The change in the vibrational density of states of a protein (dihydrofolate reductase) on binding a ligand (methotrexate) is determined using inelastic neutron scattering. The vibrations of the complex soften significantly relative to the unbound protein. The resulting free-energy change, which is directly determined by the density of states change, is found to contribute significantly to the binding equilibrium

Balog, Erika

Becker, Torsten

Daniel, Roy M.

Finney, John L.

Lechner, Ruep

Oettl, Martin

Smith, Jeremy C.

English

Name not available

Direct determination of vibrational density of states change on ligand binding to a protein

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P H Y S I C A L R E V I E W L E T T E R S week ending9 JULY 2004VOLUME 93, NUMBER 2Direct Determination of Vibrational Density of States Change on Ligand Binding to a ProteinErika Balog,1,* Torsten Becker,1 Martin Oettl,2 Ruep Lechner,3 Roy Daniel,2 John Finney,4 and Jeremy C. Smith1,†1Computational Molecular Biophysics, IWR, Universita¨t Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany2Department of Biological Sciences, University of Waikato, Private Bag 3105 Hamilton, New Zealand3Hahn Meitner Institut Berlin, BENSC, Glienicker strasse 100, 14109 Berlin, Germany4Department of Physics and Astronomy, University College London, London WCIE 6BT, United Kingdom(Received 18 September 2003; published 9 July 2004)028103-1The change in the vibrational density of states of a protein (dihydrofolate reductase) on binding aligand (methotrexate) is determined using inelastic neutron scattering. The vibrations of the complexsoften significantly relative to the unbound protein. The resulting free-energy change, which is directlydetermined by the density of states change, is found to contribute significantly to the bindingequilibrium.DOI: 10.1103/PhysRevLett.93.028103 PACS numbers: 87.15.HeDHFR from E.coli was dissolved in D2O equilibrated at4 C overnight and freeze dried. NADPH and NADPHfactors were normalized to the elastic peak height. Theerrors in Sq;! (see Fig. 1) are statistical errors of theAn understanding of how ligands bind to proteinsis of fundamental importance in biology and medi-cine [1–6]. Protein:ligand association has been assumedto be dominated by factors such as the hydrophobic effect,hydrogen bonding, electrostatic, and van der Waals inter-actions. However, as early as 1963 it was suggested thatan additional mechanism might exist, due to increasedflexibility in the protein:ligand complex manifested by achange in the spectrum of vibrations due to formationin the complex of new, intermolecular interactions[7–13]. Theoretical normal mode analyses, used to esti-mate this vibrational change on insulin dimerization[12] and on water binding to bovine pancreatic trypsininhibitor [13], have suggested that the effect is likely tobe thermodynamically important. However, experimen-tal determination of the vibrational change has beenlacking.Inelastic neutron scattering, in which the dynamicstructure factor Sq;! is measured as a function of thescattering wave vector q and energy transfer h! (where!is the angular frequency), has been used to determine thevibrational density of states (frequency distribution) g!for several proteins [14–16]. Here we present an experi-mental determination of the change in g! on binding aligand to a protein. This determination allows thermo-dynamic quantities associated with the vibrationalchange to be derived. The enzyme chosen is dihydrofolatereductase (DHFR), an important target for anticancerand antibacterial drugs [17–21]. DHFR catalyzes thereduction of dihydrofolate to tetrahydrofolate in the pres-ence of the nicotinamide adenine dinucleotide phosphate(NADPH) cofactor. The ligand used is methotrexate(MTX), a folate antagonist of DHFR that has been usedeffectively as a cytotoxic agent in the treatment of cancers[22].To minimize scattering from solvent molecules, thesystem was exchanged with D2O. To do this, lyophilized0031-9007=04=93(2)=028103(4)$22.50 MTX were added in equimolar ratios to the enzyme. Asthe dissociation constants of DHFR with NADPH andMTX are low (KNADPHd  0:01 M, KMTXd  0:15 M[23]), it can be assumed that the ligands bind quan-titatively to the enzyme. D2O was added, the solutionsequilibrated for 4 h at 4 C and freeze dried, and afinal exchange step involving dissolution in D2O andlyophilization was performed. The uncomplexed en-zyme (DHFR NADPH) and the complexed enzyme(DHFR NADPHMTX) were hydrated to a degreeof 30%, i.e., 30 mg of D2O per 100 mg of dry weightprotein. This was performed by equilibrating the samplesin a saturated solution atmosphere (KBr in D2O) at 20 Cfor 3 days.For the neutron experiments, the samples were con-tained in an aluminum sample holder. Sample amountswere 98.1 mg (uncomplexed) and 108.6 mg (complexed).The measurements were performed on the time-of-flightspectrometer IN6 at the Institut Laue-Langevin (ILL),Grenoble, with an incident neutron beam wavelengthof 5.12 A˚ . The scattering experiments were performedat 120 K to ensure that all dynamics present is harmonic.Accumulation times were 24 h=sample. Samples wereoriented at 135 with respect to the incident beam. Bothsample transmissions were 97.7%, high enough to ensurethe absence of multiple scattering effects. The raw datawere corrected using the INX program at ILL [24]. Thisprogram normalizes the detector responses with respectto an angle-independent standard vanadium sample,normalizes each data collection run to the number ofincident neutrons, performs slab corrections for self-shielding, and subtracts the cell scattering from samplecell scattering. To improve the statistics, the spectraderived from 122 scattering angles (from 10 to 114)were binned into 11 constant-angle spectra. In order tocompare the relative differences in the inelastic part ofthe spectra of the two samples, dynamical structure2004 The American Physical Society 028103-10 5 10 15 200.00.51.0g(ω) (mode/cm-1 )ω (cm-1)0 40 80 120048FIG. 2. Vibrational frequency distribution g! for un-complexed (black) and complexed (gray) forms of DHFR.Inset: enlarged frequency region of the spectra.0 20 40 60 80 100 120 140 160 180 2000.00000.00010.00020.00030.00040.0005S(q,ω) (arb. units)ω (cm-1)5 10 15 20 25 30 35 40 45 500.00020.00030.00040.0005FIG. 1. Dynamic structure factor versus frequency for un-complexed DHFR (black curve) and complexed with metho-trexate form of DHFR (gray curve) at 120 K. Data from allscattering angles are summed. Both spectra are normalized tothe elastic peak height. Inset: the low frequency region of thespectra.P H Y S I C A L R E V I E W L E T T E R S week ending9 JULY 2004VOLUME 93, NUMBER 2measurement. The errors in deduced quantities were de-termined by the error propagation.The experimental vibrational frequency distribu-tion gexp! was obtained from the spectra using thelimit [14,16]gexp!  limq!06!hq2e h!=kT  1Sq;!; (1)where h is Planck’s constant divided by 2, k is theBoltzmann constant, and T is the temperature.gexp! is on a relative scale. To determine the absolutedensity of states g!, use was made of the fact that, in theharmonic approximation at low q, the elastic scatteringintensity Sq; 0 is given by Sq; 0  expu2q2=6	,where u2 is the mean-square displacement. Thus, u2 canbe determined from the gradient of lnSq; 0 vs q2. Thecorresponding mean-square displacement u2calc calculatedfrom gexp! is obtained by integrating as follows: u2calc h2MRgexp! coth h!2kTd!, where M is the protein mass.The absolute density of states can then be derived bynormalizing as follows: g!  u2=u2calcgexp!.Figure 1 shows the dynamic structure factorSq;! of the ‘‘uncomplexed’’ (DHFR NADPH) and‘‘complexed’’ (DHFR NADPHMTX) forms of theenzyme. A significant difference can be seen in the low-frequency region of the spectra (! below 40 cm1).The fact that Sq;! is higher for the complexed in thelow-frequency region implies that the complexed form ofthe enzyme has a higher number of low-frequency modes[see Eq. (1)] and thus is more flexible than the uncom-plexed form. This is confirmed by Fig. 2, which showsthat, below15–20 cm1, g! of the complexed form issignificantly higher than that of the uncomplexed protein.028103-2For the protein to soften on binding, there must be ashift in g! from higher frequencies (in the uncom-plexed protein) to lower frequencies (in the complexed).One possibility for this that would be consistent withFig. 1 is that softened modes may be of too-high fre-quency in the uncomplexed protein to be detectable by theinstrument. However, there is evidence of a frequencyshift occurring within the frequency range shown inFig. 2. Integration of the difference between g! of thetwo samples shows that the net equivalent of about twomodes are transferred from the 40–80 cm1 region in theuncomplexed protein to the region below 20 cm1 in thecomplexed.The change in g! over the range 40–80 cm1 is notaccompanied by a statistically significant change in theSq;! in Fig. 1. The reason for this is that Sq;! isamplitude weighted. Thus, removal of a low-amplitude,higher-frequency mode from the spectrum leads to only arelatively small intensity loss, whereas adding a high-amplitude, low-frequency mode adds a relatively largeintensity. Consequently, the shifted modes scatter muchmore strongly in the complexed than in the uncomplexedmolecule, with the net result that the spectral changeappears as an increase in intensity at low frequencies inthe complexed.The vibrational partition function Zvib, i.e., the parti-tion function associated with the vibrational energy levelsin a harmonic system, is determined by g! as follows[25]:Zvib Y3N6i1e h!i=21 e h!i Y1!!mine h!=21 e h!g!;where !min is the lowest frequency in the system andb  1=kT. The associated Helmholtz vibrational freeenergy Avib is given by Avib  kT lnZvib, the energy by028103-2P H Y S I C A L R E V I E W L E T T E R S week ending9 JULY 2004VOLUME 93, NUMBER 2Evib   @@ lnZvib (this is the enthalpy change for aprocess for which the volume change can be neglected),and the entropy by Svib  klnZvib   E	.The free-energy change $Avib calculated from thedensity-of-states change in Fig. 2 is 17 4 kJ=mol at300 K, favoring binding. The free-energy change con-tains a large entropic contribution T$Svib (256 kJ=mol) that is partially compensated by the enthalpyterm $ Evib (8 2 kJ=mol) that opposes binding.The thermodynamic results are subject to errors asso-ciated with the use of the harmonic approximation andthe necessity of determining the dynamic structure factoron an absolute scale. The scattering measurements wereperformed at 120 K. At this temperature the proteinexhibits only harmonic vibrational dynamics [15], thuspermitting the direct determination of the vibrationaldensity of states.The 300 K vibrational density of states of trehalose-coated myoglobin has been found to be identical to thatat 100 K, indicating harmonic behavior [26]. For hydratedproteins at physiological temperatures, a significantcontribution to the atomic mean-square displacementsarises from anharmonic dynamics [26–28]. Theseanharmonic motions, together with overdamping of thelow-frequency modes, result in quasielastic scatteringthat renders difficult the derivation of model-independentthermodynamic quantities from experimental data [28].It is conceivable that anharmonic degrees of freedommight also be modified on ligand binding. However,molecular dynamics simulations suggest that 99:5% ofthe modes in a protein are effectively harmonic at 300 K[29]. Assuming the protein does remain harmonic, thedensity-of-states change will be the same at 300 as it isat 120 K.The dynamical change seen here indicates softening ofthe protein on complexation. Normal mode calculationson proteins have indicated that the vibrational modes inthe frequency range at which the change is seen hereinvolve mainly collective displacements of groups ofatoms distributed throughout the protein [30]. Thesemodes may be modified by environmental effects,although in the present case the sample preparation isconsistent with the environments of the complexed andthe uncomplexed forms being the same. Normal modecalculations concur with the present findings in that theyalso indicate an increase in flexibility on ligand bindingto proteins and protein:protein association [12,13].Furthermore, increased backbone conformational flexi-bility on binding a hydrophobic ligand to mouse majorurinary protein has been detected using nuclear magneticresonance (NMR) relaxation experiments [31]. However,these results contrast with other observations using NMRand crystallography of a flexibility decrease on proteinbinding to small organic ligands [32–34]. NMR andcrystallographic measurements are likely to be domi-nated by changes in anharmonic degrees of freedom not028103-3present in the conditions studied here. Moreover, thevibrational changes seen in the present work are notdetectable using NMR or crystallography [12,13].There remains much to learn about the various contri-butions to ligand binding free energies. For example,although hydrogen bonds normally must be satisfied,whether they bring any net contribution to the bindingfree energy in aqueous solution is debatable. For thepresent system, although significant ligand:protein hy-drogen bonding exists, free-energy perturbation calcula-tions suggest that hydrophobic interactions contribute asmuch to the binding free energy as do hydrophilic [35].Another effect that remains to be accurately quantified isthe loss on binding of the whole-molecule translationaland rotational entropic free energies of the protein andligand [27,36–39].The contribution elucidated here, that from vibrationalchanges, has been hitherto largely neglected in the con-sideration of binding equilibria, due largely to the ab-sence of an experimental technique for determining it.The estimation of 17 4 kJ=mol for the vibrationalfree-energy change can be compared with the experimen-tally estimated total binding free energy in the presentsystem, which is 39 kJ=mol [23]. This suggests that thevibrational change is thermodynamically significant andwould contribute a factor of103 to the binding constant.This illustrates how modifications of equilibrium internalfluctuations in a protein can have consequences for bind-ing equilibria of biomedical importance. Recently, thevibrational effect has been included together with elec-trostatic, van der Waals, and nonpolar terms in an em-pirical theoretical analysis of ligand binding free energies[40]. Whether the vibrational softening effect seen here isgeneral for protein:ligand interactions remains to be de-termined. The direct access to the vibrational density ofstates provided by inelastic neutron scattering holdspromise for the study of vibrational thermodynamicchanges in many biomolecular association processes.We gratefully acknowledge Jacques Ollivier from theInstitut Laue-Langevin for help with neutron experi-ments and Stefan Fischer for help and useful discussions.*Present address: Institut de Hautes Etudes Scientifiques,35 route de Chartres, 91440 Bures sur Yvette, France.†Corresponding author.Electronic address: biocomputing@iwr.uni-heidelberg.de[1] W. Wang et al., Annu. Rev. Biophys. Biomol. Struct. 30,211 (2001).[2] M. L. Lamb and W. L. Jorgensen, Curr. Opin. Chem. Biol.1, 449 (1997).[3] L.Y. Lian et al., Methods Enzymol. 239, 657 (1994).[4] I. M. Klotz, Q. Rev. Biophys. 18, 227 (1985).[5] S. J. Benkovic, C. A. Fierke, and A. M. Naylor, Science239, 1105 (1988).[6] M. K. Gilson et al., Biophys. J. 72, 1047 (1997).028103-3P H Y S I C A L R E V I E W L E T T E R S week ending9 JULY 2004VOLUME 93, NUMBER 2[7] I. Z. Steinberg and H. A. Scheraga, J. Biolumin.Chemilumin. 238, 172 (1963).[8] M. I. Page and W. P. Jencks, Proc. Natl. Acad. Sci. U.S.A.68, 1678 (1971).[9] J. M. Sturtevant, Proc. Natl. Acad. Sci. U.S.A. 74, 2236(1977).[10] H. P. Erickson, J. Mol. Biol. 206, 465 (1989).[11] A.V. Finkelstein and J. Janin, Protein Eng. 3, 1 (1989).[12] B. Tidor and M. Karplus, J. Mol. Biol. 238, 405 (1994).[13] S. Fischer, J. C. Smith, and C. S. Verma, J. Phys. Chem. B105, 8050 (2001).[14] S. Cusack et al., J. Mol. Biol. 202, 903 (1988).[15] W. Doster, S. Cusack, and W. Petry, Nature (London)337, 754 (1989).[16] J. C. Smith et al., J. Chem. Phys. 85, 3636 (1986).[17] M. R. Sawaya and J. Kraut, Biochemistry 36, 586 (1997).[18] D. M. Epstein, S. J. Benkovic, and P. E. Wright,Biochemistry 34, 11037 (1995).[19] E. E. Howell et al., Science 231, 1123 (1986).[20] S. R. Stone and J. F. Morrison, Biochemistry 23, 2753(1984).[21] T. Kamiyama and K. Gekko, Biochim. Biophys. Acta1478, 257 (2000).[22] F. M. Huennekens, Adv. Enzyme Regul. 34, 397 (1994).[23] J. Basran et al., Biochemistry 34, 2872 (1995).[24] F. Rieutord, Institut Laue-Langevin Report No. 90RI17T,1990.[25] D. A. McQuarrie, Statistical Mechanics (Harper & Row,028103-4New York, 1976).[26] L. Cordone et al., Biophys. J. 76, 1043 (1999).[27] A. Tournier and J. C. Smith, Phys. Rev. Lett. 91, 208106(2003).[28] J. C. Smith et al., J. Chem. Phys. 93, 2974 (1990).[29] A. Kitao, S. Hayward, and N. Go, Proteins 33, 496(1998).[30] B. Brooks and M. Karplus, Proc. Natl. Acad. Sci. U.S.A.80, 6571 (1983).[31] L. Zidek, M.V. Novotny, and M. J. Stone, Nat. Struct.Biol. 6, 1118 (1999).[32] J.W. Cheng, C. A. Lepre, and J. M. Moore, Biochemistry33, 4093 (1994).[33] C. Rischel et al., Biochemistry 33, 13 997 (1994).[34] D. Fushman, O. Ohlenschlager, and H. Ruterjans,J. Biomol. Struct. Dyn. 11, 1377 (1994).[35] U. Singh and S. Benkovic, Proc. Natl. Acad. Sci. U.S.A.85, 9519 (1988).[36] M. H. Zaman, R. S. Berry, and T. R. Sosnick, Proteins 48,341 (1999).[37] A. Tamura and P. L. Privalov, J. Mol. Biol. 273, 1048(1997).[38] M. Karplus and J. Janin, Protein Eng. 12, 185 (1999).[39] Y. B. Yu, P. L. Privalov, and R. S. Hodges, Biophys. J.81, 1632 (2001).[40] S. Schwarzl, T. B. Tschopp, J. C. Smith, and S. Fischer,J. Comput. Chem. 23, 1143 (2002).028103-4

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Direct determination of vibrational density of states change on ligand binding to a protein

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