sccdftb as a bridge between mm and high-level qm
DESCRIPTION
SCCDFTB as a bridge between MM and high-level QM. Jan Hermans University of North Carolina. 1. 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? - PowerPoint PPT PresentationTRANSCRIPT
SCCDFTB as a bridge between MM and high-level QM.
Jan Hermans
University of North Carolina
1
1. SCCDFTB better than MM
a. ExamplesSimulation of crambin (Haiyan Liu)Simulation of “dipeptides” (Hao Hu)
b. But why?Concerted changes of geometry in N-methyl acetamideHydrogen bonding between two N-methyl acetamide moleculesMore flexible
2. Develop and test MM force fields
From QM to MM via SCCDFTB
2
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
From QM to MM via SCCDFTB
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
3
amber, charmm, gromos, opls-aavs. each other and vs. SCCDFTB
SCCDFTB
Ace-Ala-Nme in explicit waterHao Hu, 2002
4
Why better accuracy with SCCDFTB?
SCCDFTB reproducesconcerted changes of geometry
charge fluctuationshydrogen bond geometry
example: N-methyl acetamide
5
6
Concerted changes of geometry inN-methyl acetamide, CH3-NH-CO-CH3
Recipe:1. Twist about NH-CO
bond2. Minimize the energy
(with SCCDFTB)
H-N-C
C-N-CA2
H-N-CA2
tetrahedral
planar
7
Fluctuation of charge in N-methyl acetamide
Fluctuations of charges and geometry are coupled
atom: C O N HN
180º (energy minimum)0.4911 -0.5082 -0.2504 0.1879
= 90º (saddle point)0.5255 -0.4257 -0.3343 0.1749
8
Non-spherical electron distribution: C=Ointeracts with H-N
Non-linear N-H…O=C hydrogen bonds
NHO prefers 180º HOC likes 130º
Cf. Side chain hydrogen bonds in proteins and by ab initio QM: Morozov, Kortemme, Baker
SCCDFTB
MM force field
9
SCCDFTB favors bent arrangementSimple Point Charge model of MM favors linear structures
Distribution of
COH in dimers of N-methyl acetamide.
Hermans, J. Hydrogen bonds in molecular mechanics force fields.Adv. Protein Chem. 72, 105-119, 2006.
1. Correlation of DFT (B3LYP/631G*) and SCCDFTB energies
10
But … SCCDFTB is too flexible:
1000 conformations from 1 ns MD simulation with SCCDFTB
2. Energy profile for internal rotation in butane
11
SCCDFTB is too flexible:
DFT B3LYP/631G*:eclipsed:E =±120 = 3.35gauche:E= ±60 = 0.83cis:E=0 = 5.69
SCCDFTB:eclipsed:E =±120 = 2.57gauche:E= ±60 = 0.45cis:E=0 = 3.80
(relative to trans, = 180)
MP2:eclipsed:E =±120 = 3.31gauche:E= ±60 = 0.62cis:E=0 = 5.51
End of part 1
, ,2 2,
12 6
0
0 ,0
,,0
( ) ( )2 2
{1 cos[ (
1{ 4 [( ) ( ) ]}
4
]
(
2
)
) }
l i ii i i i
bonds angles
ii i i
tor
i j ij ijij
i j i ij
M
sio
ij
M
n
ij
s
E
q q
r r r
K Kl l
Kn
X
Molecular mechanics energy function:how to improve it?
1. How precise is this expansion?2. How accurate is this model?3. How accurate are the implementations (amber, charmm, …
13
intramolecular
non-bonded
Assume a high-level QM method as “REALITY”:
DFT (B3LYP/631G*)
Try to reproduce its energy.
(can always choose a higher level of QM.)
The slope is very close to 1
The RMS deviation is 0.07 kcal/mol
(mean Epot = 3)15
* By minimizing the RMS deviation
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 forcefield5. Compute Epot with the new MM
force field
What are the most important energy parameters for methane?
Parameter value rmsd10
2Kl, C-H 353 1.436 1.62K, H-C-H 33.2 0.222 0.263Kl, C-H -803 0.157 263K, H-C-H -7.8 0.153 0.55
Kl,l, C-H, C-H -22.8 0.152 0.772Kd,H·H 20.5 0.066 0.69
rms residual
Standard quadraticMM terms
include these terms(not needed in simulationswith fixed bond lengths)
not very useful
16
precision
Systems studied to date (manuscript):
“rigid” moleculesmethane, benzene, water
molecules with internal rotationethane, propane, butane, methyl-benzene
Non-bonded interactionsmethane…methane, ethane…ethanewater…methane, water…water
Some results and some conclusions ….
17
Geometric parameters agree well.Transferability between related molecules
Compared with “standard” force fields
LESSONS LEARNED:
18
Coulomb interactions: (we skipped a slide)(Water: Fixed Point charges based on ESP inadequate)
Methane and ethane: ESP charges can be used
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
Methane and ethane:Lennard-Jones repulsive parameters
Conclusion: Nice agreement
Geometric parameters agree well.
Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…
methane
LESSONS LEARNED:
21
Geometric parameters agree well.
Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…
methane
Intermolecular parameters for methane and ethane are similar (and FPC model is OK).
LESSONS:
22
LESSONS LEARNED:
Geometric parameters agree well.
Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…
methane
Intermolecular parameters for methane and ethane are similar (and FPC model is OK).
Exponent of L-J repulsive term = 12 is good.
LESSONS:
23
LESSONS LEARNED:
Butane:“intrinsic” torsion termnon-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,
<E> = 14 kcal/mol* Fit several MM models:
A0* has 38 parameters, = 0.441A5 has 12 parameters, = 0.598
24
C CH H
Butane: Fit for model A5
25
Butane:
26
Critical tests:* Re-calculate DFT (B3LYP/631G*) energies* Compare energies at minima and barriers DFT vs. A5 (and 2
others)
* Simulate butane with A5 force field (and 2 others)Calculate PMF for torsion about C2-C3
red curve = MM energyblack dots = DFT energy black curve = PMF
DFT energy issystematically high
27
Simulation with A5 force field
Slope of best fit is 1.04
28
model np E=120
E=60
E=0
A=120
A=60
A=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
With more parameters (np) in the MM force field:
The slope goes down to 1.02The PMF becomes a little bit sharper
Energies and free energies at minima and maxima (relative to minimum at = 180º)
Slope and rmsd of correlation between DFT and MM energies
29
Geometric parameters agree well.Fixed point charge (FPC) model for Coulomb
energy is poor for water…water and water…
methane 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, butane:
omit terms in 1/r“messy” set of 1-4, 1-5 and 1-6 repulsive terms
LESSONS:
30
LESSONS LEARNED:
Why is SCCDFTB important in this project:
(1) Fast to run
(2) Easy to set up (need only coordinates)
(3) Equilibrium geometry agrees well with DFT
(4) Slightly more flexible: do not miss anything
Thanks to
• Weitao Yang
• Hao Hu (coauthor of paper)
Future work:I hope so
32