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

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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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SCCDFTB

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 reproducesconcerted changes of geometry charge fluctuationshydrogen bond geometryexample: N-methyl acetamide

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planar

C-N-CA2

H-N-CA2

H-N-C

tetrahedral

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:CONHN

w =180º (energy minimum)

0.4911-0.5082-0.25040.1879

w = 90º (saddle point)

0.5255-0.4257-0.33430.1749

Fluctuations of charges and geometry are coupled

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NHO prefers 180º

HOC likes 130º

Non-spherical electron distribution: C=O

interacts with H-N

Non-linear N-H…O=C 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

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.)

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

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

methane…methane, ethane…ethane

water…methane, water…water

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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Coulomb interactions:(we skipped a slide)

(Water: Fixed Point charges based on ESP inadequate)

Methane and ethane: ESP charges can be used

Methane and ethane:Lennard-Jones repulsive parameters

Conclusion: Nice agreement

LESSONS LEARNED:

Geometric parameters agree well.

Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…methane

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LESSONS:

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).

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LESSONS:

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.

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H

H

C

C

Butane:

“intrinsic” torsion term

non-bonded interactions (1/r12 and 1/r)

1-4 C,C1-5 and 1-4 C,H 1-6, 1-5, 1-4 H,H

- * In the SCCDFTB simulation forced 360º rotation about C2-C3, <dE> = 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 andfree energiesat minima and maxima (relative to minimum at = 180º)

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 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

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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

Future work:

I hope so

Thanks to

- Weitao Yang
- Hao Hu (coauthor of paper)

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