...Free Energy Simulations open close 1. Initial Path 2. Umbrella Sampling Simulations For each...
Transcript of ...Free Energy Simulations open close 1. Initial Path 2. Umbrella Sampling Simulations For each...
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
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–
–
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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•–
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•– 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•–
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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•–
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Interaction between ligand and protein
Isobe, YI, MI, Arita, Sci. Rep. 8: 7951 (2018)
Interaction between CYP1A2 and EPA
MD•–
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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•–
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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•–
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•– 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