Solvation Models for Protein Folding
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Transcript of Solvation Models for Protein Folding
Solvation Models for Protein Folding
서울대학교 화학부석차옥
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Water, everywhere!
지구 표면의 70%인체의 70%
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Water in Cell
But usual solvation model is
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Solvation Model is Important for
Protein Folding
Protein-Ligand Interaction
Protein-Protein Interaction
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Levels of Solvation Models
Continuum
(implicit water)
Molecule
(explicit water)
Surface area
Continuum electrostatics
Fixed charge models
Polarizable models
+ -++
+
--
-
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Explicit Water Models
• 용매 ( 물 ) 분자와 용질 분자 모두 explicitly 고려• Solvation effect 는 저절로 얻어짐• 계산이 비쌈 (90% 이상이 용매 계산에 소요 . 용매의 자유도에 대한 average 필요 )
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Some Fixed Charge Water Models
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Limitations
• Polarizability
• Water in first solvation shell, active site or interior (Bulk 와 다름 )
• Bond flexibility
• Temperature dependence
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Implicit Models
:)(solv iG r A Model for Solvation Free Energy
)()()( solvvac iii GEE rrr )()( vac ii EE rr
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Surface Area Based Models
Eisenberg and McLachlan, Nature 1986
i
iiAG solv
atom i of area surface accessiblesolvent :
atom i of tension surface :
i
i
A
Simple & fast
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Distance Dependent Dielectric
보통
ji ijij
ji
rr
qqGE
,Solv Coulomb )(4
rr )(
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1
: heuristic
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More sophisticated continuum dielectric models (PB, GB)
Cavity
1
80
+-
-
+
+-
SA vac GEE
charging
GB)(or PB SA vac GGEE
Partial charge
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PB (Poisson-Boltzmann)
• Solvent as a continuum dielectric: 이 가정 하에서는 정확
• 물 분자의 크기에 대한 고려는 없음 . (first-shell solvation effect 는 무시됨 )
• 미분 방정식을 수치해석적으로 품 . (Delphi)
Poisson part Boltzmann part
)(4)](sinh[)()( rrrr
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Poisson part of PB
(Reduces to Coulomb’s law for constant dielectric)
)( and )(Given rr )(for olve rSsolvG
)(4)()( rrr
ions) charges, partial(protein density charge :)(
potential ticelectrosta :)(
constant dielectric :)(
r
r
r
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Ion Contributions
Debye-Huckel Theory:
In 1:1 salt solution:
kTqii
ie /)(0 )()( rrr
Ionic density in bulk soln
kTee kTkT )(
sinh2)()()( 0/)(0/)(0ionic
rrrr rr
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Boltzmann part of PB
Nonlinear PB equation
Linear PB equation: when ionic strength is not high
)(4)](sinh[)()( rrrr
)(4)()()(
)(6
)()()(sinh
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rrrr
rr
rr
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Finite difference solution of PB
Grid size: Focusing
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GRASP
Red: negativeBlue: positive
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Examples of Application
Binding Dynamics
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GB (Generalized Born)
• Solvent as a continuum dielectric: PB 보다 계산이 빠르나 approximate (PB 결과를 아주 잘 근사하게 parametrized)
• Environment specific DDD 로 생각할 수 있음
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Born Radius
R
qGsolv
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2
1
211
2
1 qGsolv
Exact for a sphere of radius R
Effective Born radius
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GB Solvation Free Energy
i ij
pairij
i
selfisolv GGG
ji
ijjiij
jipairij
rr
qqG
4exp
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2extint
i
iselfi
qG
2
extint
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2
1
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How to get Born Radius?
selfi
i
i
i
ii
Gq
dq
E
2
extint
4
2
extint
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2
1
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3R
rR
• Volume integral• Surface integral• Analytical approximations
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EEF1
ij
jijirefi
slvi VrfGG )(
)exp(4)( 22iii xrrf
i
ii
Rrx
i
slvi
slv GG
Vj용질이 용매의 부피를 대체함으로서 발생하는solvation free energy 의 변화 고려 .
assumed to be Gaussian
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Successful example of use of EEF1
The best in the 10 year history of CASP ab initio prediction
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Break down of implicit solvation models
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Summary: Solvation Models
Implicit
Explicit Fixed-charge explicit solvent
Surface areaDistance dependent dielectric
EEF1
Generalized Born
Poisson-Boltzmann
Mo
re P
hys
ical
, M
ore
ex
pen
sive
단백질 구조예측
Dynamics Simulation
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Thank You, andEnjoy Water!!!