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）
Calculations of dynamics and polarized charges
of water molecules in ATP hydrolysis
Takuya Takahashi
Ritsumeikan University、College of Life Sciences
H2PO4
H3P2O7
H5P3O10
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
For Water molecule
SPC、TIP3P, SPC/E models were tested
Charge distribution was also varied with SPC/E
For Solute molecule
PO4、CH4,C2H6,C15H32, NH3, alkali and halogen ions
Net charge and the distribution were artificially varied
2nd layer
Biomolecules as solute：amino acids, protein
1st layer
solute
ATP hydrolysis
product
Calculated self-diffusion coefficients,Dtr,
severely depnd on the water model.
water model
Water　No.
Box length
20-40 Å
cutoff
simulation
8-12 Å
1-20 ns
temperature
density
SHAKE
NTV
NTP
SPC
SPC/E
TIP3P
Experiment
Dtr
3.83
2.49
2.
49
5.19
2.30
298.15 K
SPC/E(bond＝１→0.905)
1.0 g cm-3 SPC（charge→ SPC/E)
2.63
3.21
TIP3P (charge→ SPC/E)
4.45
TIP3P(vdw→ SPC/E)
5.40
2.57
TIP3P (bond→ SPC/E)
Myosin (PDB：1b7t) and water
effect of shape and charge of solute and water molecules on
translational self-diffusion coefficients, Dtr, and rotational
correlation time, τrot , of surrounding water molecules was
investigated exhaustively .
• 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.
2672050
Here, research target is to
investigate and reproduce the
mobility and charge of
hydrating water molecules
with 1) classical MD and 2)
QC calculations.
What determines the mobility? To find the key factor,
1. Classical MD to reproduce HMW
System
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..
Calculated self-diffusion coefficients, Dtr, and rotational
correlation time, τrot,　severely depnd on the water oxygen
atomic charge, Q, （∝ water dipole）
10
2
9
Dtr（Å/ps）
8
(１０－５cm2/s)
7
Box Size=40Å　6
2048 Water molecules
SPC/E　water
Temp=　298K
5
Polarization↓
P.M.Ewalt　Rcut=12 Å
4
⇒Mobility↑
3
SPC/E
|Qw|　１％↓
-0.8476e.u.
2
τrot（ps)
⇒Dtr～20%↑
1
0
0.5
0.6
0.7
0.8
0.9
1
|Q| (e.u.)
absolute value of water oxygen atomic charge, Q, used for MD
SPC/E　MODEL　STRUCTURE
ｔｒ of water molecules around PO4 type solute plotted
Dｔｒ
against the solute net charge Qs (-3 ~ +3) 2.8
of water molecules around PO4
Rotational correlation time, τrot,　type solute plotted against the solute net charge Qs (-3 ~ +3) 3
water molecules 2.9
Qs ~ -1　in the first layer move
2.8
faster than the bulk
region. Consistent with 2.7
Dielectric spectroscopy
Dtr [×10-5cm2/s]
2.6
water molecules
Qs ~ -1　in the first layer move
faster than the bulk
region. Consistent with
Dielectric
spectroscopy
2.5
Hydration
due to
strong
electric
1st layer field
2.4
2.3
Hydrophobic
hydration
2.2
2
-2
-1
0
1st layer
solute 3
1
4.8
nc-1
nh-1
nc-b
nh-b
PO4 type
solute
4
3.8
Nc bulk
Nc 1st
ATP hydrolysis
product
3.6
Nh bulk
3.4
2nd layer
3.2
Nh 1st
3
-5
-4
-3
-2
Qs:
-1
0
1
2
2.4
2.3
2.2
2.1
2
3
-3
-2
Solute charge is
uniformly distributed on
the O atoms
Coordination number, Nc, and hydrogen bond number, Nh of
water molecules in the bulk and the first layer plotted against the
solute net charge.　In HMW region,
4.6
both the Nh and
st
Nc of the 1 layer 4.4
is smaller than 4.2
bulk.
2.5
2
Artificially changed Qs: Solute Net Charge (e.u)
Solute charge is
uniformly distributed on
PO4　OPLS, SPC/E rigid body
the O atoms
4
Solute Net Charge (e.u)
1st layer
solute
Summary of classical MD calculations 2
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!
1st
layer
2nd
layer
3rd
layer
2.6
2nd layer
3rd layer 2nd layer
bulk
2.1
-3
Τrot (ps)　2.7
-1
0
1
2
3
Qs: Solute Net Charge (e.u)
PO4　OPLS, SPC/E rigid body
Summary of classical MD calculations 1
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 PO 4, 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.
2. Quantum Chemical Calculations
• 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
2nd layer
ions are needed.
1st layer
solute
Model Chemistry & basis set used in this calculation (Gaussian03 )
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
KeyWord
Method
HF
Hartree-Fock（HF）Self-Consistent Field （SCF）calculation
B3LYP
Becke3 (B3)-parameter functional ＋ Lee，Yang，Parr
correlation functional (LYP) DFT calculation
Basis set
Atoms
Content
6-311G
H-Kr
Pople’s valence tripe-zeta
valencetriple-zeta Effective-CorePotential（ECP）
Stevens/Basch/Krauss ECP triple-split basis set
CEP-121G H-Rn
Polarizable Continuum Model ( PCM) solvation method :ε＝ 78.2
Mulliken ＆　NBO　analysis method for charge assignment
M. P. McGrath and L. Radom, J. Chem. Phys. 94, 511 (1991)
W. Stevens, H. Basch, and J. Krauss, J. Chem. Phys. 81, 6026 (1984).
http://www.hpc.co.jp/hit/solution/gaussian_help/m_basis_sets.htm
-0.91
2
Dtr（Å/ps）
Å　Box Size=40Å
2048 Water molecules
298K
Temp=　Rcut=12 Å
P.M.Ewalt　τrot（ps)
0.5
0.6
Q (e.u.)
-0.93
SPC/E　water
Polarization↓
⇒Mobility↑
|Qw|　１％↓
⇒Dtr～
～20%↑
↑
SPC/E
-0.8476e.u.
0.7
0.8
0.9
|Q| (e.u.)
absolute value of water oxygen atomic charge, Q, used for MD
SPC/E　MODEL　STRUCTURE
Na+
|Qo| of water around
K+ is 4% smaller
than bulk water
Mobility +100%?
-0.94
-0.95
-0.96
Solute size↑
=>　|Q| ↓
-0.97
-0.98
1
|Qo| of Li >bulk |Qo|　0
-0.95
-0.96
HF/CEP-121G PCM
-0.93
IBr-
-0.97
-0.98
ClF-
-0.94
Solute size↑
⇒|Q| ↓
-0.95
|Q| for F- also
smaller than bulk
Br_CEP_d7
Cl_CEP_d7
F_CEP_d7
I CEP d7
W45 CEPpcm
-0.96
2
3
4
r (A)
5
6
Na
K
W45
W50
W55
7
-0.99
-1
-1.01
-1.02
2
4
r (A)
6
8
Averaged partial charge of water Oxygen atom, Q,
plotted against distance from the center of solute
molecule (phosphate ions) HF 6-311G　NBO
2
-0.9
-0.91
Li　-0.99
Averaged partial charge of water Oxygen atom, Q,
plotted against distance from the center of solute
molecule (halogen ions) HF CEP-121G　PCM
|Q| of water around
I- was 4% smaller
-0.92
than
bulk water
Mobility +100%?
K+
HF/CEP-121G　PCM
-0.92
(１０－５cm2/s)
Q(e.u.)
10
9
8
7
6
5
4
3
2
1
0
Averaged partial charge of water Oxygen atom, Q ,
plotted against distance from the center of solute molecule
（alkali ions）　HF CEP-121G　PCM
Calculated self-diffusion coefficients, Dtr, and
severely depnd on
rotational correlation time, τrot,　）
the water oxygen atomic charge, Q, （∝ water dipole）
3
4
5
6
Except
fot H3PO4,
PO4_6311G_d7_NBO
|Q| HPO4_6311G_d7_NBO
of surrounding
H2PO4_6311G_d7_NBO
water
was smaller
H3PO4_6311G_pcm_d7_NBO
than
bulk water
W50N631
Mobility
W45N631↑
HPO4２－
PO4３－
H2PO4－
The order of Q is
not easily explained
from the net charge
and size of solute.
H3PO4　-1.03
-1.04
d(A)
7
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.
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 "
http://www.material.tohoku.ac.jp/atpwater
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）
For more investigation
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.