Molecular Simulations of Biomolecules. Using Groningen Machine for Chemical Simulations (GROMACS)

Transcription

1 Molecula Smulaons of Bomolecules Usng Gonngen Machne fo Chemcal Smulaons (GROMACS)

2 Molecula Dynamc Smulaons: Sascal Mechancs of Classcal Sysems Assumpon: Classcal descpon s adequae fo he sysem unde obsevaon. Knec enegy Poenal enegy ρ ( q, p) H( q, exp KbT Q p) dq H( q, dpexp KbT p) Ensemble Aveage A τ 1 (, )d τ 0 ( q, p ) A q () p () Tme Aveage Egodc hypohess

3 Molecula Dynamc Smulaons Compue foces fo a gven confguaon usng Foce felds Foce Feld consss of paamees and funcons Bonded Ineacons Non bonded Ineacons Solve Equaon of Moon Compue Foce, veloces and acceleaon Scalng faco facos fo velocy and volume Apply Consans

4 Poenal Enegy Funcon Foce Felds: Relaes a gven confguaon o enegy Bonded Ineacons + Non Bonded Ineacons Bonded Ineacons Bond V Covalen b 1 (, ) k ( b) j b j Angle Va Bond 1 (,, ) k ( θ θ ) θ j k 0 θ accos j j j kj Dhedal Angle V d V ( φ) kφ ( 1+ cos( nφ φ )) 5 ( φ) ( cos( φ) ) n d C n n 0 0 φ accos n j m jk kj n nmmlk Impope Dhedal 1 ( ξ ) ( ξ ξ ) ξ V d jkl k jkl 0

5 Poenal Enegy Funcon Non bonded Ineacons Pa addve Lennad Jones v LJ 1 6 C () 1 C σ σ 6 4ε 1 6 Coulomb Ineacon v C () q q 4πε 0 ε j Reduce N Complexy by usng Cu offs Swchng funcons o swch he foces off a cu off dsances

6 Poenal Enegy funcon: Lennad Jones Ineacons Cu off s long enough ha epulson em can be negleced V l 1 Nρ 4π 0 g ( )d () V () V () c Fo plan cu off and g() 1 beyond c V l 3 πnρc6c 3 Aveage dspeson consan fo homogeneous mxues N N C C N, 6 6 ( N 1) j> ( j)

7 Poenal Enegy funcon: Coulomb neacons Aoms ousde he cuoff ae eplaced wh delecc connuum. Aoms nsde he cuoff nduce a eacon feld n he connuum ha s added o explc Coulomb neacons beween he cenal aoms and hose whn cuoffs. V cf q q ε ε q q 3 j f j ε j ε f + ε c 4πε0 πε ε c ε f + ε j 3ε f

8 Poenal Enegy funcon: Coulomb neacons Lace summaon: Poenal s spl no sho ange and long ange. Long ange poenal (n PBC) s epesened by fs few ems of s Foue sees. 1 1 qq ' j UC n4πε 0, j 1 n j + L qδ( ) q ( ) w( ) + qw( ) [ δ ] 3 β w () e 3/ π U U + U U 1 1 ( β ) s l C C C efc ( β ) j + L s ' C 4πε 0, j 1 n j + L l ( ) 1 nk k j β C j exp ε0v, j 1 0k 4β 4πε k 0 π U qq e q n

9 Foce Feld Types All aom foce felds: All aoms ae explcly Modeled OPLS (Opmzed Poenals fo lqud Smulaons) CHARMM ( Chemsy a HARvad Macomolecula Mechancs) AMBER (Asssed Model Buldng wh Enegy Refnemen) Uned aom Foce Felds: Alphac and aomac hydogen aoms ae ncluded mplcly n by epesenng cabon aoms and aached hydogen as sngle goup GROMOS Coase Ganed Foce Felds: Mulple aoms ae epesened by a sngle bead MARTINI

10 Equaon of Moon Leap fog algohm () ( ) ( ) Δ Δ Δ + Δ Δ + v m v v F Velocy Vele algohm ( ) () () ( ) () ( ) ( ) () ( ) [ ] m v v m v + Δ + Δ + + Δ Δ + Δ + Δ + FFF Consans ( ) ( ) ( ) ( ) () () [ ] () k K k k c c u N k m K k + Δ + Δ + + Δ σ λ σ ; )... (FFF( ) k K k k m Δ Δ σ λ 1 ( ) 0 d σ

11 Tempeaue and pessue couplng T N m v 3Nk B 1 Beendsen Themosa and Baosa 1 P + F 3V E kn j j dt T0 T d τ Δ T λ 1+ τ 0 T T Andesen Themosa Nose Hoove Themosa dp P0 P d τ 3 Δ χ 1 β τ ' χ 3 V ' χ V ( P P) Panello RahmanBaosa 0

12 Open Souce Fee Fas Tons of analyss ools Acve developmen Gomacs

13 GROMACS: fles and pogams Cysal Sucue fom PDB daabase (.pdb) Foce Feld Paamees ($d/shae/gomacs/op) Run npu paamees (.mdp) gompp pdbgmx Molecule s Topology (.op,.p) Run npu fle (.p) mdun Oupu fles (.xc,.,.xvg)

14 Foce Feld Paamees ($d/shae/gomacs/op) ffoplsaa.p Use LJ funcon [ defauls ] ; nbfunc comb-ule gen-pas fudgelj fudgeqq 1 3 yes #nclude "ffoplsaanb.p" #nclude "ffoplsaabon.p" ffoplsaanb.p and ffoplsaabon.p conans non bonded and bonded paamees fo he poenal enegy funcon, especvely Geneae 1 4 usng FudgeLJ and FudgeQQ Covalenly bonded aoms wh n molecules ha ae closed by n he chan, canno be modeled by LJ neacons and ae heefoe excluded (, +1, +) Fo he hd neghbou neacons ae scaled Type of C emnal (ffoplsaa c.db ) Type of N emnal (ffoplsaa n.db) Hydogen daabase (ffoplsaa.hdb) Bonded paamees fo esdues (ffoplsaa.p) pdbgmx Molecule s Topology (.op,.p)

15 Example: Smulaon of WLXLL pepdes a cyclohexane wae neface Am: To elucdae he paonng pefeences of sde chans of X ; Include focefeld paamees #nclude "ffoplsaa.p #nclude poen.p ; Include wae opology #nclude "spce.p ; Include genec opology fo ons #nclude "ons.p ; Include cyclohexane opology #nclude "cyhex_mod.p [ sysem ] ; Name Poen a neface [ molecules ] ; Compound #mols Poen K+ 4 SOL 943 chex 409 Inal Confguaon Topology fle

16 Example: mdp fle negao md d 0.00 ; me sep nseps ; numbe of seps nscomm 1 ; ese c.o.m. moon comm_mode lnea nsxou 1000 nsxcou 1000 nsvou 1000 ; we veloces nslog 1000 ; pn o logfle nsenegy 1000 ; pn eneges nsls 10 ; updae pals ns_ype gd ; pals mehod coulombype pme fouespacng 0.1 pmeode 4 ewald_ol 1.0e 6 ewald_geomey 3d consans all bonds consan_algohm lncs vdw ype swch vdw swch 0.9 vdw 1.1 ; cu off fo vdw ls 1. ; cu off fo ns coulomb 1. ; cu off fo coulomb Tcoupl beendsen ; empeaue couplng ef_ c gps SOL_IONS CYC au_ Pcoupl beensen ; pessue bah Pcouplype semsoopc ; pessue au_p.5.5 ; p couplng me compessbly 0 4.5e 5 ef_p 1 1 gen_vel no ; geneae nal veloces ;gen_vel yes ; geneae nal veloces ;gen_emp 300 ; nal empeaue ;gen_seed 1993 ; andom seed pbc xyz gompp f sample.mdp p opology.op c confguaon.go o mdun npu.p n ndex.ndx mpun np numbe_of_pocessos mdun s mdun npu.p

17 Smulaon of WLXLL pepdes a cyclohexanewae neface gompp Run npu fle (.p) mdun Oupu fles (.xc,.,.xvg) gaj, gdens COM of sdechan as funcon of me Densy as funcon of poson

18 Fee Enegy: Example Measung Wmley Whe hydophobcy scale Wmley & Whe measued paonng of Ac WLXLL no LUV membanes of POPC Expemens WLXLL ne ΔG WLXLL WLXLL bulk WLLLL ne ΔG WLLLL WLLLL bulk WLLL ne ΔG WLLL WLLL bulk ΔΔ G ΔG ΔG Leu WLLLL WLLL esdue Δ G ΔΔ G + ( ΔG ΔG ) X Leu WLXLL WLLLL

19 A β 1 ln QNVT (,, ) Alchemcal Smulaons V( λ) (1 λ) V + λv [ V( ) V( )] 1 β λ+δλ λ A( λ+δλ) A( λ) β ln e da V dλ λ Fee enegy calculaons λ A B λ Fee enegy peubaon mehod Themodynamc negaon mehod ( ) ( ) ( ) Δ A ξ A ξ A ξ β 0 ( ξ ) ( ξ ) 0 1 ln ( ξ ) ( ξ ) 1 Δ A( ξ ) β ln + [ U( ξ) U( ξ0 )] 0 Umbella Samplng Modfy ognal PEF by addng basng poenal

20 Themodynamc negaon: Example WLXLL ne Expemens ΔG WLXLL WLXLL bulk WLXLL Ine ΔG A1 Smulaon ΔG WLXLL WLXLL Bulk ΔG B1 WLLLL ne ΔG WLLLL WLLLL bulk WLD X LL Ine WLD X LL Bulk ΔG A ΔG B WLLL ne ΔG WLLL WLLL bulk WLALL Ine ΔG WLALL WLALL Bulk ΔΔ G ΔG ΔG Leu WLLLL WLLL esdue Δ G ΔΔ G + ( ΔG ΔG ) ΔΔ X Leu WLXLL esdue G ΔGWLXLL ΔGWLALL WLLLL esdue G GWLXLL GWLALL ΔΔ Δ Δ ΔG ΔG ( ΔG ΔG ) A1 A B1 B ΔG ΔG ( ΔG ΔG ) A1 B1 A B ΔG ΔG X ALA

21 Example: op fle and mdp fle [ aomypes ] ; Dummy aoms added fo fee enegy calculaons dum_sc4 SC A e e 00 [moleculeype] ;molname exclusons Poen 1 [aoms] ;N Type esn esdue aom cgn chage mass ypeb chageb massb. 9 SC4 3 PHE SCSC dum_sc SC4 3 PHE SCSC dum_sc SC4 3 PHE SCSC dum_sc fee_enegy yes n_lambda 0.00 sc_alpha 0.5 sc powe 1.0 V() (1 λ) V ( ) + λv ( ) p 6 A ( cλ + ) sc sgma 0.47 B ( p ( ) ) 6 1 λ c + A A B B 1/6 1/6 Modfes LJ neacons a all nemedae λ o avod sngulay c 6 ασ

22 Themodynamc negaon: Example Cyclohexane wae neface Smulaons ΔG WLFLL WLFLL ne WLFLL bulk ΔG A1 ΔG B1 WLF d LL ne WLF d LL bulk ΔG A ΔG B WLALL ne ΔG WLALL WLALL bulk ΔΔ Δ Δ esdue G GWLFLL GWLALL ΔG Δ G +ΔG ΔG A1 A B B ( 3.6) + ( 4.6) kJ/mol λ 1 dv Δ GA 1 λ 0 dλ 36.8kJ/mol

23 Umbella Samplng pull umbella pull_geomey poson pull_dm N NY pull_nsxou 10 pull_nsfou 0 pull_ngoups 1 pull_sa no pull_goup0 CHEX pull_goup1 Poen pull_vec pull_n pull_k1 1000

24 Umbella Samplng Smulaons ΔG WLFLL WLFLL ne ΔG A1 WLFLL bulk ΔG B1 WLF d LL ne WLF d LL bulk ΔG A ΔG B WLALL ne ΔG WLALL WLALL bulk ΔΔ Δ Δ esdue G GWLFLL GWLALL kJ/mol

25 Assumpon: Classcal descpon of he sysem s adequae fo he sysem unde obsevaon. Fne sysem sze (pocess nvolvng phase ansons) Samplng

26 Refeences Allen, M. P. & Tldesley, D. J. (1989), Compue Smulaon of Lquds, Oxfod Unvesy Pess, USA. GROMACS 4.0 Manual. Fenkel, D. & Sm, B. (001), Undesandng Molecula Smulaon, Academc Pess. Leach, A. R. (001), Molecula Modellng pncples and applcaons, Pence Hall. Chpo, C. & Poholle, A., ed. (007), Fee Enegy Calculaons. Theoy and Applcaons n Chemsy and Bology, Vol. 86, Spnge. Oen M. Becke, Beno Roux, M. W., ed. (001), Compuaonal Bochemsy and Bophyscs, CRC.