7 April 2000

Ž .Chemical Physics Letters 320 2000 316–322www.elsevier.nlrlocatercplett

23Na Solid-state NMR studies of hydrated disodiumadenosine triphosphate

Shangwu Ding, Charles A. McDowell)

Department of Chemistry, UniÕersity of British Columbia, 2036 Main Mall, VancouÕer, British Columbia V6T 1Z1, Canada

Received 24 January 2000; in final form 22 February 2000

Abstract

X Ž .The biologically important compound hydrated disodium adenosine 5 -triphosphate ATP was studied focusing on the23 Ž .Na nucleus spin quantum number Is3r2 as probe in various solid-state NMR techniques including magic-angle

Ž . Ž . Ž .spinning MAS , cross-polarization MAS CPMAS and multi-quantum MAS MQMAS at 4.7 and 9.4 T. MQMASexperiments enabled the resolution of all the four crystallographically different 23Na sites in the unit cell in the MQMASspectrum at 4.7 T, but not at 9.4 T. The four sites were successfully assigned and the principal elements of the quadrupolartensors and isotropic chemical shifts of the 23Na nuclei at each lattice site determined by analyzing and computer simulatingthe above experimental spectra. q 2000 Elsevier Science B.V. All rights reserved.

1. Introduction

X Ž .Adenosine 5 -triphosphate ATP is a well-knowncompound in biochemistry and biology because ofits crucial role in energy storage and energy transferin living organisms. Significantly, it plays an impor-tant role in more complex biological processes suchas muscle contraction and ion transport.

The crystallizable sodium salt of adenosine 5X-tri-phosphate is the hydrated form. A thorough crystal-lographic investigation of this salt using X-ray

w xdiffraction was carried out by Kennard et al. 1 . Thespace group of this crystalline compound is P2 2 21 1 1

and there are two molecules of ATP, four sodiumions and six water molecules in each unit cell. Allthe four sites of sodium ions are non-equivalent,

) Corresponding author. Fax: q1-604-822-2847; e-mail:mcdowell@chem.ubc.ca

crystallographically. The structure is shown inFig. 1. There are in this crystal two classes ofsodium ions: the first class embraces ions Na1 andNa2 which share two phosphate oxygen nuclei toform a bridge between the two sodium ions. Thesecond class, consisting of Na3 and Na4, plays a lessdominant role and is considered to have less influ-ence on the crystalline structure of ATP. The mainfunction of the atoms in this class is to link ATPdimers. Notice that the Na4 ion is only 5-coordi-nated, whereas the Na1, Na2 and Na3 ions are6-coordinated. Because of the importance of thesodium ions in coordinating the ATP dimers andtheir unique role in ionic solutions of DNA, it is,therefore, desirable to obtain the NMR interactionparameters such as the chemical shifts and quadrupo-

Ž .lar coupling constants QCCs or electric field gradi-Ž .ent EFG tensors to understand fully the effects of

such ions on the functions of ATP in biologicalfluids.

0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 00 00272-4

( )S. Ding, C.A. McDowellrChemical Physics Letters 320 2000 316–322 317

Fig. 1. The molecular and crystal structure of hydrated disodium adenosine 5X-triphosphate. Top left: Molecular formula. Top right:numbering scheme. Bottom: Coordination of the four Na ions at their lattice sites.

To our knowledge, however, no solid-state NMRŽ .or pure nuclear quadrupole resonance NQR investi-

gation of the 23 Na salt of adenosine 5X-triphosphatehas been published. In fact, few publications haveappeared which focus on odd-half-integer quadrupo-lar nuclear spins in biologically interesting com-pounds, although this type of spin species accountsfor a majority of NMR sensitive nuclei. A notewor-thy exception is the recent work on 23 Na MAS,CPMAS and quadrupolar nutation NMR spectra of

w xNa-DNA in the solid-state 2 . With the contempo-rary developments in solid-state NMR methodolo-gies, however, interesting and significant results areclearly achievable.

The goal of this work is to determine the chemicalshifts and EFG tensors of the four 23 Na lattice sitesin this compound using solid-state NMR techniquessuch as MAS, CP-MAS and MQMAS at differentapplied magnetic fields. These methods are neces-sary for this compound because our initial studyshowed that the four 23 Na sites were indistinguish-

able from the spectral results of single pulse MAS orfrom nutation MAS at two magnetic field strengths.Combining the experimental results with the quan-tification scheme for MQMAS spectra recently

w xproposed 3 , it proved possible to determine theprincipal elements of the EFG tensors and isotropicchemical shifts of the 23 Na nuclei at all the four sitesoccupied by those nuclei in the unit cell.

2. Experimental

Two NMR spectrometers, Bruker MSL-200 andMSL-400 instruments, were used with operating fre-quencies of 200.13 and 400.13 MHz for protons,respectively. To achieve optimum RF field homo-geneity and minimize the susceptibility distribution,a spherical sample of 5 mm diameter was containedwithin a 7-mm rotor in a Doty Dynamic-Angle Spin-

Ž .ning DAS probe when experiments were performedon the MSL-200 spectrometer, whereas, a 5-mm

( )S. Ding, C.A. McDowellrChemical Physics Letters 320 2000 316–322318

rotor probe was used for those experiments per-formed on the MSL-400 instrument. The spinningspeeds used were 3–6.5 kHz for the 7-mm rotor and10.5 kHz for the 5-mm rotor, respectively. Thepolycrystalline sample was purchased from Aldrichand used without further processing.

In the single pulse NMR experiments, a hardŽ .short pulse f1ms was used to obtain the best

lineshapes. In the CPMAS experiments, the conven-w xtional pulse sequences 4,5 with a contact time of

500 ms was used, longer contact times yield muchlower sensitivity, meaning the proton relaxation time

Ž .in the locking field is short f300ms . Using thew xsite population quantification method 3 , an MQ-

w xMAS 6 experiment can be performed using thew xtwo-pulse scheme 7 without invoking special re-

w xquirements on pulse lengths 8–13 pulse shapingw x w x14,15 or rotor spinning speeds, etc. 16,17 , al-though these techniques, particularly when some areapplied simultaneously, may improve sensitivity and

w xspectral resolution 18 . High-power proton decou-Ž .pling approximately 70 kHz was used for all exper-

iments.While only MAS and MQMAS results are re-

quired in determining the interaction parameters, CP-MAS and nutation MAS spectra can be studied toprovide supportive information and data for the siteidentification. The experimental parameters varieddepending on the experimental method and the NMRspectrometer used, details of which can be found inthe caption of each of the figures shown below.

3. Computer simulation methods

MAS and MQMAS spectra were used to obtainthe NMR interaction parameters while other spectrasuch as NUTMAS and CPMAS were used to verifythe obtained parameters and to study spin dynamics.Here the principles and practical procedures are out-lined. More elaborated expositions are given in pre-

w xvious publications 3,14,15,19–23 .There are three principal coordinate systems

needed to describe the quadrupolar spin system,namely, the EFG axis system, the rotor axis systemand the laboratory axis system. Two sets of Eulerangles are required for the description of the trans-formation relationships between these coordinate

systems, and these are: EFG ™ Ža ,b ,g . ROTOR™

Žv r t,u ,0. LAB, where v is the sample spinningr

speed and u is the rotation axis direction which isusually 54.748 relative to the direction of the mainmagnetic field.

3.1. MAS spectra

The computer simulation of MAS spectra is ac-complished by starting from the initial density matrixŽ .r 0 immediately after the short RF excitation pulse

Ž . Ž23.and which is given by r 0 s I , corresponding tox< : < :the central transition 1r2 l y 1r2 , of the

quadrupolar spin 3r2 energy level diagram. The spinensemble then evolves under the followingquadrupolar Hamiltonian

H sv 3 I 2 y1 qH Ž1. 1Ž .Ž .Q q z Q

where the first term is the first order quadrupolarHamiltonian while the second term is the secondorder interaction Hamiltonian which can be found in

w xRefs. 19,23 . The quadrupolar frequency v is givenqQ'by v s 2r3 V withq 20

q2Q Ž2. Ž2. QV s" DD v t ,u ,0 DD a ,b ,g rŽ . Ž .Ý2 j m j r nm 2 n

m ,nsy2

js0,"1,"2 2Ž .where DD is the Wigner rotational transformationmatrix, r Q represents the principal elements of the2 n

electric field gradient tensor and h is the asymme-Q

try parameter: r sh v , r s0 and r s20 Q Q 2 "1 2 " 2' Ž .6 v where v sQCCr8 I 2 Iy1 .Q Q

The contributions of the RF offset and the isotropicchemical shift interaction can be included in theHamiltonian d I . The time domain signal of the0 z

central transition is calculated from the equation

t tŽ . Ž .yi d t H qd I i d t H qd IH HQ 0 z Q 0 zS t sTr e r 0 e 3Ž . Ž . Ž .0 0

Ž .From Eq. 3 the MAS spectrum is then obtained byapplying a Fourier transform.

3.2. MQMAS spectra

In this case, the density matrix of initial state ofŽ .the system, r 0 , can be chosen as I , and the totalz

( )S. Ding, C.A. McDowellrChemical Physics Letters 320 2000 316–322 319

Hamiltonian can be expressed in the rotating frameas

HsH qH 4Ž .Q RF

H sv t IŽ .RF 1 f

where v and f are the amplitude and the phase of1

the RF pulse, respectively.From the Liouville equation, the density matrix

Ž . Ž .r t at any time t )0 is given byy1

r t sU t ,0 r 0 U t ,0 5Ž . Ž . Ž . Ž . Ž .For the spin evolution during the RF pulsing, the

Ž . ŽyiH0t d tX H Ž tX ..evolution operator U t,0 sT e while for

‘free’ evolution of the spin between the pulses, it isŽ . ŽyiH0

t d tX HQŽ tX ..U t,0 sT e . Here T is the Dyson time-ordering operator.

For the two-pulse scheme MQMAS experiment,P y t yP y t , which is mostly used, the phases1 1 2 2

of the two pulses P and P are systematically1 2Žchanged so that the triple quantum coherences for

. w xspin-3r2 are selected in the first dimension 6,7 .The time-domain two-dimensional MQMAS signalis thus given as,

t q t q t q t X X1 2 p1 p 2 Ž ..Žyi d t H tH QS t ,t sTr T e r tŽ . Ž .t q t q t1 p1 p 21 2 14 1

=t q t q t q t X X1 2 p1 p 2 Ž ..Ž i d t H tH Qe 6Ž .t q t q t1 p1 p 2

where t and t are the width of the first andp1 p2

second pulses, respectively. The triple quantum co-Ž .herence r t can be calculated according to Eqs.14 1

Ž . Ž . w x6 and 7 . The final 2D ‘FID’ is sheared 6,7accordingly. For spin-3r2 like 23 Na, it is realized byusing the equation

yi 7v t r92 1S t ,v sFT S t ,t e 7Ž . Ž . Ž .1 2 2 1 2

where FT is the Fourier transform with respect to2Ž .t . The Fourier transform of S t ,v with respect to2 1 2

t gives the required MQMAS spectrum. For higher1Ž .quadrupolar spin systems, the faction 7r9 in Eq. 7

Ž . Ž . Ž w x.should be changed to C I rC 1r2 Refs. 6,74 4

where I is the order of the MQC excited in the firstdimension. The MQMAS spectrum can be used todetermine the principal values of the quadrupolar

Ž .interaction tensor EFG as well as the isotropicchemical shift. The simulation programs were writ-ten in FORTRAN code and run on an IBM RISC-6000computer.

4. Results and discussions

The QCCs and asymmetry parameters h s of theQ

different 23 Na nuclei at all four resolved lattice sitescan be obtained by simulating the F2 dimension of

w xthe 2D MQMAS spectrum 3,6–18 . The second-order isotropic contribution can be calculated pre-cisely from the QCCs and the asymmetry parametersw x24 . The isotropic chemical shifts can then be found

Ž .from the F1 dimension isotropic dimension of the2D MQMAS spectrum. Therefore, in principle, todetermine the isotropic chemical shifts, QCCs andasymmetry parameters, one MQMAS spectrum suf-fices. In practice, however, for good precision andfreedom from ambiguity in interpretation, other spec-tra or another MQMAS spectrum at a different mag-netic field may be required. Moreover, to verifyfurther the parameter values, more information otherthan from MAS and MQMAS spectra can be instruc-tive and may make the assignment problem simpler.In this work, apart from 1D MAS and 2D MQMASspectra and CPMAS are also used to ensure thecorrectness of the parameter evaluations and peakassignments.

The 1D experimental MAS spectra at differentrotor spinning speeds and magnetic fields are shown

Ž . Ž . 23Fig. 2. The experimental f and simulated e Na MAS spectraof hydrated disodium ATP obtained at rotor spinning speeds of

Ž . Ž .3.5 left and 10 kHz right , respectively. The asterisks indicatespinning sidebands. The site-separated sub-spectra are shown inŽ . Ž .a–d . The left experimental spectrum f was acquired at 4.7 T

Ž .while the right experimental spectrum f at 9.7 T. The parametersused were from computer simulating the MQMAS spectra shownin Fig. 3.

( )S. Ding, C.A. McDowellrChemical Physics Letters 320 2000 316–322320

at the top of Fig. 2. Obviously, from these spectra itis impossible to identify how many magneticallyinequivalent sites exist in this compound. But bycomparing the spectra observed at two differentmagnetic fields, it seems reasonable to infer that theEFG tensors at these 23 Na nuclei are similar. The

Ž .subspectrum corresponding to each site Fig. 2a–dwas calculated with the parameter values obtainedfrom computer simulating the experimental MQMASspectra at two different magnetic fields shown inFig. 3. The interesting phenomenon shown in Fig. 3

Fig. 3. The experimental 23 Na MQMAS spectra of hydrateddisodium ATP obtained at a rotor spinning speed of 4.5 kHz and

Ž . Ž .4.7 T a and at a rotor spinning speed of 10 kHz and 9.4 T b ,respectively. F1 is the isotropic dimension and F2 is the anisotropic

23 Ž .dimension. The four Na sites are resolved in a and the slicescorresponding to the four sites are displayed and data from whichare used to calculate the quadrupolar parameters. The asterisk inthe diagram denotes the first order rotational sideband. The foursites are overlapped in the MQMAS spectrum at 9.4 T as shown

Ž .in b .

Table 1The 23 Na quadrupolar interaction parameters and isotopic chemi-cal shift of disodium ATP salt by computer simulating 1D MASand 2D MQMAS spectra

Site Isotropic chemical Quadrupolar coupling AsymmetryŽ .shift constant parameter hQ

1 2.8"0.8 ppm 1.40"0.06 MHz 0.88"0.052 9.0"0.8 ppm 1.35"0.06 MHz 0.92"0.053 14.6"0.8 ppm 1.45"0.06 MHz 0.95"0.054 y3.2"0.8 ppm 1.38"0.06 MHz 0.85"0.05

is that the isotropic dimension of the MQMAS spec-trum at 4.7 T is well resolved while that at 9.4 T isnot. Theoretically, this is because for quadrupolarnuclei, the isotropic contribution arises from two

Ž .sources: a the chemical shift which is proportionalŽ .to the applied magnetic field, and b second-order

quadrupolar interaction which is inversely propo-rtional to the magnetic field. This effect usuallynecessitates MQMAS experiments at different mag-netic fields. This simulation of the MQMAS spec-trum at 4.7 T gives the values of the isotropicchemical shifts, QCCs and asymmetry parameters ofthe 23 Na nuclei at each site. The details of the com-

w xputer simulation can be found in Ref. 3 . The valuesof the parameters deduced are given in Table 1.

The good agreement between the experimentaland computer simulated spectra at different rotorspinning speeds and magnetic fields confirms theaccuracy of the estimated values of the interactionparameters. Four 23 Na sites are clearly resolved inthe MQMAS spectrum at 4.7 T shown in Fig. 3. Thefour isotropic chemical shifts can be readily calcu-lated as well as the QCCs and asymmetry parametersŽwhich are obtained by computer simulating the F2dimension slices corresponding to each peak and the

.peak positions in the F1 dimension . The assignmentof these four peaks, however, is not obvious. Theoxygen atoms which carry a nominal charge of y2clearly play a predominant role in determining theelectric field gradient and thus the QCC, and also thechemical shift tensor of each of the 23 Na nuclei inthe unit cell. From the molecular and crystal struc-

w xture 1 ,therefore, we may tentatively make the fol-Žlowing assignments according to the positions of the

. Ž .isotropic peaks : 1 Na3)Na4 because the oxygenatoms bonded to Na3 are closer to the Na3 nuclei

( )S. Ding, C.A. McDowellrChemical Physics Letters 320 2000 316–322 321

Ž . Ž .Fig. 4. The experimental left and computer simulated rightproton™ 23 Na CPMAS spectra of hydrated disodium ATP ob-

Ž .tained at two matching conditions: a v s67 kHz, v s671 H 1 NaŽ .kHz and b v s67 kHz, v s25 kHz. The contact time1 H 1 Na

was 500 ms for both spectra. The sample spinning speed was 3.5kHz. The experimental spectra were recorded at 4.7 T. Thesidebands are marked with asterisks. The theoretical spectra werecalculated with the parameter values listed in Table 1. A cross-re-

Žlaxation time of 5 ms and quadrupolar relaxation time in RF.field of 500 ms were used.

Ž .than are those bonded to Na4. 2 Na3)Na1,Na2because there are five oxygen atoms bonded to Na1and Na2 but there are six oxygen atoms bonded to

Ž .Na3. 3 Na2)Na1 because the oxygen atomsbonded to Na2 are closer to Na2 than those to Na1.Ž .4 Na4 is least deshielded because it is only five-co-ordinated. Therefore, the tentative assignment is Na3)Na2)Na1)Na4. The assignments can be justi-fied by the fact that the four sets of QCC and

Ž .asymmetry parameters h s are analogous.Q

Moreover, from the values of quadrupolar param-eters listed in Table 1 and the second order isotropiccontribution of the quadrupolar interaction which is

h2Q QCCŽ .given by 0.025 1q QCC, it can be found that3 v 0

the four second-order contributions are almost theŽ .same 2.6 ppm for the main magnetic field of 4.7 T ,

each being much smaller than the separations be-tween adjacent spectral peaks. Therefore, we can bereasonably sure of the correctness of the assignmentsgiven in Table 1 and Fig. 3 based on MAS, MQMASspectra and the available molecular and crystal struc-tural information. The 1H–23 Na CPMAS spectra canqualitatively describe the distances between thesodium and hydrogen and the lineshape changes withthe strength of the RF field and the magnitude of

w xQCC 23,25–28 . The spectra shown in Fig. 4 ex-hibit two typical lineshapes with ‘high’ and ‘low’

w xmatching conditions 23 . The experimental spectracan be well reproduced with computer simulation asshown on the right-hand side of Fig. 4. From these

w xspectra and an earlier theoretical description 23 , itis clear that the hydrogen environments of thesesodium ions are similar, evidently the protons form auniform dipolar reservoir.

5. Conclusions

Using MAS and MQMAS NMR techniques sup-plemented with other methods such as nutation andcross-polarization, it was possible to resolve all four23 Na lattice sites in the unit cell of polycrystalline5X-adenosine triphosphate in the experimental spectrataken at 4.7 T. Those spectra measured at 9.4 T werenot well-resolved for reasons explained in the text.The assignments were made possible by comparingthe experimental MAS and MQMAS spectra withthose obtained by computer simulations based on thetheoretical treatment given above and employing anearlier described computer program for calculatingthe 23 Na ion populations at the various lattice sites.From the MQMAS spectral simulations it was alsopossible to obtain the principal values of thequadrupolar coupling tensors, asymmetry parametersand isotropic chemical shifts of the individual 23 Nanuclei at the assigned sites. The assignments of the23 Na resonances in the MQMAS spectra were con-firmed by theoretical simulations and using datafrom other solid-state NMR spectral techniques suchas MAS and CPMAS.

Acknowledgements

We are grateful to the Natural Sciences and Engi-neering Research Council of Canada for researchgrants to C.A.McD. We thank Professor Colin A.Fyfe for permitting us to use his MSL-400 spectrom-eter and high spinning speed probe to record MASand MQMAS spectra.

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