SCCDFTB as a bridge between MM and high-level QM.

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SCCDFTB as a bridge between MM and high-level QM.

• Jan Hermans
• University of North Carolina

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From QM to MM via SCCDFTB

• 1. SCCDFTB better than MM
• Examples
• Simulation of crambin (Haiyan Liu)
• Simulation of dipeptides (Hao Hu)
• b. But why?
• Concerted changes of geometry in N-methyl
  acetamide
• Hydrogen bonding between two N-methyl acetamide
  molecules
• More flexible
• 2. Develop and test MM force fields

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From QM to MM via SCCDFTB

• Simulation of crambin (Haiyan Liu 2001)
• Liu, HY, Elstner, M, Kaxiras, E, Frauenheim, T,
  Hermans, J, Yang, W. Quantum mechanics
  simulation of protein dynamics on long time
  scale. Proteins, 44 484-489, 2001.
• Improved agreement of backbone geometryin folded
  state

Simulation of dipeptides (Hao Hu 2002) Hu, H,
Elstner, M., Hermans, J. Comparison of a QM/MM
force field and molecular mechanics force fields
in simulations of alanine and glycine
"dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in
water in relation to the problem of how to model
the unfolded peptide backbone in solution.
Proteins, 50, 451-463 (2003). Improved agreement
of backbone geometryin solution
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Ace-Ala-Nme in explicit water Hao Hu, 2002
amber, charmm, gromos, opls-aavs. each other and
vs. SCCDFTB
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Why better accuracy with SCCDFTB?SCCDFTB
reproduces concerted changes of geometry
charge fluctuations hydrogen bond
geometryexample N-methyl acetamide
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Concerted changes of geometry inN-methyl
acetamide, CH3-NH-CO-CH3
Recipe 1. Twist about NH-CO bond 2. Minimize the
energy (with SCCDFTB)
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Fluctuation of charge in N-methyl acetamide

• atom C O N HN
• w 180º (energy minimum)
• 0.4911 -0.5082 -0.2504 0.1879
• w 90º (saddle point)
• 0.5255 -0.4257 -0.3343 0.1749

Fluctuations of charges and geometry are coupled
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Non-spherical electron distribution
CO interacts with H-N
Non-linear N-HOC hydrogen bonds
Cf. Side chain hydrogen bonds in proteins and by
ab initio QM Morozov, Kortemme, Baker
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Distribution of ?COH in dimers of N-methyl
acetamide.
SCCDFTB MM force field
SCCDFTB favors bent arrangement Simple Point
Charge model of MM favors linear structures
Hermans, J. Hydrogen bonds in molecular mechanics
force fields.Adv. Protein Chem. 72, 105-119,
2006.
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But SCCDFTB is too flexible
1. Correlation of DFT (B3LYP/631G) and SCCDFTB
energies
1000 conformations from 1 ns MD simulation with
SCCDFTB
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SCCDFTB is too flexible
2. Energy profile for internal rotation in butane
DFT B3LYP/631G eclipsed DE? 120
3.35 gauche DE? 60 0.83 cis DE?0 5.69
SCCDFTB eclipsed DE? 120 2.57 gauche
DE? 60 0.45 cis DE?0 3.80
(relative to trans, ? 180)
MP2 eclipsed DE? 120 3.31 gauche DE?
60 0.62 cis DE?0 5.51
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• End of part 1

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Molecular mechanics energy function how to
improve it?
intramolecular
non-bonded
1. How precise is this expansion? 2. How accurate
is this model? 3. How accurate are the
implementations (amber, charmm,
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• Assume a high-level QM method as REALITY
• DFT (B3LYP/631G)
• Try to reproduce its energy.
• (can always choose a higher level of QM.)

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Recipe STEP 1 1. Simulate (1 ns with SCCDFTB) 2.
Save 1000 conformations
Example methane, CH4
Recipe STEP 2 3. Compute Epot with
B3LYP/631G 4. Fit a new MM forcefield 5.
Compute Epot with the new MM force field
By minimizing the RMS deviation
The slope is very close to 1 The RMS deviation is
0.07 kcal/mol (mean dEpot 3)
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What are the most important energy parameters for
methane?
rms residual
Parameter value r rmsd10
2Kl, C-H 353 1.436 1.6
2Kq, H-C-H 33.2 0.222 0.26
3Kl, C-H -803 0.157 26
3Kq, H-C-H -7.8 0.153 0.55
Kl,l, C-H, C-H -22.8 0.152 0.77
2Kd,HH 20.5 0.066 0.69
Standard quadraticMM terms
not very useful
include these terms (not needed in
simulationswith fixed bond lengths)
precision
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Systems studied to date (manuscript) rigid
molecules methane, benzene, water molecules with
internal rotation ethane, propane, butane,
methyl-benzene Non-bonded interactions methaneme
thane, ethaneethane watermethane, waterwater
Some results and some conclusions .
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LESSONS LEARNED

• Geometric parameters agree well.
• Transferability between related molecules
• Compared with standard force fields

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Nonbonded interactions
Results of different fits for Coulomb interactions
with independent values according to mean ESP
charges with charge neutrality with one
fixed value
System r C free r ltDEgt CESP r ltDEgt Cneutral r Cfix 1
H2O,H2O 1.004 200 -10548.1 1.336 0.65 (215)(-108)(54) 1.210 0.2 298-14975.5 1.004 (215)-10246.5
CH4, CH4 0.166 190-4912.7 0.171 -0.1 (95)(-23.75)(5.94)


ltDEgt ltEMM - EQMgt
acceptable
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Coulomb interactions (we skipped a
slide) (Water Fixed Point charges based on ESP
inadequate) Methane and ethane ESP charges can
be used
Methane and ethaneLennard-Jones repulsive
parameters
Parameter methanedimer (1) methanedimer (2) ethanedimer
12BC,C 1,200,000 1,200,000 1,110,000
12BC,H 60,000 62,000 52,000
12BH,H 1,100 700 840
Conclusion Nice agreement
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LESSONS LEARNED

• Geometric parameters agree well.
• Fixed point charge (FPC) model for Coulomb energy
  is poor for waterwater and watermethane

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LESSONS
LESSONS LEARNED

• Geometric parameters agree well.
• Fixed point charge (FPC) model for Coulomb energy
  is poor for waterwater and watermethane
• Intermolecular parameters for methane and ethane
  are similar (and FPC model is OK).

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LESSONS
LESSONS LEARNED

• Geometric parameters agree well.
• Fixed point charge (FPC) model for Coulomb energy
  is poor for waterwater and watermethane
• Intermolecular parameters for methane and ethane
  are similar (and FPC model is OK).
• Exponent of L-J repulsive term 12 is good.

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Butane intrinsic torsion term non-bonded
interactions (1/r12 and 1/r) 1-4 C,C 1-5 and
1-4 C,H 1-6, 1-5, 1-4 H,H
In the SCCDFTB simulation forced 360º rotation
about C2-C3, ltdEgt 14 kcal/mol Fit several MM
models A0 has 38 parameters, r 0.441 A5 has
12 parameters, r 0.598
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Butane Fit for model A5
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Butane
Simulate butane with A5 force field (and 2
others) Calculate PMF for torsion about C2-C3
Critical tests Re-calculate DFT (B3LYP/631G)
energies Compare energies at minima and
barriers DFT vs. A5 (and 2 others)
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Simulation with A5 force field
red curve MM energy black dots DFT energy
black curve PMF
DFT energy issystematically high
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Slope of best fit is 1.04
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With more parameters (np) in the MM force
field The slope goes down to 1.02 The PMF
becomes a little bit sharper
Energies and free energies at minima and maxima
(relative to minimum at ? 180º)
model np DE??120 DE??60 DE?0 DA??120 DA??60 DA?0 slope rmsd
A0h 32 3.88 0.76 5.81 3.87 0.86 6.08 1.02 0.700
A1 23 3.85 0.72 5.83 3.89 0.86 6.17 1.02 0.696
A5 12 3.71 0.67 5.63 3.65 0.80 5.91 1.04 0.734
DFT 3.35 0.83 5.69
Slope and rmsd of correlation between DFT and MM
energies
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LESSONS
LESSONS LEARNED

• Geometric parameters agree well.
• Fixed point charge (FPC) model for Coulomb energy
  is poor for waterwater and watermethane
• Intermolecular parameters for methane and ethane
  are similar and FPC model is OK.
• Exponent of L-J repulsive term 12 is good.
• Torsion in ethane, propane, butaneomit terms in
  1/rmessy set of 1-4, 1-5 and 1-6 repulsive
  terms

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• Why is SCCDFTB important in this project
• Fast to run
• Easy to set up (need only coordinates)
• Equilibrium geometry agrees well with DFT
• Slightly more flexible do not miss anything

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Future work I hope so

• Thanks to
• Weitao Yang
• Hao Hu (coauthor of paper)

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