gs bNX
Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]ëR1,2CûF²1,2CRTM1,2C¬Ñ ü1,2C
Ê Â1Câ{[¾1Cg¯ 3Crû¿38522 _Þì§¡ls`kæúg 3_14_1
§223_

1

cä`måwHw¨wÈ2»w¤d¤úËõÈw¤Z^[îÕ¤3¡ls§åwåw@¶½imVXeÈw¤È

v |§679_5148 ºÉ§²pS²p¬õs 1_1_1§230_0045 _Þì§¡lsß©æL¬ 1_7_29

Rq[g X üñÜC[WOÍC»»ª´IÉsÂ\Èñ»±qÌ§Ì\¢ðÍÉLøÈè@ÅèCñÜp^[©ç¾çêé\¢UÌÝ©ç±qÌe\¢CgOtB[À±ÉæÁÄO³dq§xðÄ\¬Å«éB{eÅÍC±êÜÅÉñÄ³ê½Rq[g X üñÜC[WOÁLÌ\¢ðÍðUèÔéB
Ü½C®«nß½ XFEL {ÝÅÌ«ÌÀ±Éü¯ÄCV½ÉlÄµ½n}ï±qÌ\¢ðÍvgRÌTvð¦µÈªçC¡ãð·×«âèð¢µ½B

Ép¢çêÄ«½ªCCXDI ÅÍ»êçðÛ²ÆÏ@·

1. Í¶ßÉ

é±ÆªúÒ³êÄ¢éBm[x»wÜÍC2003NÈ~ 3 NüúÅCÁÊÉd

{eÅÍC±êÜÅÌ CXDI \¢ðÍÌ´ðZßévÈ­«ðÂ¶ÌªqÌ\¢ðÍÉö^³êÄ¢éBÆÆàÉCX ü©Rdq[U[iX­ray Free Electron±Ì±ÆÍCX ü\¢ðÍªg»»Â\ÈªqhÌ´

Laser: XFELjðp¢½ CXDI \¢ðÍvgRJ­ÌqðxÅÌ§Ì\¢ðÍÉå«­v£µÄ¢é±Æð½»óðÐîµÈªçC«IÈ­WðëÕ·éBfµÄ¢éBêûÅCîbÈwªìâÞ¿ÈwªìÅ­©
é¢Ín¶³ê½Cg»»sÂ\Èªqâ±qhª½¶Ý·éB¶½ÈwÅÌáð°éÆC×EjÉÇÌ

2. Ç§±q©çÌ X üñÜ­x
Maxwell ûö®ðc¡Ég¢±ÈµÄ¢éwïÇÒæ¤È`ÔÅ DNA ªi[³êÄ¢éÌ©ðªð\ÅÂ»µ½áª³¢½ßC×EªôúÌõFÌ`¬JjYÉÍ¸ç©Æv¢ÂÂàCÃTdq¼aÈÇðxOµ½

ÍËRÆµÄs¾Å

\¢¶¨wÒ©çÌï­ÈñÄ9)ð©éÉÂ¯C¸¦Ä XéBßNCPx X üõ¹ðp¢éRq[g X üñÜüÌe«UÉÂ¢ÄÈPÉZßé±ÆÉµ½B
Li áenar­Wiechert |eV10) É]¦ÎCO©çüC[WO@iCoherent X­ray Diraction Imaging:
CXDI)1_3)Éæéñ»±qÌ\¢ðÍÉúÒªÄéó

Ë·é X üdêªdqðU®^®³¹éÆCdq©çÍµÉÈÁÄ«½BCXDI ÅÍCóÔRq[X X üüË X üÆ¯g·ÌoÉqúËª¶¶CX ügUhªðÇ§¿±qÉÆËµÄóÔªð\oíÅñÜp

Ïª³êéB½Êg X üð¨¿ÉÆË·éÆC^[ðL^µC½IÊñ@4)ðp¢ÄCÏª\¢¿çÌdq©çgUghª¶¶CMaxwell ûö®Ìü¿ç±UÌÝ©ç±qÌüË X üûüÖÌedq§xðÄ`«ªÛØ·ég«µí¹hÉæÁÄCdqªzÉNö¶·éiFig. 1jBóÔRq[X X ür[ªÂ·é±ÂÈªÏª³êéBg· l ÅüË­x Iincident Ì X\ÈúËõ{ÝÅÍCimÞ¿â¶Ìà±qÈÇÌ\¢¤üðCüËûü©ç©½ÅåTCY A Ì±qÉÆË·éÉKp³ênßÄ¢é5_8) BCXDI ÅÍCdq°÷¾Åêðl¦éBüË`dxNg k0 ÆÏªûü`dxNâèÆÈéYû·ÉÏí³êé±Æ³­CZg· Xg k Åè`³êéUxNg Si S( k| k0)/2p, | S|üÌ§ß«ÉæÁÄCdq°÷¾ÌKpÍÍð´¦½úÝ

2 sin u/ljÅÌ X ü­x I( S) ÍCFraunhofer ßº11)ÌÅCX üÆËæÌdq§xªz r(r) Ì Fourier Ï·iFTj

é±qÌà\¢ðCõw°÷¾ÅÍBsÂ\ÈðxÅÂ»Å«éBá¦ÎCdq°÷¾Éæé×EØÐ

Åé\¢öq F( S) Æ»Ì¡f¤ðÌÏÅ\í³êéB

Ï@ª×EâIKlÈÇÌ½Kw«@\óÔÌ\¢¤úËõ Jan. 2013 Vol.26 No.1  11(C) 2013 The Japanese Society for Synchrotron Radiation Research`dxNgÌå«³ªÏ»µÈ¢½ßCÏª³êéñÜp^[ÍtóÔÌ¼a 1/l Ì½Ë

iEwaldjÆð··é­xÉÀè³êéiFig. 1(b))12) B¬³ÈUfÊÏÌÉÍ´Px X üðp¢éBPF X üÀ±Åæ
ñÌ_ÉÎ·éÉÍC¿ðñ]µÄ EwaldÆtóÔ­xªzÌð·ðÏ»³¹CñÜ­xf[^ðûW·éB3. CXDI É¨¯éÊñ
3.1

ñÜp^[ÆîñÊeèÉæêÎCO³dq§xÌeÌñ³
FT ÍCdq§xÌO³ FT É¨¯é´_ðÊß·éêfÊÆÈéBf

F(Sx, Sy, Sz0)

frP(x, y)zx, yrP(x, y) exp [2pi(Sxx{Syy)]dxdyr(x, y, z)dyz(3_1)æÁÄCtóÔ´_ðÊèCüË`dxNg k0 É¼È½ÊÌ\¢U |F(Sx, Sy, Sz 0)| ÍC¿±qàdq§xªz r( r) ð z ûüÉeµ½ rP (x, y) Ì FT ÌâÎlÆÈé13) BÈºÅÍC±Ìeèð¼èµÄc_ð
ÈPÉ·é½ßCEwald

ð½ÊÉß·éB±êÍñÜpª¬³¢©Cg·ªZ¢êÉÎ·éBFig. 1(color online) (a) Photograph of apparatuses for cryogenic
CXDI experiment at BL3 of SACLA20). (b) Schematic illus­
tration of CXDI experiment and analysis. The CXDI patternfrom a cluster of 250 nm Au­colloid was recorded by a 10­fs
pulse.

±qÌedq§x rP(x, y) ð Nx~Ny sNZðxÅÄ »·éê ðl¦é BÏªµ½ñ Üp^[ ãÌiSx, Sy, Sz0jsNZÅÌ\¢UÍ|FOBS(Sx, Sy, Sz0)||

N x|1 N y|1

I( S)Iincident r 2ef

   rP(x, y) exp

( )

2

l
F( S)ÞF( S)
s1A

x0

y0

[2pi(S N {S N )]DxDy|
x

x

x

y

y

y

(3_2)

F( S) r(r) exp (2pi SÉr)d 3r|F( S)| exp [ia( S)] (2_1)Å^¦çêéB±±ÅCDxDy ÍtóÔÊÏfÐÅ

éB

¡C\¢U |FOBS (Sx, Sy, Sz 0)| ð Nx ~Ny sNZÅ±±ÅCs1 Íãq·éê³ÌI[o[TvOä¾éêCñÜ­xªzÌSÎÌ«iFriedel ¥CI(Sx,ÆÄÎêép[^[Cre ÍÃTdq¼ai2.8179~

Sy)I(|Sx, |Sy))12)Ì½ßÉCûö®Íe}Ä»É

10|15 m)10)Å

éB\¢öq F( S) Ìå«³ |F( S)| ð\KvÈÌ¼ªiNx~Ny/2jÆÈÁÄCrP(x, y) ªÜç¢UCÎp a( S) ðÊ ÆÄÔBa( S) ÍñÜ­xp

È¢iFig. 2(ajjBêûCñÜp^[ðCx ûüÉ sx(sx^[©ç¸íêéªC¨¿àdq§xªzÉË¶µÄ±1) {©Â Sy ûüÉ× sy(sy1) {Æ×©­TvµÂp^[Ìâ­³ðè·éB\¢öqÌt Fourier

Äªè·éêiFig. 2(ajjCs2sxsy2 ÅêÎSÎÏ·iIFTjÉæÁÄdq§xªzðÄ»·éÉÍCÊÌ«ÉNö·éîñ¹ðâÁÄCe\¢ª¾çêéBðè·éKvª±Ìðð OversamplingiOSjðCs2 ðñ³ÅÌ

èCX ü\¢ðÍÉ¨¯éÊâèOS äCsx â sy ðê³ÅÌ OS äÆÄÔB

ÆÄÔ12)B
À±ðs¤ãÅåÏdvÈñ_ÉÓ·×«ÅéBæêÉCüË X üdêÉæÁÄ¶¶édq©çÌ X ügU

3.2

ñÜp^[©çÌÊñhÌm¦iUfÊÏjÍCÃTdq¼a re Ì©æÉ{eÌ\¢ðÍÅÍCOS ðÅ¾½\¢UÉÎµÄ

äáµÄÉßÄ¬³¢BæñÉCe«UÅÍüËÆU½IÊñASYiFig. 2(b))4) ðKpµÄ rP

12  úËõ Jan. 2013 Vol.26 No.1

gsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]àå«È sxNx~syNy àÉªÄ¶³êéiFig. 2(ajjBT|[gOdq§xÍëÅé×«ÈÌÅC»Ì±Æðl¶µ½ÀóÔS©ðªÌp³êÄ¢éBû©«üPÉü¯½wÍ4)ÉæèC»ÝÅÍCHybrid­Input­Output (HIO)4)ASYâ»ÌÏ@6,7)ªp¢çêéBHIO ÌÀóÔS©ðÍ

rk{1(r)

{r (r)|br(r) otherwise

r¸support and r
k(r)Z0

r
k(r)
k

Å

(3_4)

k

èCè b ðp¢ÄT|[gOdq§xð¸¦Äë

É¹¸Éâ¯ðh¢Å¢éB\¢UÌÝðp¢éÌÅCû©ðªUÌÂ\«àè¤éªCñ³ÈãÌâèÅU

éÆ³êÄ¢é14) BTCN½ðJðÌo»ÍóÅ

èÔ·ÆCT|[gàÍ³µ¢dq§xÉû©µCT|[
gOdq§xÌaÍëÉQß·éÅë¤B»Ì»èÉÍT|[gàOÌdq§xaÌäÉCT|[gàOÌÊÏ
äi1/(s|1jjðæ¶½g

 r(r)
1 r/̧ Support(s|)  r(r)(3_5)

r¸Supportðp·éiFig. 2(cjjBGÈúdq§x©çJnµÄàC\ªÈ S/N Å¾½ |FOBS (Sx, Sy, Sz 0)| ©çÍ rP(x, y) ðñÅ«éB

3.3

T|[g`óÌXV

{C±qÌÝªdq§xðÂ½ßC±qe`óðT|[gÆ·é±ÆÅÊñ¬xâ¸xÌüPª©ÜêéB±q\¢ªs¾ÈñTCNÅÍCñÜ­xp^[Ì FT Åé©ÈÖÖªëÉûÊ·éÌæðT

|[gÆ·éÌªÇ¢iFig. 3(ajjB³çÉiñ¾û@ÆµÄ Shrink­WrapiSWj@15)ªñÄ³ê½BÊñT
Fig. 2(Color online) Theoretical background of phase­retrieval
analysis used in CXDI. (a) Oversampling of diraction pat­tern increase the amount of information necessary to solve
the phase problem. (b) Schematic illustration of the phaseretrieval algorithm4). (c) Example of phase retrieval calcula­tion for the diraction pattern from a cartoon monitored by
the g­value.

CNÉCèúIÉñedq§xÉ[pXÉtB^[ÆµÄìp·éKEXÖ

G(x, y)

1
exp
2pa2

ðôÝÞB»ÌÊC

[

]

x2{y2
2a2

|

(3_7)

élÈãÌdq§xðÂÌ(x, y) ðÄ¶µÄ¢éB¯ASYÅÍCÀóÔÆt

æðV½ÈT|[gÆ·éBKEXÖWÎ·ClC

óÔð FT Æ IFT ÉæÁÄðÝÉµÈªçCZo³XVÔÌÊññªKØÈêCT|[g`óÍ±q( r) â \ ¢ö q Gk ( S) É S ©ð 
ê½  e dq § x r kO`Éû©·éiFig. 3(ajjBSW @ÍC^pN¿»

irestraintjðÛ·BtóÔS©ðÅÍCíÉ\¢U\¢ðÍÅÌn}Ìædq§x½»12) ÉÄC±q«

ðÏªl |FOBS( S)| Éu··éBEÌ¾m»ÅC³µ¢ÊÌgð^¦éåæðÖÌÚßð

ÀóÔÅÌS©ðÉÂ¢ÄÍCû©«ðüã³¹é½¬ßÄ¢éBäXÍCSW ÉæÁÄ®IÉXV³êéÅKßÉlXÈàÌªlÄ³êÄ«½4) BOS ðÅ¾çê½

T|[gÌæðgp·é HIO ÊñvOðì¬\¢öqÌ IFT eÉÍCtóÔÆÀóÔÌ½«©

µÄCÀ±âV~çCßé×« Nx~Ny ÌæiÊíT|[gÆÄÔjæè

ÞÀ±f[^ÉÎµÄÍCFig. 3(b)ÌtÎÌ±qÌæ¤É

[VÉp¢Ä¢éBmCYðÜ

úËõ Jan. 2013 Vol.26 No.1  13

4. XFEL_CXDI À±XFEL pXÍ´­õqêÅé½ßCpXÊßãÉÍ´qà©dqª¬æçêCc³ê½´qjÔÌÃ
d½­ÉæÁÄ´qcªN[­ðN±·Æ\z³êÄ¢é19)BÀÛCüË­xª1012 photons/mm2/pulse öxÆ © Ï à ç ê é SACLA © ç Ì X ü p  X ð p ¢ ½
CXDI À±iFig. 1(ajjÅÍCÆËÌæªÁ¸·éÉà©
©íç¸CñÜp^[©çW¿Ìdq§xªñ³
êéB±Ì±Æ©çCÉ­ZÔÌ¤¿É´qàdqªoÉqúËð¶¶C´qªóêéOÉñÜ»Ûª¶¶Ä¢é
idiraction before destroyjÆl¦éÌª©RÅé20)B±ÌlÉCXFEL À±ª´¥´qxÅÌjóIªèÅé½ßC¿±qðÆËìÉü·éKvªéBÜ½CÒ­Ì XFEL {ÝÉ¨¯é X üpX­¶
Í10_100 Hz ÈÌÅCåÊÌñÜp^[ðZÔÅæ¾·éÉÍCà¯ÜèÌ¢¿ÆËðÂ\Æ·éñÜuÌJ­ª]ÜêéB
n}Â«Å@\·é¶Ì±qâ@\«imÞ¿±qÅÍCn}Â«ð®¦½óÔÅÌ¿ì»ªsÂÅèC±q¿ð¼Ú^óÉ·±ÆÍð¯ËÎÈçÈ¢BêûCobNOEhUðá¸·é½ßÉÍC¿ð^óÉu­×«ÅéÆ¢¤fB}ªéB±Ì_ð

ðÅ«éû@ÆµÄCtHÉ¿±qðüêÄÆËì
É±üµCn}ªöU·éOÉ X üÆË·éuªÀp
Fig. 3(Color online) (a) Variation of support shape during HIO­SW phase retrieval calculation. (b) Projection electron den­sity map of a spinach intact chloroplast phase­retrieved froma cryogenic CXDI diraction experiment at BL29XU of SPr­
ing­841). The density map at a resolution of 182 nm is com­pared with its image viewed using optical microscope16). (c)Schematic illustration of three­dimensional phase retrieval
analysis for structure amplitude distribution reconstructed inreciprocal space17).

»³ê½21) BÆËÌà¯ÜèÍÉßÄá¢ªC\¢ðÍ
À±Ép³êÄ¢éB±êÉÎµÄCäXÍ¶ÌªqÉ±qÌdq°÷¾Ï@ÅZpîÕªm§³êÄ¢éXï@ÉÚµCòRÌ±qðXïµ½¿ðêè¬xÅÚ®³¹ÄC¿±qÉ
 X üÆË·éá·¿ÅèÆËugæëh20,22)ð
J­µ½iFig. 1(ajjB¿±qÍCdq°÷¾psz[ÂÉ\èt¯½z£iYfãÉ¼x§ä¿ì»ugóbíUlh16)ðp¢ÄWJµCtÌG^
1000ñÌÆ§µ½ HIO_SW ÊñvZðs¢Cñ³Å}¬·éBtÌfÅ¿sz[Âðê½1000Ìedq§xÔÌÝÖâ g lð¢µê½z_[ÍCêpUuÉæÁÄ¸·ÉÄÅIÌedq§xð¾é16)BÆÈ­Cæë^ó

³·é±àÌt»KX|bgÉÀ³êéB±êçJ­uÆVKÉlÄµ½¿ì»û@ðp¢é±

3.4

O³dq§xÌñüË`dxNgÉÎµÄlXÈzüÉ

ÆÅCSACLA Å¾çêéüË XFEL pXÌ20_60÷ªé^óÇ§

¿±qÉqbg·éóµÉéB±qÌñÜp^[ð½¾ÄCtóÔÅÌO³ OS äð«Å«éóÔªð\Å\¢UªzðÄ\¬Å«êÎCO³½IÊñÉÄ±qÌO³dq§xðÄ5. n}ï±qÌ\¢ðÍë¤17) iFig. 3(cjjB¾çêéñÜp^[n}ï±q¿ÌñÜp^[ðl¦éBÆËìÉ¶ÍtóÔ´_ðÊß·éÌÅCCÓÌ 2 gÌp^[ÉÝ·éSÄÌ´qÉªqðl¶·éÆCÏª³êéñÜ­ÍC¯êÌ­xð¦·¤Ê~Ê common line18)ª©o³êxÍÈºÌlÉÈéB»Å«éÅ

éB3 gÌñÜp^[ÉÂ¢ÄÎIzüªè³êêÎCcèÌzüàèÅ«CtóÔÅÌ\¢UªzðÄ»·é±ÆªÅ«éB

14  úËõ Jan. 2013 Vol.26 No.1

gsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]I( S)I0r2e

( )

l 2
[|FP( S)|2{|Fw( S)|2sA{FP( S)ÉFw( S)Þ{FP( S)ÞÉFw( S)](5_1)±±Å FP( S) Æ Fw( S) ÍC»ê¼êC¿±qÆn}Ì
æÌ\¢öqÅéBA Í(2_1)ÆÙÈèCû`fÊðÂ X üªÆË³êén}ÌæêÓÌ·³ÅéBFw ( S)ª³Å«È¢êCFw ( S) Ìñ^Æ FP ( S) ÆÌ±ÂÉæÁÄC^óÌ¿±qÆÍÙÈéñÜp^[ª¶¶C±qÌ\¢ðÍÉsÂÈæêÌÝðæèo¹È
¢BÜ½C¿Ìn}dSÆ±qdSð§ä·é±ÆÍÅ«È¢µC»êçªíÉêvµÄ¢éÛØàÈ¢B
ãLð¦·ÈPÈáÆµÄCdq§x r0 Ìû`Ìæ A
Ædq§xª Dr ¾¯]èÈû`Ìæ B Å`¬³ê½ñ¬ª¿iFig. 4(ajjÌñÜp^[ðl¦éBÌæ A Ì\¢öqð FA(Sx, Sy)CÌæ B Ì]èdq§xÉR·é\¢öqð FB(Sx, Sy) Æ·éÆCñÌæÌdSªêvµ½
¿ 1 ÆÌæ B ª²ûüÉ D Ú®µ½¿ 2 ÅÍCñÜ­xÌ±ÂªÙÈéBI1(Sx, Sy)|FA(Sx, Sy)|2{|FB(Sx, Sy)|2{2FA(Sx, Sy)FB(Sx, Sy)
I2(Sx, Sy)|FA(Sx, Sy)|2{|FB(Sx, Sy)|2{2FA(Sx, Sy)FB(Sx, Sy)~exp [2piSxD] exp [2piSyD]
FA(Sx, Sy)r0(2L)2sin (2pSxL) sin (2pSyL)
2pSxL
2pSyL

FB(Sx, Sy)Dr(2a)2sin (2pSxa) sin (2pSya)
(5_2)
2pSxa
2pSya

»ÌÊCcommon line @iFig. 3(cjjÉæétóÔÅÌ
\¢UªzÌÄ\¬ÍsÂ\ÆÈéBäXÍC±ÌâèððµÄn}±qÌdq§xð¾
é×­CÊñ@4)ÆP±qO³Ä\¬@13)ðgÝí¹ ½Vµ ¢\ ¢ðÍ XL [ ðlÄ µ½23) B± ±ÅÍCÜ¸CX ü\¢ðÍÅp³êé±ÆÌ³¢P±qO³Ä\¬@ðTàµCÉCïÌIÈV~[VÊðð¦ÈªçVXL[ððà·éB

5.1

P±qðÍÉ¨¯éO³Ä\¬P±qðÍÍC¶Ì´ªq¡ÌÈÇÌdq°÷¾ÌðÍðs¤ÛÉL­p¢çêÄ¢éO³Ä\¬è@Åé13) BÁ¬d³200_300 keV Ìdq°÷¾ÅÍCãÊ¨¿Ìdq°÷¾ðdqüüË`dxNgûüÖÌÃ
d|eVÌeÆ©ô·±ÆªÅ«é13) BP±qðÍÅÍClXÈûü©çÏªµ½½Ì±qeÉÎµÄCeèÉËµ½ common line @ÉæÁÄeà±qÌÎzüðèµCFourier Reconstruction

Fig. 4(Color online) Theoretical background of three­dimensional
reconstruction method for single particle used in the present
study. (a) Example demonstrating the signicant dierence
in diraction patterns caused by the positional shift of innerparticle in a medium. (b) An image of L~M pixels is ex­pressed as a point in the L~M­dimensional hyper space bytreating the density of each pixel as variable. (c) Schematic
illustrations of multiple data analysis applied for clas­sication­averaging and three­dimensional Fourier recon­
struction using the common line method in reciprocal space.
(d) Renement of reconstructed density model using the
projection matching method.

(FR) @24)ÈÇÅO³ðÄ\¬·éBúËõ Jan. 2013 Vol.26 No.1  15

Ïª³êéeÉÍmCYª¬Ý·é½ßC½ÏÊð
ÍiMultiple Data AnalysisjÉæÁÄC

ªÀè»·éÜÅ±ÌßöðJèÔ·BépxÍÍÅ

½Ï»ãCzüèµ½e©ç FR @ÉÄO³Ä¯¶züÆ©ô¹é±qÌeÌggNXhÉªÞµC\¬ðs¤BFR @ÍCeèð¼Úpµ½O³Ä

½ÏìÉæÁÄG¹ðá¸µ½¿eð¾é25) B\¬Å±Ì Û C ± q  e ð Ü Þ L ~M s N Z Ì æ  1 ÉæÁÄzüðßCtóÔÌCÓ_Ì\¢öqðâÔµðCesNZÌ§xðÏÆµÄC JL~M ³´óÄ26)\¢öqªzðÄ\¬ãC»Ì FT ©çO³dq§èCæÌ FT p^[ÉÎ·é common line

ÔÌê_Æ©ô·iFig. 4(bjjBN Ìæð¾½êC

xð¾éBêxÌsÅ¾çêéfÍ³m³É¯éf[^SÌðCsNZÔðñCæÔðsÆ·ésÌÅCúfð projection matching @13) ÈÇÉæÁÄ¸§»·éiFig. 4(djjB^¦çê½ú\¢©çvZñ³êéeÉÎµÄCeÏªeÌÝÖÖðv] c11 c c1J `^_C P S P

ZµCÅåÖð^¦é Euler pia, b, gjyÑÀWÉæ

a

(5_3)

cN1 c cNJb

ÁÄ±qzüðXVµÄCFR @Æ¯lÈÅV½ÈO
³\¢ðÄ\¬·éTCNðJèÔ·BO³Ä\¬É¨¯éªð\Ì]¿ÉÍCFourier Shell

ÆµÄ\·B±ÌsñÌÁ¥t¯ÉÍCÈºÌ½³óÔ
Å Ì Å L l â è ð æ è µ ¤ Correspondence

Correlation (FSC)27)

Analysis(CA) ðp·éBt

FSC(S
)

^_

M

0 `

N

/

0`

S
0

nNJ

ab

/

³êéñÂÌfÌO³\¢öqÅi

J, nii1 cij
j

(5_6)

|S|¸S

ðp¢éBF1( S) Æ F2( S) ÍCf[^ðñªµÄÄ\¬N, mjj1 cij,

mNJb

]n11

^_

a

S
0

|S|¸S

 |F1( S)|2  |F2( S)|2|S|¸S

CNCMulu]m11

Re  F1( S)ÉF2Þ
( S)éBFSC(S)ª0.143(1/7) ÆÈé SÌtðªð\Æ·éªC±êÍ X ü»\¢ðÍÉ¨¯éÊÌm©çµ³ÌwWÅ
(5_4)

é gure­of­merit É¨¢ÄCÊÌsm©³ª60xöxÅ

é±ÆÉÎ·éBÈºÉq×éV~[VÉ¨¢ÄÍC±êç½Ï

CA ÅÍCÎpsñ M ÉæÁÄeæÌKi»CÎpsÊðÍÉæéæâO³Ä\¬ðZß½dq°÷¾ñ N ÉæÁÄesNZdq§xÌKi»ð{µ½ãÅpP±q\¢ðÍvOpbP[W EMAN28)ðgp

ÅLlûö®ðð­B±êÉæÁÄCæÔRgXgµ½BÌe¿ðó¯È¢ªÞªÂ\ÉÈéBÅLlªélð´¦Ä¢éÅLxNgðV½ÈîêÆµÄCá³óÔ
ÅÌå²ðp¢ÄnðÁ¥Ã¯éiFig. 4(cjjB

5.2n}ï±qÌ\¢ðÍ 1\Poisson mCYðz
èµÈ¢ê

á³óÔÅÌNXª¯ÉÍCK­Means ClusteringäXÍCn}ï±qÌ\¢ðÍÉü¯CñÜp^[

(KMC) ðp¢C³óÔÅLq³êéÏª_ðC»Ì©çÊñµ½eð¾Cn}dq§xðãÉCÚßxÉ¶Ä K ÂÌNXÉª¯éBwIÉÍCó

P±qðÍO³Ä\¬@ðKp·éÆ¢¤vgRðÔIÉß¢¨Ì¯mªÇê¾¯¯êÌNXÉUèª¯çlÄµ½23) B±ÌvgRÌÀp«ð¢·é½ßC
Ü¸CñÜp^[L^Ì Poisson mCYðl¶µÈ¢êÄ¢é©ÌwWÆÈé

V~
K

V (xj|mi)2i1 xj¸Si(5_5)

[VðCñÎÌÈ`óÆ¾mÈhC\¢ðLµ½ protein disulde isomerase (PDI)29)ÉÎµÄsÁ½iFig. 5jBÙÈézüÉé^óÌ PDI ÉÂ¢ÄiFig. 5(ajjCðÅ¬»·é±ÆÉÈéB±±ÅBK ÍNXCSi

0.21 nm ªð\ÅÌñÜp^[ I(Sx, Sy, Sz0) 10000Í i ÔÚÌNXÌæCmi Í i ÔÚÌNXÌdSCxj Íð OS ä 4 ÅvZµ½B

Si NXÉÜÜêéÏª_ÌÀWÅéBKMC NXàÌÞæðdËí¹Ä½Ï»µCmCYðá¸·éB

I(Sx, Sy, 0)FÞ(Sx, Sy, 0)ÉF(Sx, Sy, 0)³çÉCæÌñ]©Rxðl¶·é½ßÍCêUè³
ê½½Ï»ÉNXª¯æðñ]³¹ÈªçeæÆÌ

F(Sx, Sy, 0)fj( S 2x{S 2y) exp [2pi(Sxrjx{Syrjy)] (5_7)

ÝÖWðvZ·éBÖWª¯êÎ½Ï»ÉN±±ÅCj ÔÚ´qÌÊuð rj C´qUöqð fj (S) ÅXª¯æª³çÉ¸§»³êéÌÅCeæÌñ]péBñÜp^[ÉÍC^pN¿Ìå«³ð½fµ½

16  úËõ Jan. 2013 Vol.26 No.1

j

gsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]

XybNp^[ª»êiFig. 5(djjCHIO_SW Êñ\¬@ÉæèCFSC èªð\0.21 nm Ìdq§xfÉæÁÄñÜp^[©çñ³eðñµ½B

ª\zÅ«½iFig. 5(fjjB±Ì^óV~

0.21 nm ªð\ÅÌÀóÔO³Ä\¬ÉKvÆ³êékÉæèC\¢UªzÌÄ\¬ðoé±ÆÈ­CVµ¢ÞÌ³¢epxÌgÝÍ6842ÈÌÅCgpµ½evgRÅ\¢ðÍªÅ«é±Æª¦³ê½B
ÉC¼a12.6 nm ÌÍ\ªÆ¾¦éBNXª¯Æ½Ï»ðoÄO³Ä[VótHÉ^pN¿ªq 1 ÂªÜÜêéêÌ\¢ðÍðÝ½iFig. 5(bjjBtHÍC
zÈ TIP3Pªqf30)Åßs­³ê½§ûÌ©ç

KÉØè¾·ÌÅC¯¶ªqzuÌtHÍ³¢BÜ½CtHÉßÞ^pN¿ªqÌ X ür[ÉÎ·ézüÉd¡Í³­C^pN¿

aÉ¨¯é

fÌ

ô½w31) ÉîÃ¢Ä^pN¿\ÊÉÚßµ·¬½ªqð¢½B^pN¿ªqðÜÞtHð10000ÂpÓ
µC^óÌV~[VÆ¯lÉñÜp^[ðvZµ½Bn}ÌæÌñÜ­xÖÌñ^Í^pN¿ªqPÆÌêÌñ100{ÆÈèC¬p­xvt@CiFig. 5(d)ÌÔüjÍC¼a D Æ§x r0 ðàÂ[

I(S) 4pD3r0{

ÌUÖ32)}]sin (2pSD)|2pSD cos (2pSD)(2pSD)32(5_8)
ÅßÅ«½BÀÛCU­xÉ¬Êu©ç D12.6 nmÆ©Ïàçê½BÇÌp^[ÅàótHÌUÖª»êCÜ½CFig. 4(a)Æ(5_2)Åðàµ½ªqÌÊuÏ»é½ßCCÓÌ 2 ÌñÜp^[Å common lineªðT·±ÆÍsÂ\ÅÁ½B

HIO_SW ÊñÅ¾½e}ÉÍCn}Ìædq§x Ì ñ^ ªå Å

è CPDI d q §x Ì o Íe ÕÅ È

¢Bi5_8)®Æ¬pñÜvt@C©çß½§x r0 ðp¢C

¼aÆÌedq§xªrwater(x, y)2r0 D2|x2|y2(5_9)

Æ\í¹é±ÆðpµÄC±êðñp^[©ç·µø­ÆC©·©É PDI Ìdq§xðmFÅ«éæ¤É
ÈéB±Ìð{·OãÅÌedq§xÌvt@CÌÏ»ð Fig. 5(e)É¦µ½B±ÌáRgXgeÉÎµÄCe»ÆóÔügmCYÉLøÈ

Fig. 5(Color online) Course of structure analysis for particles insolvent by the combinational use of HIO­SW phase retrieval,density modication and three­dimensional structure analy­
sis for single particle23). Simulations for particle in vacuum(a), in spherical­shaped water drop (b), and in cubic­shaped
vitreous ice (c). Small­angle diraction patterns are shownin the magnied view at 0.83 nm resolution. The line prolesof the in­vacuum, in­sphere and in­cube simulations are plot­
ted as black, red, blue lines, respectively (d). (e) Line pro­les of electron density before (orange) and after (green)
density modication. The eective resolution of each elec­tron density model is estimated using the FSC function (f).

úËõ Jan. 2013 Vol.26 No.1  17[pXÉtB^[ð{µÄ PDI ÌRgXgðß½ÊCCA Æ KMC ÉæéNXª¯ªÂ\ÆÈèC½Ï»³ê½æ©çúdq§xð\zÅ«½B³
çÉC5.1ßÅq×½\¢¸§»ðCn}dq§x¸Zµ½eæÉÎµÄs¢CÅIfð¾Ä¢éB±ÌfÌÀøIªð\ÍCFSC æè0.28 nm Æè³ê½
iFig. 5(fjjB^óÉä×ÄLøªð\ª«»·é´öÆµÄCn}dq§x¸ZÉæÁÄ^pN¿ªq\Ê\¢ÌÚ×ª¸íêCªqzüÌ©ÏàèÉB³ª¶¶é±Æª°çêéB
OÔÚÉCKXóXï¿ðzèµCêÓ16.2 nmÉßÜê½ PDI ÉÎ·é\¢ðÍðÌ§ûÌ

Ý½iFig. 5(cjjBñÜp^[ÌÔ¹ÉqßüãÌ¬p­xvt@CiFig. 5(d)ÌÂüjÍCêÓ D §x
r0 Ì³û`¨Ì©çÌñÜÖ11)[

I(Sx, Sy) 4A2r20]

sin (2pSxD) sin (2pSyD)
2pSxD
2pSyD

2

(5_9)

ÅÇ­ß³êCvt@CÌÉ¬Êu©ç D Æ r0ªè³ê½BHIO_SW Êñ©ç r0 ð¸ZãCtHÌêÆ¯lÉ[pXÉtB^[ð{µ½ÍNXª¯Â\Å

èC½Ï»æ©çÌúfÉ\¢¸§»ð{µCLøªð\0.29 nmiFig. 5(fjjÌdq§xfð¾½B

5.3n}ï±qÌ\¢ðÍ 2\Poisson mCYðl
¶µ½êOßÅÍCVK\¢ðÍvgRªn}±qÌ§Ì\¢ðÍÉLøÅ

é±Æª¦³ê½B±±ÅÍCæè»ÀIÈÀ±Ì X üoÅ¶¶é Poisson mCYðl¶µ½V~

[VÊÉÂ¢ÄLq·é23)B^óiFig. 6(ajjÅÍCüË­xª1021 ©ç1019 É 2¸­·éÆCÊñeÌÚ×ª¸íêC±qzü

Fig. 6(Color online) Inuences of Poisson noise in detecting X­raydiraction patterns on the reconstructed three­dimensional
electron density model in the in­vacuum (a) and the in­
sphere (b) simulations23).

èÉsè«ª¶¶ÄC0.21 nm ªð\f[^Éà©©íç¸CFSC Løªð\Í0.52 nm Æå«­«»µ½BêûÅCüË­x10

21 ÌêÉÍCmCYðl¶µÄ¢Èï±qÌO³\¢ðÍªÂ\ÅéàÌÅé±Æð­­¦´·

Á½B¢ Fig. 5(a)Æ¯Ìdq§xfª0.21 nm ÌLøªð\ÅÄ\¬Å«½B
tHiFig. 6(bjjÅÍC^óÉä×ÄmCYÌe¿ª³çÉ°Å

Á½BüË­x1020 ÅÍCLøªð\0.31

nm ÅO³Ä\¬ªÂ\ÅÁ½ªCüË­xª 1

6. ¶Ìªq¡Ì±qÌ\¢ðÍ
XFEL pXÉÎµÄ_ÈzüÌ¶ÌªqðË¸oµC\P±qñÜp^[ðæ¾µÄ¶ÌªqÌ­µ½¾¯ÅCÊñeªNXª¯¢ïÈöxÉ

O ³\¢ð ÍªÂ\Å ÍÈ¢©Æ¢ ¤ñÄªÈ ³ê

ò»µC2 ññ]ÎÌðÂªO³Ä\¬ÉcÁ½17)Bµ©µCi2_1)Åàq×½æ¤ÉdqÌ X üUf

½B±ÌlÈ_ðüP·éÉÍCÊñASYÅÊÏªÉßÄ¬³¢½ßC»óÌ XFEL õ¹ÅÍC¶ÌÌ¬ FT [`ÌüÇCmCYÉ­¢ÀóÔS©ð

ªq 1 Â©çÌñÜp^[ðL^·éÌÍwÇsÂ\

Ì±üÈÇªsÂÅÆl¦çêéBáÆµÄCªq¿Ê 1 MDa Ì^pN¿

éBêûÅC±êçêAÌV~­x³¦\ªÅ[VÍCüË X üêÎCPoisson mCYÉÅ¿ÁÄn}18  úËõ Jan. 2013 Vol.26 No.1´ªqWÌðzèµC»Ì´_U­xð®ðp¢Ä©ÏàéBgsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]

Ielec( S0)r2e

( )|
l
sa

2

rmol

VM M M 2~Iincident
NA

|

(6_1)

^pN¿ªqÌ½Ïdq§x rmol i0.4 e/Å3 jCÎäe VM i0.74 cm3 /gjCAvogadro  NA i6.0~1023 /moljCÃTdq¼a re i2.82~10|12 mmjCªq¿Ê
iMM j1~106 g/molCªqTCYiaj10 nmCX üg·
i l j 0.1 nm C OS ä i s j 2 Æ · é Æ ü Ë ­ x Iincident ª
1012 photons/mm2/pulse ÌêÉÍC´_U­x Ielec( S0) ÍC50 photons/pulse Åµ©È¢Bªð\ðÚw·ÌÅ

êÎC±ÌüË­xÅÍ«è¸C´qUöqÌªð\ÅÌUé¢ðl¶·êÎC­È­Æà104 {ÌIincident Ì­ªsÂÅ

éB±±ÅÍC±ÌÊð¥Ü

¦C»ÀIÈr[TCYC¿`Ôâoí«\ðl¶µÈªçCn}±qÌ\¢ðÍvgRðg£µ½´ªq¡ÌÌ nm ªð\\¢ðÍÌÂ\«ðc_·é33)B¡ñÌV~[VÅÎÛÆµ½¶Ì´ªqÍC{\[±qi70S {\[jÌ\¬vfÅbZW
[ RNA Ìâ`ÃÉµ½ªÁÄ|yv`h¬ð¨±È¤50S {\[Tujbg34)Å

éB¯Tujbg229Âð500~500~50 nm3 ÌAt@XXÉïµ½¿ðl¦éiFig. 7(a))33) B±Ì¿ÍCcåÈªqðÜÞÌÅC¿SÌÌUfÊÏÍ\ªå«¢B¿ÊÉ¼É X üðüËµ½êÌñÜp^[ÍCi ÔÚÌ¶Ì´ªqÌ\¢öqð FPi( S) Cn}ÌæÌ

Fig. 7(Color online) (a) Structure analysis protocol for macro­molecular assemblies embedded in vitreous ice33). In thiscase, 229 50S ribosomal subunit particles in 500~500~50
nm3 vitreous ice plate. From 1832 images of 50S subunit
oriented variously to incident X­ray, a three­dimensional
electron density model at a resolution of 0.8 nm is recon­
structed. Diraction pattern of 70S ribosome collected at
SACLA suggested diculties to perform the proposed pro­
tocol. (b) Electron density contrast between 50S ribosomal
subunit and vitreous ice region became worse when the thick­ness of the ice reaches to approximately 10­fold of the size of
50S subunit.

\¢öqð FW( S) ÆµÄC( ) [|{}

2l 2 Np Np
FPi( S)ÞFPi( S) {|Fw( S)|2


sA
i
j
Np
Np
Þ
{ FPi( S) ÉFw( S){ FPj( S) ÉFw( S)Þ|I( S)Iincident r2e

i

{

}

j

]

(6_2)
Å^¦çêéB±ÌêC¿TCY A Í±qÌå«³
ÅÍÈ­CXÌå«³500 nm Å
æ 7 ßÅà¾·é Ewald

é_ÉÓ·éB\zµ½Bªð\ð3.2, 1.6, 0.8 nm ÆXÉã°ÈªçÌâèðl¶µCªð\0.8¸§»ð{µCFSC Løªð\0.8 nm ÌÅIdq§xnm ÜÅÌñÜp^[ÉÎµÄ\¢ðÍV~[Vfð¾½BfÍC»\¢©çvZµ½0.8 nm ªðsÁ½B0.8 nm ªð\ÅÌ\¢ðÍÉKvÈzuÌ

ð \ Ì d q § x } Æ Ç ¢ ê v ð ¦ µ ½ B Á É C Crown

ÙÈé50S Tujbg1832ÂðpÓµC8 ÌXÉview ÆÄÎêézüÅ­ß½êCCrown Ìæ[ð`¬229Â¸ÂC¶»wÀ±Å²®Â\ÈZxi46 mg/mljÅ·é50S {][å\¬vfÅUzµ½B¿ 1 ÉÍCñ4.3­ÂÌªqÆC2.1çÂÌ50S Tujbg´qªÜÜêÄ¢éB

é 5S ribosomal RNAÌÁ¥IÈñdù\¢C50S {][Ìyv`Wg
XtF[[½Å¬³ê½|yv`h½ªÊèOS ä 4 Å Poisson mCYðl¶µ½êC0.8 nm ªð²¯églC\¢ãÌÁ¥ªÇ­Ä»³êÄ¢½B\Å\¢ðÍ·éÉÍCIincident 5~1016 photons/500~

ÅßC70S {\[ÌZx¿ðì¬µÄ SACLA É

500 nm2/pulse ÌüË­xªKvÅ

Ä±ÌlÈÀ±ªÂ\©ð²×nßÄ¢éiFig. 7(a)EºÁ½BXÌñÜp

^[ÉÍCFig. 5(c)æè³çÉ×©¢é`JûRÌX}jB

ybNª»ê½BHIO_SW ÊñÉæÁÄ¾½ 8 ñ³ê½O³dq§xÅÍCFig. 5_6 Ìn}ÌV[VÆ¯lC±qOÉ¶Ý·é ribosomeÌXe©ç1832ÂÌ50S Tujbgeð~¾ÄCæ 5 ßÌèÉ]ÁÄ3.2 nm ªð\Åúf^pN¿Ìdq§xªêµÄ¢½Bedq§xúËõ Jan. 2013 Vol.26 No.1  19ÅÍCn}Ìæàdq§xªzÌhç¬ªeûüÖÏZ

ÖÆµÄ Gaussian ªp¢çêÄ¢éB³êC±qdq§xÉà«µÜêÄµÜ¤iFig. 7(bjjB
M( S)exp [|( S|a)2x2/2]»ÌÊCXÌæÌdq§xÏ®ªXú³ºÁÄåµC
20 nm TCYÌ50S Tujbgð500 nm ÌXÉüêÄ

IFT[M( S)]expedq§xð­ßéÆC50S TujbgÌÁ¥ªå«(| x ) exp (|2pirÉa) (7_2)
2p2r 22­¹ÈíêéB
{V~

[VÊ©çC¼x§äu16,20)ðp

±±ÅCa ÍñÜp^[ÅÌ}XNÖÌSÊuC¢Äú³§äµÄì¬µ½X¿ÉÎµÄ\ªÈ­xx Í}XNÖÌWÎ·ÅéBÃìÍ¡fÆµÌ XFEL pXªÆËÅ«êÎC´ªq¡ÌÌÉ÷Ê

ÄÄ¶³êé½ßCHIO ÀóÔS©ðÅÍÀÆ¿÷t©çCáªð\\¢ðÍðÂ\Æ·éñÜ­x

Ì¼ûðl¶·éBÃìÊñÅÍC\¢Uîñªf[^ð\ñöxÌIõÅûWÅ«é±Æª¾ç©ÆÈ}XNÌæÉÀè³êCpÌæñÜ­xÌ¸­ÉæéÁ½BPoisson mCYÌe¿ª°ÉÈéB±êçÉÎ·é½ßCmCYÉ­¢ÀóÔS©ðªñÄ³êÄ¢é36)B

7. XFEL É¨¯é\¢ðÍÌWJ

ir
k(r)

n}ï±qÌ\¢ðÍÉÂ¢ÄÍCÀHIÈªàÜk

rk{1(r)jrk(r)|brk(r)kßÄCO 2 ßÉÄñÄµ½û@ðp¢ÄðÅ«»¤Ål0¸Support/̧ Support ¿|r
k(r)|3dnoise/̧ Support ¿|r
k(r)|[3dnoise(7_3)éBêûÅCCXDI ÉÍC\¢ðÍÌãÅðµÄä­×«âèªôÂ©c³êÄ¢éB±ÌßÅÍCXFEL Å¾çêéñÜp^[ÌñÅÌâè_â»ÌðôÆ±±Ål dnoise ÍCPoisson vÉ]ÁÄñÜ­xð]«IÈW]ÉÂ¢ÄZß½B¿·é±ÆÅè·éB
PDI Ì0.21 nm ªð\ÜÅÌñÜp^[iFig. 8(ajj

7.1ÃìÊñÉ} XNÖ ðæ¶C pÌÃìÌ æÌÝðc µ½

CXDI À±ÅÍCüË X üÉÎ·ér[XgbvC

iFig. 8(bjjB±Ì}XNp^[ÉÃìÊñð{·ñ¶UXgbp[CoífqÌ£èí¹MbvÆÆCFig. 8(c)Ìdq§xð¾é±ÆªÅ«½B³çÉC±¢Á½ô½wIvöâoíÌOaÉæÁÄC´_¨æÌdq§xðúT|[gÆµC´_tßª¹µ½ Fig.

ÑápxÌæÌñÜp^[ðL^Å«È¢iFig. 1jB8(a)Ìp^[ÉÎµÄ HIO_SW Êñð{µ½ÊC¿O`ÉÖ·éîñðÜÞápxÌæÌñÜUª¸íê

Fig. 8(d)Ìedq§xªÄ¶Å«½B

Ä¢éÆC]Ì HIO_SW Êñ@ÅÍCT|[gÌå«È¿âæ 6 ßÉ¦µ½ÆËìÉ½Ì±qª¶

æð³mÉè·é±Æªïµ­CMÅ«éñª¢ïÉÈéB±ÌlÈ CXDI p^[©çÌñâèð·é½ßCpÌæÌ\¢UÌÝ©çC¿ÌO`ðè·é dark­eld phase retrievaliÃìÊñ@jªñÄ³êCÀ±f[^ÌðÍÉp¢çênß½35) BpÌæÌñÜUà¿±qdq§xSÌÌ FT ÉR·éÌÅC¿SÌÉÖ·éîñðÜÝC´IÉÍCpÌæf[^ÌÝ©çÌñÍsÂ\ÅÍÈ¢B±±ÅÍ»Ì_ÌTvÆCäXÌì¬µ½ÃìÊñ\tgEGAÌKpá©ç»ÌLø«ðl¦ÄÝ½¢BpÌæf[^ÌÝðp¢½ñÌ½ßÉC\¢öqÉpÌæÌÝIðÂ\È}XNÖ M( S) ðæ¶éBR{[VèÉæèC}XNÖÆ\¢öqÌÏð IFT ·éÆCdq§xªzÆ}XNÖð IFT µ½
Fig. 8Ö m(r) ÌôÝÝÆÈéB~r(r)rdark(r)IFT[M( S)~F( S)]m(r)

(7_1)

ÀpãCOª}sÈ}XNÖðgp·éÆCIFT
µ½ÀóÔÖÉ Gibbs »Ûª¶¶ÄT|[g`óèð¢ïÉ·éÌÅCOªç©ÉëÉQß·é}XN

20  úËõ Jan. 2013 Vol.26 No.1

(Color online) Dark­eld phase retrieval method is a useful
to obtain the initial support shape for HIO­SW calculation.
Original diraction pattern from PDI (a) is masked by aGaussian (b). The dark­eld phase retrieval applied to themasked pattern gave a Gaussian­smeared projection density(c) to be used as the starting model in the HIO­SW phaseretrieval for the diraction pattern in panel (a). The nal
projection map displays structural details of PDI.

gsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]Ý·é¿©çÌñÜp^[ÅÍCXybNTCYª¬³­Èé½ßCS¨æÑ»ÌüÓÌXybNðÏª·é±ÆªZpIÉà¢ïÅéB»Ìæ¤ÈêCÃìÊñ@ªÀpã½¢ÖñLøÅ

éÆl¦çêéB

äXÍC»ÝCKEXÖðp¢½ÃìÊñÉÂ¢ÄCXybNTCYCªð\â§äp[^[ÌÏ»ªÇÌæ¤ÉÊñÊÉe¿ðyÚ·©ð¢µÄ¨èCæèg¢èÌÇ¢ÃìÊñ@Ì\zðÚw
µÄ¢éB

7.2

Ewald

ÉÖíéâè

5C6 ßÌðÍÅÍCeèðp·é½ßCüË X
ü`dxNgÉ¼ÈÊÌñÜp^[©çÌæñðåÆµÄæèµÁÄ«½Bµ©µCÀ±ÅÍ Ewald
Æð·µ½ñÜ­xªzªñÜp^[ÆµÄÏª³êé
iFig. 9(ajjÌÅCÈºÌô½wIl@ªíÉsÂÅéBX üüËûüÌ¿TCYª A ÌêCEwaldÊãÌ_ Sobs Æ Sz0 ½ÊÔÌ£iFig. 9(a)àÌÔ¾üj
ª 1/2A æèàå«­ÈéÆCeèðKp·é±Æª¢ïÉÈèCñ³êédq§xðeÆß·é±Æª¢ïÆÈéBá¦ÎCA ª20 nm Ì±qÉÎµÄ0.1
nm Ì X üðp¢éêCeèðp¢½ðÍÍ 1 nmöxÜÅÌ¬pñÜp^[É§À³êéB nm g·Ì
X üÍC¿ÌUfÊÏðßé½ßÉÍLÅªCEwaldéFig. 9Ì¼aª¬³­Èé½ßÉCeèÌpÍÍª·ÜéiFig. 9(bjjB
XFEL ðp¢½ñÜÀ±ÍjóÀ±Å

èC1 ÂÌ±qÉÎ·égOtB[ªsÂ\È±Æ©çCÅ«êÎC
1 VbgÅÌñÜp^[©ç¢ªð\ÅO³\¢(Color online) (a) Geometrical condition in elastic scatter­ing and Ewald sphere. The cyan­colored line indicates thereciprocal distance between the plane normal to incident X­
ray and Ewald sphere. (b) Variety of the Ewald sphere de­pending on wavelength of X­ray. For PDI molecule, the IFTof structure factor on Ewald sphere is calculated numericallyand visualized.

ðñµ½¢BÀÛCzIðÍÉü¯½C¢³³©­øÈðÍû@ªñÄ³ê½37) B·g· X üÈÇðp¢½\¢¤ÖÌpªÈ³êÄ¢éªClXÈá»ðÑÄ¢

7.3}jtH[hÉæé_Ci~NXÉXibvVbgÌXFEL ðp¢½À±ÍjóÀ±ÅéBé½ßC1 ÂÌ±q±±ÅÍC±ÌâèððÍIÉl¦ÄÝ½¢BEwald

É½xàÆËo¸C]ÁÄ½Ì±qðXï·éÈÇÊãÌñÜ­xÆ±qÌdq§xÌÖWÍCÈºÌ 2µÄC»ê¼êÌ±qÉÔÉ XFEL ðÆË·éÉÈ_ÉÂ¢ÄÌl@ªKvÅéBFig. 7(a)ÌÀ±É¨¢ÄCXàÌ±qªÝ¢ÉÙ

éB

P
ò

Ewald

ÊãÌ\¢UÌÝ©çÌ\¢öqèÈézü¨æÑ\¢ðÆéêl¦ÄÝ½¢BeñÜp

Q
ò

Ewald

Êã\¢öqÌ IFT Å¾çêédq§x^[©çCÆ±qÌdq§xÆÌÖW

éûü©ç©½±qÌXibvVbgª¾çêéÆl¦çêéBæÁÄCcåÈÌñÜp^[

äXÍC±êçÌâèÉÂ¢ÄðÍIÈl@ðÝÄ«½©çñ³êéð®É·é±ÆÅC±qÌ_Ci

P ÉÂ¢ÄÍ¢¾¾é¢©Êµª§ÁÄ¢È¢Bò
QÉªCò~NXð²×é±ÆªÅ«é©àµêÈ¢BÖµÄÍðÍI_WJªÂ\Å( r) Æ Ewald

èC±qÌdq§x r½ÏÊðÍi5.1QÆjðp¢éÆC\¢ªå«­ÙÈÊãÌ\¢öq©çvZ³êédq§xéªqª¬ÝµÄàC2 ÂÌNXÉª¯é±ÆªÅ«½) ðp¢Ä
rEwald ( r)iFig. 9(bjjÍCHermit sñ H(r, r

iFig. 10(ajjBêûC÷­ÉÙÈé\¢ª¡ÜÜêéê

)r( r) Ìæ¤ÉÖWÃ¯ªÂ\ÅrEwald ( r)H(r, rCñíÉ½ÌNXª¯ªKvÅªC\ªÈªð\ÜÅf[^ûWðs¤Kvª

é

PÌ
éBò

èCNXÔÌÖ

Wªs¾Ì½ßC¾çê½½ÌNX©ç_Ci~NXâèÉÂ¢ÄÍCeèð¼èµ½ðÍÆ¯lCHIO_

ð²×éÍÙÚsÂ\ÅSW ðp¢½vZ@ÉæéAv[`ª³ïÈæ¤Å éB

jtH[hhÌTO38_40) ðp¢êÎ±qÌ_Ci~Në¤B±Ìæ¤ÈêCg}

Xð¾ç©ÉÅ«é©àµêÈ¢Æl¦çênß½Bg}

úËõ Jan. 2013 Vol.26 No.1  21

Éü¯¤ðißÄ¢éB^pN¿ÉÀç¸C×EÈÇ
lXÈnÉKpoéêÊIÈû@Ì\zðÚwµÄ¢éB
XFEL ÅÍ½­ÌXibvVbgªªè³êéÆzè³êéÌÅCX[p[RsÍvZ@ÆÌAgàdvÅ

[^uvÌæ¤ÈåKë¤B}jtH[hðp¢½ 2 ³ñÜf[^ÌVµ¢ðÍû@ª®¬·êÎCVµ¢¶½Èw¨æÑvZÈwª©¦Ä­éÌÅÍÈ¢©Æl¦Ä¢éBÓ«{eÉLµ½uJ­ÆÀ±ÉÍC¶ÈwÈ XFELpi¨æÑd_íªÛè¤CÁèÌæ¤CVwp
Ìæ¤Cú{wpU»ïÌîÕ¤iAjC§íIGè¤C¨æÑC»w¤©çÌ SACLA puñÄÛèÌxðó¯Üµ½BFig. 1C3C7 É¦µ½À±Ê Í C SPring­8  ¤r [   C   p Û è i Û è Ô 
20110006 j ¨ æ Ñ SACLA  p ¤  Û è i Û è Ô 
2012A8006jÅ¾çêÜµ½B

Ql¶£
1)
2)
Fig. 10(Color online) (a) The classication and averaging pro­
tocol is able to distinguish PDI molecules in two dierent
conformations29,42) in the in­vacuum simulation. (b)Schematic illustration of manifold in multi­dimensional
space used to describe the dynamics of molecular systems.

jtH[hhðp¢éÆCá¦ÎC®¬µ½pp
æðOãÌÖWª»çÈ¢æ¤ÉooÉµ½ãCæððÍf[^ðàÆÉ³ÌppæðÄ\¬Å«éB
}jtH[hÌTOðCN ´qÅ\¬³êé^pN¿Ì_Ci~NXðáÉl¦ÄÝéBFig. 10(b)Ìæ¤Ée´qÌix, y, zjÀWÅ£çêé 3N ³óÔizÊ
óÔjðl¦éB^pN¿Ìé\¢ÍCzÊóÔÌ

3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)

1 _ÆµÄ^¦çêéB±±Å´qÔÌÉæèC·×
ÄÌ_ÍzÊóÔÌéS©óÔãÉ¶Ý·éÆl¦ç

êéB±ÌS©óÔÌ±Æð}jtH[hÆÄÔBÚ·×«ÍC^pN¿Ì\¢Ï»Í}jtH[hãÌ

14)
15)
16)

éB]ÁÄ½ç©Ìû@Å}

17)

jtH[hðÁ¥t¯çêêÎC^pN¿Ì_Ci~

18)_ÌÚ®ÉÎ·é±ÆÅNXð²×é±ÆªÂ\ÆÈéBÁ¥t¯ðs¤û@ÆµÄ Isomap38), Diusion Map39) ÈÇª

éBÜ½zÊóÔ

ÉÀç¸Cá¦Î 2 ³ñÜf[^ÌesNZÉ¨¯éU­xð²Æ·éóÔÅà}jtH[hðl¦é±Æªoé40)BäXÍ»ÝC}jtH[hÌTOðpµ½½Ì 2
³ñÜf[^©çnÌ_Ci~NXð²×éû@Ì\z

22  úËõ Jan. 2013 Vol.26 No.1

19)
20)
21)
22)
23)
24)

J. Miao, D. Sayre and H. N. Chapman: J. Opt. Soc. Am. A
15, 1662 (1998).
J. Miao, P. Charalambous, J. Kirz and D. Sayre: Nature 400,
342 (1999).
J. Miao, T. Ishikawa, Q. Shen and T. Earnest: Annu. Rev.
Phys. Chem. 59, 387 (2008).
J. R. Fienup: Appl. Opt. 21, 2758 (1982).
C. Song, et al.: Phys. Rev. Lett. 101, 158101 (2008).
Y. Nishino, et al.: Phys. Rev. Lett. 102, 018101 (2009).
H. Jiang, et al.: Proc. Natl. Acad. Sci. USA 107, 11234(2010).
Y. Takahashi, et al.: Phys. Rev. B 80, 054103 (2009).
http://www.mext.go.jp/b_menu/shingi/chousa/shinkou/
022/attach/1308353.htm»ìdMF_d¥CwæñÅ (IÉ ®XC1973).
M. Born and E. Wolf: Principles of Optics 7th (expanded)
edition (Cambridge University Press, Cambridge, 1999).
J. Drenth: Principles of Protein X­ray Crystallography(Spriger­Verlag, New York, 1994).
J. Frank: Three­Dimensional Electron Microscopy of Macro­molecular Assemblies (Oxford University Press, Oxford,2006).
R. Barakat and G. Newsam: J. Math. Phys. 25, 3190 (1984).
S. Marchesini, et al.: Phys.Rev. B. 68, 140101 (2003).
Y. Takayama and M. Nakasako: Rev. Sci. Instrum. 83
054301 (2012).
J. Miao, K. O. Hodgson and D. Sayre: Proc. Natl. Acad. Sci.
USA 98, 6641 (2001).
R. A. Crowther, D. J. DeRosier and A. Klug: Proc. R. Soc.
Lond. 317, 319 (1970).
R. Neutze, et al.: Nature 406, 752 (2000).
ëRçF[U[¤ 40, 680 (2012).
U. Weierstall, et al.: Exp. Fluids 44, 675 (2008).
ëRçFOptronics 31, 101 (2012).
W. Kodama and M. Nakasako: Phys. Rev. E 84, 021902(2011).
M. Radermacher, et al.: Biophys. J. 61, 936 (1992).

gsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]

25)
26)
27)
28)
29)
30)
31)
32)
33)

L. Lebert, A. Maurineau and K. M. Warwick: ``Multivariate
Descriptive Statistical Analysis'' (Wiley, New York, 1984).
P. Penczek, R. Renka and H. Schomberg: J. Opt. Soc. Am.
21, 499_509 (2004).
P. B. Rosenthal and R. Henderson: J. Mol. Biol. 333, 721(2003).
S. J. Ludtke, P. R. Baldwin and W. Chiu: J. Struct. Biol. 128,82 (1999).
G. Tian, et al.: Cell 124, 61 (2006).
W. L. Jorgensen, et al.: J. Chem. Phys. 79, 926 (1983).
M. Nakasako: Phil. Trans. Roy. Soc. Lond. B 359, 1191
(2004).
O. Glatter and O. Kratky: Small­angle X­ray Scattering(Academic Press, London, 1980).
ûF²CëRFæ25ñú{úËõwïNïÉúËõ

34)
35)
36)
37)
38)
39)
40)
41)
42)

Èw¯V|WE\eWi2012N 1 j8P126.
T. M. Schmeing, et al.: Mol. Cell 20, 437 (2005).
A. V. Martin, et al.: Opt. Express 20, 13501_
13512 (2012).
A. V. Martin, et al.: Opt. Express 20, 16650_16661 (2012).
K. S. Raines, et al.: Nature 463, 214 (2010).
J. B. Tenenbaum, V. de Silva and J. C. Langford: Science
290, 2319 (2000).
R. R. Coifman and S. Lafon: Appl. Comput. Harmon. Anal.
21, 5 (2006).
R. Fung, V. Shneerson, D. K. Saldin and A. Ourmazd: Nat.
Phys. 5, 64 (2008).
K. Tamasaku, et al.: Nucl. Instrum. Meth. A 467_468, 686(2001).
G. Tian, et al.: J. Biol. Chem. 283, 33630 (2008).

úËõ Jan. 2013 Vol.26 No.1  23

ÒÐî
ëR

cä`måwHw¨wÈ³öC»w¤d¤úËõÈw¤Z^[îÕ¤qõåÇ¤õE­mail: nakasakophys.keio.ac.jpêåFX üimC[WO
mªðn
1990NCkåwåw@w¤È¨wæñêUmãúÛöPÊæ¾ÞwB
1990NCåwÉòwÉèB1994
NC»w¤É¤õB1997NC
åwªq×E¶¨w¤utB1996_
1999NCJST ³«ª¯±¤õB2002
NCcä`måwHw¨wÈ³öB
2005Næè»EBï¡Í¼ÊC_[
J[hûWBÊÂ

2011Ncä`måwåw@îbHwêU¨wêCCmÛöC¹â{[¾2010N cä`måwåw@îbHw
êU¨wêCCmÛöC¹ûF²

cä`måwHw¨wÈC»w¤
d¤úËõÈw¤Z^[îÕ¤qõ¤õE­mail: oroguchiphys.keio.ac.jpêåF¶¨¨mªðn
2007NC¡ls§åw¶Ì´ªqVXeÈwêUm¤õB2011NCcä`
måwHw¨wÈ³B

RTM

cä`måwåw@îbHwêU¨wêCm 3 NC»w¤d¤úËõÈw¤Z^[îÕ¤¤C¶êåFX üñÜC[WO
mªðn
2010NCcä`måwåw@îbHw
êU¨wêCCmÛöC¹Bï¡ÍhCcbNÆ±ÑÆÃ©ñB¬Ñ ücä`måwHw¨wÈ 4 NC
»w¤d¤úËõÈw¤Z^[îÕ¤¤C¶êåFX üñÜC[WO

24  úËõ Jan. 2013 Vol.26 No.1g¯¡ls§åw¶½imVXeÈw¤ÈÁC³E­mail: t4yoshidometsurumi.yokohama­cu.ac.jpêåF¨wC¶¨¨wCv¨wCtÌ_mªðn
2007NCsåwGlM[Hw¤m¤õB2009NCsåwGlM[Hw¤Áè³B2012Næè
»EB

rû¿

¡ls§åwåw@¶½imVXeÈw¤Èy³öC»w¤d¤úËõÈw¤Z^[îÕ¤qõ¤õE­mail: iketsurumi.yokohama­cu.ac.jpêåF¶ÌªqV~ [Vmªðn
1994NCåwåw@_wn¤ÈmÛöC¹B1994NCåw_wèB2001NC¡ls§åwåw@w¤È³öB2009Næè»EB

gsbNX ¡ Rq[g X üñÜC[WO\¢ðÍ_ÌJ­ÆW]

Development and prospect of theory incoherent X­ray diraction imaging
Masayoshi NAKASAKO1,2, Tomotaka OROGUCHI1,2, Yuki TAKAYAMA1,2,
Amane KOBAYASHI1,2, Wataru KODAMA1, Keita SAKAMOTO1,
Takashi YOSHIDOME3, Mitsunori IKEGUCHI3
1Department of Physics, Faculty of Science and Technology, Keio University

3_14_1 Hiyoshi, Kohoku­ku, Kanagawa, Yokohama 223_8522, Japan

2Infrastructure Research Group, Synchrotron Radiation Research Center, Harima Institute, RIKEN

1_1_1 Kouto, Sayo­cho, Sayo­gun, Hyogo 679_5148, Japan

3Department of Supramolecular Biology, Yokohama City University

1_7_29 Suehiro­cho, Tsurumi­ku, Yokohama, Kanagawa 230_
0045, Japan

Abstract

Coherent X­ray diraction imaging is an useful technique to visualize the three­dimensional struc­tures of non­crystalline particles, which have not been crystallized. The projection structures ofsample particles are obtained only from the structure amplitudes of diraction patterns, and thethree­dimensional structures are reconstructed from tomography experiments. In this review, werevisit the structure analysis theories specic to this technique. In addition, we introduce our pro­
tocol, which is developed for structure analyses of particles/molecules embedded in water drops
and vitreous ice. We also summarize problems to be solved for future application of this tech­nique.

úËõ Jan. 2013 Vol.26 No.1  25