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

+ -++

+

--

-

=80

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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 )(

80

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

3

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

80

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Born Radius

R

qGsolv

211

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

11

2

1

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How to get Born Radius?

selfi

i

i

i

ii

Gq

dq

E

2

extint

4

2

extint

11

2

1

11

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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!!!