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1. Brooks et.al, PNAS,80,pp6571Biol., 9, e1003003 (2013)
6575 (1983)
7. Zhao et al., Nature, 497, pp6432. Duan et al., Science,282,
646 (2013)
pp740-3744 (1998)
8. Clementi et al.. JMB, 298, pp
3. de Groot et al., Science,294,
937-953 (2000)
pp2353-2357 (2001)
9. Yao et al., Nature Comm. 1:117
4. Shaw et al., Science,330,(2010)
pp341-346 (2010)
10. Yao et al., JACS, 135, pp74745. Piana et al., PNAS,110,7485 (2013)5pp5915–5920 (2013)7hĥǰȝɀɅɋɐȝɇɎńĊw(õǲɃȪɊ)ȇ]ǽǬ3ƫǭÈPx^ÙmĠÞǭŸľ6^ÙmĠÞŬǂļǲ ǃȇ¾ƷǠǬǍȲɊȖǲªƎȇî+ǡȄȫȾɌȞɐĥǱǳ3ñ/ȫɐɈȟ(ñȻɐȞ)7Žɘñ/^ÙmĠÞǲȫȾɌȞɐǳȫɐɈȟ

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Y. Matsunaga and Y. Sugita, in preparation9ȤɎȳȖƎ8qǲĨ$ĝQđɘ ąǱǖǜȄēȏȯɊȕɐ  0.6kcal/mol
Interaction

Typical distance

EnergyC

1.5 Å~ 100 kcal/mol

Salt bridge

H
N H +
H

O
– C
O

3.0 Å

~ – 4.0 kcal/mol(in water)

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N H

O

C

3.0 Å

~ – 1.0 kcal/mol(in water)van der Waals

HH
C H H CHH

3.5 Å

~ – 0.1 kcal/mol(in water)

various

Depend on
distance andenvironment

non-covalent interactions

Covalent bondElectrostatic

Example
C

H
N H +
H

O
– C
O

ƲƔƾĨ$ĝǘůƽǱŎǻZǩǬĜ"=xǲïŝǘĤÆǟȅǬǓȄ

10

MDǱ%ȆȅȄŋǈĥǰȾȩɎȝɄɊƵÈV ( r ) = ∑ kb ( ri,i+1 − r0 )2

Bonded interactions
O(N) interactionsbonds+ ∑ ka (θ i,i+1,i+2 − θ 0 )2angles+ ∑ kt ⎡⎣1 + cos ( nφi,i+1,i+2,i+3 − ω )⎤⎦torsions⎡⎛ σ ⎞ 12 ⎛ σ ⎞ 6 ⎤interactions+∑ ∑ ε ⎢⎜ ⎟ − ⎜ ⎟ ⎥ vdW term Non-bonded
2) interactionsO(Nrr⎢⎝ ij ⎠⎝i j>i
ij ⎠ ⎥⎣⎦
qi q j+∑ ∑i j>i 4πε 0 rij

Electrostatic term

Bottleneck
11

Bonded interactions• Bond stretching term
b

0

bonds

(Kb; force constant, r; bond length,r0; equilibrium bond length)

Bond energy [kcal/mol]å K (r - r )

2

200
160
120
80
40
0
0.5

1

1.5

2

2.5

r (bond length) [Angstrom]• Angle bending termθ0angles(Kθ; force constant, θ; bond angle,
θ0; equilibrium bond angle)

8

Angle energy [kcal/mol]å K (θ - θ )

2

7
6
5
4
3
2
1
0
100

110

• Torsion termφdihedrals(Kφ; force constant, φ; torsion angle,
n; multiplicity, γ; phase)

130

0.35

Dihedral angle energy[kcal/mol]å K [1 + cos(nφ - γ )]120

θ (bond angle) [deg.]

0.3
0.25
0.2
0.15
0.1
0.05
0
0

100

200

300

Φ (dihedral angle) [deg.]

The number of pairs examined in the bonded interaction terms grows only linearly withnumber of atoms, O(N).
12Non-bonded interactions
æ Aij Bij ö
ç
- 6÷
å
12
ç
rij ÷ø
van der Waals è rij
i , j pairs

van der Waals energy [kcal/mol]• van der Waals term
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
2

(Aij and Bij; force constants,
rij; distance between atoms i and j)

4

6

8

10

r (distance) [Angstrom]åqi q jer

electrostaticij
i , j pairs(qi and qj; atomic charges of atoms iand j, respectively, ε; dielectric
constant, rij; distance between atoms iand j)

Electrostatic energy [kcal/mol]• Electrostatic term
100
NO
HO

50
0
-50
-100
0

2

4

6

r (distance) [Angstrom]

810

Opposite charges

Same charges

Unlike the van der Waals interaction, the electrostatic term islong-range interaction!

The number of pairs examined in the non-bonded interaction terms grows
quadratically with number of atoms, O(N2).
13Non-bonded interactionsȇIęȁǛŸľǡȄǦ
ǽǲtɘ Ewald summationƾÇĥǰƿŦ=ȇµǨĂǡċȂǗǰ¬ƿŦ=ȇ2ǡȄǝǮǱȁȃǍ  ż>żE{AżTżȖɐɌɎĨ$ĝȇ2ǪǱ=ǜȄ
Frenkel & Schmit, “Understanding Molecular Simulation”

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'+ċ :‫ڈڈ‬-‫ڈڈ‬(ƧǓƿŦǲ ǃǳµǨĂǟȅǬǓȄǍcutoffǭŶǛ)ǦˮƲз¬ĥǰƿŦ=ǲ 2

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ɂȧȝɅǭƛǠǬ3D-FFTǭŶǛ)‫ڈڈ ڈ   ڈڈ ڈ‬-‫ڈ  ڈ‬

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WIREs Computational Molecular Science?Kǲ

Algorithm improvements for molecular dynamics simulations

ǅi=Eǲ&

Larsson, et al., WIREs (2011)15

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ƬƘƤǍèƌúǍâMťǍàö!Ǎ|ŨåoɒěısɓǍİƊjXǍ'ĞƸtɒƲĀȲȌȑsɓǍMichael FeigɒɀȝȓɎĺsɓ
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Comput. Mol. Sci., 5, 310-323 (2015).

n aǓZȆǣ0genesis@riken.jp
20

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23

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tual site group.
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24
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NAMD

2048

8192

32768

șɎȶɅɐȤǭǲŸľ
K computer8sŲîƍĈǭǲǉ
?IęȇĚ
2048
8192
32768
25

(f)

Crowding (103.7 million)

GENESIS+șɎȶɅɐȤǲ°ãŉ
I. Yu, T. Mori, T. Ando, R. Harada, J. Jung, Y. Sugita, and M. Feig, Elife 5, e19274 (2016).

Cytoplasm of Mycoplasma genitalium
Animal cell

Model for MD simulation

10 μm
50 nm

Mycoplasma genitalium# of atoms: 11,737,298# of macromolecules: 216 (43 types)# of metabolites: 4,212 (89 types)
Conc. : 298 mg/ml
Vol. fraction: 0.315 (Calculated by 3V (Neil etc, 2010))

300 nm26

List of macromolecules in the systemname (number)

RP (2)

R50P (1)

GROL (3)PYK (2)IF2 (1)

EFP (2)FUSA (3)

APS0 (1)SERS (1)

LEPA (1)GAPA (5)

LYSS (1)RR5 (1)

ACKA(13)

EFTU (1)

PTA (4)FBA (4)

RIBF (1)

ENO (13)

TRXB (1)FOLD (1)

PGI (5)

METK (1)

MANB(3)

UDK (1)

NOX (20)RF (1)

TRNA (2)ATRN(25)

PGK (18)

CDD (1)

ACK1 (1)

PDHC(28)

PDHA(11)

PDHD(21)

PDHB(4)

FBA1 (1)

YID2 (1)

TIG (2)

CMK (2)

ADK (2)

MTHF (1)1F1 (3)

I. Yu, T. Mori, T. Ando, R. Harada, J. Jung, Y. Sugita, and M. Feig, Elife 5, e19274 (2016).

27

List of metabolites (ƈĔƎ) in the system name (number)PO42 (161)

GLBP (29)

GLAP (3)

RB5P (1)

CDP (4)

DAMP (2)

PCYS (21)PPHE (2)

PO41 (194)DHAP (7)

GLCO (7)

SAHC( 29)

CMP (25)DATP

PGLN (290)

PPRO (28)POP (30)

FR6P (8)HCYS (25)

SAMT (13)CTP (142)

DGTP (6)PGLU (157)

PSER (5)

ADP(17)

AMM1 (1)

FAD (15)NAD (175)

UDGL (5)GDP (6)

TDP (28)

PGLY (60)

PTHR (13)

GTP(334)

H2O2 (1)

FRBP (28)

NDPH (6)UDPG (34)

GMP (1)

TMP (3)

PHSE (9)PTPF (3)

DCDP (1)

GL3P (76)

FMN (4)PYRP (7)

UDGF (7)GUN (10)

TTP (6)

PHSD (4)PTYR (1)

NUSC (1)

ACET (63)

FOR A (14)

PRPP (7)DRB1 (1)

UDP (134)

PALA (162)

PILE (17)

SPMD(80)

DCTP (1)

ADPG (1)

GL1P (140)PYRV (8)AMP (13)

UMP (6)

PARG (43)

PLEU (18)ETOH(116)

DGDP (1)

COA (165)

GOLP( 16)

RB1P (6)ATP (673)

RNUU (145)

PASN (42)

PLYS (23)

ACTP(73)

DGMP(3)

ACOA (38)

GL6P (7)

DRB5 (2)CYN (2)

UTP (612)

PASP (144)

PMET (17)

RBFL(4)

PVAL(162)

I. Yu, T. Mori, T. Ando, R. Harada, J. Jung, Y. Sugita, and M. Feig, Elife 5, e19274 (2016).

water(2,944,143)
Na+ (1,505)
Cl- (3,76)
K+ (20,792)
Mg2+ (376)28100 ns MD
performed by
GENESIS on K
computerI. Yu, T. Mori, T. Ando, R. Harada, J. Jung, Y. Sugita, and M. Feig, Elife 5, e19274 (2016).

29

I. Yu, T. Mori, T. Ando, R. Harada, J. Jung, Y. Sugita, and M. Feig, Elife 5, e19274 (2016).

30

GENESISǲ8Ĕɒ1ɓ
n MDȹɌȗɈɁ‒ ATDYN (ATomic decomposition DYNamics simulator):• atomic decompositionȇ%ĝ
• łųKɃȪɊɒCa-GO, all atom GO)ǘŸľWŝ
• ȆǗȃÐǓșɐȬǭɆɐȜǱȁȄƳĤWŝ

‒ SPDYN (SPatial decomposition DYNamics simulator):ŚǭǳǝǨȂȇ

• domain decompositionȇ%ĝ
%ĝ• Ƒ ?ɏǉơǰɊɐȦɎ (Midpoint cell/3ñ/=EFFT/ ? I/Oɓ

ĕ¦

ATDYN

SPDYN

ȝȟȩɁǲ=EüPx=EȬɂȌɎ=ENew lookup tableǌ

ǌɋȹɉȒÅü

ǌ

ǌ

łųKɃȪɊ

ǌ

ǋ

3ñ/=EFFT

ǋ

ǌ

?I/O

ǋ

ǌ

r-RESPA (1.1.0)

ǋ

ǌ

31

GENESISǲ8Ĕɒ2ɓ
XY-fixed)n ATDYN/SPDYN5Ơ
•
•

•

ÖƨK
² Steepest Decentü
Integrator² Leapfrog² Velocity VerletȊɎțɎȸɊ
² NVE² NVT– Langevin– Bussi– Berendsen² NPT– Langevin Piston– Bussi– (Isotropy of Simulation box:
Isotropic, Semi-iso, An-iso,•¸ÝŸľ(constraint)² SHAKE (Leapfrog)² RATTLE (Velocity Verlet)² SETTLE• FFT (PME)² FFTE• Restraint functions² Position² Bond² Angle² Dihedral angle² RMSD• REMD/REUS• String methodƏyǳN£ǲŚǭ%ǔǾǲ

32

GENESISǲ8Ĕɒ3ɓ
n ǤǲŶáȨɐɊ••ȫɈȞȎȖȫɉpÅɒtrjcnvɓ
² crd_convert² pcrd_convertɒ ?I/OĝŸľĝɓ² remd_convertɒREMDŸľĝɓȫɈȞȎȖȫɉŶáɒtrjanaɓ² mbar_analysis² pathcv_analysis² pmf_analysis² gval_analysis² rmsd_analysisɒRMSDǍRMSFɓ
² trj_analysisɒƔƾǍŵǰǯɓ
² wham_analysis•ɉȟȤɐȫȷȉȌɊpÅɒrstcnvɓ
² rst_convert² rst_upgrade•PCAŶáɒpcaanaɓ
² avecrd_analysis² eigmat_analysis² flccrd_analysis² prjcrd_analysis• S©ŋƕÁŇƵƣ
ɒrpath_generatorɓ• Ŷá5ƠɒlibanaɓƏyǳN£ǲŚǭ%ǔǾǲ

33ǝȅȂȇ%ǩǬǭǙȄǝǮ (&1)ƠǲMDȝɀɅɋɐȝɇɎõĊªȤɎȳȖƎ

şȤɎȳȖƎ

łųKɃȪɊ

ȼɐɁȻɐȞǱȦɅɐȫɉȊɊǘǒȄ
http://www.aics.riken.jp/labs/cbrt/tutorial/basic_md_tutorials/
34ǝȅȂȇ%ǩǬǭǙȄǝǮ (&2)ɋȹɉȒÅüǱȁȄIęĥǰțɎȹɉɎȗǮ¥ȂȅǦȪɐȤŶáąɋȹɉȒÅüȾȩɎȝɄɊ(ȊɎȸɋɈ)ɋȹɉȒÅü

ȼɐɁȻɐȞǱȦɅɐȫɉȊɊǘǒȄ
http://www.aics.riken.jp/labs/cbrt/tutorial/remd-tutorials/
35ǝȅȂȇ%ǩǬǭǙȄǝǮ (&3)?I/OǱȁȄsǰȝȟȩɁǲMDëƢpKǲȳȟȍȎȌÁŇ

ȼɐɁȻɐȞǱȦɅɐȫɉȊɊǘǒȄ
http://www.aics.riken.jp/labs/cbrt/tutorial/advanced_md_tutorials/36Ìǲ8
n 10:00 – 11:30 Ƈř• Ĝ"=xǲ=xJG{Ÿľ• GENESISǲŉ• ŚǱ¨ŰǰěƆǲƁÏ

n ǖÑ®ɒ90=ɓ
n 13:00 – 16:00 Ś
••••GENESISǲșɎȳȌɊŪ&(1) =xJG{üŸľGENESISǲȫɈȸɊȝɅɐȩȋɎȗŪ&(2) ɋȹɉȒÅ=xJG{üŸľǮšğȏȯɊȕɐŸľ
37IęĥǰțɎȹɉɎȗüɘɋȹɉȒÅü
38ɋȹɉȒÅüǲêŰ
ɋȹɉȒÅüǮǳǍĢǰȄąɏȾȩɎȝɄɊǲɋȹɉȒȇ ?Ǳ=xJG{ȝɀɅɋɐȝɇɎǠǍ~ƴƺǭɋȹɉȒƴǲíȇ~ǲɊɐɊǭÅǟǣȄ´üǎšğȏȯɊȕɐǲɌɐȒɊɀȮȿɁȇŞ<ǠǍñǲ|~Ė­ȇÁŇǡȄǲǱv
GȇĤÆǡȄǎ
GENESISǲɂȌɎïŝǲǵǮǪɏ
ǉǓą

MD

?ŸľïȇØIǱ%ĝǭǙȄ

MD

Ǔą

ȏȯɊȕɐ

íÅ

ëƢĹƴ

39

ɋȹɉȒÅüǲƨĝ&ɘȤɎȳȖƎǱɈȺɊǠǦũ1Ťņ=xǲJǙÓƠǲMDȝɀɅɋɐȝɇɎɋȹɉȒÅü

ɋȹɉȒÅüǱȁȃũ1Ťņ=xǲrǛǲĖ­ȇțɎȹɉɎȗǡȄǝǮǘǭǙǬǓȄ
40ěƆǲƁÏɘĉ-ȝȟȩɁǲȾȩɎȝɄɊȏȯɊȕɐȇ V(x) ǮǡȄǎǝǝǭ x ǳ3PxǲȪȒɊȫíǎ
A(x)ȇ í x Ǳ'zǡȄĔěƮǮǡȄǮǍȝɀɅɋɐȝɇɎǭǳ
A(x)ǲÙ¢,ȇ÷ǽǦǓǝǮǘrǓǎA ( x ) = ∫ A ( x ) P ( x ) dx =− βV ( x )
A
x
e
dx
(
)
∫

∫e

− βV ( x )dx=− βV ( x )
A
x
e
dx
(
)
∫

Z
β =

1
kBT

41

MDǮMCMC=xJG{ü(Molecular Dynamics; MD)=xȝȟȩɁǲGl(ȾȩɎȝɄɊȏȯɊȕɐ)ǱjǫǓ
ǬǍȮɅɐȫɎËĵȇŶǓǬțɎȹɊȇĜ°ǡȄ´üțɎȹɊĜ°ü = ȮɅɐȫɎËĵ + ēāȿɊșȷƣƱɃɎȩȒɊɌü(Markov Chain Monte Carlo; MCMC)~=(ū=)ȇćǦǡȿɊșȷƣƱǱȁȃțɎȹɊȇĜ°ǡȄËüțɎȹɊĜ°ü = *ŮëƢǲĜ° + ɂȫɌȾɉȟ@~ŜǮǾǍȏɊȚɐȬªǘ°ȃĺǪǰȂǴ

1 T
A ( x ) ≈ ∑ A ( xt )
T t=1
42

MCMCǲŶƁ

ȿɊșȷƣƱǮǳǍñǲĖ­ǭí x’ ȇǮȄĮęǘǍħCǲĖ­ x ǲǻǱ'zǡȄɊɐɊǭJǛȝȟȩɁǲǝǮƩĴĮęπ ( x → x ')ǭźƝǭǙȄ

~=(ū=)ȇțɎȹɊǡȄȿɊșȷƣƱȇŻŸǭǙȄǗəƩĴĮęǘćǦǡǸǙªƎɏŰƅǳǒȄǗə43

MCMCǲŶƁĽǕɘ žňƯȃZǓȇćǦǣǴţǓ( ) ( x → x ') = P ( x ') π ( x ' → x )P ( x ) = ∫ e ( )dx Z
π ( x ' → x) P( x)=ZǘȔɄɎȡɊǟȅȄɑπ ( x → x ') P ( x ')žňƯȃZǓ P x π− βV xžňƯȃZǓȇćǦǡƩĴĮęŻŸǲŬ´üɘɂȫɌȾɉȟü
1. ĳªQ(x, x’) = Q(x’, x)ȇćǦǡȁǔǰĮęǭñǲëƢ*Ůȇ$°
2. r = P(x’)/P(x)>1ǰȂǴ ¨Ǣ*ŮȇVěr = P(x’)/P(x)<1ǰȂǴ Įęrǭ*ŮȇVěǝȅǘžňƯȃZǓȇćǦǡǝǮǳ
ÐǱĮſǭǙȄ

44

ƠǲMDǲțɎȹɉɎȗǱǖǜȄaǇĎ
šğȏȯɊȕɐfǧ:;ǠǬǓȄǮǍɌɐȒɊɀȮȿɁǱȫɈȧȹǟȅȄǝǮǭ
œ`ÒƴǘƲǛǰȃǍȝɀɅɋɐȝɇɎÒƴǲĿc8ǭȏɊȚɐȬªǘ°ȃĺǦǰǓ

ȏȯɊȕɐ

1 T
A ( x ) ≠ ∑ A ( xt )T t=1

ɌɐȒɊɀȮȿɁëƢĹƴ

45ąɋȹɉȒÅüɘąǲĢǰȄɋȹɉȒǲ2ąǲĢǰȄ=xȝȟȩɁǲɋȹɉȒ M)ȇǺǮǽǦ[Ò=ȇ 2ǡȄǎYɋȹɉȒƴǱǳĨ$ĝǳǰǓǲǭǍ[Ò=ǲ~=(ū=)ǳOǰȄ¿ǜľ[Òū=

(

)

M

( )

M

P x (1) , x ( 2 ) ,..., x ( M ) = ∏ Pm x ( m ) = ∏
m=1

m=1

e

( )

− β ( m )V x( m )Z (m))ǏǲɋȹɉȒǱǪǓǬ=xJG{ü(MD)ȇƨĝǠǬțɎȹɉɎȗǡȄǮ→ [Ò~(ū)=ǱǪǓǬțɎȹɉɎȗǠǬǓȄǝǮǱǰȄ→ ǓąǲȫɈȞȎȖȫɉǳ'ĐǮǠǬȫɈȧȹǟȅȄWŝªǘǒȄǉǓą MD
( 3)

MD

MD

x

x (1)
Ǔą

ȏȯɊȕɐ

x(2)

ëƢĹƴ

46

ɋȹɉȒÅȇMCMCǮǠǬ

2MDǲƟ ǭǍMCMCĥǰÒƴĤɊɐɊȇ 2ǡȄǎǦǧǠǍ
*ŮëƢȇÊǦǱĜ°ǡȄǲǭǳǰǛǍɋȹɉȒmǮm+1ǲíȇÅǡȄǝǮȇśǕȄǎ
ǝǲǮǙǍɂȫɌȾɉȟüǲÅĮę r ǳǍǲȁǔǱÕǜȄ

P ( x( ) ) P ( x( ) )()⎡( β ( ) − β ( ) ) (V ( x ( ) ) − V ( x ( ) )) ⎤
r=
=
=
exp
⎣
⎦
P ( x ( ) ,..., x ( ) , x ( ) ,..., x ( ) ) P ( x ( ) ) P ( x ( ) )P x (1) ,..., x ( m+1) , x ( m ) ,..., x ( M )
1

m

m+1

m+1

m

M

m

m+1

m

m

m+1

m

m+1

m

m+1

m+1

¹ȊɎțɎȸɊǲžňƯȃZǓǳćǦǠǬǓȄǲǭǍū=ǲțɎȹɉɎȗǱǰǩǬǓȄǎ
)ǏǲɋȹɉȒǲóǱĩĦǡȄǮǍÍǉąǱǩǬǍąǱǖȃȄWŝªǘǒȄǎǪǺȃǝǲlZǍȫɈȧȹȇīÒƴǭŞ<ǭǙȄǎǉąǧǮȇƒǕǿǡǓɑ
ǉǓą
MD
MD
( 3)

x

x (1)
Ǔą

ȏȯɊȕɐ

x(2)

íÅ
(MCMCĥ)ëƢĹƴ

47

ąɋȹɉȒÅüǲAĎǮðĎ
ąɋȹɉȒÅüǲAĎǮðĎ• AĎ– øĝĥǭǒȄɘȝȟȩɁǱǪǓǬǲ
Ǳ%ǕȄ

CĪƉǰǠ

• ðĎ
– ȝȟȩɁțȌȠ(PxÈ)ǘsǙǛǰȄǮǍÅǆǘǘȄǦǽǍ¨ŰǮǟȅȄɋȹɉȒÈǘsǙ
ǛǰȄŶùüɘǒȄšğǱōǩǬ¹ȊɎțɎȸɊȇśǕȄ→ȾȩɎȝɄɊɋȹɉȒÅü(REUS)
Y. Sugita, A. Kitao, and Y. Okamoto, J. Chem. Phys. 113, 6042 (2000).
H. Fukunishi, O. Watanabe, and S. Takada, J. Chem. Phys. 116, 9058 (2002).

48

ȾȩɎȝɄɊɋȹɉȒÅü(REUS)ɘ
ĢǰȄɋȹɉȒǲ 2
ǒȄ1ñ/íyǱšğȏȯɊȕɐȲɉȊǘǒȄǮ=ǗǩǬǓȄlZ
ąǭǳǰǛǍĢǰȄyƖǲÝŕȾȩɎȝɄɊȇǾǪɋȹɉȒȇ 2ǡȄǎ6"ĥǱǳǍɋȹɉȒmǱǠǬǍymȇ §ǮǡȄƄ`ȾȩɎȝɄɊȇ¬~ǡȄɘ

Vm

()

()

(

ȝȟȩɁǲȾȩɎȝɄɊȾȩɎȝɄɊ3
MD
( 3)

)

( )

()

2
1
x =V x +y( x )−ym = V x + U m y( x )2MDÝŕȾȩɎȝɄɊ

MD

x

x (1)
ȾȩɎȝɄɊ1

ȏȯɊȕɐ

x(2)

yƖ

y3

y2

y1

49

ɋȹɉȒÅȇMCMCǮǠǬ

2CǮ[ìǱǠǬǍɋȹɉȒmǮm+1ǲíȇÅǡȄǝǮȇśǕȄǎ
P ( x( ) ) P ( x( ) )()
r=== exp ⎡ β ( −U ( y ) − U ( y ) + U ( y ) + U ( y )) ⎤()( ) ( )
( )
( )
( )
⎦
P ( x ,..., x , x,..., x ) P ( x ) P ( x) ⎣P x (1) ,..., x ( m+1) , x ( m ) ,..., x ( M )
1

m

m+1

m+1

m

M

m

m+1

m

m

m+1

m

m

m+1

m+1

m

m

m+1

m+1

m+1

rǳyǲǻǱ'ȄǲǭǍȝȟȩɁțȌȠǘsǙǛǬǾÅǆǳǘȂǰǓÝŕȾȩɎȝɄɊǭȇƒǕȄɑȾȩɎȝɄɊ3
MD
( 3)

MD

x

x (1)
ȾȩɎȝɄɊ1

ȏȯɊȕɐ

x(2)

íÅ
(MCMCĥ)

yƖ

y3

y2

y1

50

ȾȩɎȝɄɊɋȹɉȒÅ(REUS)ǘ¡ǱĺǪlǂ:ŧDǲŌZɃɐȬǲÁŇ
Journal of Chemical Theory and ComputationyƖǮǠǬǐŧDǲŌZțȌȫǗȂǲƔƾǑȇǮȄǮ
Journal of Chemical Theory and ComputationŌZɃɐȬǲÁŇǱØIǭǒȄǝǮǘįǟȅǬǓȄ

ŌZɏŶƾȇ#ǾŗȃƜǠǬŌZɃɐȬȇÁŇɑȏȯɊȕɐ

Figure 3. Time series of (a) the reaction coordinate ξ (the distances fprotein pocket, (c) RMSD (in Å) from the correct binding mode (a blu
potential (k3 = 1.0 kcal/(mol Å2) and d3 = 6.0 Å) obtained from the R(blue), 6 (green), 12 (orange), and 16 (pink) are shown for (a), (b), andshow the correct binding distance from the PDB.

We additionally used one of the typical docking software
GLIDE40 for the comparison. The initial structures wereprepared using Protein Preparation Wizard by the default
setting. OPLS2005 force ﬁeld parameter was used, and theminimization was performed with the restraints on all the heavy
atoms. The obtained structures were used for the docking
templates. First, we used the SP mode to obtain 20 docking
modes. Second, the obtained 20 modes were further reﬁned by
the XP mode. The binding modes were sorted according to theyƖ=ŧDǲŌZțȌȫǗȂǲƔƾ
scores.
Bothself- andcross- Comput.
docking
performed.
Figure 3. Time series H.
of (a)
the reaction
coordinate
ξ Okamoto,(thedistancesfromtheTheory
proteinpocket),were(b)4660
themidpoint
Kokubo,T. Tanaka,
and Y.XPJ. Chem.
9,(2013).Inof
self-docking,the
receptor
conformation
bindingtotheligandexw
protein pocket, (c)Figure
RMSDÅ) fromthe correctbindingmode(a J.blue
ligand in
Figure6c below),and (d) (green)
replica6.(inComparisonsof thepredicted
bindingmodes
by
the REUS
simulations
H. Kokubo,
T. Tanaka,andY. Okamoto,Comput.
Chem.
32,
2810
(2011).
2
was
used
as
the
docking
template,
and
on
the
other
hand,
in s
kcal/(mol Åﬁgures) and were
d3 = 6.0
Å) obtained
from the26REUS simulation of the 1PMV system. Timepotential (k3 = 1.0(blue).The
createdusing PyMOL.
cross-docking
thereceptor
conformation
bindingtoanother(blue), 6 (green), 12 (orange), and 16 (pink) are shown for (a), (b), and (c) as representatives. The bold horizontal red
51that theshow the correct binding distance from the PDB. ligand was used as the docking template. We conﬁrmed
in o
independently by diﬀerent replicas
as the REUS
simulation
docking software
successfully
reproduced thetrapped
experimental

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GENESISǭǲɋȹɉȒÅüǲŭ8ǉǓą or ȾȩɎȝɄɊ4x(4)x ( 3)x(2)x (1)Ǔą or ȾȩɎȝɄɊ1
1. (m, m+1) Ǯ (m-1, m)ȇ2ȅƦǓǱǠǬÅȇżǻȄ
2. ƻǳǍíǭǳǰǛą/ȾȩɎȝɄɊȇÅǠǬǓȄ
ȫɈȞȎȖȫɉǲą/ȾȩɎȝɄɊǘÅǞǮǱpK
ɆɐȜǘȣɐȫǠǬǍ[ą/ȾȩɎȝɄɊǲȪɐȤǱǡȄ¨Ű52ňǗǰŽɘąɋȹɉȒÅüǱǖǜȄ
ÅÒǲơǲUȃ¶ǓňǗǓǝǮȇŷǕǴǍMDǮŊǻZȆǣȄlZǍÅÒǱíǧǜǭǰǛǍơȇǯǔǲȁǔǱUȃ¶ǔǗǾśǕǰǜȅǴǰȂǰǓǎ
žňƯȃZǓǲǱǍȾȩɎȝɄɊȏȯɊȕɐǧǜǭǰǛǍ
ơȇ]ǽǦȱɀɊȫȮȊɎǲǱÕǛǝǮǾǭǙȄǘǍ
ǘĒƽǱǰȄǮǮǾǱǍí+ơÅħ£ǲȝȟȩɁǲ|~ªļǱģřǘǒǩǦǎ
ǤǝǭǍSugita and Okamoto (1999)ǳÅǲƻǱǍơȇβ (m)β ( m+1)

Y. Sugita and Y. Okamoto, Chem. Phys. Lett. 314, 141 (1999)ǺǦǳǤǲƞǲȷȉȖȤɐǭȟȘɐɉɎȗǡȄǝǮȇÄæǠǦǎǝǲȁǔǱ
ǡȅǴǍơǳȔɄɎȡɊǠǬǍɂȫɌȾɉȟǲÅĮę r ǳCȻɐȞǲȁǔǱȝɎȹɊǱǰȄǎơǲUȃ¶ǓǱƵǠǬǳǍǝǲǱÅÒǱȿȖȟȍȎɊɏȽɊȨȿɎ=ǗȂțɎȹɉɎȗǡȄ´üļǘÄæǟȅǬǓȄǎ
GENESISǭǳǍȟȘɐɉɎȗǡȄ´üǘŭǟȅǬǓȄǎ

53

ňǗǰŽɘąɋȹɉȒÅüǱǖǜȄ
ąEȃǬɏɋȹɉȒÈȇu#ǱùǽȄǗəŋǈĥǰ 
1. ɋȹɉȒ m Ǯ m+1 ǘÅǡȄĮęǳ m ǱȂǢ~ǮǰȄąEȃǬǘţǓǎ → ąĹƴȇɈɎȥɁɏȍȐɐȖǡȄȁǔǱǰȄǦǽǎ
2. ÅĮęǳ0.20.3ƛǘţǓ (ŋǈB)ąEȃǬǲűķȃË
CǱĢǰȄąǭÅǰǠǲȝɀɅɋɐȝɇɎȇÿǠǬǍ
YąǭǲȾȩɎȝɄɊȏȯɊȕɐǲ=ȇ¥Ȅǎǲȇ%ǩǬÅĮęȇűķǾȄ

( ) (

)

Pexchange ( β m , β m+1 ) = ∫ ∫ Pm V ( m ) Pm+1 V ( m+1) min [1,r ] dV ( m ) dV ( m+1)β m β m+1

g,+Ů}ǱȁȄƛ K. Y. Sanbonmatsu and A. E. García, Proteins 46, 225 (2002).
ȓȍȝȊɎǱȁȄƛ N. Rathore, et al., J Chem Phys 122, 024111 (2005).

ƶąǳǍȝȟȩɁǘnȅǰǓ ǗǪ ȝɀɅɋɐȝɇɎȊɊȚɉȠɁǘĭŐǠǰǓąȤɎȳȖƎȷȐɐɊȪȋɎȗ Tmax = 600KƛşȤɎȳȖƎȝɀɅɋɐȝɇɎ Tmax = 400KƛÅĮęɏƶąȇjǱǠǬǍɋȹɉȒÈȇù~ǡȄǖ´ƗǰǲǳǲțɐȲ http://folding.bmc.uu.se/remd/54ňǗǰŽɘɋȹɉȒÅüǱǖǜȄǤǲǲŽǇ• ą~ȊɎțɎȸɊqǭǲREMD– NPTÞ (GENESISǱŭă)– NPγTÞ γT REMD (GENESISǱŭăǍşȤɎȳȖƎǱØI)T. Mori, J. Jung, and Y. Sugita, JCTC 9, 5629 (2013).

• REMDǲȫɈȞȎȖȫɉǲŏŸ9ě– WHAM, Parallel tempering WHAM (PTWHAM)ǱȁȄůÈȫɈȞȎȖȫɉȇ%ǩǦ9ě
J. D. Chodera, et al., JCTC 3, 26 (2007).
– Markov State ModelǱȁȄlong time-scale kinetics«kǲÃ~
N.-V. Buchete and G. Hummer, Phys. Rev. E 77, 030902 (2008).

55ɋȹɉȒÅüǲQśÉĘ
• MCMCɏɋȹɉȒÅüǲěƆŶƁ
, ĶÜòŘ , ŸľŏŸ 2 ȿɊșȷƣƱɃɎȩȒɊɌüǮǤǲ^ƙ (ŏŸı{ǲȷɌɎȩȋȊ 12) ýÕ
(2005)• ɋȹɉȒÅüǲPƆÉ
K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604
(1996).
• ąɋȹɉȒÅüǮ=JG{üȇŊǻZȆǣǦƆÉ
Y. Sugita and Y. Okamoto, Chem. Phys. Lett. 314, 141 (1999)

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WHAM
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ǽȄǗə– ĢǰȄÝŕȾȩɎȝɄɊǘǗǗǩǦńǲȪɐȤȇǯǲȁǔǱǠǬŏZǡȄǗəŶùüɘƭǻǜ(~K)ǠǬŏŸÃ~(ÖÃ~)→Weighted Histogram Analysis Method (WHAM)
58ąɋȹɉȒÅüǲAĎǮðĎÖÃ~ÖÃ~ǮǳɃȪɊȳɈɂɐȤÃ~üǲǵǮǪǎ
ǒȄȳɈɂɐȤǲǾǮǭǍȪɐȤ (ŹŔíÚ)ǘĜƐǡȄĮęȇśǕǬǍ
ǤȅȇȳɈɂɐȤǲƵÈǮűǦǾǲȇ(Likelihood)ǮȁǶǎ
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http://qiita.com/kenmatsu4/items/b28d1b3b3d291d0cc698

60ąɋȹɉȒÅüǲAĎǮðĎÖÃ~• ÖÃ~ǲěƆĥªƎ– čƛÓƥªɘȪɐȤÈǘďƶsǲéƶǭǍÃ~,ǲȲȌȊȟǳȢɌǱǰȄ– čƛØIªɘȪɐȤÈǘďƶsǲéƶǭǍÃ~,ǲȏɈɐ(ȲɉȊɎȟ)ǘÖǱǰȄ
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(=)<:∝ <: exp(IJ= (K: ))yiǳȵɎiǲ§íǺǦǍÝŕȾȩɎȝɄɊUm(y)ǲǾǮǭŴĆǟȅǦYȵɎǲ
ȴȟȫȗɈɁȇhiǮǡȄǮǍȳɈɂɐȤpiǲǳ<(=)ℎ$ , ℎ& , … , ℎ? <$ , <& , … , <?

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62

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Histogram Analysis Method (WHAM)
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CȻɐȞǲp(m)ȇǍ3ǬǲÝŕȾȩɎȝɄɊm=1,…,MǱǪǓǬėĺ ƋǮǠǬķȇǮȄǮǍȫɐȤɊǲpǘ <ǟȅȄL< ℎ$ , ℎ& , … , ℎ? <$ , <& , … , <? = 0 <(=) ℎ$ , ℎ& , … , ℎ? <$ , <& , … , <?
=;$ǝǲȇȳɈɂɐȤpiǱǪǓǬÖsKǠǬǍÖÃ~ǡȄǲǘWHAMǭǒȄ
piȇÃ~ǠǦǭǍyƖǱǖǜȄšğȏȯɊȕɐpKǳǲǭŸľǭǙȄ

M: = − IN$ ln <:C. Bartels and M. Karplus, J. Comput. Chem. 18, 1450 (1997).
S. Kumar, D. Bouzida, R. H. Swendsen, P. A. Kollman, and J. M. Rosenberg,
J. Comput. Chem. 13, 1011 (1992).

63ąɋȹɉȒÅüǲAĎǮðĎ
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©Dr. Kobayashi (RIKEN)

64ąɋȹɉȒÅüǲAĎǮðĎ
ǺǮǽ• =xJG{üǮGENESISǱǪǓǬŀOǱŉǠǦ• ŚǱ¨ŰǰɋȹɉȒÅüɏWHAMǲěƆ
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