Calculations of dynamics and polarized charges

of water molecules in ATP hydrolysis

　水を主役としたATPエネルギー変換（科研費：新学術領域研究）

H5P3O10H3P2O7H2PO4

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溶媒和ダイナミクスの計算手法開発とＡＴＰ加水分解過程への応用高橋卓也　　立命館大学・生命科学部・生命情報学科

Takuya Takahashi

Ritsumeikan University、College of Life Sciences

Introduction　of　Hyper Mobile Water (HMW) • Physico-chemical property of the water molecules around

biomolecules are supposed to change during enzymatic reactions.

• For example, in ATP hydrolysis, number of hydration water drastically changes. Moreover, in many solutions, enhanced motion of water molecules (i.e., faster than bulk water) are observed with dielectric spectroscopy (Suzuki et al.).

• This hyper mobility of water has already been investigated in several systems such as

alkaline halide solution of KI

and urea solution etc..

Here, research target is to

investigate and reproduce the

mobility and charge of

hydrating water molecules

with 1) classical MD and 2)

QC calculations.Myosin (PDB：1b7t) and water

1. Classical MD to reproduce HMW

• A previous MD study showed

hyper mobility in translational

self-diffusion coefficient (Dtr)

near the oxygen atom only in

urea solution (not in tetra

methyl urea), although the

system size was small, water

model was poor, and the

rotational motion was not

investigated(Tovchigrechko ’99).

• Here, we tried MD simulations

exhaustively to elucidate

dynamical properties of

hydrating water molecules

around many types of solutes.

effect of shape and charge of solute and water molecules on

translational self-diffusion coefficients, Dtr, and rotational

correlation time, ττττrot , of surrounding water molecules was investigated exhaustively .

For Water molecule

　SPC、TIP3P, SPC/E models were tested　Charge distribution was also varied with SPC/EFor Solute molecule

PO4、CH4,C2H6,C15H32, NH3, alkali and halogen ions Net charge and the distribution were artificially varied

Biomolecules as solute：amino acids, protein

1st layer

2nd layer

solute

What determines the mobility? To find the key factor,

ATP hydrolysis

product

2.572.572.572.57TIP3P (bond→ SPC/E)

5.40 5.40 5.40 5.40 TIP3P(vdw→ SPC/E)NTVNTP

4.45 4.45 4.45 4.45 TIP3P (charge→ SPC/E)SHAKE

3.213.213.213.21SPC（charge→ SPC/E)g cm-31.0density

2.632.632.632.63SPC/E(bond＝１→0.905)K298.15temperature

2.30Experimentns1-20simulation

5.195.195.195.19TIP3PÅ8-12cutoff

2.2.2.2.49494949SPC/ESPC/ESPC/ESPC/EÅ20-40Box length

3.833.833.833.83SPC267-2050Water　No.

DtrDtrDtrDtrwater modelSystemSystemSystemSystem

Calculated self-diffusion coefficients,Dtr,

severely depnd on the water model.

0

1

2

3

4

5

6

7

8

9

10

0.5 0.6 0.7 0.8 0.9 1

τrot（ps)

Dtr（Å/ps）2

Calculated self-diffusion coefficients, Dtr, and rotational

correlation time, τrot,　severely depnd on the water oxygen atomic charge, Q, （∝ water dipole）

Box Size=40Å　　　　 2048 Water molecules

Temp=　298KP.M.Ewalt　Rcut=12 Å

|Q| (e.u.)

absolute value of water oxygen atomic charge, Q, used for MD

SPC/E　MODEL　STRUCTURE

　(１０－５cm2/s)

SPC/E　waterPolarization↓⇒Mobility↑|Qw|　 １％↓⇒Dtr～20%↑

SPC/E

-0.8476e.u.

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

-3 -2 -1 0 1 2 3

Solute Net Charge (e.u)

1st layer

2nd layer

3rd layer

bulk

　 D

tr [×

10

-5cm

2/s

]

Dｔｒｔｒｔｒｔｒ of water molecules around PO4 type solute plotted against the solute net charge Qs (-3 ~ +3) 　　　　　

Qs ~ -1　　　　water molecules in the first layer move

faster than the bulk

region. Consistent with

Dielectric

spectroscopy

PO4　OPLS, SPC/E rigid body

Solute charge is

uniformly distributed on

the O atoms

1st layer

2nd layer

solute

Hydrophobic

hydration

Hydration

due to

strong

electric

field

Artificially changed Qs:

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

-3 -2 -1 0 1 2 3

Solute Net Charge (e.u)

1stlayer2ndlayer3rdlayer

Qs ~ -1　　　　water molecules in the first layer move

faster than the bulk

region. Consistent with

Dielectric spectroscopy

Τro

t (p

s)　

Rotational correlation time, ττττrot,　　　　of water molecules around PO4 type solute plotted against the solute net charge Qs (-3 ~ +3) 　　　　

PO4　OPLS, SPC/E rigid body

Solute charge is

uniformly distributed on

the O atoms

Qs:

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

-5 -4 -3 -2 -1 0 1 2 3 4

nc-1

nh-1

nc-b

nh-b

Solute Net Charge (e.u)

In HMW region,

both the Nh and

Nc of the 1st layer

is smaller than

bulk.

Coordination number, Nc, and hydrogen bond number, Nh of

water molecules in the bulk and the first layer plotted against the

solute net charge.　

PO4 type

solute

Qs:

Nh 1st

Nc 1st

Nh bulk

Nc bulk

1st layer

2nd layer

solute

ATP hydrolysis

product

　Hyper mobility was observed in specific solute charge region (Qs ~ -1 e.u.) especialy in small solutes (PO4, CH4, CO2, OH, NH3 ).

In case of PO4, this was consistent with dielectric spectroscopy (HMW for NaXHYPO4).

• Mobility decreases as solute becomes larger ( P2O7, P3O10, C2H6 ) . Is this a reason of entropy change in ATP hydrolysys? No HMW for C15H32

• Shape of solute molecule was important , that is, no HMW was observed without LJ potential on H or O atom.=> No HMW for alkali and halogen ions .

• Effect of charge distribution is negligible in CH4,NH3 type solute, but not negligible in PO4 type solute.

• The reason of the hyper mobility was explained with the lower coordination number (density) and hydrogen bond network than bulk water.

Summary of classical MD calculations 1

MD for amino acids as solute

• No HM Water was observed

• τrot was effected by each chemical group but Dtr was not　＝＞Due to cooperative motion of water around solute

MD for proteins (pepsin, 1f32, and lysozyme, 6lyz)

• Mw and ASA almost same, net charge largely different

• No HM Water

• No difference for τrot and Dtr

Model or parameters used in this MD study was not enough => Improvement is needed!

Summary of classical MD calculations 2

• On the other hand, the hyper mobility of hydrating water for very simple solutes such as I－ and K+ ions in alkaline halide solution were also difficult to quantitatively reproduce with simple classical MD.

• To improve MD simulations and reproduce more realistic hydrating water properties in ATP hydrolysis,

quantum chemical (QC) calculations of water molecules around several solutes such as phosphates, three alkali ions and four halogen ions are needed.

2. Quantum Chemical Calculations

1st layer

2nd layer

solute

Previous Quantum Chemical Calculations

＊Previous Car-Parrinello MD : alkali ions（（（（Li+,Na+,K+ ） with 62 water molecules （T.Ikeda, M.Boero, K.Terakura,’07）

　Water molecules around K+ ion :Compared with bulk water

　　 Water dipole(∝polarization)↓ 　 Mobility ↑　

　But..still problems

Water molecules around Na+ ion also the same result

　　Absolute value of Dtr was much smaller than experiment

Results are only alkali ions.

Therefore,

we tried more calculation conditions (system size, basis set function, model chemistry) and more solutes such as halogen ions and phosphate ions

valencetriple-zeta Effective-CorePotential（ECP） Stevens/Basch/Krauss ECP triple-split　basis set

H-RnCEP-121G

Pople’s valence tripe-zetaH-Kr6-311G

ContentAtoms Basis set

Becke3 (B3)-parameter functional ＋ Lee，Yang，Parr correlation functional (LYP) DFT calculation

B3LYP

Hartree-Fock（HF）Self-Consistent Field（SCF）calculationHF

MethodKeyWord

Model Chemistry & basis set 　　　　used in this calculation (Gaussian03 )

W. Stevens, H. Basch, and J. Krauss, J. Chem. Phys. 81, 6026 (1984).

M. P. McGrath and L. Radom, J. Chem. Phys. 94, 511 (1991)

http://www.hpc.co.jp/hit/solution/gaussian_help/m_basis_sets.htm

Polarizable Continuum Model (PCM) solvation method :ε＝ 78.2

Mulliken ＆　NBO　analysis method for charge assignment

0

1

2

3

4

5

6

7

8

9

10

0.5 0.6 0.7 0.8 0.9 1

τrot（ps)

Dtr（Å/ps）2

Calculated self-diffusion coefficients, Dtr, and

rotational correlation time, ττττrot,　　　　severely depnd on the water oxygen atomic charge, Q, （（（（∝∝∝∝ water dipole））））

Box Size=40ÅÅÅÅ　　　　　　　　　　　　　　　　 2048 Water molecules

Temp=　　　　298KP.M.Ewalt　　　　Rcut=12 ÅÅÅÅ

|Q| (e.u.)

absolute value of water oxygen atomic charge, Q, used for MD

SPC/E　MODEL　STRUCTURE

　(１０－５cm2/s)

SPC/E　waterPolarization↓⇒Mobility↑|Qw|　 １１１１％％％％↓↓↓↓⇒Dtr～～～～20%↑↑↑↑

SPC/E

-0.8476e.u.

-0.99

-0.98

-0.97

-0.96

-0.95

-0.94

-0.93

-0.92

-0.91

0 2 4 6 8

Li　 Na

K W45

W50 W55

HF/CEP-121G　PCM

r (A)

Averaged partial charge of water Oxygen atom, Q ,

plotted against distance from the center of solute molecule

（alkali ions）　HF CEP-121G　PCM

Solute size↑=>　|Q| ↓

|Qo| of Li >bulk |Qo|　　

|Qo| of water around

K+ is 4% smaller

than bulk water

�Mobility +100%?

K+

Na+

Q (

e.u

.)

-0.96

-0.95

-0.94

-0.93

-0.92

-0.91

-0.9

2 3 4 5 6 7

Br_CEP_d7

Cl_CEP_d7

F_CEP_d7

I CEP d7

W45 CEPpcm

r (A)

HF/CEP-121G PCM

Averaged partial charge of water Oxygen atom, Q,

plotted against distance from the center of solute

molecule (halogen ions) HF CEP-121G　PCM

I-

Br-

Cl-

F-

Solute size↑⇒|Q| ↓

|Q| for F- also

smaller than bulk

|Q| of water around

I- was 4% smaller

than bulk water

�Mobility +100%?

-1.04

-1.03

-1.02

-1.01

-1

-0.99

-0.98

-0.97

-0.96

-0.95

2 3 4 5 6 7

d(A)

Q(e

.u.)

PO4_6311G_d7_NBOHPO4_6311G_d7_NBOH2PO4_6311G_d7_NBOH3PO4_6311G_pcm_d7_NBOW50N631W45N631

Averaged partial charge of water Oxygen atom, Q,

plotted against distance from the center of solute

molecule (phosphate ions) HF 6-311G　NBO

HPO4２－

　PO4３－

H2PO4－

H3PO4　　　　The order of Q is not easily explained

from the net charge

and size of solute.

Except fot H3PO4,

|Q| of surrounding

water was smaller

than bulk water

�Mobility ↑

Summary of QC calculations

＊Except for Li+ ion, electric dipole (polarization) of surrounding water decrease (Mobility increase) �K+, I-, Br- OK, but inconsistent with Na+ ion

＊Size dependence (number of water ) was small

＊Model Chemistry（HF､MP2,B3LYP） and basis set dependence was small and not esential .

＊Natural Bond Orbital analysis (NBO) also showed the same tendency as Mulliken charge analysis and showed much smaller dependence for the calculation conditions.

＊We could also obtained charge parameters of phosphate ions, which are applicable to classical MD simulations.

At present, we are calculating

• MD and QC for Poly phospates （HxP3O10、HxP2O7） with counter ions.

Hydrogen bond analysis in detail

Starting

• Model improvement for MD

• MD for ATP＝＞ADP＋Pi reaction.

• MD with enzyme protein such as ATPase.

• Analysis of protein surface group effect on the hydration water dynamics.

For more investigation

http://www.material.tohoku.ac.jp/atpwater

Acknowledgement

Mr. Morishita, Mr. Komatani (Ritsumeikan Univ.)

This study is partly supported by MEXT.

"Development of calculation methods of solvation

dynamics and application to ATP hydrolysis"

is a research thema in A01 group of

"Water as a key player in ATP energy transduction "

　水を主役としたATPエネルギー変換（科研費：新学術領域研究）