2018年11月7日横浜市立大学 生命医科学研究科

池口 満徳

•

•–

– Force Field

•–

–

–

–

Conformational Changes of β subunit upon ATP binding

βTPβE βE βTP

γ γ

AcrB

H+BindingExtrusion

AccessBinding

ExtrusionAccess

H+

H+

Binding

Extrusion

Access

Drug

DrugDrug

Drug

Drug

S. Murakami, PNE, 52 (2007), 406-414

Drug

90

by

QM

QM MD

MD

MD

MD

MD

MD

MD

分子動力学シミュレーションとはー基本アルゴリズム、力場(force field)ー

MD

Bond Angle Torsion

http://www.nobelprize.org/

Nonbond (Elec, vdW)

MD Karplus2013

MD MD

MD

ü 16

ü

ü

Hashido, Ikeguchi, Kidera, FEBS. Lett., 579, 5549, 2005Hashido, Kidera, Ikeguchi, Biophys. J., 93, 373, 2007

ü MD1 2 fs 10-15s)

ü 1 186,400 =86 ps

ü 1 186,400,000 =86 ns

ü 1 MD12

t x t f t

t-Δt/2 v t-Δt/2

t+Δt/2 v t+Δt/2

t+Δt x t+Δt

v(t +Δt 2) = v(t −Δt 2)+Δt ⋅ f (t) m

x(t +Δt) = x(t)+Δt ⋅ v(t +Δt 2)

(leap frog)

Force Field

M. Levitt, The birth of computational structural biology, Nature Struct. Biol. 8, 392, (2001)

1969-1977

MD

• (Force Field)

•• MD

MD

•

force fieldAMBER (Kollman), CHARMM (Karplus), GROMOS (Berendsen), OPLS (Jorgensen), etc.

-0.2

-0.1

0

0.1

0.2

0 2 4 6 8 10

ener

gy [k

cal/m

ol]

distance [Å]

0

20

40

60

80

100

0 5 10 15 20

ener

gy [k

cal/m

ol]

distance [Å]

( ) i jq qE r

r=

•

•• Ewald

––– FFT Particle Mesh Ewald (PME)

•––– Fast Multipole Method; FMM

分子動力学シミュレーションの解析・応用

MD•–

•–

•–

•–

•–

•– NMR SAXS

MD•–

MD : RMSD, RMSFRoot Mean Square Deviation (RMSD)

ü

ü

ü

üRMSD % = ∑( )((%) − )-./,(

1

2

RMSD from crystal structure)

Time (ns)

RM

SD (Å

)

domain Adomain B

MD RMSD

RCBRCA

Oroguchi, MI et al., Biophys. J., 96, 2808 (2009)

Root Mean Square Deviation (RMSD)

RMSD =

√(∑

i xi xref i)2

N

üü MDü

RMSDRMSD

MD : RMSD, RMSFRoot Mean Square Deviation (RMSD)

ü

ü

ü

üRMSD % = ∑( )((%) − )-./,(

1

2

Root Mean Square Fluctuation (RMSF)

ü

ü

ü

ü

ü

RMSF 4 = ∑5 )((%) − )67.,(1

8

Conformational Changes of β subunit upon ATP binding

βTPβE βE βTP

γ γ

Protein Fluctuation (RMSF)

ü Fluctuation of C-terminal domain: βE>βTP>βDP

ü Despite fairly similar conformations of βTP and βDP,fluctuations of C-terminal domain are different.

Y. Ito & M. Ikeguchi, J. Comp. Chem. 31, 2175 (2010)

βE βTP

Empty; Open)ATP bound; Closed)ADP bound; Closed)

MD•–

•–

MD : , PCA

Correlation Matrix

Cij =Δri ⋅ Δr jΔri

2 Δr j2

Cij = 1

Cij = 0

Cij = −1

ü

ü

ü

Correlated Motion in Protein

Y. Ito & M. Ikeguchi, J. Comp. Chem. 31, 2175 (2010)

Cij = 1

Cij = 0

Cij = −1

MD : , PCA

Correlation Matrix

Cij =Δri ⋅ Δr jΔri

2 Δr j2

Cij = 1

Cij = 0

Cij = −1

ü

ü

ü

Principal Component Analysis (PCA)

∆"#∆"$% = 1⋯3*

ü

ü

ü

PCA

MD PCA

ü PCAü

Computational Biochemistry and Biophysics, Becker et al. eds., 2001.

Principal Component Analysis (PCA)

PCA F1-ATPase βü Top mode 30 % ü Top ten modes 70 %

ü 4 ATP

Y. Ito & M. Ikeguchi, Chem. Phys. Lett. 490, 80 (2010)

Principal Component Analysis: Mode 1-4Mode 1: magentaMode 2: yellowMode 3: cyan

Mode 4: greenβE→βDP: red

üRelaxation from interactions with adjacent subunits

ü Intrinsic flexibility is well correlated with structural transition

Y. Ito & M. Ikeguchi, Chem. Phys. Lett. 490, 80 (2010)

MD•–

•–

•–

Interaction between ligand and protein

Isobe, YI, MI, Arita, Sci. Rep. 8: 7951 (2018)

Interaction between CYP1A2 and EPA

MD•–

•–

•–

•–

MD

A B

λ=0 λ=1

A B

i=0 i=Nλ=0.01 λ=0.02i=1 i=2

∆" = −%&'()

*+,ln exp −2)3, − 2)%&' )

= 45

, 6267 8

97

Free Energy Perturbation

Thermodynamic Integration

Bennett Acceptance Ratio (BAR)

ΔGbind

ΔGligandΔGcomplex MD FEP, TI, BAR

ΔGbind ΔGligandΔGcomplex= −

=

=

ΔGcomplexΔGligand

MDFujitani et al., JCP, 2005

ΔΔG

relative binding free energyFEP+

Wang et al. JACS, 2015

MDMD MD

Replica 1

Replica 2

Replica 3

Replica 0

Replica 0

Replica 3

Replica 2

Replica 1

Replica 3

Replica 0

Replica 2

Replica 1

…

…

…

…Te

mpe

ratu

re

High

Low

MD

Tem

pera

ture

High

Low

17.2

17.6

18

18.4

0 50 100 150 200

MD(REMD)

MD: REMD:

ΔSC

laus

ius

[cal

/mol

/K]

Time [ns]

Tors

ion

angl

e [θ

]

Tors

ion

angl

e [

]

Time [ns]Time [ns]

MD REMD: Oseltamivir

MD

Hikiri, MI, et al. J Chem Theory Comput. 2016 12: 5990.

UnfoldFold

ΔSc

Folding/Unfolding MD(REMD)

0

20

40

60

80

100

250 280 310 340 370 400

Temperature [K]

P Fol

d(T)

[%]

Tm( )

Tm(REMD)

• REMD Folding/Unfolding• Folding/Unfolding• REMD (Tm=305K) (315K)

RM

SD (Å

)

Simulation time [ns] RMSD (Å)

(T=305K) Fold/Unfold

(10 )

< >

0

4000

8000

12000

16000

0 1 2 3 4 5 6 7

FoldUnfold : Fold :

Unfold

REMD(255K-400K)

UnfoldFold

ΔSc

-30.0 -25.0 -20.0 -15.0 -10.0

-5.0 0.0

250 280 310 340 370 400

Folding ΔSc(T)

Temperature [K]

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

250 280 310 340 370 400

Temperature [K]

ΔGU

nfol

d(T)

[kca

l/mol

]Fo

ldΔS

Unf

old(T)

[cal

/mol

/K]

Fold

:ΔS:ΔSUnfold

Fold

Temperature [K]

ΔSc(T

) [ca

l/mol

/K]

-40

-30

-20

-10

0

285 295 305 315 325 335

Hikiri, MI, et al. J Chem Theory Comput. 2016 12: 5990.

MD•–

•–

•–

•–

•–

Hierarchy of Protein Dynamics

10-15 10-12 10-9 10-6 10-3 100 103 106femto pico nano micro milli second hour day

bondvibration

methylrotation

loopmotion

domainmotion

protein folding

slow dynamics

side chain rotamers

drug binding

Conventional MD Simulations

Enhanced Sampling, Ensemble Simulations, etc.

Basin around open structure

eq. MD eq. MD

Umbrella Sampling MD

µs - ms

Method: umbrella sampling simulations

Conformations

Free energyBasin around closed structure

Method: umbrella sampling simulations

Conformations

Free energy

MD

MDReplica Exchange Umbrella Sampling (REUS )

Reaction Coordinate

Method: umbrella sampling simulations

Conformations

Free energy

Reaction Coordinate

Free Energy Simulations

open close

1. Initial Path

2. Umbrella Sampling SimulationsFor each intermediates along path, simulations with restraint,

3. WHAM

Weighted Histogram Analysis Method was used for removing restraints and calculating free energy profiles along structural transition between open and closed conformations.

C.L. Brooks PNAS (2007)B. Roux JACS (2005)

w j = K rmsd (ΔDrmsd − ΔDmin )2

ΔDrmsd = rmsd(X,Xopen ) − rmsd(X,Xclosed )

was carried out.Restraint potential is applied to both main chains and side chains.

Nudged Elastic Band

Free Energy Profiles for Open-Close Transition

open close

blue: openyellow: closedgreen: ATP

ü Meta-stable state is found:ATP-bound open conformation.

encounter complex

open close

Ito, Oroguchi, Ikeguchi, JACS, 133, 3372 (2011)

transition: H-bond in P-loop

Open Closed

H-bond partner of Asp256 is changedfrom Lys162 to Thr163 (P-loop).Mutation of Asp256, Lys162, or Thr163 results in remaining open conformation even with ATP bound.

MD•–

•–

•–

•–

•–

•– NMR SAXS

MDMD

MD

MD

ØØØ

MD

Ø MDØ MDØ

MD

MD

Yamane, Okamura, Ikeguchi, Nishimura, Kidera, Proteins, 71, 1970 (2008)

PhoBDNA

CNS NMR

MARBLE NMRCHARMM27/CMAP

PME300K→800K→0K

the same water position in

NMR and crystalstructures

control DNA binding activity

Water-mediated interactions between PhoB and DNA

Glu159

red lines: NMR structuresgreen lines: crystal structures

MDMD

MD

MD

ØØØ

MD

Ø MDØ MDØ

MD

( )

2

222 3 12 2

, , ,

i jr rr

S tr tr

i j x y z

F =

= F - F

=

ij

N

H

rC

H

r

C

H

S2NH S2axis

H

NMR: Order Parameterbackbone side chain

NMR provides information on dynamics of both backbone and side chains.

Order parameters (S2) represent the amplitude of fluctuation of bond vectors.

MD simulations without any restraints were conducted for 10 ns x 20 structures.

Calculated S2NH and S2

axiswere compared with experimental data.

Best, Clarke, Karplus, J. Mol. Biol. 349, 189, (2005)

Model-free order parameter S2NH-backbone dynamics-

R=0.91

R=0.88

« Agreement with experiments« Small changes between

free and complexexcept for β6-β7 loop

« Flexible regions:ütransactivation loop

(α2-α3 loop)üArg172 in β5üβ3-β4 loop

Yamane, Okamura, Kidera, Nishimura, Ikeguchi, J. Am. Chem. Soc.132, 12653, 2010

Calculations of I(q) at t = tn

MD Simulation

2q

ProteinSolution

Simulation time

Average of I(q): I(q)MD-SAXS

Structure ensembleof protein

t=t1I(q)

q

q

Principle of MD-SAXS

InitialStructure

t=t2 t=tn

SAXS

q

q q

CompareI(q) I(q)

……

……

I(q)EX

PDB id: 2ZLCPDB id: 2ZXM

Coactivator

/

VDR

Helix 12

Helix 12

VDR

1,25D3 /rVDR-LBD

H12

JB/rVDR-LBD

12

H12

D

Antagonist

I(q)EX

SAXS Ab-initio

χ=0.8

Antagonist

χ=0.7I(q)EX

Ab-initio

GASBOR Ab-initio

AgonistPDB id: 2ZLC

Antagonist

PDB id: 2ZXM

Helix12

H12 H12

DY. Anami, N. Shimizu, T. Ekimoto, D. Egawa, T. Itoh, M. Ikeguchi, and K. Yamamoto; J. Med. Chem. 59, 7888 (2016).

MD-SAXS

MD

MD

SAXS

MD

χ=0.29χ=0.8

MDχ

Apo 100 ns

H11

100 ns MDχ

D

MD-SAXS

MD

MD

SAXSAntagonist

Antagonist

MD

χ=0.29χ=0.7

χ

100 ns MDχ

D

Loop11-12

まとめ• 生体分子の動きが機能に重要• 分子動力学シミュレーションでは、様々な力

場が提案され、今も継続して改良中である• 分子動力学シミュレーションの解析は、その

機能ごとに様々である‒ 例：RMSD, RMSF, 相関行列, PCA等

• 分子動力学シミュレーションは、様々に応用されている。‒ 実験との連携も重要な点‒ 超並列計算への展開：レプリカ系の計算