Born-Oppenheimer ab initio QM/MM

Molecular Dynamics Simulations of

Enzyme Reactions

Yingkai Zhang

Department of Chemistry

New York University

Dr. Po Hu

Dr. Shenglong Wang$$$ NIH

$$$ NSF

Dr. Yihan Shao (Q-Chem Inc.)

Two Key Requirements for Reliably

Simulating Enzyme Reactions

• 1. A reasonably accurate potential energy surface

A. Describing bond forming/breaking

B. Modeling heterogeneous

enzyme environment.

Combined Ab initio Quantum Mechanical and Molecular

Mechanical (QM/MM) Approach

MM

QM

Interaction

Enzyme reactive site: small The rest: large

Allows for modeling the chemistry at the enzyme active site

with the state-of-the-art quantum mechanical methods

Properly including the heterogeneous enzyme environment

bondedMM

MMQM

vdw

MMQM

ele

MMQMMMQM

MMQMMMQMtotal

EEEE

EEEE

////

/

QM/MM Covalent Boundary Problem

How to treat the boundary that bisects the covalent bond?

C

C

C

C

C

N

H

H

O

HH

H H

N

H

Protein

O

Protein

H

Active part

Environmental Part

Link Atom Approach

• Additional atoms to cap the free valence

• Introducing additional degree of freedoms

C

C

C

C

C

N

H

H

O

HH

H H

N

H

Protein

O

Protein

H

Active part

Environmental Part

C

C

C

C

C

N

H

H

O

HH

H H

N

H

Protein

O

Protein

H

QM

MM

HL

The Pseudobond Approach

• Cps: a seven-valence-electron atom with an effective core potential

• Cps-C: a pseudobond mimics the original C-C bond with the similar bond length and strength, and the similar effects on the rest of the system

• No additional atoms or degrees of freedom

• Offers smooth connection between the QM and MM regions

Y. Zhang, T. S. Lee, W. Yang, J. Chem. Phys, 1999,110,46-54

C

C

C

C

C

N

H

H

O

HH

H H

N

H

Protein

O

Protein

H

C

Cps

C

C

C

N

H

H

O

HH

H H

N

H

Protein

O

Protein

H

QM

MM

HL

QM

MM

Link atom Pseudobond

• Significantly improved C(sp3)-C(sp3) pseudobonds for cutting of protein side chains for 6-31G* basis set

• Developed C(sp3)-C(sp2) and C(sp3)-N(sp3) pseudobonds for the cutting of protein backbones, DNAs and RNAs for the first time

• Independent of force field

• DFT (B3LYP, BLYP, PW91), HF , MP2

HH

CH2

OH

H H

O

N

NN

N

NH2

5'

3'

C

C

Side-chain

HN

C

O

HN

O

C

H

C

C

C

C

C

C

N

H

H

O

HH

H H

N

H

Protein

O

Protein

H

Active part

Environmental PartY. Zhang, J. Chem. Phys., 122, 024114 (2005)

New Development: the Cps with its own basis set

Two Key Requirements for Reliably

Simulating Enzyme Reactions

• 1. A reasonably accurate potential energy surface

Describing bond forming/breaking

Modeling heterogeneous enzyme environment

• 2. Extensive sampling due to the complexity of

energy landscape

Free energy change instead of potential energy change

Molecular dynamics instead of minimization

Allows for modeling the chemistry at the enzyme active site with the state-of-the-art quantum mechanical methods, while properly including the heterogeneous enzyme environment

• It takes account of dynamics of the reaction active site and its environment on an equal footing.

Born-Oppenheimer ab initio QM/MM MD simulation

At each time step, the atomic forces as well as the total

energy of the whole QM/MM system are calculated with

the ab initio QM/MM method on the fly, and Newton

equations of motion are integrated..

On-the-fly Born-Oppenheimer ab initio QM/MM MD

simulations are becoming increasingly feasible !

One pico-second MD simulation ( 1000 force and energy evaluations)

[intel 64 linux cluster (2.33Ghz, quad core) ], [Q-Chem3.0/Tinker4.2]

• A highly dissociative and concerted mechanism for the nicotinamide cleavage reaction in Sir2 enzymes

B3LYP/(6-31G*) QM/MM

QM: 65 atoms, 562 basis

Functions. MM: more than

9000 atoms.

720 ps QM/MM MD simulations

SIR2

P. Hu, S. Wang, Y. Zhang, J. Am. Chem. Soc., 130, 16721-16728 (2008) .

What can we really learn from such

advanced simulations ?

On-the-fly Born-Oppenheimer ab initio QM/MM MD

simulations are becoming increasingly feasible !

Histone Lysine Methyltransferase (HKMT)

Containing a novel structural fold, and not sharing sequence or

structural similarity with other methyltransferases.

What is the origin of its catalytic power ?

A prerequisite is to reliably compute free energy barriers

for chemical reactions in enzymes and solutions

Ab initio QM/MM Molecular Dynamics Simulation

with Umbrella Sampling

Enzyme free energy barrier estimated from experiment: 20.9 kcal/mol

Calculated free energy profiles

in enzyme and in water

Whole ab initio QM/MM simulation length for each reaction ~ 1 ns

One million

fold rate

enhancement

S. Wang, P. Hu, Y. Zhang, J. Phys. Chem. B, 111, 3758-3764 (2007).

How does SET7/9 achieve such one million fold

rate enhancement ?

• Is it due to the mechanism difference ?

Compression hypothesis (The TS is more compressed in enzyme than in solution)

Near-attack conformer hypothesis (the reactant conformations in enzyme are more ready for reactions than in solutions)

LYS4

N

H

H

S

C

H

H

H

CH2

CH2

AdoMet

Geometries of pre-reaction states and

transition states

The transition state of

the solution reaction is

a little more compact.

Mechanism difference is very small, and is not likely to be

a key source of enzyme catalytic power.

LYS4

N

H

H

S

C

H

H

H

CH2

CH2

AdoMet

• Does it come from electrostatic interactions ?

Electrostatic field in the reaction center

LYS4

N

H

H

S

C

H

H

H

CH2

CH2

AdoMet

S

N

A positive charge migrates

from S to N during the methyl

transfer reaction

A positive electrostatic field

along S-N direction deter

the methyl transfer

A negative one facilitates the

reaction

In solution reaction, there is a strong shift in electrostatic field from

the pre-reaction state to the transition state

For enzyme reaction, SET7/9 provides a pre-organized electrostatic

environment

Hydrogen network around the reaction center

in solution

It undergoes a significant change from the pre-reaction state

to the transition state

Summary (I)

• A combination of the electrostatic pre-

organization in enzyme and the hydrogen

bond network reorganization in solution is a

key source to the enzymatic power of

HKMT

S. Wang, P. Hu, Y. Zhang, J. Phys. Chem. B, 111, 3758-3764 (2007)

Methylation State Specificity

Methylation state specificity: a distinct HKMT often

only transfers a certain number of methyl group(s) to its

substrate lysine residue.

Different methylation states have differing effects on

chromatin structure and gene transcription

Each lysine residue can be either mono-, di-, or tri- methylated.

A hallmark of histone lysine methylation

Steric Hinderance Hypothesis

The active site of mono-HKMT is quite

tight, while that of tri-HKMT LSMT is very

roomy.

• The methylation state specificity is

dependent on the ability of accommodating

the increasing bulk of the lysine group

How can such a steric effect be imposed given

that a protein structure in water is very dynamic

in nature and the methyl group is very small ?

SET7/9 is a mono-methyltransferase

Free energy barrier for the mono-methylation estimated from experiment: 20.9 kcal/mol

(Exp. kcat is 0.004 s-1)

Di-methylation reaction is about

500 fold slower than the mono-

methylation reaction.

What is the key difference between mono- and di-methylation

in SET7/9 ?

The AdoMet binding

channel.

The access of solvent

water molecules

to the active site

What is the consequence for the access of solvent water

molecules? A water chain

The lone pair of N atom of the lysine substrate forms a direct

N…H-O hydrogen bond with a water molecule. The break of

this HB requires extra energy.

Why does the di-methylation have a higher barrier ?

The catalytic power of SET7/9 is impaired in the di-methylation

due to the access of solvent water molecules to the active site.

LSMT: a SET-domain tri-methyltransferase

(more spacious active site than SET7/9)

The estimated experimental barrier for mono- and di-methylation are

23.3 and 22.5 kcal/mol respectively.

In LSMT, mono- and di- methylation are very similar

The active site of LSMT is larger, so that the methylated lysine can

be accommodated without interfering with its catalytic power.

Summary (II)

• A dynamic mechanism is emerged regarding how the methylation state specificity is achieved.

• The binding of Me-lys in SET7/9 opens up the binding channel so that solvent water molecules get access to the active site, which leads to a higher reaction barrier.

• The active site of LSMT is more roomy so that it can accommodate Me-Lys substrate without disrupting its catalytic power.

• These detailed insights take account of protein dynamics, consistent with available experimental results as well as the theoretical findings regarding the catalytic power.

P. Hu, S. Wang, Y. Zhang, J. Am. Chem. Soc., 130, 3806-3813 (2008). .

Conclusion

• We have advanced the frontier of Born-

Oppenheimer ab initio QM/MM molecular

dynamics simulations.

• Novel insights have been provided into

important biological problems.

Acknowledgement

Dr. Shenglong Wang

(currently at NYU-

ITS)

Dr. Po Hu ( currently

at UC Berkley)

$$$ NIH (R01-GM079223)

$$$ NSF (CAREER Award, MRI)

$$$ NYSTAR (James D. Watson Young Investigator Award)

$$$ NYU (Whitehead Fellowship, start-up fund)

Computing NSF-MRI, NYU-ITS, NCSA

Dr. Yihan Shao (Q-Chem Inc.)