BIOORGANIC &
`;\:iEDICINAL
`CHEM:ISTRY
`
`Pergamon
`
`Bioorganic & ~fcdicinal Chemistry 7 (1999) 851-860
`
`Estitnation of the Binding Affinities of Fl(BP12 Inhibitors Using
`a Linear Response Method
`
`Michelle L. Lamb,1 Julian Tirado-Rives and William L. Jorgensen*
`Depart111e11t ofC'he111istry, Yale Unfrersity, 1Vew Haw!n, C'T06520-8JU7, USA
`
`Received 15 September !998; accepted 2 November 1998
`
`Abstract---1\ series ofnon-inununosuppressivc inhibitors of FK506 binding protein (FKBP12) arc investigated using ~vlonte Carlo
`statistical 1nechanics si1nulations. These s1nall 1nolecu\es 1nay serve as scaffolds for che111ical inducers of protein di111erization, and
`have recently been found to have FK BPI 2-dcpendent ncurotrophic activity. A linear response inodel was developed for csti1nation
`of absolute binding free energies based on changes in electrostatic and van der \Vaals energies and solvent-accessible surface areas,
`which are accu1nulated during sin1ulations of bound and unbound ligands. \Vith average errors of 0.5 kcal/11101, this inethod pro(cid:173)
`vides a relatively rapid way to screen the binding of ligands 'Nhile retaining the structural infonnation content of 1nore rigorous free
`energy calculations.© 1999 Elsevier Science Ltd. 1\1! rights reserved.
`
`Introduction
`
`'!'he binding protein of the ilntnunosuppressant natural
`product FK506 (Fig. I) has been the target of extensive
`investigation by both bioche1nical and theoretical tech(cid:173)
`niques during the last 10 years. Discovery of the cis(cid:173)
`trans peptidyl-prolyl iso1ncrase (PPiase or rotatnase)
`activity of FKBPl2 (MW~ 12 kDa) led to dissection of
`the rota1nase 1nechanis111 1 4 and hopes for the rapid
`design of lo\V n1olecular \veight inununosupprcssant
`n1olccules that inhibited this activity. The crystal struc(cid:173)
`ture of FK506 bound to FKBP12 was crucial to this
`endeavor, as it de111onstrated that the pcptido1nin1etic a(cid:173)
`ketoa1nide and pipecolyl portions of the ligand \Vere
`buried but that n1uch of the 1nacrocycle re1nained
`exposed to solvent. 5 Ho,vever, in later studies rota1nasc
`inhibition \Vas found to be insufficient for inununosup(cid:173)
`pression; the FK506--1 .. KBPI2 con1plex associates \vith
`the surface of calcineurin (CN), a serine/threonine
`phosphatase, and hinders binding of subsequent pro(cid:173)
`teins in the T-ccll signaling patlnvay. 6 The "effector"
`region of FI(506, \Vhich contacts CN, is opposite the a(cid:173)
`ketoa1nidc-pipecolic acid 1noiety.7,8 Thus, the PPlasc
`inhibitors developed
`through structure-based design
`efforts (e.g. compounds 1-7 in Table I) formed a set of
`potential scaffolds
`for
`inununosuppressive effector
`con1ponents. 9•10
`
`Key words: Monte Carlo; linear response; FKBP12; rotamasc inhibi·
`tors.
`*Corresponding author. Fax: + 203-432-6299; e-mail: bill@adrik.d1em.
`yale.edu
`t Current address: Dept. of Phannaccutical Chemistry, University of
`California, San Francisco, Box 0446, San Francisco, CA 94143-0446.
`
`these non-itnn1unosuppressive FKBPl2
`Many of
`ligands are also able to protnote neuronal gro\vth in
`vitro and in vivo through binding to FKBP12. 11 " 13
`Dose-response studies of neurite outgro\vth in chick
`dorsal root ganglia resulted in an ED50 of 0.058 nM for
`co1npound 10, for exatnple. 11
`In addition, tethered
`ditners of n1olecules sin1ilar to 4 have been used to
`"chc1nically-induce" ditneriza ti on 14 of targeted cellular
`proteins that had been adapted to include FKBP12
`do1nains. 15 N1odiflcation of targets in appropriate sig(cid:173)
`naling path\vays can result in apoptosis or the induction
`of transcription; the prospects of this technology for
`gene therapy are intriguing.
`
`Consequently, \VC have used theoretical techniques to
`probe this class of small molecules (Table 1) to gain
`insight
`into
`the physical basis
`for differences
`in
`FKBPI2-binding activity and to evaluate ne\V n1ethods
`for the calculation of protein-ligand binding affinities.
`In previous \Vork, 16 re/a ave free energies of binding
`(1'1'Gb) for compounds 2, 4, and 8--10 were calculated
`by the free energy perturbation (FEP) technique using a
`Metropolis Monte Carlo (MC) algorithm for config(cid:173)
`urational san1pling. 17 'l'he para1netcrs and gco1nctry of
`one ligand \Vere transfonned into those of another \Vi th
`these si1nulations, both in solution and \Vhile bound to
`the protein. At each step of the transfonnation, the
`syste1n \Vas brought to equilibriun1 and the free energy
`difference relative to the previous step \Vas con1puted.
`The difference in binding free energy for the two ligands
`\Vas then found fro1n the difference in the total free
`energy change for each (bound and unbound) transfor-
`1nation. While theoretically rigorous and accurate, cal(cid:173)
`culations of this type arc con1putationally de1nanding
`
`0968-0396/99/S - see front mallcr C(: !999 Elsevier Science Ltd. All rights reserved.
`Pl/ S0968-0896(99)00015-2
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 001
`
`

`
`852
`
`,\/. L. Lamb et al./ Bioorg. ,\fed. Chem. 7 ( 1999) 851··860
`
`Meo 13
`
`MeO, 15
`,,,
`
`18
`
`9 04
`
`OH8 0 N7
`~02
`
`0
`
`QH Ol
`
`24
`
`:/
`
`31 OMe
`
`3l'OH
`
`Figure 1. The in1munosuppresent drug FK506.
`
`and i1npractical for a large set of structurally diverse
`ligand"
`
`An attractive alternative has e1nerged in linear interac(cid:173)
`tion energy or linear response techniques (LR), as
`recently revie\ved. 18 Unlike n1ost FEP calculations,
`ahsolute free energies of binding (.6.Gb) for protein(cid:173)
`ligand systen1s are esti1nated, and si1nulations of non(cid:173)
`physical states (interrnediatc steps) are not required. In
`other respects, the n1olecular dyna1nics (MD) or ~11C
`si1nulation protocols arc the satne.
`
`As first proposed, the linear interaction energy n1ethod
`c1nploys eq (I) for the estitnation or binding free encr(cid:173)
`gics.19
`.6.Gb = P{.6.ECoulomb} + o:{.n.ELenn.ird-Jom.•s)
`
`(l)
`
`These tenns represent the change in interaction bet\veen
`a ligand and its environ1nent (solvent and/or protein)
`upon binding. The electrostatic energy differences are
`obtained fro111 average Coulo1nbic interaction energies
`bct\veen the ligand and solvent (E~~~~;:b) and the ligand
`and protein (Ef~l:~t) accun1ulated during siinulations
`of the bound and unbound ligands. The Lennard-Jones
`(van der Waals) energy differences are found in an ana(cid:173)
`logous tnanner. 'fhe original value of p = 0.5 is con(cid:173)
`sistent \Vith analyses of the response of polar solutions
`to changes in electric fields, such as the charging of an
`ion in \vater. Observed linear correlations bet\veen the
`niolecular size (surface area, chain length) and salvation
`free energies of hydrocarbons suggested van der \\'aals
`interactions n1ight respond linearly as \Veil. ;\ scale fac(cid:173)
`tor a= 0.161 \Vas obtained e1npirically frotn fitting to
`cxperilnental binding data for a. stnall set of endothia(cid:173)
`pepsin inhibitors. 19 R.ecently, Aqvist and co-\vorkers
`have advocated the assignn1cnt of one of four reduced
`values of~ according to the charge-state or polarity of
`the ligand and have obtained an appropriate value for a
`by fitting to data for a larger set of protein-ligand
`pairs. 20 22 An extended linear response equation,23 •24 in
`\vhich a cavitation tenn based on solvent-accessible sur(cid:173)
`face areas (SASA) is added and all para1neters are
`e111pirically detennined, is given in eq (2) belo\v. This
`111odel \Vas first applied to the calculation of free energies
`of hydration for organic solutes; ho\vever, opti1nization of
`
`Tab!(' I. FKBPl2 inhibitors"
`
`Compound
`
`Ki.app. ni\'[
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`
`11
`
`186, 17ob
`
`110, 2sob
`
`250
`
`10, 17b
`
`7
`
`300-600
`
`300
`
`165, 13ob
`
`?,sh
`
`23QQC
`
`aRotamase inhibition data taken from refs 9 and 10 unless otherwise
`noted.
`hOata from ref 11.
`cK; reported !Or a mixture of Rand S isomers.
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 002
`
`

`
`,\[. L. Lamb et al./ Biaarg. Afed. Chem. 7 ( 1999) 851-860
`
`853
`
`scale factors to ~~0.131, a~0.131 and y~0.014 yielded
`acceptable esti1nates of thro1nbin-binding affinity as
`\Vell. 25 In addition, the extended linear response equation
`has potential for predictions of other properties in1portant
`for phannacological activity, such as the cstin1ation of
`ligand lipophilicity.24 It has been observed that the con(cid:173)
`tribution of the 6.SASA tennis often nearly constant, so
`the case in \Vhich the silnple addition of a constant
`improves the fit has also been considered [eq (3)]-'°.25
`
`b.Go = ~(.6.Ecoulomh} + a(.6.ELeunard- Jones}+ y(.6.SASi\}
`(2)
`
`In contrast to 1nost proteins studied previously \vith this
`technique, FKBP12 has a distinctly hydrophobic binding
`pocket lined \vith aro1natic residues, and only t\vo inter-
`1nolccular hydrogen bonds are observed in the crystal
`structure of inhibitor 4 \Vith the protein.9 Consequently, it
`\Vas expected that the electrostatic behavior of these 1nole(cid:173)
`cules n1ight deviate fron1 linear response and that the van
`der \Vaals contributions to binding n1ight be larger than
`previously observed for other syste1ns. To detennine the
`suitability of the linear response approxi1nation for binding
`to FKBP12, MC silnulations of the bound and unbound
`states for all 11 inhibitors in l'able I \Vere perfonned.
`
`Contpntational Details
`
`The 1nodeling strategy e1nployed here \Vas consistent
`\Vith the FEP study described previously, 16 based on the
`4-FKBP12 crystal structure (IFKG)9 and the OPLS
`force field. 26- 28 (A full listing of parameters for these
`molecules may be found in ref 29) The first five inhibi(cid:173)
`tors \Vere easily built fro1n 4. Ato1ns of the I-phenyl
`substituent \Vere si1nply re1novcd to obtain 2, and for
`co1npound 1, a united-ato1n cyclohexyl groupJo \Vas
`positioned in the plane of the original 3-phenyl ring.
`rfhc Vinyl group Of 3 \VaS also represented \Vith Unitcd(cid:173)
`atOIH paran1eters and \Vas positioned at the 1ninin1un1 of
`the CH3-C-CH=CH 2 torsional energy profile (180.0°)
`and aligned \Vith an edge of the 1-phepyl ring of 4.29
`One side of this ring \Vas \Vi thin 3.2 A of His87 and
`·ryr82 , \Vhile the other \Vas positioned 1nore than 3.5 A.
`fro1n Phe46 and Glu 54
`. Accordingly, the orientation
`\Vhich 1naxi1nized hydrophobic contact bet\veen the
`protein and 3 \Vas chosen. Inhibitor 5 incorporated the
`crystal structure orientations of the cyclohexyl and tert(cid:173)
`pentyl groups from 5-FKBP12 (IFKH). 9 In 1 and 5, the
`cyclohexyl groups \Vere treated as rigid units, as \Vere all
`ligand and protein arotnatic groups. It \Vas thought that
`the confonnational flexibility \Vithin the rings of these
`substituents \vould be less i1nportant to binding than the
`overall flexibility of the ligand, and thus sa1npling \Vas
`focused accordingly. Starting geo1netries
`for
`the
`unbound ligand siinulations \Vere
`taken front
`these
`initial bound confonnations.
`
`All si1nulations \Vere perfonned using the MCPR.0
`prognun and i\1onte Carlo configurational sa111pling. 31
`
`The ligands and protein-ligand co1nplexes \Vere solvated
`with 22A spheres of TIP4P water molecules. First,
`Ix 106 (IM) configurations of water-only equilibration
`\Vi th preferential sa1npling of n1olecules close to the inhi(cid:173)
`bitor was performed, followed by 16 M configurations of
`sa1npling of the entire syste1n \Vith all solvent 1nolecules
`sampled uniformly. Next, data was collected for 8 M
`configurations averaged in blocks of 2x 105 configura(cid:173)
`tions. ·ro ensure convergence, averaging for all unbound
`ligands \Vas extended to 16 1\rf configurations.
`
`To obtain protein-bound structures of 6 and 7, the final
`confonnations of 4 and 5 above \Vere cpi1ncrized \Vithin
`the FK BP 12 binding pocket via a slo\v perturbation
`protocol. Eight sequential double-\vide \Vindo\vs \Vith
`/'.),~ 10.0625 were used. ln each window, 4M config(cid:173)
`urations \Vere san1pled to slo\vly transfonn bet\vcen the
`t\vO ligands in an energetically reasonable \Vay. 'l'his
`procedure \Vas repeated \vith the free ligands in solution.
`'J'he si1nulations of ligands 8-11 \Vere started fron1 the
`final structures of FEP si1nulations reported pre(cid:173)
`viously.16·29 In each case, energy con1ponents \Vere
`averaged over 8 M
`I GM (unbound)
`(bound) and
`configurations of the syste111.
`
`As \vas 1nentioned above, the initial structure for 2 had
`been generated fro1n the bound confonnation of 4 \Vith the
`I-phenyl ato1ns re1noved. Follo\ving an FEP calculation
`fron1 4 to 2, further sa1npling \Vas carried out \vithin the
`first windows of both a phenyl~pyridyl FEP 16 and a car(cid:173)
`bonyl~hydroxyl FEP. 29 The final confonnations of these
`\Vindo\vs \Vere then used to start t\VO additional linear
`response N1C siinulations, 2a and 2b, respectively. These
`additional data points provide one gauge of precision.
`
`Solvent-accessible surface areas for the ligands in both
`aqueous and protein environn1ents
`\Vere calculated
`using the SA VOL2 prograin. 32 l'his algorith1n has been
`incorporated into tv1CPRO, and the necessary ato1nic
`radii are calculated fro1n the corresponding OPLS a
`paran1eters via 1/2 (2 116a). Using the standard solvent
`radius for \Valer, 1.4 A, the SASAs of the ligands \Vere
`calculated for the structure at the end of each block of
`i\1C configurations and \Vere averaged.
`
`Average energy and solvent-accessible surface area dif(cid:173)
`\Vere fit
`ferences
`to
`the cxpcri1ncntal binding data
`(Table l) to obtain linear response para1neters a, p, and
`y according to cqs (1)-(3). This procedure was per(cid:173)
`fonncd \Vith a Siinplex-based algorith1n. As inhibition
`data for the 1najority of the ligands in this set has been
`reported by Holt and co-\vorkers,9•10 in cases \Vhere t\vo
`the values fro1n
`these
`values have been 1neasured
`authors \Vere used for fitting.
`
`Results and Discussion
`
`1\ vcrage interntolcculnr energy contponents and SAS1\s
`
`Each ligand and protein-ligand con1plex \Vas solvatcd
`\vi th a sphere of explicit \Vater 1110\ecules and sa1npled as
`described above. Average energy con1poncnts and
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 003
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`

`
`854
`
`1\f. L. l.amb et al./ Bioorg. i\fed. Chem. 7 ( 1999) 851--860
`
`ligand SASAs accu1nulated during the sin111lations arc
`reported in Table 2. As has been observed with throm(cid:173)
`bin inhibitors, the ligand-solvent Coulon1bic energy
`con1ponents, Ef~~~~~;:b, fluctuate the n1ost during the
`siinulations. 25 Ho\vcver, both the 1nagnitude of the
`energy contribution and the 1nagnitude of the fiuctua(cid:173)
`lion are reduced co1npared to the positively charged or
`Z\vittcrionic protease inhibitors, as expected for the
`neutral ligands of this set. All of the ligands in solution
`have undergone hydrophobic collapse relative to their
`bound confonnations but to differing extents, as sig(cid:173)
`nificant flexibility is observed in the propyl side chain.
`The Lennard-Jones interactions for the o:-ketoa1nide
`1nolecules in solution scale generally \Vith molecular
`size; 1 and 2 (and 8-10) have the least favorable average
`energies, follo\ved by co1npound 3, and finally there is a
`s111all range of energies for 4-7. 'fhe solvent accessible
`surface area of an1ide carbonyl 03 is generally ca. IO A.2
`Jess than that of the keto (04) or ester (02) atoms, and
`usually only one \vatcr 1nolecule is found to interact
`\Vith 1nolecular
`this ato1n. This is consistent
`\vith
`dyna1nics results for trans-.FK506. 29 Often, 04 interacts
`stropgly \vith one \Yater 1nolecule (H-04 dist.ance, ca.
`1.8 A), while a second molecule hovers 0.5 A further
`a\vay. Also, \Vater 1nolecules are found to interact \Vith
`the faces of aro1natic rings. In the case of 2, an unusual
`long-lived salvation pattern is noted. The \Vater 1nole(cid:173)
`culc that hydrogen bonds to 03 further associates \Vith
`one directed into the center of the less-accessible face of
`the phenyl ring (Fig. 2).
`
`'f'ypical of 1nany FKBP12-ligand con1plexes,33 the crys(cid:173)
`tal structure of 4-FKBP12 contains contacts bet\veen
`
`Figure 2. The hydrogen bonding nelwork in 2, with waters that bridge
`between the amide 03 and phenyl ring.
`
`04 and aro111atic hydrogens of Tyr26, Phe36, and Phe99,
`\Vith the pipecolyl ring sitting over Trp59 •9 The 3-phe(cid:173)
`nylpropyl moiety binds in the solvent-exposed FK506-
`cyclohcxyl groove of FKBPJ2 between IJe 56 and Tyr82 ,
`and these residues fonn hydrogen bonds \Vith the ester
`and amide carbonyl oxygens of the ligand. The !-phenyl
`substituent interacts \Vith Phe46 and the tertiary pentyl
`group of the inhibitor. The two crystallographic inter(cid:173)
`n1olecular hydrogen bonds arc 1naintained throughout all
`of the FKBPI 2-ligand si1nulations, and none of the
`ligands deviates significantly fron1 the original orientation
`
`Tahir- 2, Average interaction energies (kcal/n10!) and solvent-accessible surface areas of the inhibitors (..\:2) from the aqueous and FKDPl2 l\·fC
`si1nulations 3
`
`Compound
`
`I aq
`IFKBP
`2 aq
`2n aq
`2h aq
`2FKBP
`2aFKBP
`2hFKBP
`3 aq
`3FBKP
`4 aq
`4FKBP
`S aq
`SFKBP
`6 aq
`6FBKP
`7 aq
`7FKBP
`8 aq
`8FBKP
`9 aq
`9FBKP
`10 aq
`IOFKBP
`11 aq
`llFKBP
`
`£-"oulomh
`'/--hd/U
`
`-23.16(0.32)
`-0.24(0.15)
`. -31.28(0.46)
`29.91 (0.35)
`-27.11(0.38)
`-5.15(0.31)
`-2.14(0.19)
`-1.62(0.19)
`-27.68(0.36)
`-1.41 (0.20)
`-31.89(0.42)
`-5.30(0.38)
`-28.43(0.50)
`-6.49(0.19)
`·-32.84(0.55)
`·-8.00(0.19)
`-29.64(0.34)
`-3.92(0.23)
`--30.53(0.43)
`-ll.5t(0.48)
`-29.88(0.50)
`-1.43(0.19)
`-33.45(0.40)
`-11.95(0.31)
`. 42.57(0.43)
`-2.72(0.34)
`
`EL-·1
`'l-kul<r
`
`-35.96(0.15)
`-15.09(0.12)
`-34.59(0.21)
`-33.90(0.16)
`-33.26(0.16)
`-13.74(0.09)
`-13.99(0.12)
`-13.95(0.14)
`-36.52(0.16)
`-15.31(0.13)
`-39.63(0.22)
`-17.84(0.11)
`-40.12(0.19)
`-16.54(0.10)
`-38.35(0.12)
`-18.10(0.13)
`-38.48(0.15)
`-16.10(0.15)
`-32.75(0.18)
`-12.03(0.15)
`·-31.67(0.17)
`-14.04(0.09)
`-32.89(0.22)
`-12.82(0. l 0)
`-31.24(0.21)
`-15.19(0.10)
`
`~oulc,mh
`/ .. n:.sP
`
`Ef:./KRP
`
`··19.14(0.16)
`
`··39.53(0.14)
`
`-19.73(0.21)
`-21.56(0.16)
`-20.97(0.20)
`
`-40.29(0.13)
`-38.01(0.17)
`-37.92(0.21)
`
`-21.15(0.20)
`
`-44.06(0.15)
`
`-21.25(0.15)
`
`-42.73(0.19)
`
`-20.58(0.14)
`
`··44.00(0.16)
`
`-17.26(0.15)
`
`-38.46(0.20)
`
`-17.09(0.18)
`
`-43.65(0.21)
`
`-18.03(0.16)
`
`-38.80(0.19)
`
`-23.59(0.16)
`
`-39.40(0.17)
`
`-·20.02(0.18)
`
`-38. 77(0.15)
`
`-18.23(0.151
`
`38.61(0.13)
`
`SASAb
`
`665.4(1.2)
`202.1(1.6)
`653.9(1.9)
`629.3(2.3)
`620.6(2.3)
`202.9(5.l)
`222.4(6.8)
`188.6(7.0)
`680.9(1.2)
`221.2(3.0)
`715. l( 1.4)
`248.8(2.5)
`728.3( 1.8)
`244.9(2.l)
`712.2(1.6)
`232.4(3.0)
`688.3(1.9)
`282.3(7.l)
`618.4(1.8)
`176.0(4.7)
`624.9(2.2)
`179.3(6.4)
`630.8(2.2)
`183.2(6.5)
`626.7(1.4)
`185.5(4.4)
`
`.
`"'The standard error of the means is given in parentheses.
`l'>C;llculated from slrw:Lures saYed every 2 x 105 configunttions, N = 40 (8 ,lf) or 80 (16 1\D. (Standard deviations range from 10-50 A 1
`
`.)
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 004
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`

`
`,\{. L. La111b et al./ Bioorg. ;\fed. Chem. 7 ( 1999) 851-860
`
`855
`
`of 4. In general, the aro1natic rings of the inhibitors are
`oriented perpendicularly to the ring ofTyr 82, although a
`clearly 'f-shaped interaction is not don1inant. Consistent
`with the hydrophobic binding pocket, the largest con(cid:173)
`tribution to the protein·-ligand interaction energy in all
`cases co1nes fro1n the Lennard-Jones tenns. In addition,
`the 1nost favorable van der \Vaals interactions \Vith
`FKBP12 are observed for the more hydrophobic 3, 5,
`and 7 co1npared to their 1nore aro1natic or s1naller
`counterparts.
`
`An estirnate of the prec1s1on of the sin1ulations \Vas
`dctennined fro1n the three sitnulations of 2 in solution.
`One model was derived directly from the 4-FKBP12
`crystal structure, while the others (2a and 2b) were
`obtained through earlier FEP si1nulations fro111 4. In
`solution, there is a 4 kcal/11101 range in the Ef~u.10/;1b
`,
`[-}
`na,tr
`k
`I/
`con1poncnts and a 2 ca 11101 range 111 E 1'_
`•01t•r' Vana-
`tions an1ong the average energy con1ponents reported
`for all simulations of 2-FKBPI 2 are on the order of 2-
`3 kcal/11101. It 111ust be noted that the ten11s fron1 sin111-
`lations 2a and 2b are 1norc si111ilar to each other than to
`those fron1 the original 2 siinulation.
`
`11
`
`1\s energy and S1\SA dij}'ercnces bet\veen the protein
`and aqueous environ111ents are the quantities that arc
`scaled to esti111ate binding allinity, these values arc
`recorded in '{'able 3. T\vo of the lo\vcst affinity inhibi(cid:173)
`tors, 3 and 11 have the largest van dcr Waals energy
`differences bet\veen bound and unbound
`ligands.
`Ligands 6, 7, and 11 have
`the 1nost unfavorable
`6,t,-Coulomh, \Vhile only 8 has a net favorable electrostatic
`interaction upon binding. Approxiinately 450 A 2 of each
`ligand is buried upon binding to FKBP12. This repre(cid:173)
`sents 65o/o of the surface of inhibitor 4, for exa1nple. The
`largest change is noted for inhibitors 5 and 6 (ca. 480 A.2
`buried), while the smallest difference is found for 7 (ca.
`4IOA 2).
`
`Opti1nization of the Lil equations
`
`'rhe energies and surface areas of Table 2 \Vere used first
`\Vith previously detennincd scaling paratneters to co1npute
`
`FKBP12-binding affinities. The original paran1eters of
`Aqvist 19 do not describe binding to this protein well at
`all; the free energies of binding are underesti1nated \Vi th
`an average unsigned error ( < lerrorl >)of 9.3 kcal/11101.
`Results \Vith the thro111bin-derivcd paran1eters are of
`more appropriate magnitude (-9.3 (5) to -6.3 (11) kcal/
`mo!, < lerrorl > ~ 1.4 kcal/mo!), although both the set
`of ato1nic radii for SASAs and the all-ato111 representa(cid:173)
`tion of the thro1nbin inhibitors differed fron1 the study
`presented here. Ho\vever, to itnprove the correspon(cid:173)
`dence \Vith experi111ent for FKBP12, ne\v values for a,~.
`and y \Vere found by fitting the average energy and sur(cid:173)
`face area differences to the experiinental binding free
`energies. The results for the various 1nodels investigated
`arc sun11narized in Table 4.
`
`The first step was to employ eq (I) with B~0.5 and
`derive an appropriate value for a, as \vas done originally
`for cndothiapepsin. 19 l'his 111odel resulted in a= 0.626
`and yielded free energies \Vhich deviated significantly
`frotn expcrin1ent. In particular, the 1naxi1nu111 unsigned
`error for 1nodel I \vas 4.4 kcal/1110!, \Vhich di1ninishes its
`predictive value given that the range of experi111ental
`binding affinities is 3.4 kcal/11101. Furthennorc, co111-
`pound 3, a poor inhibitor, \Vas predicted to bind as \Vell
`as the highest affinity ligand, 8.
`
`As expected, the linear response assun1ption for elec(cid:173)
`trostatic energies, 0 = 0.5, does not appear to hold \\1Cll
`for binding to FKBP12. When the value of B is set
`based on ligand co1nposition 20 and u derived e1npiri(cid:173)
`cally with eq (I) (model 2) or both p and o: treated as
`free paratneters (1nodel 3), average unsigned error and
`RMS to experitnent \Vere i1nproved but the 111axinnn11
`errors are still greater than 2kcal/mol. With model 2, the
`o:-ketoamide ligands required B ~ 0.43; II called for
`p ~ 0.37 due to its single hydroxyl substituent.2°
`
`Fitting the data with three parameters yielded an RMS
`deviation of 0.7 kcal/mo!, whether or not the SASA dif(cid:173)
`ference was included explicitly (eq (2) versus eq (3)).
`Values of B~0.139, o:~0.194, and y~0.0145 (model 4)
`ranked the ligands in a qualitatively reasonable \Vay
`
`Table 3, Calculated energy and surface·area differencesa with representative binding affinities
`
`Compound
`
`t'.lt<°"ulnnih
`
`t'lEL-1
`
`t'lSASA
`
`b.Gh. kca!/11101
`
`t
`3.8
`6.4
`2
`6.2
`2a
`4.5
`2b
`5.1
`J
`5.3
`4
`1.4
`5
`7.6
`6
`8.6
`7
`-1.0
`8
`4.8
`9
`L5
`IO
`2L6
`11
`au nits: kcal/1110! and A. 2 , respectively.
`0 Reforcnccs given in notes to Table I, t'lG = RT/11K1.
`"Compound 3 not included in the derivation of this model.
`<lFrce energy estimated using K; = 450 n}.f.
`
`-18.7
`-19.4
`·-18. l
`·-18.6
`-22.7
`-20.9
`-20.4
`· 15.2
`-·21.3
`-18.l
`·21.8
`-18.7
`-22.6
`
`-463.3
`-451.0
`-406.9
`-432.0
`459.7
`-466.3
`-483.4
`-479.8
`-406.0
`-442.4
`-445.6
`-447.6
`-441.2
`
`model 2
`
`model 4
`
`-9.6
`-8.9
`-8.2
`-9.2
`-1 l.5
`- 10.2
`-11.6
`-·7.6
`-9.0
`-11.3
`--11.0
`-10.6
`-5.5
`
`·-9.8
`- 9.4
`-8.5
`·9.2
`-J0.4
`-IO.I
`-t0.8
`-9.4
`··8.8
`· IO.I
`-10.0
`·9.9
`-7.8
`
`model 6
`
`9.7
`-9.4
`-8.6
`-9.3
`(·-10.9)'
`-10.3
`-10.9
`-9.0
`-9.3
`-10.2
`-10.5
`-10.0
`- 7.8
`
`cxpt"
`
`-9.2(-9.2)
`-9.5(-9.0)
`-9.5(-9.0)
`-9.5(-9.0)
`·9.0
`-10.9(-10.6)
`·-11. I
`-8.7<1
`-8.9
`-9.2(-9.4)
`-IO.I
`-!Lt
`-7.7
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 005
`
`

`
`856
`
`,\f. L. Lamb et al./ Bioorg. i\led. Chem. 7 ( 1999) 851-860
`
`Table 4, Summary of the a, p, and y parameters determined by fitting to the expcriincntal .6.Gb dataa
`
`!V{odcl
`
`eq
`
`I
`I
`I
`2
`
`J
`2
`
`l
`2
`J
`4
`
`5
`6
`
`7
`
`~
`a.sod
`0.43'1."
`0.201
`0.139
`0.138±0.016
`0.145
`0.176
`/J.174::±:0.(JIJ
`0.180
`
`a
`
`0.626
`0.599
`0.536
`0.194
`0.191 ±0.006
`0.134
`0.348
`0.348 ± 0.04 I
`0.328
`
`0.0145
`U.0146±0.0003
`-7.75
`0.0084
`OJJ085 ± OJJ002
`-4.21
`
`max. lcrrorlc
`
`< lerrorj > c
`
`R!\1S to e.xptc
`
`4.39
`2.49
`2.22
`1.39
`
`1.12
`l.09
`
`1.12
`
`1.24
`I.OJ
`0.71
`0.57
`
`0.55
`0.47
`
`0.47
`
`1.75
`1.25
`0.90
`0.72
`
`0.69
`0.58
`
`0.59
`
`·'Energy components and SASAs from ?-.1C sinntlations of I, 2, 2a, 2b, and J--11 were fit unless otherwise noted in the text. Cross-validation values
`with uncertainties given in ilallL'S.
`"eq (2), kcal/mol·A1 , cq (3). kcal/mo!.
`~1vraximum unsigned error, average unsigned error, and R~·fS deviation to experiment in kcal/11101.
`JFixed value.
`~p=O.J7 for hydroxyl-containing ligand 11 (see text).
`
`('fable 3); again 3 \Vas predicted to bind too \vell and
`\Vas responsible for the largest deviation fro111 experi(cid:173)
`tnent (l.4kcal/111ol). In perfon11ing the "leave-one-out"
`cross-validation of these scaling paran1eters, it beca111e
`clear that con1pound 3 \vas the notable outlier. Thus,
`the fitting \Vas repeated \Vithout including data for this
`coin pound, resulting in opti1nal parameters P = 0.176,
`a~ 0.348, and y ~ 0.0084 (model 6). The predicted order
`of affinities for the re111aining ligands in1proved slightly,
`and there \Vas a corresponding decrease in RMS devia(cid:173)
`tion to 0.6 kcal/11101. The average unsigned error in this
`case improves by 0.1 kcal/mo! to 0.5 kcal/mo!. A plot of
`calculated versus cxperitnental binding free energies based
`on 111odcl 6 is sho,vn in Figure 3. Additional justification
`
`for setting aside co1npound 3 111ay be found \Vhen y is a
`constant tenn in the linear response 1nodcl. \Vhen 3 is
`included in the data set (model 5), the predicted binding
`energy results largely fro1n the constant rather than the
`scaled energy tern1s (Table 4). Ho\vever, \Vhcn the fitting
`is performed without 3 (model 7), the value of y
`(-4.21 kcal/mo!) accurately reflects the nearly constant
`value of y* 1'SASA found with model 6.
`
`Overall, with or \Vithout 3, the LR calculations arc
`ordering the binding affinities \Vell. Tn vie'v of the sta(cid:173)
`tistical noise in the sin1ulations and the cxpcri1ncntal
`uncertainties, average errors of 0.5 kcal/1110! arc as good
`as can be hoped for.
`
`-6.0
`
`-7.0
`
`-8.0
`
`0
`E
`~
`
`-9.0
`
`u "' r5
`<1
`1l
`~
`~ -10.0
`u
`
`-11.0
`
`•
`
`•
`
`• •
`
`•
`•
`
`•
`•
`•
`
`•
`
`-12.0
`-12.0
`
`-11.0
`
`-10.0
`-9.0
`Experin1entnl L\G, kcal/11101
`
`-8.0
`
`-7.0
`
`-6.0
`
`Figure 3. Calculated versus experimental 6.Gb plotted for all ligands. The binding free energies were estimated using optimal parameters ~= 0.176,
`~=0.348, and ·1=0.0084 and eq (2). Con1pound 3, not included in this model. is not shown.
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 006
`
`

`
`,\I. !,. f_amh <'I al./ Bioorg. 1\fed. Chem. 7 ( 1999) 85 f.-860
`
`857
`
`Structural obscr\'ations
`
`\\1ith reasonable reproduction of the observed binding
`free energies, \Ve no\v turn to structures obtained during
`the si1nulations for possible insights into the origins of
`the predicted affinities. The benchtnark exa1nple in our
`earlier \York \Vas the difference bet\veen the 3-phenyl(cid:173)
`propyl compound, 2, and the (R)-1,3-diphenylpropyl, 4.
`The reduced binding for 2 \Vas attributed to a loss of
`hydrophobic contacts and specific aryl C-H ... N,O
`interactions \Vith the protein upon re1noval of the !(cid:173)
`phenyl substituent. 16 ~rhe relative free energy of binding
`con1puted \Vi th the Lil n1ethod for any simulation of 2
`and 4 (l'll'lGb ~ 0.9-1.8 kcal/mo!) is in excellent agree-
`1ncnt \Vith the experi1nental and FEP-calculated values
`of 1.4 kcal/mo!. Appropriately, the conformations of 2
`and 4 bound to FKBP12 resemble those reported pre(cid:173)
`viously, although at the end of the sin1ulations, the
`phenyl rings in these co1nplexes are found nearer to
`Tyr82 than Glu 54 (not shown). The mobility of the
`\Vithin
`that region of the protein
`is seen
`ligands
`throughout the N[C sin1ulations.
`
`1\111011g the final structures of the bound silnulations of
`co1npound 2, the t\VO fro1n the FEP-generatcd struc(cid:173)
`tures (2a and 2b) are 1nore sin1ilar to one another than
`to that of 2, especially \vith regard to the dicarbonyl
`o~c-c~o dihedral angle, which is -108' in 2a and 2b
`and -125° in 2. Ho\vcvcr, the electrostatic energy dif(cid:173)
`ferences for 2 and 2a arc very si1nilar (6.4 and 6.2 kcal/
`mo!, respectively), while 2b yields 4.5 kcal/mo!. There is
`also variation in the 6.SASA tenns for each rnodel of 2
`that parallels the trend in contribution to binding fro1n
`D.EL-J for these ligands, in that 2 is n1ost favorable, 2b
`is intennediate, and 2a is the least favorable. As a result,
`the predicted binding free energies for 2 and 2b agree
`well with the experimental values (Table 3), while 2a is
`estimated to bind I kcal/mo! less well.
`
`As one \Vould expect, con1pound 1, \Vhich contains no
`aron1atic ring, has the least favorable average electro(cid:173)
`static interaction of all ligands in solution (-23.16kcal/
`1110\); ho\vever, its van der \Vaals interactions \Vith sol(cid:173)
`vent are con1parable to those of 2. 'fhe flexible propyl
`side chain allo\vs the cyclohexyl ring of 1 to pack
`against the side chain of Ilc 56 (Fig. 4). It is also observed
`that 1nuch less \Vater is found \Vithin 3 A of the cyclo(cid:173)
`hexyl group than the phenyl group, in both bound
`(Fig. 4) and unbound structures.
`
`One of the best inhibitors, 5, is notable for its packing
`<ln1ong aro1natic side chains of the protein. 'fhis is
`found both in its crystal structure \Vith FKBPl29 and in
`the structures 1nodclcd here. One Ht: of 1'yr82 is 2.8 A
`fro111 the ligand phenyl ring center and this protein side
`chain fills the space between the tert-pentyl and phenyl
`groups (Fig. 5). Furthermore, the pipecolyl and cyclo(cid:173)
`hexyl rings are parallel to one another and separated by
`Phe46 . The cyclohexyl 1noicty has 1nore contact \Vith
`Phe46 than docs the analogous aron1atic group of 4.
`Without these contacts in solution, the cyclohexyl ring
`is free to rotate ca. 30° into a position still parallel to
`but displaced from the pipecolyl ring.
`
`Figure 4. Final siinulate<l strueturcs of l·FKBPl2 and 2-FKBP\2.
`Protein residues and solvent molecules within 3 A of the ligands arc
`displayed.
`
`Figure S. Snapshots front bound and unbound simulations of S.
`
`The cxpcri1ncntal and calculated binding affinities of 6
`and 7 are 111uch reduced fro1n their (R)- counterparts, 4
`and 5; the scaled electrostatic and van der \Vaals energy
`differences fro1n 1nodel 6 each contribute ca. I kcal/11101
`to the less favorable 6.Gb for these 1nolcculcs. Thus, it
`appears that the bound confonnations found for these
`ligands through epilnerization of their counterparts
`(Fig. 6) are reasonable models. When bound to the
`protein, the t\vo phenyl rings of 6 fonn a "parallel(cid:173)
`stacked and displaced" structure \Vi th one
`another; and
`the distance bet\veen ring centers is 4.7 A. This align-
`1nent of arotnatic rings has also been noted previously
`for benzene ditner in solution 27 but is not seen in the
`simulations of 4-FKBPl2. In 7-FKBP12, the Tyr82H'1-
`03 ohydrogen bond is the shortest of all complexes,
`1.7 A, and the interaction bet\veen Ile 56H and 02 is the
`longest at 2.6A. Unlike the I-phenyl group of 6, the
`cyclohexyl ring in 7 interacts \Vith Phe46 1nore closely
`than \Vith its O\Vn tert-pcntyl 1noicty.
`
`0
`
`Roxane Labs., Inc.
`Exhibit 1020
`Page 007
`
`

`
`858
`
`1\/. L. Lamb et al,/ Bioorg. 1\/ ed. (,'hem. 7 ( 1999) 851-860
`
`the protein. This "bump-hole" design could be used to
`avoid unproductive binding of ligand by wild-type
`FKBP12 in
`the cytoplas1n
`in a chcrnically-induccd
`din1erization scheme. 34