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