The Polarizable Pseudo-Particles Solvent Model

Transcription

1 LAMBE, UMR 8587 The Polarzable Pseudo-Partcles Solvent Model Nathale Basdevant, Tap Ha Duong, Danel Borgs LAMBE, Unversté d Evry and CNRS (UMR 8587) Ateler CFBo, 14 Ma 006

2 Solvaton: Some ssues

3 Solvaton: Forces n play Dfférent water molecules: The bulk Frst solvaton shells Lnked, specfc molecules Three keywords: Hydrophobc nteractons Electrostatc nteractons Hydrogen bondng

4 Coarse-graned models (mplct solvent) Macroscopc descrpton (electrostatcs, ) Φ( r) Explct solvent

5 Coarse-graned models (mplct solvent) Classcal DFT ρ( r), Polarzable Pseudo- Partcules (PPP) Explct solvent

6 Les méthodes de solvant mplcte L approxmaton délectrque contnu (Posson-Boltzmann) ε = 80 ε = ε φ( r) [ ε ( ) φ( r) ] = 4πρ ( r) r 0 électrostatque + hydrophobcté F 1 = dr ρ 0 r + ()() r φ γ A Surface accessble au solvant Méthode PB-SA: Posson-Boltzmann/Surface Area ou GB/SA ou autres (avec approxmatons supplémentares) γ = 0.05kJ / Mol / A

7 Forces hydrophobes: vson mult-échelle Davd Chandler, Nature, 417, 491 (00) + nsght revew artcle Hydrophobcté dfférente à pette et grande échelle a < 1 nm a > 1 nm Effet entropque Effet enthalpque

8 = tenson superfcelle G solv = γ A γ 0.5 kj / Mol / A G solv = α V

9 Dzubella, Hansen, JCP, 003 F contact = Cγ R Théore macroscopque: C = 4,8 Dynamque moléculare: C= 3,9

10 Polarzaton densty functonal Electrostatcs can be dscussed n terms of the Polarzaton densty P(r), and the Non-Local Polarzaton free-energy Functonal (NLPF) F NL [ P( r )] 1 P( r ) 1 = dr dr P( r ) E 0 χ () r () r drdr' P( r ) T( r r' ) P( r' ) ( r) = ( ε ( r) 1) / π = χ 4 E 0 ( r) = T( r r' ) solute electrc feld = dpolar tensor electrc susceptblty ε s _1 χ = 4π χ = 0 See Marcus (56 ), Felderhof (77 )

11 Polarzaton densty functonal (Cont.) Mnmzng wth respect to P(r) P( r) = χ ( r) E( r) Consttutve equaton ( r) + dr T( r r') E( r) = E0 P( r' ) Maxwell feld Equvalent to Posson equaton [ ε( ) Φ( r) ] = 4πρ ( r) r 0

12 Polarzaton densty functonal (Cont.) F NL [ P(r) ] can be represented on a 3D-grd and mnmzed Usng conjugated gradents Usng on-the fly Car-Parrnello technque, wth fcttous dynamcs of P(r) coupled to real dynamcs of the atomc coordnates. P(r), ρ(r) M. March et al. Delectrc contnuum Molecular Dynamcs (DCMD), J. Chem Phys. (001) Can be generalzed to more refned functonals F [ ρ( r), P( r) ] «hydrophobc» and electrostatc contrbutons ncludng both R. Ramrez et al Densty functonal theory of solvaton n polar solvents, Phys. Rev. E (00), J. Phys. Chem. B (005).

13 Polarzaton densty functonal Non-Local Polarzaton free-energy Functonal (NLPF) F NL [ P( r )] 1 P( r ) 1 = dr dr P( r ) E 0 χ () r () r drdr' P( r ) T( r r' ) P( r' ) ( r) = ( ε ( r) 1) / π = χ 4 E 0 ( r) = T( r r' ) solute electrc feld = dpolar tensor electrc susceptblty ε s _1 χ = 4π χ = 0

14 The Coulomb feld approxmaton Suppose longtudnal polarzaton: P( r) = f ( r) Local Polarzaton free-energy functonal F L [ r) ] At the mnmum ( r) 1 ε P( r) ( = r r P( r) E d d χ P 0 ( r) () r () r () r χ 1 1 P( r) = E r ε 8π ε ( r) ths amounts to: r) E ( r) () r, = dr 1 E ( 0 F L 0 ) D 0 ( = CFA See computaton of self-energes n GB method

15 Coulomb feld approxmaton: Tests 196 confguratons «Varatonal» CFA «Renormalzed» CFA

16 Polarzable PseudoPartcles model Contnuous functonal «Coarse-graned» functonal ρ(r), Functonal represented on a (fne) grd. Boundary problem between contnuous and dscrete world Functonal represented by dscrete pseudopartcles wth par nteractons yeldng correct thermodynamcs and electrostatcs All-partcle algorthms

17 R k, q k r, µ Polarzable PseudoPartcles model V ( r, µ ) = Φ k ( Rk ) + Φ ss ( rj ) + Fel ( r, µ ; R k ), k < j Two parameters σ s and ε s : ftted on compressblty and lqud-gas surface tenson of water

18 R k, q k r, µ Polarzable PseudoPartcles model V ( r, µ ) = Φ k ( Rk ) + Φ ss ( rj ) + Fel ( r, µ ; R k ), k < j Nonlocal model Local model F el ( r µ, µ ; R k ) = µ α T( r r j ) µ j µ < j E q ( r ) Fel ( r, µ ; R k ) µ = µ α eff E Q ( r Q= «dressed» charges ) 4π ρα = 3 x( ε 1) 9ε ε + + ( x 1) ε + 1 4π ( ε 1) ρα eff = 3 3ε

19 Applcaton of the PPP solvent model: MD smulaton of RNA Antcodon loop of trna 17 nucleoddes, helx + loop Extremely senstve to solvaton and extremely charged (16 Na + ) Comparson of «on-the-fly» electrostatc free-energy to contnuum delectrc calculaton

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22 Proten and solvent coarse-graned models U j λj ε j rj 6 rj exp σ j =

23 CG solvent model: Electrostatcs

24 CG solvent model: Hydrophobc nteractons

25 Concluson The «smplest» partcle-based model ncludng electrostatcs. Presently scales as N N p In development: s -- Numercal scalng N p -- Estmaton of hydrophobc free-energes -- Hard-core MD smulatons of proten-proten assocaton... Haduong et al, J. Chem. Phys. (00), Basdevant et al, J. Comp. Chem. (004), JCTC (006).