Distance Dependent Hydrogen Bond Potentials for Nucleic Acid Base Pairs from ab Initio Quantum Mechanical Calculations (LMP2/cc-pVTZ)

Transcription

1 J. Phys. Chem. B 1997, 101, Distnce Dependent Hydrogen Bond Potentils for Nucleic Acid Bse Pirs from b Initio Quntum Mechnicl Clcultions (LMP2/cc-pVTZ) Ken Brmeld, Siddhrth Dsgupt,* nd Willim A. Goddrd III* Mterils nd Process Simultion Center, Beckmn Institute (139-74), DiVision of Chemistry nd Chemicl Engineering, Cliforni Institute of Technology, Psden, Cliforni ReceiVed: Jnury 13, 1997; In Finl Form: Mrch 17, 1997 X Hydrogen bonding between bse pirs in nucleic cids is key determinnt of their structures. We hve exmined the distnce dependence of the hydrogen bonding of AT-WC (Wtson-Crick), GC-WC, nd AT-H (Hoogsteen) bse pirs using b initio quntum mechnics, LMP2/cc-pVTZ(-f) energies t HF/cc-pVTZ(-f) optimized geometries. From these curves, we hve extrcted Morse potentils between the H toms nd the cceptor toms tht ccurtely reproduce the quntum mechnicl energies for rnge of geometries. Using these prmeters, we hve clculted the complextion energies of the remining 26 possible pirwise combintions, nd the greement with previously reported b initio clcultions is excellent. We hve lso extrcted off-digonl Lennrd-Jones 12-6 prmeters to be used with the populr AMBER95 nd CHARMM95 force fields tht significntly improve their descriptions of the bse-piring energy nd optimum geometry. 1. Introduction Hydrogen bonds ply key role in mintining structure nd specificity of biologicl systems. In prticulr, the bse piring of nucleic cids (stemming from the specific formtion of hydrogen bonds between Wtson-Crick bse pirs) is essentil for the trnsfer of genetic informtion. We exmine here the three of gretest biologicl relevnce; the Wtson-Crick bse pirs, in which denine hydrogen bonds to thymine (AT-WC) or gunine hydrogen bonds to cytosine (GC-WC), nd the Hoogsteen denine-thymine pir (AT-H). Given the importnce of hydrogen bonding in biologicl systems, considerble theoreticl ttention hs been focused on exploring the nture nd strength of these interctions. Extensive clcultions hve been crried out on the nucleic cid bse pirs using semiempiricl or b initio quntum mechnicl (QM) methods. For recent review covering the current stte of the field nd discussing the extensive progress from semiempiricl to b initio QM methods, see ref 1. It is now estblished tht the determintion of ccurte hydrogen bond energies nd geometries requires lrge diffuse bsis set nd the inclusion of electron correltion. 2,3 Mny of the erlier studies of the nucleic cid bse pirs did not include electron correltion effects, or estimted correltion energies with empiricl methods. Recently, series of studies hve been reported in which dispersion energies hve been evluted using second-order Møller-Plesset perturbtion theory (MP2) 4-8 or density functionl theory (DFT). 9 Experimentlly, nucleic cid bse piring hs been difficult to study, nd there is little dt with which theoreticl results my be compred. Gs phse ssocition energies hve been reported for some systems, 10 nd solution studies hve been undertken in nonpolr solvents. 11 The limited experimentl dt leds to uncertinty in the ccurcy of empiricl potentils. We report b initio QM clcultions (LMP2/cc-pVTZ(-f)) on the complextion energies of the AT-WC, GC-WC, nd AT-H nucleic cid bse pirs. In ddition to determining the minimum energy nd geometry of these complexes, we used QM to clculte the strength of these interctions s function *To whom correspondence should be ddressed. E-mil: sdg@wg.cltech.edu nd wg@wg.cltech.edu. X Abstrct published in AdVnce ACS Abstrcts, My 15, S (97) CCC: $14.00 of intermoleculr distnce. These potentil energy curves were used to determine distnce dependent hydrogen bond functions (described s Morse potentils). We find tht force fields (FFs) incorporting these hydrogen bond potentils in conjunction with stndrd vn der Wls nd Coulombic terms ccurtely reproduce the full QM potentil curve. This differs from the pproch of current stndrd FFs (AMBER95, 12 CHARMM, 13 nd OPLS 14 ), which hve been prmetrized to reproduce only the energy nd geometry t the bottom of the potentil curve. 2. Methods Clcultions involving the nucleic cid bse pirs were crried out with the PS-GVB softwre pckge. 15 Optimum geometries (HF/6-31G**) of the free bses 1-(hydroxymethyl)cytosine, 9-(hydroxymethyl)gunine, 1-(hydroxymethyl)thymine, 9-(hydroxymethyl)denine, 1-methylthymine, nd 9-methyldenine were determined while mintining plnr C s symmetry. This constrint ws lso imposed for the optimiztion of the AT- WC, GC-WC, nd AT-H bse pirs. For the unpired bses contining n exocyclic mino group, the optimum geometry hs been reported to be nonplnr. 16 However, it hs been shown tht for the three bse-pired structures we exmine, the optimum structure is plnr, 5b nd hence the errors due to the symmetry constrint re negligible. Initilly we obtined the optimum bse pir geometries by grdient optimiztion (HF/6-31G**) while keeping internl bse coordintes fixed in the optimum monomer conformtion. These HF/6-31G** results proved to be indequte nd yielded geometries tht did not mtch experimentl structures. Full optimiztion with more diffuse cc-pvtz(-f) bsis set gretly improved the results. 17 For these clcultions no symmetry constrints were used. Energetics were obtined using locl second-order Møller- Plesset perturbtion theory (LMP2) 18 with frozen core orbitls for geometries determined t the HF/cc-pVTZ(-f) level. The LMP2 method differs from cnonicl MP2 by limiting ech occupied orbitl s spce of correlting virtul orbitls to be loclized on the toms of the occupied HF orbitl. A Boys locliztion 19 of the HF reference wve function is used to determine the locl MP2 reference wve function. This locl correltion method hs been reported to be essentilly free from 1997 Americn Chemicl Society

2 4852 J. Phys. Chem. B, Vol. 101, No. 24, 1997 Brmeld et l. Figure 1. Digrm of the nucleic cid bses; thymine, denine, cytosine, nd gunine including force field tom types nd prtil chrges. Chrges were determined from LMP2/cc-pVTZ(-f) quntum mechnicl clcultions. The methyl nd methoxy groups in the lst row re common to ll bses nd re bbrevited s R in the bse structures. correltion bsis set superposition error (BSSE) nd offers significnt computtionl svings. 18c Strting from the optimum geometry, energies were clculted t the LMP2/cc-pVTZ(-f) level s the centrl N-H N hydrogen bond length ws systemticlly incresed. This yielded potentil energy curve s function of distnce for ech bse pir. 19 The HF BSSE correction ws clculted for ech geometry, using the counterpoise method of Boys nd Bernrdi. 20 To simplify the clcultions, we wnt to replce the deoxyribose sugr with either methyl or hydroxymethyl substitution on the bse. To estblish which is best, we crried out clcultion on 2 -deoxydenosine, including the sugr explicitly. Compring the potentil-derived chrges for the 2 -deoxydenosine cse with those of 9-methyldenine nd 9-(hydroxymethyl)denine, we found tht the hydroxymethyl substitution gve results closer to tht with the complete sugr (see Figure 1). Since these hydrogen bond potentils re intended for prmetriztion of force field (FF) tht will include the sugr, the hydroxymethyl-substituted bses were used for ll subsequent clcultions. This hydroxymethyl substitution is expected to led to complextion energy similr to tht of the full sugr becuse the chrges for ll toms in close contct re quite similr. Experimentl hydrogen bond energies hve been mesured for the methyl-substituted bse pirs. In order to compre our clcultions directly with these experiments, we lso exmined the methyl substituted AT Hoogsteen bse pir. The effects of this substitution re discussed in greter detil in sections nd The complextion enthlpies for bse pir dimeriztion hve been mesured experimentlly using mss spectrometry. 10 To compre between these experimentl vlues nd theoreticl clcultions, severl corrections must be mde. The free bses undergo smll conformtionl chnge upon forming bsepired complexes, resulting in positive deformtion energy ssocited with bse piring. Thus, the QM energy my be defined s E QM ) E HF - BSSE HF + E cor + E def where E HF is the HF energy, BSSE HF is the bsis set superposition error, E cor is the LMP2 correltion energy, nd E def the deformtion energy. Finlly, H 300 my be determined from H 300 ) E QM + ZPE + H 0f300 (1) (1b) in which ZPE is the chnge in zero-point energy between the free bses nd the dimer, while H 0f300 is the temperture dependence of H from 0 to 300 K. ZPE nd H 0 f300 were clculted from the vibrtionl frequencies obtined from the FF. The two terms hve opposite sign, with ZPE decresing the vlue of E while H 0f300 increses E. Atomic point chrges were determined from the electrosttic potentil (ESP) derived from the electron density distribution (constrined to reproduce the moleculr monopole nd dipole moments) clculted from the converged LMP2/cc-pVTZ(-f) wve functions (Figure 1). 21 MM clcultions were performed with the POLYGRAF 22 softwre pckge using the Dreiding FF 23 with n exponentil-6 vn der Wls potentil (2). E vdw ) Ae -CR - BR -6 (2) The procedure for determining the b initio derived hydrogen bond potentils ws s follows: 1. The totl nonbonded potentil energy for the complex ws determined for ech geometry excluding the specific vn der Wls contribution between hydrogen-bonding toms. This steeply ttrctive potentil mtches the hydrogen bond energy t lrge distnces.

3 Distnce Dependent Hydrogen Bond Potentils J. Phys. Chem. B, Vol. 101, No. 24, The difference between the electrosttic potentil nd the hydrogen bond curve determined from QM is fit with simple Morse function (3). E morse ) D 0 [χ 2-2χ] (3) χ ) exp[ - ζ 2( 1 - R R 0 )] This off-digonl Morse function is specific for ech pir of hydrogen bond donor nd cceptor toms nd enbles the MM clcultions to reproduce energies nd geometries obtined from QM over the full rnge of hydrogen bond distnces. Thus, the nonbonded interctions involve superposing twobody vn der Wls (E vdw ), hydrogen bond (E morse ) nd electrosttic terms: E nonbond ) E vdw + E morse + ( ) Q i Q j R ij (4) Hydrogen bond curves for the FF were obtined nlogous to the QM methods. The hydrogen-bonded complexes were optimized while keeping the internl degrees of freedom fixed t the HF/6-31G** optimum geometry. The intermoleculr distnce ws then incresed nd single-point energies clculted. We chose to keep the internl bse geometry fixed so s to compre to the nonbonded potentils of the AMBER95, 12 CHARMM, 13 nd OPLS 14 FFs without correcting for vlence distortions Results nd Discussion 3.1. Quntum Mechnicl Clcultions for Nucleic Acid Bse Pirs LeVel of Theory. QM clcultions on systems s lrge s nucleic cid bse pirs re still computtionlly intensive. Our initil pproch ws to crry out ll clcultions t the HF level with 6-31G** bsis set. Erlier optimiztions reported for the 6-31G* bsis set yielded hydrogen bond lengths tht were n verge of 0.1 Å too long. 8 We obtined similr results with the 6-31G** bsis set. Using the cc-pvtz(-f) bsis set gve much better geometries when compred to experiment. HF/6-31G** energies were determined for ll points nd corrected for BSSE. These energies were found to underestimte the H of dimeriztion. To improve upon both the optimum geometries nd energies obtined from QM, we used lrger bsis set nd included electron correltion for the single-point energy clcultions (LMP2/cc-pVTZ(-f)). The results of these HF/cc-pVTZ(-F)// LMP2/cc-pVTZ(-f) clcultions with BSSE corrections re discussed in detil in sections nd Geometry Optimiztion. The optimum hydrogen bond lengths for the AT-WC, GC-WC, nd AT-H bse pirs re reported in Tble 1. The HF/6-31G** geometries led to hydrogen bond lengths tht re consistently too long by 0.15 Å. Incresing the bsis set size [cc-pvtz(-f)] gve much better results with n verge difference of only 0.05 Å from the experimentl geometry (some differences my be expected between the gs phse geometries of isolted bses nd the crystl structure of two-bse-pir dimer). As discussed in section 2, hydroxymethyl ws used to replce the full ribose or deoxyribose sugr. For the AT-H bse pir, both the methyl nd hydroxymethyl substitutions were exmined. The effect this substitution hs on the HF/6-31G** geometry is worth noting. The optimum distnces for N7 (H)N3 nd N6(H) O4 hydrogen bonds in the hydroxymethyl cse re 3.09 nd 2.98 Å, respectively, wheres in the methyl cse they TABLE 1: Hydrogen Bond Lengths of the DNA Bse Pirs (Å) tom pir HF/3-21G HF/6-31G** b HF/cc-pVTZ(-f) c X-ry d GC Wtson-Crick O6-N N1-N N2-O AT Wtson-Crick N6-O N1-N AT Hoogsteen N6-O N7-N As reported by Gould et l. 8 b Internl geometry held fixed. c Full geometry optimiztion with no constrints. d From experimentl X-ry crystllogrphy dt. 37 TABLE 2: Root Men Squre Comprsion between b Initio [HF/cc-pVTZ(-f)] nd Experimentl Nucleic Acid Bse Structures bse coordinte (Å) bond (Å) ngle (deg) 1-methylcytosine methylthymine methyldenine methylgunine TABLE 3: DNA Bse Pir Energies for HF Optimized Geometries (kcl/mol) GC Wtson- Crick AT Wtson- Crick AT Hoogsteen HF/6-31G** HF/6-31G**[BSSE] HF/cc-pVTZ(-f) HF/cc-pVTZ(-f)[BSSE] LMP2/cc-pVTZ(-f) LMP2/cc-pVTZ(-f)-[BSSE] E QM ZPE b H c 0f H d H e exp f E QM, the LMP2/cc-pVTZ(-f) interction energy t the HF/ccpVTZ(-f) minimum geometry corrected for the deformtion energy, def. b ZPE, the zero-point energy correction determined from vibrtionl frequencies clculted with moleculr mechnics. c H 0f300, the difference in temperture dependence of H. d H 300 ) E QM + ZPE + H 0f300. e H exp, experimentl H from mss spectrometry dt. 10 f This experimentl H hs been corrected to reflect the effects of the multiple conformtions possible for the AT bse pir. 25 re 2.96 nd 3.12 Å, respectively. This mrks reversl in the the reltive lengths for both hydrogen bonds, yet this effect is not observed for the HF/cc-pVTZ optimized structures. These observtions further support the need for lrge bsis set to correctly describe nonbonded interctions. The individul bses were lso optimized (HF/cc-pVTZ(-f)) so s to determine internl strin energies ssocited with bse piring. These geometries were found to compre fvorbly with crystl structures of the free bses. Tble 2 lists the rms difference in coordintes, bond lengths, nd ngles for ech bse. The verge rms difference in coordintes for the pyrimidine bses ws 0.02 Å nd for the purine bses 0.05 Å Bse Pir Complextion Energies. HF/6-31G** complextion energies were clculted for the optimized bse pirs nd corrected for BSSE. The bse pir energies re listed in Tble 3 nd found to be substntilly weker thn the reported experimentl H, even before tking ZPE corrections into ccount. The BSSE ws found to be 2.1 nd 2.4 kcl/mol for

4 4854 J. Phys. Chem. B, Vol. 101, No. 24, 1997 Brmeld et l. the AT-WC nd GC-WC bse pirs, respectively. This compres fvorbly with the reported results of Gould et l. 8 in which the effects of BSSE corrections re discussed in detil for vrious methods nd bsis sets. Using cc-pvtz(-f) bsis set improves upon these results. However the inclusion of correltion energies is necessry to dequtely describe the system. The HF/cc-pVTZ(-f) BSSE is reduced to 1.1 nd 1.3 kcl/mol for the AT-WC nd GC-WC bse pirs respectively. With the LMP2 method, there is no dditionl correction to the dispersion energy due to BSSE. 18c This offers distinct dvntge over stndrd MP2 methods, for which BSSE corrections re difficult to estimte nd computtionlly intensive. As discussed erlier, LMP2/cc-pVTZ(-f) energies cn be compred to experimentl complextion enthlpies only fter number of fctors hve been tken into ccount. Tble 3 lists E QM, ZPE, nd H 1f300, the sum of which ( H 300 ) my be compred directly to experimentlly determined enthlpies ( H exp ). For the GC-WC bse pir, the clculted vlue of kcl/mol is in excellent greement with the experimentl vlue of kcl/mol. The clculted hydrogen bond energy of the AT-H bse pir is considerbly lower thn the experimentl results, versus kcl/mol. These energies differ from those of Gould et l., 8 who found good greement with the AT-H bse pir but reported GC-WC bse pir energy 4.4 kcl/mol too negtive when compred with experiment. The H energies reported by Sponer et l. 5c re within 1 kcl/mol of the energies we report. We exmined the AT-H complextion enthlpies in greter detil to understnd the discrepncy between the theoreticl nd experimentl energies. A methyl versus hydroxymethyl substitution for the full sugr mkes no difference in the complextion energy. The HF/cc-pVTZ(-f) energy for methyl-at-h is kcl/mol compred to kcl/mol for hydroxymethyl substitution. This is lso in greement with the experimentl report tht H is independent of methyltion. 10 The AT bse pir my ssume one of four conformtions; Wtson-Crick, reverse Wtson-Crick, Hoogsteen, or reverse Hoogsteen, ll of which hve been reported to hve energies within 1 kcl/mol of ech other. 5c Experimentl gs phse complextion enthlpies were not corrected for contributions from ll four possible orienttions. 25 At 60 C, this leds to n overestimtion of H by 0.9 kcl/mol. Thus the experimentl AT complextion enthlpy should be kcl/mol. While this correction reduces the difference between our theoreticl energies nd experiments, the discrepncy of 1.6 kcl/mol is still significnt. Although stbiliztion between bse pirs is dominted by electrosttics, dispersion energies contribute significntly more to the AT-H nd AT-WC bse pirs versus GC-WC. For the GC-WC bse pir dispersion energies ccount for only 3% of the totl complextion energy, wheres for the AT-WC nd AT-H pirs this contribution is incresed to 15% nd 18%, respectively. It my be the cse tht n LMP2 geometry optimiztion of the AT nd GC bse pirs would be found to preferentilly stbilize the AT pir Distnce Dependent Potentil Energy Surfces. Given n optimum geometry for ech of the Wtson-Crick nd Hoogsteen bse pirs, it is possible to determine the complextion energy s function of distnce. For ech bse pir, the distnce between toms of the centrl (N H-N) hydrogen bond ws incresed nd single-point energy clcultions were performed followed by BSSE corrections. Complete HF/6-31G** curves were obtined for ll the bse pirs. The AT- WC nd GC-WC curves re shown in Figure 2. As discussed Figure 2. Potentil energy curves for the AT-WC nd GC-WC bse pirs. The bse pir seprtion is defined s the distnce between heterotoms of the centrl hydrogen bond, toms N1 of the pyrimidines, nd N3 of the purines. Note the overestimtion of the complextion by the Hrtree-Fock clcultion t distnces greter thn 4 Å. TABLE 4: LMP2/cc-pVTZ(-f) Totl nd Component Energies (kcl/mol) for the GC-WC Bse Pir t Vrible N1(H) N3 Distnces (Å) N1(H) N3 E HF BSSE HF E cor E LMP TABLE 5: LMP2/cc-pVTZ(-f) Totl nd Component Energies (kcl/mol) for the AT-WC Bse Pir t Vrible N1 (H)N3 Distnces (Å) N1 (H)N3 E HF BSSE HF E cor E LMP TABLE 6: LMP2/cc-pVTZ(-f) Totl nd Component Energies (kcl/mol) for the AT-H Bse Pir t Vrible N7 (H)N3 Distnces (Å) N7 (H)N3 E HF BSSE HF E cor E LMP bove, these hydrogen bond lengths re slightly too long nd the energies too wek to be used to fit FF. For completeness, the energies of the HF/6-31G** clcultions my be found in the Supporting Informtion Tble S1. For ech bse pir, six single-point LMP2/cc-pVTZ energies were clculted: one t the HF/cc-pVTZ optimum geometry nd five dditionl points up to hydrogen bond length of 5 Å. A finl distnce of 5 Å between heterotoms ws chosen, s the dispersion energies re nerly zero nd the totl potentil energy is lrgely determined by electrosttics. For ech geometry, the component nd totl energies re listed in Tbles 4-6 for the GC-WC, AT-WC, nd AT-H bse pirs, respectively. To compre with the HF/6-31G** results, the points for the AT-WC nd GC-WC pirs re plotted in Figure 2.

5 Distnce Dependent Hydrogen Bond Potentils J. Phys. Chem. B, Vol. 101, No. 24, TABLE 7: Dependence of Correltion Energies (kcl/mol) for the H 2 O Dimer on O O Distnces (Å) nd Level of Theory, Using the cc-pvtz Bsis Set O O MP2 MP3 MP4 LMP2 b All clcultions use frozen core pproximtion. The optimum geometry hs n O O distnce of 2.97 Å. b LMP2 clcultions were crried out with the cc-pvtz(-f) bsis set, s discussed in the Methods section. Exmintion of the correltion energies revels positive contribution to the totl energy t intermedite distnces. Clcultions on the CC nd GG dimers, the only other DNA systems for which distnce dependent hydrogen bond potentils hve been reported, show the sme tendencies. 5c The LMP2 electron correltion energies my be decomposed s in (6). 26,27 E LMP2 cor ) E disp + E rep (6) where E disp is the dispersion energy nd is lwys negtive, while E rep represents the remining repulsive terms, which include the intrsystem correltion correction to the electrosttic effect, the induction correltion, nd exchnge terms. MP2 clcultions hve been reported for simple hydride dimers such s (HF) These clcultions indicte tht E rep is slightly smller in mgnitude thn E disp, with the two terms lrgely cnceling ech other, leding to smll totl correltion correction. A fine blnce is mintined between these components, which individully re sensitive to the intermoleculr seprtion, yet vry slowly once summed. At intermedite to long hydrogen bond distnces, where E disp becomes negligible, E rep still contributes slightly to the totl energy, resulting in positive E cor. Thus the HF clcultion overestimtes the electrosttic energies nd hs lower reltive energy for these points. Similrly, FF which incorportes chrges determined from isolted monomers will overestimte the electrosttic energy t points where there is positive chnge in electrosttic energy, with decresing distnce, due to electron correltion. To exmine whether such positive correltion energies observed using MP2 or LMP2 methods re generl, we crried out extensive clcultions on wter dimer system. The optimum dimer geometry used in these clcultions ws the sme s tht determined by Sebo et l. 18 The intermoleculr distnce ws then vried, nd for ech geometry the LMP2/ccpVTZ(-f) energies were compred to MP2, MP3, nd (SDTQ)MP4/cc-pVTZ energies fter full BSSE corrections. The correltion energies s function of distnce re listed in Tble 7, nd the totl energies plotted in Figure 3. All levels of theory show the sme distnce dependent behvior with positive correltion energy t intermedite intermoleculr distnces. The complextion energy determined with LMP2 (4.67 kcl/mol) is within the rnge of experiment, ( 0.7 kcl/mol (MP2 with ugmented cc-pvtz bsis set leds to 5.58 nd 4.65 kcl/ mol when corrected for BSSE nd monomer relxtion) Force Field Prmetriztion. Using the curves clculted from QM, we sought simple FF description for use in moleculr mechnics (MM) clcultions tht could correctly describe both the inner wll of the minimum energy well nd the curvture s the hydrogen bond length is incresed. Exmintion of the hydrogen bond potentils determined from QM revels tht t lrge distnces the energies re dominted Figure 3. Potentil energy curves for the H 2O dimer t vrious levels of theory. The LMP2/cc-pVTZ(-f) minimum energy is closer to the experimentl ssocition energy of 5.4 ( 0.7 kcl/mol. In ddition, ll clcultions tht include electron correltion effects show the sme behvior t intermedite distnces, with ssocition energies tht re weker thn the Hrtree-Fock clcultion predicts. by electrosttics. We find tht using chrges derived from QM for ll toms, it is only necessry to define repulsive Morse potentil between the tom pirs directly involved in hydrogen bonding to reproduce the QM curves. This method hs been used successfully in the prmetriztion of specilized FF for nylon. 30 Prmetriztion of the Morse potentils is closely relted to the vn der Wls description of the FF used. For these clcultions we hve used the Dreiding FF with the exponentil-6 (Exp-6) vn der Wls (vdw) option. All vdw interctions re included explicitly except the specific vdw interction between two toms tht form hydrogen bond. This energy is set to zero. For ech geometry, MM energy is clculted with nonbonded energies comprised of n Exp-6 vdw term nd stndrd Coulombic function. The difference between the QM energy nd the FF Exp-6 + Coulomb energy my be fit with Morse potentil. The Morse potentil is specific for the selected pir of toms forming the hydrogen bond nd replces the norml Exp-6 vdw energy clculted from combintion rules. We report two sets of Morse prmeters for the MSC FF, which differ in ccurcy nd generlity. The best prmeters (MSC1 FF) require different potentils between the AT (-WC nd -H) bse pirs nd the GC-WC bse pir. While this gives n excellent fit to the QM dt, it is not s useful for studies of uncommon bse pir geometries or non-nturl bses. A stisfctory fit using globl set of prmeters (MSC2 FF) for ll the bse pirs ws lso obtined. The MSC2 FF leds to systemtic differences from the QM dt, probbly becuse of coopertive effects in hydrogen bonding. The AT-WC nd AT-H bse pir energies re too strong by 0.6 nd 0.4 kcl/ mol, respectively, nd the GC-WC energy is underestimted by 1.1 kcl/mol. The prmeters for both MSC1 FF nd MSC2 FF re listed in Tble 8. The optimum energies nd geometries obtined using these new FF re listed with the QM results in Tbles 9 nd Moleculr Mechnics Force Field Evlutions Distnce Dependent Potentil Energy Surfces. Hydrogen bonding hs been ddressed in number of wys in vrious FFs. Erlier versions of AMBER, 31 CHARMM, nd Dreiding used Lennrd-Jones (LJ) potentil for hydrogen-bonding tom pirs. The current releses of AMBER (AMBER95), 12 CHARMM, 13 nd OPLS 14 ll use LJ 12-6 potentil, but differ in the derivtion of tomic chrges nd the specific LJ

6 4856 J. Phys. Chem. B, Vol. 101, No. 24, 1997 Brmeld et l. TABLE 8: Morse Potentil Prmeters for the DNA Bse Pirs tom pir tom types R 0 D 0 ζ MSC1 FF GC O6-N4/N2-O2 O 2-H A N1-N3 N RL-H A MSC1 FF AT N6-O4 O 2-H A N1-N3 N RL-H A MSC2 FF (ll pirs) O2-H A NRL-H A TABLE 9: Optimum Hydrogen Bond Lengths of the DNA Bse Pirs (Å) As Determined by Moleculr Mechnics with the AMBER95.1*, CHARMM*, nd MSC Force Fields; Internl Bse Geometries Were Defined by the Optimum HF/6-31G** Structures nd Held Fixed during Optimiztion by Ech Force Field tom pir AMBER95.1* CHARMM* b MSC1 MSC2 X-ry c GC Wtson-Crick O6-N N1-N N2-O AT Wtson-Crick N6-O N1-N AT Hoogsteen N6-O N7-N AMBER95* force field prmeters nd chrges from ref 12 with specific off-digonl hydrogen bond vn der Wls terms dded. b CHARMM* 13 with specific off-digonl hydrogen bond vn der Wl terms dded. c From experimentl X-ry crystllogrphy dt. 37 TABLE 10: Optimum Complextion Energies for the DNA Bse Pirs (Å) As Determined by Moleculr Mechnics with the AMBER95.1*, CHARMM*, nd MSC Force Fields; Internl Bse Geometries Were Defined by the Optimum HF/6-31G** Structures nd Held Fixed during Optimiztion by Ech Force Field GC Wtson-Crick AT Wtson-Crick AT Hoogsteen AMBER95.1* CHARMM* b MSC MSC QM c AMBER95* force field prmeters nd chrges from ref 12 with specific off-digonl hydrogen bond vn der Wls terms dded. b CHARMM* 13 with specific off-digonl hydrogen bond vn der Wl terms dded. c LMP2/cc-pVTZ(-f)[BSSE] quntum mechnicl energies for the HF/cc-pVTZ(-f) optimized structure. prmeters. AMBER95 nd CHARMM both use QM-derived chrges. AMBER95 uses the restrined electrosttic potentil (RESP) 32 method nd lters the LJ prmeters of the hydrogenbonding toms to fit experimentl energies nd geometries. The OPLS FF uses generl LJ prmeters bsed on element type only nd uses chrge-fitting scheme which reproduces the energy nd geometries of wter-bsed complexes s determined from b initio quntum mechnics. We find tht these stndrd MM FFs led to n inccurte description of the curvture of the hydrogen bond potentil nd usully do not predict correct complextion energies nd geometries. For ech FF (including MSC1 FF) we hve evluted the bse pir complextion energies s function of distnce. The internl geometry of ech bse ws held fixed in the HF/6-31G** optimum conformtion. Intermoleculr geometries were determined by grdient optimiztion of the nonbonded energies, Figure 4. Comprison between potentil energy curves for the DNA bse pirs () GC-WC, (b) AT-WC, nd (c) AT-H s determined with different moleculr mechnics force fields nd quntum mechnicl results. The AMBER95.0 FF uses chrges from ref 33, while AMBER95.1 uses chrges from ref 12. followed by single-point energy clcultions t fixed intermoleculr distnces. Two sets of chrges re vilble for the AMBER95 FF: (i) AMBER95.0 denotes clcultions using the originl RESP chrge scheme (listed in the supplementry mterils of ref 33), for which the complextion energies re reported in the FF pper, ref 12, nd (ii) AMBER denotes the chrge scheme relesed with the full FF, 12 which does not mtch the energies in ref 33. The results of this nlysis, plotted in Figure 4-c nd listed in Tbles S2-S4, revel tht FFs tht employ b initio QMderived chrges re more successful t reproducing the QM

7 Distnce Dependent Hydrogen Bond Potentils J. Phys. Chem. B, Vol. 101, No. 24, energies. For ll three cses exmined, AMBER95.0 nd AMBER95.1 overestimte the hydrogen bond energies by 3-5 kcl/mol. CHARMM describes GC-WC to within 1 kcl/mol, but overestimtes the AT-WC nd AT-H energies by 3 nd 2.5 kcl/mol, respectively. The OPLS FF underestimtes the complextion energies by 1-2 kcl/mol nd is considerbly worse t reproducing the QM energies wy from the optimum geometry. All FF incorporting LJ6-12 description suffer from the sme shortcoming intrinsic to the form of the potentil. Specificlly, the ttrctive portion of the potentil is too steep, creting minimum energy well tht is too nrrow. In comprison, the Morse potentil used with the MSC FF leds to softer inner wll nd broder minimum energy well tht better describes the true curve. In spite of this improvement, the MSC1 Morse potentil does not reproduce the exct QM energies for the AT-H nd AT- WC pirs t longer hydrogen bond distnces (see Figure 5bc). As discussed erlier, inclusion of electron correltion decreses the electrosttic energy, leding to weker bonding t the longer distnces. An electrosttic model bsed on independent monomers correctly describes the system round the minimum, but overestimtes the stbiliztion energy t longer distnces. For the GC-WC pir, where dispersion contributes less to the totl bonding, this effect is negligible, but for AT complexes, which depend more strongly upon dispersion, it is significnt Additionl Prmeters for the CHARMM nd AM- BER95.1 Force Fields. In ddition to determining optimum off-digonl nonbonded prmeters for the MSC FF, we crried out similr optimiztions for CHARMM nd AMBER95.1. For both FFs we report the optimum LJ12-6 prmeters needed to define the vdw potentils between the heterotoms involved in hydrogen bonding. These off-digonl vn der Wls terms replce the stndrd R e nd D e determined using combintion rules. No chrges or vlence terms hve been ltered. The prmeters re listed in Tble 11. We denote clcultions using these modified terms s CHARMM* nd AMBER95*. The new optimum geometries nd energies re compred in Tbles 9 nd 10, respectively. Full potentil curves re plotted in Figure 5-c. Incorporting these specil off-digonl terms gretly improves both FFs. For AMBER95.1* (which uses the chrge scheme distributed with AMBER95), the minimum geometry nd energy for ll three bse pirs could be djusted to reproduce the QM results with quite stisfctory distnce dependence. Due to the dditionl number of tom types used by the CHARMM FF, ll three bse pir complexes could be fit independently; however, this ws not sufficient to ttin stisfctory fit for AT-WC. Here the finl optimum hydrogen bond lengths re too long by 0.1 Å nd the energies too strong by 0.4 kcl/mol. As with AMBER95.1*, both the GC-WC nd AT-H complexes could be fit nd yielded similr distnce dependent curves shown in Figure 5-c. These off-digonl vn der Wls prmeters re simple to include during MM nd dynmics simultions nd gretly improve the ccurcy of these two populr FFs Bse Pir Complextion Energies of 26 Possible Geometries. The stbiliztion energies of 26 possible geometries for the DNA bse pirs, in which minimum of two hydrogen bonds re formed, hve been evluted using b initio QM (MP2/6-31G**). 5c These energies hve been compred to those obtined from empiricl potentils such s AMBER95, CHARMM, nd OPLS FFs. 35 A liner regression nlysis of ech of these potentils compred to the MP2 results simplifies the tsk of ssessing which FF best reproduce the QM energies. Such n nlysis hs been previously reported for the potentils Figure 5. Comprison between potentil energy curves for the DNA bse pirs () GC-WC, (b) AT-WC nd (c) AT-H s determined by b initio quntum mechnics, the MSC FF, nd modified versions of AMBER95 nd CHARMM. The AMBER95* force field prmeters nd chrges re from ref 12 with the specific off-digonl hydrogen bond vn der Wls terms listed in Tble 11 included. The CHARMM* FF is stndrd CHARMM 13 with the specific off-digonl hydrogen bond vn der Wl terms listed in Tble 11 included. listed bove, 35 nd we hve now extended this work to include the generl MSC2 FF. The MP2 nd MSC2 FF energies of ech complex re plotted in Figure 6, nd the liner regression plot is shown in Figure 6b. The MSC2 FF energies correlte very well with the QM results. The specific liner regression prmeters for ech of the FFs re listed in Tble 12. The correltion coefficient is n overll mesure of how well the MM potentils nd QM methods re correlted, with vlue closest to 1.0 representing

8 4858 J. Phys. Chem. B, Vol. 101, No. 24, 1997 Brmeld et l. TABLE 11: LJ12-6 Prmeters for the DNA Bse Pirs Used To Correct the AMBER95.1 nd CHARMM Force Fields tom types R 0 D 0 AMBER95.1 NA-NC N2-O NA-NB CHARMM NN3-NN2G NN3A-NN2U NN4-NN2U NN1-ON TABLE 12: Liner Regression Anlysis of Complextion Energies for 26 Hydrogen-Bonded DNA Bse Pir Geometries Using the AMBER95.1, CHARMM, nd MSC Force Fields Compred to b Initio Energies t the MP2/ 6-31G** level: The Eqution Is Y ) A + BXwhere X E MP2 MSC2 FF AMBER95 b CHARMM b OPLS b R c SD d A B AAE e MP2/6-31G** energies reported by Hobz et l. 5c b Liner regression nlysis reported by Hobz et l. 35 c Correltion coefficient. d Stndrd devition (kcl/mol). e Averge bsolute error (kcl/mol). AAE ) (1/26) 26 i E MP2 - E FF. the highest possible correltion. In ddition, the stndrd devition reflects the difference in energies between the two methods for ech geometry. The MSC2 FF hs the highest correltion coefficient (0.98) of the FFs exmined nd the smllest stndrd devition (0.83 kcl/mol). Other prmeters my lso be exmined such s the intercept (A) or slope (B) of the liner fit, which should be close to 0.0 nd 1.0, respectively. Finlly, the MCS2 FF leds to the smllest verge bsolute error. Since none of the MP2 energies were used to prmetrize the MSC2 FF, this represents n independent test of both the method of prmetriztion nd the qulity of LMP2 complextion energy clcultions compred to the MP2 method. It is evident tht generlized hydrogen bond potentil derived from the full LMP2 potentil energy surfces of three bse pir geometries is sufficient to ccurtely describe ll possible bse pir interctions. 4. Conclusion We exmined the distnce dependent hydrogen bond energies of the AT-WC, GC-WC, nd AT-H bse pirs using b initio QM (LMP2/cc-pVTZ(-f)//HF/cc-pVTZ(-f)). Using these energies s stndrd, n lterntive hydrogen bond potentil for use in MM nd dynmics simultions is presented. This new FF incorportes Morse potentil to describe the nonbonded energies between hydrogen bonding toms nd reproduces the QM energies for rnge of geometries. In ddition to prmetrizing the new FF, we exmined the ccurcy of two commonly used FFs, AMBER95 nd CHARMM95. Neither FF ws found to correctly describe the optimum geometry or energy of the bse-pired complexes. The ccurcy of these FFs ws gretly improved by replcing the LJ12-6 potentil between the heterotoms directly involved in hydrogen bonding with n off-digonl LJ12-6 potentil tuned for the bse pirs. The new prmeters nd the resulting complex energies nd geometries re reported. Figure 6. () Complextion energies for 26 possible bse pir conformtions determined with b initio quntum mechnics (MP2/6-31G**) nd the generl MSC2 FF. See ref 5c for specific geometries. (b) For ech complex, the MSC2 FF energies re plotted ginst the MP2 energies. The dshed line represents the idel cse in which the two energies re equl. The solid line is the lest squres best fit through ll points. These b initio clcultions nd nlyticl hydrogen bond potentil energy functions re prt of n ongoing effort to develop generl first principles FF for biologicl systems. The gol of this work is to provide reltively simple set of functions which hve been fit to reproduce b initio clcultions on smll model compounds. Prmeters thus defined re generl nd my be esily extended to new systems including non-nturl mino cids nd nucleic cid bses. Such new genertion FF my be extended using QM theory nd is thus independent of experimentl prmeters. Acknowledgment. This reserch ws funded by DOE-BCTR (DE-FG36-93CH105 81). The fcilities of the MSC re lso supported by grnts from NSF (CHE nd ASC ), Chevron Petroleum Technology Co., Armco, Ashi Chemicl, Owens-Corning, Chevron Chemicl Compny, Ashi Glss, Chevron Reserch nd Technology Co., Hercules, BP Chemicl, nd Beckmn Institute. Some clcultions were crried out t the NSF Sn Diego Supercomputer Center (SDSC).

9 Distnce Dependent Hydrogen Bond Potentils J. Phys. Chem. B, Vol. 101, No. 24, Supporting Informtion Avilble: Tbles of HF/6-31G** complextion energies nd MM evlution of the complextion energies (4 pges). Ordering informtion is given on ny current msthed pge. References nd Notes (1) Sponer, J.; Leszczynski, J.; Hobz, P. J. Biomol. Struct. Dyn. 1996, 14, (2) () Delbene, J. E.; Shvitt, I. J. Mol. Struct. (THEOCHEM) 1994, 307, (b) Delbene, J. E. J. Phys. Chem. 1993, 97, (c) Delbene, J. E.; Shvitt, I. Int. J. Quntum Chem. 1989, (d) Delbene, J. E. Int. J. Quntum Chem. 1987, (e) Delbene, J. E. J. Comput. Chem. 1987, 8, (f) Delbene, J. E. J. Chem. Phys. 1987, 86, (3) () Szczesnik, M. M.; Ltjk, Z.; Scheiner, S. J. Mol. Struct. (THEOCHEM) 1986, 28, (b) Ltjk, Z.; Scheiner, S. J. Chem. Phys. 1984, 81, (c) Clrk, T.; Chndrsekhr, J.; Spitzngel, G. W.; Schleyer, P. V. R. J. Comput. Chem. 1983, 4, (d) Spitzngel, G. W.; Clrk, T.; Chndrsekhr, J.; Schleyer, P. V. R. J. Comput. Chem. 1982, 3, (4) Sponer, J.; Leszczynski, J.; Hobz, P. J. Comput. Chem. 1996, 17, (5) () Sponer, J.; Hobz, P. Chem. Phys. 1996, 204, (b) Sponer, J.; Florin, J.; Hobz, P.; Leszczynski, J. J. Biomol. Struct. Dyn. 1996, 13, (c) Sponer, J.; Leszczynski, J.; Hobz, P. J. Phys. Chem. 1996, 100, (6) Sponer, J.; Leszczynski, J.; Hobz, P. J. Phys. Chem. 1996, 100, (7) Sponer, J.; Leszczynski, J.; Vetterl, V.; Hobz, P. J. Biomol. Struct. Dyn. 1996, 13, (8) Gould, I. R.; Kollmn, P. A. J. Am. Chem. Soc. 1994, 116, (9) Hutter, M.; Clrk, T. J. Am. Chem. Soc. 1996, 118, (10) Ynson, I. K.; Teplitsky, A. B.; Sukhodub, L. F. Biopolymers 1979, 18, (11) Myevsky, A. A.; Sukhorukov, B. I. Nucleic. Acids Res. 1980, 8, (12) Cornell, W. D.; Cieplk, P.; Byly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Cldwell, J. W.; Kollmn, P. A. J. Am. Chem. Soc. 1996, 118, (13) Mckerell, A. D.; Wiorkiewiczkuczer, J.; Krplus, M. J. Am. Chem. Soc. 1995, 117, (14) Prnt, J.; Wierschke, S. G.; Jorgensen, W. L. J. Am. Chem. Soc. 1991, 113, (15) () Ringnld, M. N.; Lnglois, J-M.; Greeley, B. H.; Murphy, R. B.; Russo, T. V.; Cortis, C.; Muller, R. P.; Mrten, B.; Donnelly, R. E.; Minz, D. T.; Wright, J. R.; Pollrd, W. T.; Co, Y.; Won, Y.; Miller, G. H.; Goddrd, W. A., III; Friesner, R. A. PS-GVB 2.34 from Schrödinger Inc., (b) Muller, R. P.; Lnglois, J-M.; Ringnld, M. N.; Friesner, R. A.; Goddrd, W. A., III. J. Chem. Phys. 1994, 100, (c) Murphy, R. B.; Friesner, R. A.; Ringnld, M. N.; Goddrd, W. A., III. J. Chem. Phys. 1994, 101, (d) Lnglois, J.-M.; Ymski, T.; Muller, R. P.; Goddrd, W. A., III. J. Phys. Chem. 1994, 98, (e) Greeley, B. H.; Russo, T. V.; Minz, D. T.; Friesner, R. A.; Lnglois, J.-M.; Goddrd, W. A., III; Donnelly, R. E.; Ringnld, M. N. J. Chem. Phys. 1994, 101, (16) Sponer, J.; Burcl, R.; Hobz, P. J. Biomol. Struct. Dyn. 1994, 11, (17) The PS-GVB implementtion of this triple-ζ correltion-consistent Dunning 36 bsis set does not include diffuse f functions on second-row elements [thus the nottion cc-pvtz9-(f)] nd d functions on hydrogen; however this hs been shown to hve little effect on hydrogen bond energies. 2 (18) () Sebo, S.; Puly, P. Theor. Chim. Act 1986, 69, 357. (b) Sebo, S.; Puly, P. Annu. ReV. Phys. Chem. 1993, 44, 213. (c) Sebo, S.; Tong, W.; Puly, P. J. Chem. Phys. 1993, 98, (19) Foster, J. M.; Boys, S. F. ReV. Mod. Phys. 1960, 32, 300. (20) Boys, S. F.; Bernrdi, F. Mol. Phys. 1970, 25, 553. (21) Tnnor, D. J.; Mrten, B.; Murphy, R.; Friesner, R. A.; Sitkoff, D.; Nicholls, A.; Ringnld, M. N.; Goddrd, W. A., III; Honig, B. J. Am. Chem. Soc. 1994, 116, (22) Distributed by Moleculr Simultions Inc., Sn Diego, CA. (23) Myo, S. L.; Olfson, B. D.; Goddrd, W. A., III. J. Phys. Chem. 1990, 94, (24) Quntum mechnicl clcultions were performed on either HP 9000/735 CRX worksttions, Cry C90 (Sn Diego Super Computer Center), or IBM SP2 (Cornell Theory Center). Moleculr mechnics clcultions were performed on either Silicon Grphics 4D/480 SMP server or Silicon Grphics Indigo2 Extreme worksttions. (25) If four conformtions of the AT bse pir contribute eqully, the experimentlly mesured ssocition constnt (K obs) will be overestimted by fctor of 4. Tht is K obs ) 4K true. A substitution for K where K ) Ae -( H/KT) leds to Ae -( H obs /KT) ) 4(Ae -( H true ) ). If T ) 333, then KT ) kcl/mol leding to H obs+ KT ln(4) ) H true. If H obs )-13.0 kcl/mol, this leds to H true ) ) kcl/mol. (26) Ltjk, Z. J. Mol. Struct. (THEOCHEM) 1991, 251, (27) Ltjk, Z. J. Mol. Struct. (THEOCHEM) 1992, 253, (28) Curtiss, L. A.; Frurip, D. J.; Blnder, M. J. Chem. Phys. 1979, 71, (29) Xnthes, S. S.; Dunning, T. H., Jr. J. Chem. Phys. 1993, 99, (30) Dsgupt, S.; Hmmond, W. B.; Goddrd, W. A., III. J. Am. Chem. Soc. 1996, 118, (31) Weiner, S. J.; Kollmn, P. A.; Nguyen, D. T.; Cse, D. A. J. Comput. Chem. 1986, 7, (32) Cieplk, P.; Cornell, W. D.; Byly, C.; Kollmn, P. A. J. Comput. Chem. 1995, 16, (33) Cornell, W. D.; Cieplk, P.; Byly, C. I.; Kollmn, P. A. J. Am. Chem. Soc. 1993, 115, (34) The chrges for HC1 were set to , nd the chrge t C1 ws djusted so s to hve net neutrl chrge for ech bse. (35) Hobz, P.; Hublek, F.; Kbelc, M.; Mejzlik, P.; Sponer, J.; Vondrsek, J. Chem. Phys. Lett. 1996, 257, (36) Dunning, T. H. J. Chem. Phys. 1989, 90, (37) Senger, W. Principles of Nucleic Acid Structure; Springer- Verlg: New York, Berlin, Heidleberg, Tokyo, 1984; pp , nd references therein.