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1 Supplmtary Ifrmati Cctrati-Dpdt Bidig f Small Ligad t ultipl Saturabl Sit i mbra Prti Ltícia Stck, Juliaa Hum ad Wrr Trptw Labratóri d Bilgia Tórica Cmputacial (LBTC, Uivridad d Braília DF, Brail SUPPLEENTARY ATERIALS AND ETHODS mbra Equilibratd Chal Structur. Th Kv. tructur i th p tat wa btaid frm Trptw ad Tark. Th ctruct wa prviuly acquird via mlcular dyamic (D imulati f th publihd x-ray crytal tructur. dlig dtail ad validati ca b fud i th rigial papr. Th chal tructur wa mbddd i th lipid bilayr fr D rlaxati ad ubqut mlcular dckig f vflura. Spcifically, th tructur wa irtd i a fully hyatd ad utral (zwittriic all atm palmityllylphphatidylchli (POPC phphlipid bilayr. Aftr ambld, th macrmlcular ytm wa imulatd vr a D imulati paig ~ 0, at ctat tmpratur (300 K ad prur ( atm, utral ph, ad with applid T lctrtatic pttial. Th chal tructur rmaid tabl i it tartig p cfrmati thrughut th imulati. I th Kv. imulati, th rt ma-quar dviati (rmd valu fr th whl T dmai, a wll a fr gmt S5S6 (pr ad th S4S5 likr, rag frm.0 t 3.5 Å, which agr with th tructural ift quatifid i prviu imulati f th chal. lcular Dckig. Uig AutDck Via,3 vflura wa dckd agait a D-gratd mbl f 00 tructur f th chal. Dckig luti wr rlvd with a xhautiv paramtr f 00, by archig a bx vlum f 50.0 x 50.0 x 00 Å3 ctaiig th pr dmai rgi f th prti rcptr (vltag r wr xcludd frm dckig. Svflura wa allwd t hav flxibl bd fr all calculati. Clutrig f dckig luti wa carrid ut fllwig a maximum ighbrhd apprach. lcular Dyamic. All D imulati wr carrid ut uig th prgram NAD.9.4 Lagvi dyamic ad Lagvi pit mthd wr applid t kp th tmpratur (300 K ad th prur ( atm f th ytm fixd. Th quati f mti wr itgratd uig a multipl tim-tp algrithm.5 Shrt- ad lg-rag frc wr calculatd vry ad tim-tp rpctivly, with a tim tp f.0 f. Al, pridic-budary cditi wr mplyd. Chmical bd btw hyg ad havy atm wr ctraid t thir quilibrium valu. Lg-rag lctrtatic frc wr tak it accut uig th Particl h Ewald (PE apprach.6 Th CHAR36 frc fild7 wr applid ad watr mlcul wr dcribd by th TIP3P mdl. 8 All th prti chargd ami acid wr imulatd i thir full-iizd tat (ph7.0. All D imulati icludig FEP calculati ( xt wr prfrmd lcal HPC facility at LBTC. Fr-Ergy Prturbati (FEP. Th xc chmical pttial μ aciatd with cuplig f th ligad frm ga pha t watr ad W aciatd with cuplig f ligad frm ga pha t it udr rtrait wr quatifid via FEP. Bcau cmputati f μ d t dpd up th chic f cctrati, lg a th am thrmdyamic tat i ud fr th luti ad ga pha, w timatd th xc pttial by cidrig vflura mlcul mbddd it a watr bx f 60 x 60 x 60 Å3. W wa cmputd hr by takig it cidrig th whl ligad-chal-mmbra ytm. All FEP calculati wr prfrmd i NAD.94 by cidrig th Charmm-bad paramtr fr vflura a dvid by Barbr t al.9 Startig frm chal-mmbra quilibratd ytm ctaiig bud vflura a rlvd frm dckig, frward trafrmati wr carrid ut by varyig th cuplig paramtr i tp f 0.05 (r fr cvrgc purp, i tp f 0.05 at fial tag f th prc. Each trafrmati th ivlvd a ttal f 80 widw, ach paig vr 35 tp f imulati. Fr th purp f imprvig tatitic, fr-rgy timat ad aciatd tatitical rrr wr dtrmid uig th impl vrlap amplig (SOS frmula0 bad at lat tw idpdt FEP ru. Spcifically fr ligad-prti calculati, th fr-rgy chag W fr igly-ccupid it wa cmputd a a FEP prc that ivlv ligad cuplig t a vacat it. Diffrtly, fr dubly-ccupid it, W wa cmputd a a tw-tp FEP prc ivlvig ligad cuplig t a vacat it W fllwd by bidig f a cd ligad at th prccupid it W. Bcau i a W tat fucti, th tpwi apprach i quivalt t a igl-tp prc ivlvig imultau cuplig f tw ligad t th prti it that i, W W +W. Th clvar mdul i NAD.9 wa ud t apply th harmic rtrait pttial wh cmputig th quatiti. A dcribd i th mai txt, th valu f W dpd th paramtr f th rtrait pttial adptd i th FEP calculati i., th rfrc piti f th ligad i th bud tat {R,..., R } ad th magitud f frc ctat {k,..., k }. By miimizig th ctributi f th rtrait pttial t th bidig fr-rgy W, Rux ad cwrkr dvid ptimum chic fr th paramtr

2 {R R,..., R R } ad {k 3β 3β,..., k } δ R δ R i which, R,..., R ad δ R,..., δ R ar rpctivly th quilibrium avrag piti fr ach f th bud ligad at it ad thir crrpdig ma-quar fluctuati. Hr, th paramtr wr timatd frm th dckig cfigurati pac ad th rultig frc ctat, i th rag f.0 t 0.0 kcal/ml/å, wr cidrd fr cmputati f th bud tat. Cvrgc f amplig. Hr, a pr-it maur fr th mbl f dckig luti ffctivly ampld i FEP wa dtrmid by quatifyig th vrlap ( A, B btw th cfigurati pac i bth calculati3 ( A, B tr(( A / B /, tr A +tr B / / fr A ad B dtig cvariac matric aciatd rpctivly t FEP ad dckig ampl at it ad, A ad B thir quar rt. Spcifically, A ad B wr dtrmid a ymmtric 33 cvariac matric fr ctrid piti R f th ligad at it T X (R R.(R R ad thir quar rt / / T X / R diag(λ /,λ, λ 3 R wr lvd frm th clum mar igvctr { Rl, R, R3 } f th rtati matrix R ad th aciatd igvalu { λl,λ, λ 3 }. Nt that th vrlap quati ( A, B i xpctdly fr idtical amplig ad 0 fr rthgal pac. Drivati f mai txt quati (5. Drivati f quati (5 i tadard ad fllw frm th crdiat trafrm (r ( R,Ω, I ivlvig th ctrid piti R, ritati Ω ad itral I dgr f frdm f th ligad. β W (R d r δr (r R... d r δ R (r R V d r N d r N βu (r N N β U (r + u (R β U (r + u (R d r V d r N d r N d r δ R(r R... d r δr (r R V d r δr (r R... d r δ R (r R V d r N d r N βu (r d rn d r N N d r N βu (r N N d r βu (R... d r βu ( R d r δ R(r R... d r δr (r R d r δr (r R... d r δ R (r R V β U (r + u (R d r N d r N β U (r β U (r + u (R d R βu (R... d R β u (R 3 ( π i β k i 3 d r δr (r R... d r δ R (r R V N N β U (r + u (R N d r N βu (r π ( βw i β k i I thi ca, th Jacbia f th trafrmati d t dpd th R dgr f frdm allwig fr cacllati f (Ω, I π 3 ctributi. Th ffctiv vlum ( thu rult frm th 3 -dimial Gauia itgral apparig i li 4. β ki i Drivati f mai txt quati (6. Th patial prcti alg th z dircti f th ytm hw i quati (6 driv a

3 ρ(z d R δ z (R z ρ(r+ d Rδ z (R z ρ (R max ρ A(z + ρ( δ V 0 d R δ z ( R z ρ ( R ρ A(z + ρ (z whr, A (zδ x Δ y i th ttal ara f th watr-mmbra rgi alg th Cartia x ad y dircti. Car-graiig vr tat O(,...,. Dcripti f th bidig prblm i trm f macrtat O( ca b f itrt fr macrcpic maurmt. Cidr ay macrtat O( f th ytm mappig a mbl f accibl tat O(,..., i which ligad bid th rcptr rgardl thir pcific ditributi vr th bidig it. Bcau O( i dgrat, th prbability dity f th macrtat ρ( δ, ρ(,...,,..., (S ca b dtrmid by car-graiig vr th rcptr tat O(,..., faturig xactly bud ligad. Hr, th Krckr dlta fucti δ, ur ummati vr tat accibl t O( ly. Th cquc i that th quilibrium ctat Κ( fr th prc O(0+ L O (, Κ( δ, Κ (,...,,..., (S ca b fully rctructd frm Κ(,..., ctat. Supplmtary quati (S ad (S ur th xti f th prviu rult t macrtat O(, whr ρ( ρ Κ( (S3 ρ Κ( giv th prbability dity ad Δ G ( β l Κ((C tablih th lik btw Κ( ad th tadard bidig fr-rgy Δ G ( aciatd t ach f th tat atifyig upplmtary quati (S.. Trptw, W. & Tark,. Evirmt f th gatig charg i th Kv. Shakr ptaium chal. Biphy. J. 90, L64-66 (006.. Lg, S. B., Campbll, E. B. & acki, R. Crytal tructur f a mammalia vltag-dpdtshakrfamily K+chal. Scic 309, ( Trtt, O. & Ol, A. J. AutDck Via: Imprvig th pd ad accuracy f dckig with a w crig fucti, fficit ptimizati, ad multithradig. J. Cmput. Chm. 3, ( Phillip, J. C. t al. Scalabl mlcular dyamic with NAD. J. Cmput. Chm. 6, ( Izaguirr, J. A., Rich, S. & Skl, R. D. Lgr tim tp fr mlcular dyamic. J. Chm. Phy. 0, ( Dard, T., Yrk, D. & Pdr, L. Particl mh Ewald: A N lg(n mthd fr Ewald um i larg ytm. J. Chm. Phy. 98, ( Huag, J. & ackrll, A. D. CHAR36 all-atm additiv prti frc fild: Validati bad cmpari t NR data. J. Cmput. Chm. 34, ( Jrg, W. L., Chaakhar, J., adura, J. D., Impy, R. W. & Kli,. L. Cmpari f impl pttial fucti fr imulatig liquid watr. J. Chm. Phy. 79, ( Barbr, A. F., Carval, V., Kli,. L., Eckhff, R. G. & Cvarrubia,. dulati f a vltag-gatd Na+ chal by vflura ivlv multipl it ad ditict mchaim. Prc. Natl. Acad. Sci., ( Lu, N., Kfk, D. A. & Wlf, T. B. Imprvig th fficicy ad rliability f fr rgy prturbati calculati uig vrlap amplig mthd. J. Cmput. Chm. 5, 8 40 (004.. Firi, G., Kli,. L. & Héi, J. Uig cllctiv variabl t iv mlcular dyamic imulati. l. Phy., (03.. Rux, B., Nia,., Pmè, R. & Smith, J. C. Thrmdyamic tability f watr mlcul i th bactrirhdpi prt chal: a mlcular dyamic fr rgy prturbati tudy. Biphy. J. 7, ( H, B. Cvrgc f amplig i prti imulati. Phy. Rv. E 65, 0390 (00.

4 SUPPLEENTARY FIGURES Supplmtary Figur. S. Cfigurati pac vrlap ( A, B btw FEP ad dckig calculati (cf. Supplmtary atrial ad thd. Nt that vrlap i largr tha 0.5 fr th marity f igly- (cya ad dubly-ccupid (gray it upprtig that FEP ampl uccfully th vlum δv dtrmid frm dckig. Supplmtary Figur S. Cl viw f vflura itracti it at Kv. at th S4S5 likr (A, S6P-hlix itrfac (B ad arby th lctivity filtr (C. Th mlcular urfac i ach f th bidig it i clrd by phyical-chmical prprti f th ctitutig ami acid: hyphbic (whit, plar (gr ad chargd (blu r rd. Nt that it (A ad (B ar primarily dhyatd hyphbic pckt whra th it arby th lctivity filtr i amphiphilic ad largly hyatd.

5 Supplmtary Figur S3. Avrag atmic ditac btw th ctrid f vflura ad phtlabld Kv. ridu. Ditac wr maurd cidrig mbl f bth quilibrium prti tructur iputd it dckig arch, ad vflura dckig p prtaiig t a giv bidig it. A highlightd i th imag, avrag ditac btw vflura gmtric ctr wh bud t S6P-hlix it ad Thr384 i 0.6±.Å; avrag ditac f th ligad wh bud t S4S5-likr it t ridu Lu37 ad G39 ar rpctivly 5.5±.Å ad 6.3±0.9Å.

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