

/(kcal/mol/A o2 ) /Ao/Ao

/(kcal/mol/rad 2 ) /deg

/(kcal/mol)/deg

Algorithms for Molecular Dynamics Runge-Kutta methods: x(t+  t) = x(t) + (dx/dt)  t Fourth-order Runge-Kutta x(t+  t) = x(t) + (1/6) (s 1 +2s 2 +2s 3 +s 4 )  t +O(  t 5 ) s 1 = dx/dt s 2 = dx/dt [w/ t=t+  t/2, x = x(t)+s 1  t/2] s 3 = dx/dt [w/ t=t+  t/2, x = x(t)+s 2  t/2] s 4 = dx/dt [w/ t=t+  t, x = x(t)+s 3  t] Very accurate but slow!

Algorithms for Molecular Dynamics Verlet Algorithm: x(t+  t) = x(t) + (dx/dt)  t + (1/2) d 2 x/dt 2  t x(t -  t) = x(t) - (dx/dt)  t + (1/2) d 2 x/dt 2  t x(t+  t) = 2x(t) - x(t -  t) + d 2 x/dt 2  t 2 + O(  t 4 ) Efficient & Commonly Used!