Introduction to single crystal X-ray analysis XIII. Phase determination in protein structure analysis

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1 Technical articles Intrductin t single crystal X-ray analysis XIII.Phase determinatin in prtein structure analysis Akihit Yaman 1.Intrductin The principle single crystal X-ray structure analysis is the same r rganic/inrganic materials and prteins. Hwever, althugh the steps structural analysis are the same, there are mar dierences in the methd executing each step between structural analysis small mlecules and prteins. One the steps where there is a mar dierence is the phase determinatin methd r slving the phase prblem, regarded as the central prblem single crystal X-ray structure analysis. The main methd phase determinatin in small mlecule structure analysis is the direct methd inerring phase via statistical prcessing diractin intensity. In prtein structure analysis, n the ther hand, phase determinatin using the direct methd is impractical, and thus phase is determined experimentally. In the direct methd, a rughly assigned initial phase is imprved by using a phase relatin which takes the magnitude diractin intensity as a clue. Therere, in prtein crystals, which have a cmparatively large lattice, and limited atmic species and deviatin the electrn distributin in the crystal, the magnitude diractin intensity is small cmpared with a small mlecule crystal, and thus it is diicult in principle t apply the direct methd. As an experimental phase determinatin methd r prtein structure analysis, the MIR (Multiple Ismrphus Replacement) methd serves as the classical apprach. The MIR methd derives the phase the target (native) prtein by using the slight shits in phase which ccur when heavy atms are incrprated. This paper explains the MIR methd, and the MAD (Multiple Anmalus Dispersin) methd which uses the wavelength dependence anmalus dispersin. have been incrprated r nt by actually measuring data, and there are many cases where, t btain ne derivative, it is necessary t repeat steps rm saking t measurement/evaluatin at least a ew times t as many as a ew tens times. As a mdiied methd preparing a heavy atm derivative, there is a technique using vaprized idine (1). In particular, the methd using slid idine is extremely easy. The prcess invlves simply cutting a piece idine t the apprpriate size under a micrscpe, aixing it t the side a crystallizatin drp with grease r a similar substance, and then resealing (Fig. 1(b)). It is als pssible t use an idine slutin r a mixed slutin idine and ptassium idide. The methd preparing a heavy atm derivative using vaprized idine has the llwing advantages nt available with ther methds: The crystal yellws as incrpratin prceeds, s it is easy t cnirm prgress.preparatin heavy atm derivative.1. Saking The irst stage experimental phase determinatin is preparatin heavy atm derivative. The typical methd preparing the heavy atm derivative is a technique called saking where the native prtein crystal is saked in heavy atm slutin. The saking prcedure itsel is simple (Fig. 1(a)), but there are many parameters t be varied, such as the heavy atm type, cncentratin, and saking time, therere a cnsiderable amunt labr is required. This is because there is a need t evaluate whether the heavy atms Applicatin Labratries, Rigaku Crpratin. Fig. 1. Schematic diagram prcedure r preparing heavy atm derivative. (a) Methd preparing rdinary heavy atm derivative. (b) Methd preparing heavy atm derivative using vaprized idine. A piece idine is attached t cver glass with grease etc., and sealed. Instead the piece idine, it is als pssible t use an idine slutin, r an idine + KI slutin. Rigaku Jurnal, 34(1),

2 Intrductin t single crystal X-ray analysis XIII. Phase determinatin in prtein structure analysis Saking can be stpped and resumed at any time Only tyrsine side chains expsed t the slvent are idized Ismrphism is high When determining phase, it is pssible t use the high electrn density and large anmalus dispersin idine The likely reasn r the gd ismrphism is that the heavy atm slutin is nt added directly t the crystallizatin drp, and thus there is little change in the envirnment arund the crystal, such as smtic pressure, and nly the rth psitins the tyrsine residue expsed t the slvent are idized, and as a result there is little eect n the direct and indirect intermlecular cntact attributable t the change in structure the prtein mlecule itsel. Since the lcatin where idine is present is tyrsine, this als serves as clue r mdel cnstructin. The drawback the methd using vaprized idine is that it cannt be used in cases where PEG is the precipitant, r in cases where a tyrsyl residue expsed t the slvent is nt present. Vaprized idine absrbed int a crystallizatin drp cntaining PEG ends up crystallizing in the drp. In phase determinatin using the MAD methd, selenmethinine is nrmally incrprated using genetic engineering techniques, and thus heavy atm saking is unnecessary. Althugh this als depends n the quality data cllectin, it has been reprted that phase can be determined i abut ne atm selenium is present r every 150 amin acid residues ()... Determinatin pssibility incrprating heavy atms via measurement X-ray lurescence In Sectin.1, it was nted, as ne the diiculties preparing a heavy atm derivative, that the pssibility incrpratin must be evaluated by actually measuring data. One way aviding this is the methd measuring X-ray lurescence (XRF). An attachment r measurement X-ray lurescence r single crystals (Fig. (a)) can be munted nt an existing single crystal X-ray diractmeter, and XRF can be measured while carrying ut data cllectin. T eliminate the pssibility XRF signal cntaminatin rm the heavy atm slutin part in the case a crystal munt, it is necessary t perrm back-saking, in which the heavy atm derivative crystal is saked berehand in a slutin that des nt cntain heavy atms. Derivatives prepared using the vaprized idine abve are als advantageus regarding this pint. This is because the incrprated idine has cvalent bnds t a speciic site in the tyrsyl residue side chain, and thus it is nearly impssible that heavy atms are remved during back-saking, a requent prblem with derivatives btained using the rdinary saking methd. I XRF is btained crrespnding t the incrprated atmic species, then heavy atms exist in the crystal (Fig. (b)). In heavy atm derivatives that cntribute t phase determinatin, it is nt enugh r heavy atms t simply be present; they must be bnded regularly t speciic sites acrss the entire crystal. The ccupancy is als crucial. Hwever, i n XRF signal is present, this means heavy atms are nt present in the crystal, and the crystal can be reected withut data cllectin. Using the XRF attachment enables signiicant labr-saving. 3.Principle phase determinatin 3.1. MIR methd As the name indicates, in the MIR (Multiple Ismrphus Replacement) methd a crystal cntaining n heavy atms (knwn as a native crystal) is prepared, tgether with derivative crystals in which the native crystal has been saked in slutin cntaining heavy atms s that the heavy atms are incrprated, and the phase the native crystal is derived rm the shit in phase between the tw. Figure 3 shws the principle phase determinatin using the MIR methd. Structure actrs can be regarded as waves, and therere it is cnvenient t cnsider these n the cmplex plane. Inrmatin rm the native crystal is indicated in blue. The diractin intensity the native crystal can be measured thrugh data measurement, but phase cannt. This situatin crrespnds t the act that the length the arrw r the structure actr, in itsel a vectr, is knwn, but its endpint psitin is unknwn. Here is where the heavy Fig.. (a) XRF attachment r single crystal X-ray diractmeter. (b) Results measurement with (a) ater saking native crystal r 10 min in 10 mm K PtCl 4 slutin. Rigaku Jurnal, 34(1),

3 Intrductin t single crystal X-ray analysis XIII. Phase determinatin in prtein structure analysis Fig. 3. Diagram shwing principle the MIR methd (Argand diagram). The ideal phase relatinship r a speciic diractin pint is shwn. F p : Structure actr native prtein, F ph1 : Structure actr 1st heavy atm derivative, F ph : Structure actr nd heavy atm derivative, F h1 : Structure actr nly heavy atms 1st heavy atm derivative, F h : Structure actr nly heavy atms nd heavy atm derivative. The values F p, F ph1, and F ph are, respectively, the magnitudes the structure actrs the native prtein, 1st heavy atm derivative, and nd heavy atm derivative, and these can be measured thrugh diractin intensity measurement. Fig. 4. Diagram shwing principle the MAD methd (Argand diagram). The ideal phase relatinship r a speciic diractin pint is shwn. F B : Structure actr all atms withut anmalus dispersin, F A : Structure actr parts that d nt cntribute t anmalus dispersin all atms with anmalus dispersin, F A : Amng structure actrs parts that cntribute t anmalus dispersin all atms with anmalus dispersin, structure actrs parts with the same phase as parts that d nt cntribute t anmalus dispersin, F A : Amng structure actrs parts that cntribute t anmalus dispersin all atms with anmalus dispersin, structure actrs parts having a 90 degree phase dierence with parts that d nt cntribute t anmalus dispersin. atm derivative cmes int play. I the psitin the heavy atm is knwn, the structure actr the heavy atm part can be calculated. The structure actr is expressed as a vectr, and therere it can be written in like Fh 1 in Fig. 3. Hwever, r parts ther than heavy atms in the heavy atm derivative, the nly thing knwn is the diractin intensity, and thus a circle is drawn, whse radius is the magnitude the structure actr, centered at the endpint the structure actr the heavy atm (red circle in Fig. 3). At the intersectin pints the red circle and blue circle, deriving rm the derivative and native crystal, structure actr vectr peratins are satisied nly r the heavy atm derivative, native crystal, and heavy atm. Hwever, there are tw intersectin pints, and tw pssibilities r the phase angle. Thus a secnd heavy atm derivative is prepared, and the same prcess is repeated. Fr the secnd derivative t, the psitin the heavy atm is determined, and the structure actr the heavy atm part is calculated (Fh in Fig. 3). I a circle is drawn, centered at the endpint Fh and with the magnitude the heavy atm derivative as its radius, then in this case t there are tw intersectin pints, but nly ne intersectin pint des nt cnlict with the tw intersectin pints btained with the irst derivative (thick arrw in Fig. 3). This results in determinatin a single pssibility r the tw phase angles, and thus the phase the prtein crystal is determined. 3.. MAD methd The MAD methd tends t be regarded as a newer technique than the MIR methd, but the thery itsel was develped at the same time as the MIR methd (3), (4). The MAD methd appeared later because measurement must be dne at dierent wavelengths, and thus its practical applicatin required the advent synchrtrn radiatin beamlines r prtein structure analysis. Whereas the MIR methd uses the act that the structure actr changes depending n dierences in the atmic species, and dierences in the bnding site and ccupancy, the MAD methd uses the act that the structure actr changes because the anmalus dispersin diers r dierent wavelengths. Figure 4 shws the phase relatinship r a single diractin pint when there is a surce anmalus dispersin. The principle phase determinatin in the MAD methd (5) will nw be derived rm this diagram. Assuming that all the heavy atms which serve as surces anmalus dispersin are the same atm, and letting F H be the structure actr r heavy atms as a whle, F A be the part that des nt cntribute t anmalus dispersin, F' A be the wavelength dependent part that has the same phase as F A and cntributes t anmalus dispersin, and F A be the wavelength dependent part with a 90 degree phase dierence rm F' A that cntributes t anmalus dispersin, then: i FH = FA+FA +FA = FA+ FA+ FA FA = FA, FA = FA (1) 0 0 Because, Rigaku Jurnal, 34(1),

4 Intrductin t single crystal X-ray analysis XIII. Phase determinatin in prtein structure analysis { π( } π { π( } π { π( } F = exp i h r )+ exp i i h r ) H 0 + i exp i i h r ) = F + exp i h r ) { π( } A i 0 exp{ i h r } π( ) 0 = F + F +i F A A A 0 0 The ABC is a right triangle, and thus i the Pythagrean therem is applied, and Equatin (1) is substituted in, = + = () + y FA FA F A Als, rm the ABC and Equatin (1), ycsδ = FA = FA, ysinδ = FA = FA (3) 0 0 Here, i the law csines is applied t OAB, { + } + T = T + - T cs( - a) T F F y F y π φ φ Since (πϕ a )+δ+ϕ A =π, i.e., ϕ a =ϕ A +δ, and cs(πα)=cs α and cs(αβ)=cs α cs βsin α sin β, { φ φ δ} T + + T cs( T A) T + + T csδ cs φt-φa FT ysinδ sin ( φt-φa) = F y F y - - = F y F y ( ) + Substituting in Equatin () and Equatin (3), + T = T +( + ()/ ) A + / 0 FT FA cs φt-φa + / 0 FT FA sin φt-φa F F F ( ) ( ) ( ) ( ) I F T is calculated in the same way, and it is assumed that a(λ)=( + )/( 0 )), b(λ)=( / 0 ), and c(λ)= ( / 0 ), + T T + λ A + λ T A cs φt-φa ± c λ FT FA sin φt-φa F = F ( a ) F ( b ) F F ( ) ( ) ( ) (4) In Equatin (4), it is pssible t ind a(λ), b(λ), and c(λ) r a speciic wavelength rm the absrptin spectrum, and thus the number unknwns dependent n the wavelength is three: F T, F A, and (ϕ T ϕ A ). Therere, i Friedel pairs can be measured r tw r mre dierent wavelengths, then ur r mre equatins can be btained r the three unknwns, and thus it is pssible t determine F T, F A, and (ϕ T ϕ A ). The largest change in diractin intensity ccurs near the absrptin edge, and thus measurement is rdinarily dne at Fig. 5. (a) Structure r heavy atm derivative, (b) structure r native crystal, (c) structure r heavy atms nly. three wavelengths: immediately bere (Edge) and immediately ater (Peak) the absrptin edge (Edge), and distant (Remte) rm the absrptin edge. 4.Derivatin heavy atm psitin T calculate the phase the native prtein using the MIR methd, it is necessary t knw the structure actr the heavy atm. Als, the phase btained with the MAD methd is ϕ T ϕ A, and thus ϕ A must be subtracted in rder t calculate ϕ T. That is, whether the MIR methd r MAD methd is used, it is necessary t determine heavy atm parameters such as heavy atm psitin using sme methd. This crrespnds t determining the substructure the heavy atms nly. T determine the psitins heavy atms with the MIR methd, the expressin Fph 1 Fp is used, in which the diractin intensity the native crystal is subtracted rm the diractin intensity the heavy atm derivative crystal. This is because, i the ismrphism the heavy atm derivative is suiciently high, then Fph 1 Fp nly includes the cntributin rm the heavy atm part, and therere the derived structure crrespnds t the structure the heavy atms nly. This is easy t understand i it is cnsidered in actual space. Fr bth the structure the native prtein and the structure the heavy atm derivative, it is diicult t directly calculate the phase because the prtein part is included. Hwever, i the native prtein structure is subtracted rm the structure the heavy atm derivative, the result is the structure the heavy atms nly, and this becmes extremely simple (Fig. 5). I this is the case, it shuld be pssible t smehw determine the structure. Until arund the 1990, determinatin the heavy atm psitins was dne thrugh hand calculatin, by calculating the Pattersn unctin, a superpsitin vectrs between heavy atms. This wrked well as lng as the applicable structure was simple, but as the applicable prtein mlecules grw large in size, the number sites where heavy atms are bnded als increases, and thus the prblem can n lnger be handled with hand calculatin. At present, the typical apprach is t use the direct methd, r stware where the Pattersn unctin is analyzed autmatically, e.g., using SOLVE, SHELXD, SHARP, r CRANK (6). Rigaku Jurnal, 34(1),

5 Intrductin t single crystal X-ray analysis XIII. Phase determinatin in prtein structure analysis 5.Cnclusin With the MIR methd, it is pssible t determine phase i diractin data can be measured r a native crystal and tw types dierent heavy atm derivative crystals. Hwever, the preparatin a single heavy atm derivative that cntributes t phase determinatin requires a search r cnditins and measurement/ evaluatin multiple times, and thus is the stage invlving the mst labr. This situatin has nt changed even tday, when there has been signiicant prgress in measurement equipment. Hwever, at present, i ne heavy atm derivative can be btained, it is als pssible t determine phase using the SIR (Single Ismrphus Replacement) methd, the SIRAS methd which cmbines the SIR methd with anmalus dispersin, and the SAD (Single-wavelength Anmalus Dispersin) methd. In particular, phase determinatin is pssible with a native crystal nly i the SAD methd can be applied while using the S-S bnds in prteins r using anmalus dispersin sulur cntained in side chains methinine. With the MAD methd, multiple data cllectins at dierent wavelengths are required, but this methd has the advantage that nly ne heavy atm derivative crystal is needed. Therere, the MAD methd is eective in cases where the MIR methd cannt be used because acquiring a native crystal is diicult either in principle r technically, where the prtein cntains metals t begin with, and ther similar situatins. Als, the MAD methd is nt aected by the quality the ismrphism because it des nt use a native crystal, and thus the phase quality depends n the data quality alne. Generally speaking, measurement using synchrtrn radiatin and its high cunt rate enables measurement data with high reliability, and thus phase determined with the MAD methd has high quality, and tends t acilitate the mdel cnstructin which is the next step structural analysis. Reerences ( 1 ) H. Miyatake, T. Hasegawa and A. Yaman: Acta Cryst., D6 (006), ( ) W. Hendricksn, J. Hrtn and D. LeMaster: EMBO J., 9 (1990), ( 3 ) J. Karle: Int. J. Quant. Chem. Symp., 7 (1980), ( 4 ) W. Hendricksn: J. Synchrtrn Rad., 6 (1999) ( 5 ) Fr example, J. Drenth: Principles Prtein X-ray Crystallgraphy, Springer-Verlag, New Yrk, (1994), ( 6 ) S. R. Ness, R. A. G. de Graa, J. P. Abrahams and N. S. Pannu: Structure, 1 (004), Rigaku Jurnal, 34(1),