(197)Bodey,A.J.;Kikkawa,M.;Moores,C.A.J.Mol.Biol.,218.(198)Amos,L.A.;H - PDF document

(197)Bodey,A.J.;Kikkawa,M.;Moores,C.A.J.Mol.Biol.,218.(198)Amos,L.A.;Henderson,R.;Unwin,P.N.T.Prog.Biophys.Mol.Biol.,183.(199)Henderson,R.;Baldwin,J.M.;Ceska,T.A.;Zemlin,F.;Beckmann,E.;Downing,K.H.J.Mol.Biol.,899.(200)Mitsuoka,K.;Hirai,T.;Murata,K.;Miyazawa,A.;Kidera,A.;Kimura,Y.;Fujiyoshi,Y.J.Mol.Biol.,861.(201)Crowther,R.A.;Henderson,R.;Smith,J.M.J.Struct.Biol.,9.(202)Nogales,E.;Wolf,S.G.;Downing,K.H.J.Struct.Biol.,119.(203)Gipson,B.;Zeng,X.;Stahlberg,H.2DCrystalDataMicrosc.,1290.(204)Schenk,A.D.;Castano-Díez,D.;Gipson,B.;Arheit,M.;Zeng,X.;Stahlberg,H.MethodsEnzymol.,101.(205)Hoppe,W.Annu.Rev.Biophys.Bioeng.,563.(206)Xiong,Q.;Morphew,M.K.;Schwartz,C.L.;Hoenger,A.H.;Mastronarde,D.N.J.Struct.Biol.,378.(207)Zanetti,G.;Riches,J.D.;Fuller,S.D.;Briggs,J.A.J.Struct.,305.(208)Rosenthal,P.B.;Henderson,R.J.Mol.Biol.,721.(209)Henderson,R.Q.Rev.Biophys.,3.(210)Saxton,W.O.;Baumeister,W.J.Microsc.,127.(211)vanHeel,M.;Schatz,M.J.Struct.Biol.,250.(212)Frank,J.;Al-Ali,L.,376.(213)Unser,M.;Trus,B.L.;Steven,A.C.,39.(214)Unser,M.;Sorzano,C.O.;Thevenaz,P.;Jonic,S.;El-Bez,C.;DeCarlo,S.;Conway,J.F.;Trus,B.L.J.Struct.Biol.,243.(215)Penczek,P.A.J.Struct.Biol.,34.(216)Cardone,G.;Grunewald,K.;Steven,A.C.J.Struct.Biol.,117.(217)Sousa,D.;Grigorie,N.J.Struct.Biol.,201.(218)Schmid,M.F.;Sherman,M.B.;Matsudaira,P.;Tsuruta,H.;Chiu,W.J.Struct.Biol.,51.(219)Gabashvili,I.S.;Agrawal,R.K.;Spahn,C.M.;Grassucci,R.A.;Svergun,D.I.;Frank,J.;Penczek,P.,537.(220)Orlova,E.V.;Saibil,H.R.MethodsEnzymol.,321.(221)Halic,M.;Becker,T.;Pool,M.R.;Spahn,C.M.;Grassucci,R.A.;Frank,J.;Beckmann,R.,808.(222)Heymann,J.B.;Cheng,N.;Newcomb,W.W.;Trus,B.L.;Brown,J.C.;Steven,A.C.Nat.Struct.Biol.,334.(223)Valle,M.;Zavialov,A.;Sengupta,J.;Rawat,U.;Ehrenberg,M.;Frank,J.,123.(224)Klaholz,B.P.;Myasnikov,A.G.;VanHeel,M.,862.(225)Fischer,N.;Konevega,A.L.;Wintermeyer,W.;Rodnina,M.V.;Stark,H.,329.(226)White,H.E.;Orlova,E.V.;Chen,S.;Wang,L.;Ignatiou,A.;Gowen,B.;Stromer,T.;Franzmann,T.M.;Haslbeck,M.;Buchner,J.;Saibil,H.R.,1197.(227)White,H.E.;Saibil,H.R.;Ignatiou,A.;Orlova,E.V.J.Mol.,453.(228)Elad,N.;Clare,D.K.;Saibil,H.R.;Orlova,E.V.J.Struct.Biol.,108.(229)Elad,N.;Farr,G.W.;Clare,D.K.;Orlova,E.V.;Horwich,A.L.;Saibil,H.R.Mol.Cell,415.(230)Fu,J.;Gao,H.;Frank,J.J.Struct.Biol.,226.(231)Briggs,J.A.;Huiskonen,J.T.;Fernando,K.V.;Gilbert,R.J.;Scotti,P.;Butcher,S.J.;Fuller,S.D.J.Struct.Biol.,332.(232)Penczek,P.A.;Frank,J.;Spahn,C.M.J.Struct.Biol.,184.(233)Penczek,P.A.;Yang,C.;Frank,J.;Spahn,C.M.J.Struct.Biol.,168.(234)Rossmann,M.G.ActaCrystallogr.,Sect.D:Biol.Crystallogr.,1341.(235)Chacon,P.;Wriggers,W.J.Mol.Biol.,375.(236)Jensen,G.J.,Ed.MethodsinEnzymology:Cryo-EM,PartC,;AcademicPress,Elsevier:SanDiego,CA,2010;Vol.484(237)Suhre,K.;Navaza,J.;Sanejouand,Y.H.ActaCrystallogr.,1098.(238)Topf,M.;Lasker,K.;Webb,B.;Wolfson,H.;Chiu,W.;Sali,A.,295.(239)Yuan,S.;Yu,X.;Topf,M.;Ludtke,S.J.;Wang,X.;Akey,C.W.,571.(240)Trabuco,L.G.;Villa,E.;Mitra,K.;Frank,J.;Schulten,K.,673.(241)Grubisic,I.;Shokhirev,M.N.;Orzechowski,M.;Miyashita,O.;Tama,F.J.Struct.Biol.,95.(242)Al-Amoudi,A.;Díez,D.C.;Betts,M.J.;Frangakis,A.S.,832. (116)Tang,G.;Peng,L.;Baldwin,P.R.;Mann,D.S.;Jiang,W.;Rees,I.;Ludtke,S.J.J.Struct.Biol.,38.(117)Frank,J.;Radermacher,M.;Penczek,P.;Zhu,J.;Li,Y.;Ladjadj,M.;Leith,A.J.Struct.Biol.,190.(118)Sorzano,C.O.;Marabini,R.;Velazquez-Muriel,J.;Bilbao-Castro,J.R.;Scheres,S.H.;Carazo,J.M.;Pascual-Montano,A.J.Struct.,194.(119)Dube,P.;Tavares,P.;Lurz,R.;vanHeel,M.EMBOJ.,1303.(120)Penczek,P.;Radermacher,M.;Frank,J.,33.(121)Schatz,M.;vanHeel,M.,255.(122)Stewart,A.;Grigorie,N.,67.(123)Joyeux,L.;Penczek,P.A.,33.(124)Frank,J.Three-DimensionalElectronMicroscopyofMacromo-lecularAssemblies;OxfordUniversityPress:Cary,NC,2006.(125)Yang,Z.;Penczek,P.A.,959.(126)Sigworth,F.J.J.Struct.Biol.,328.(127)Scheres,S.H.;Valle,M.;Nunez,R.;Sorzano,C.O.;Marabini,R.;Herman,G.T.;Carazo,J.M.J.Mol.Biol.,139.(128)Roseman,A.M.ActaCrystallogr.,Sect.D:Biol.Crystallogr.,1332.(129)Frangakis,A.S.;Rath,B.K.InPrinciplesofElectronTomo-;Frank,J.,Ed.;Springer:NewYork,2006;pp401(130)Brandt,S.;Heikkonen,J.;Engelhardt,P.J.Struct.Biol.,10.(131)Masich,S.;Ostberg,T.;Norlen,L.;Shupliakov,O.;Daneholt,J.Struct.Biol.,461.(132)McEwen,B.F.;Downing,K.H.;Glaeser,R.M.1995,357.(133)Castano-Diez,D.;Al-Amoudi,A.;Glynn,A.M.;Seybert,A.;Frangakis,A.S.J.Struct.Biol.,413.(134)Forster,F.;Pruggnaller,S.;Seybert,A.;Frangakis,A.S.J.Struct.Biol.,276.(135)Bartesaghi,A.;Sprechmann,P.;Liu,J.;Randall,G.;Sapiro,G.;Subramaniam,S.J.Struct.Biol.,436.(136)Lebart,L.;Morineau,A.;Warwick,K.M.MultivariateDescriptiveStatisticalAnalysis;Wiley:NewYork,1984.(137)Saxton,W.O.;Frank,J.,219.(138)vanHeel,M.;Frank,J.,187.(139)vanHeel,M.;Portugal,R.;Schatz,M.MultivariateStatisticalAnalysisinSingleParticle(Cryo)ElectronMicroscopy.InHandbookonDVD3D-EMinLifeSciences;Orlova,E.,Verkleij,A.,Eds.;3D-EMNetworkofExcellence,EuropeanCommission:London,2009.(140)Jollie,I.T.PrincipalComponentAnalysis;Springer:NewYork,1986.(141)vanHeel,M.;Harauz,G.;Orlova,E.V.;Schmidt,R.;Schatz,J.Struct.Biol.,17.(142)Ward,J.H.J.Am.Stat.Assoc.,236.(143)Scheres,S.H.;Gao,H.;Valle,M.;Herman,G.T.;Eggermont,P.P.;Frank,J.;Carazo,J.M.Nat.Methods,27.(144)Radermacher,M.;Wagenknecht,T.;Verschoor,A.;Frank,J.J.Microsc.,113.(145)Crowther,R.A.Philos.Trans.R.Soc.,B,221.(146)Baker,T.S.;Cheng,R.H.J.Struct.Biol.,120.(147)Orlova,E.V.;vanHeel,M.InProc.13thInt.CongressElectron;Jourey,B.,Colliex,C.,Eds.;LesEditionsdePhysique,LesUlis.:Paris,1994;Vol.1,pp507(148)Radermacher,M.;Wagenknecht,T.;Verschoor,A.;Frank,J.EMBOJ.,1107.(149)Radermacher,M.J.ElectronMicrosc.Tech.,359.(150)Radermacher,M.;Rao,V.;Grassucci,R.;Frank,J.;Timerman,A.P.;Fleischer,S.;Wagenknecht,T.J.CellBiol.,411.(151)Fernandez,J.J.;Li,S.;Crowther,R.A.,587.(152)Leschziner,A.E.;Nogales,E.J.Struct.Biol.,284.(153)Radon,J.Math.Phys.Klasse,262.(154)vanHeel,M.,111.(155)Fuller,S.D.,923.(156)Fuller,S.D.;Butcher,S.J.;Cheng,R.H.;Baker,T.S.J.Struct.,48.(157)Serysheva,I.I.;Orlova,E.V.;Chiu,W.;Sherman,M.B.;Hamilton,S.L.;vanHeel,M.Nat.Struct.Biol.,18.(158)vanHeel,M.;Orlova,E.V.;Harauz,G.;Stark,H.;Dube,P.;Zemlin,F.;Schatz,M.ScanningMicrosc.,195.(159)Penczek,P.A.;Grasucci,R.A.;Frank,J.,251.(160)Grigorie,N.J.Struct.Biol.,117.(161)Sinkovits,R.S.;Baker,T.S.Three-DimensionalImageReconstructionofIcosahedralVirusesfromCryo-electronMicroscopyData.InHandbookonDVD3D-EMinLifeSciences;Orlova,E.,Verkleij,A.,Eds.;3D-EMNetworkofExcellence,EuropeanCommission:London,2009.(162)Sorzano,C.O.;Jonic,S.;El-Bez,C.;Carazo,J.M.;DeCarlo,S.;Thevenaz,P.;Unser,M.J.Struct.Biol.,381.(163)Prasad,B.V.;Hardy,M.E.;Dokland,T.;Bella,J.;Rossmann,M.G.;Estes,M.K.,287.(164)Navaza,J.ActaCrystallogr.,Sect.D:Biol.Crystallogr.,70.(165)Chandran,V.;Fronzes,R.;Duquerroy,S.;Cronin,N.;Navaza,J.;Waksman,G.,1011.(166)Penczek,P.MethodsinEnzymology:Cryo-EM,PartB,3-D;AcademicPress,Elsevier:SanDiego,CA,2010;Vol.482(167)Lyumkis,D.;Moeller,A.;Cheng,A.;Herold,A.;Hou,E.;Irving,C.;Jacovetty,E.L.;Lau,P.W.;Mulder,A.M.;Pulokas,J.;Quispe,J.D.;Voss,N.R.;Potter,C.S.;Carragher,B.MethodsEnzymol.,291.(168)Yan,X.;Sinkovits,R.S.;Baker,T.S.J.Struct.Biol.,73.(169)Jiang,W.;Li,Z.;Zhang,Z.;Booth,C.R.;Baker,M.L.;Chiu,J.Struct.Biol.,214.(170)Herman,G.T.ImageReconstructionfromProjections:TheFunda-mentalsofComputerizedTomography;AcademicPress:NewYork,1981.(171)Ramanchandran,G.N.;Lakshminarayanan,A.V.Proc.Natl.Acad.Sci.U.S.A.,2236.(172)Shepp,L.S.;Logan,B.F.IEEETrans.Nucl.Sci.,21.(173)Orlov,S.S.Sov.Phys.Crystallogr.,429.(174)Orlov,S.S.Sov.Phys.Crystallogr.,312.(175)Harauz,G.;VanHeel,M.B.,146.(176)Herman,G.T.;Lent,A.;Rowland,S.W.J.Theor.Biol.1973,1.(177)Herman,G.T.;Rowland,S.W.Comput.GraphicsImage,151.(178)Herman,G.T.Math.Programming,1.(179)Kak,A.C.;Slaney,M.PrinciplesofComputerizedTomographic;IEEEPress:NewYork,1988.(180)Gordon,R.;Herman,G.T.Commun.Assoc.Comput.Mach.,759.(181)Gilbert,P.J.Theor.Biol.,105.(182)Penczek,P.A.MethodsEnzymol.,1.(183)Andersen,A.H.;Kak,A.C.Ultrason.Imaging,81.(184)Bracewell,R.N.Aust.J.Phys.,198.(185)Bracewell,R.N.FourierAnalysisandImaging;KluwerAcademic/PlenumPublishers:NewYork,2003.(186)Bracewell,R.N.;Riddle,A.C.Astrophys.J.,427.(187)DeRosier,D.J.;Klug,A.,130.(188)Crowther,R.A.;DeRosier,D.J.;Klug,A.Proc.R.Soc.London,Ser.A,319.(189)DeRosier,D.J.;Moore,P.B.J.Mol.Biol.,355.(190)Amos,L.A.J.Mol.Biol.,65.(191)Carragher,B.;Whittaker,M.;Milligan,R.A.J.Struct.Biol.,107.(192)Beroukhim,R.;Unwin,N.,57.(193)Yonekura,K.;Toyoshima,C.,15.(194)Egelman,E.H.,225.(195)Kikkawa,M.J.Mol.Biol.,943.(196)Metlagel,Z.;Kikkawa,Y.S.;Kikkawa,M.J.Struct.Biol.,95. (39)Studer,D.;Michel,M.;Muller,M.ScanningMicrosc.,Suppl.,253.(40)Sartori,N.;Richter,K.;Dubochet,J.J.Microsc.,55.(41)Dahl,R.;Staehelin,L.A.J.ElectronMicrosc.Tech.,165.(42)Hawes,P.;Netherton,C.L.;Mueller,M.;Wileman,T.;Monaghan,P.J.Microsc.,182.(43)Nixon,S.J.;Webb,R.I.;Floetenmeyer,M.;Schieber,N.;Lo,H.P.;Parton,R.G.,131.(44)Grabenbauer,M.;Geerts,W.J.;Fernadez-Rodriguez,J.;Hoenger,A.;Koster,A.J.;Nilsson,T.Nat.Methods2005,857.(45)Leis,A.;Rockel,B.;Andrees,L.;Baumeister,W.Biochem.Sci.,60.(46)Plitzko,J.M.;Rigort,A.;Leis,A.Curr.Opin.Biotechnol.2009,83.(47)Marko,M.;Hsieh,C.;Schalek,R.;Frank,J.;Mannella,C.,215.(48)Rigort,A.;Bauerlein,F.J.;Leis,A.;Gruska,M.;Homann,C.;Laugks,T.;Bohm,U.;Eibauer,M.;Gnaegi,H.;Baumeister,W.;Plitzko,J.M.J.Struct.Biol.,169.(49)Hanszen,K.J.Adv.Opt.Microsc.,1.(50)Glaeser,R.M.;Taylor,K.A.J.Microsc.,127.(51)Knapek,E.;Dubochet,J.J.Mol.Biol.,147.(52)Glaeser,R.M.PhysicalAspectsofElectronMicroscopyandMicrobeamAnalysis;Siegel,B.,Beaman,D.R.,Eds.;JohnWiley&Sons:NewYork,1975;p205.(53)Unwin,P.N.J.Mol.Biol.,657.(54)Berriman,J.A.;Li,S.;Hewlett,L.J.;Wasilewski,S.;Kiskin,F.N.;Carter,T.;Hannah,M.J.;Rosenthal,P.B.Proc.Natl.Acad.Sci.U.S.A.,17407.(55)Unwin,P.N.;Henderson,R.J.Mol.Biol.,425.(56)Glaeser,R.M.J.Struct.Biol.,271.(57)Ziegler,A.;Kisielowski,C.;Ritchie,R.O.ActaMater.2002,565.(58)Gonen,T.;Cheng,Y.;Sliz,P.;Hiroaki,Y.;Fujiyoshi,Y.;Harrison,S.C.;Walz,T.,633.(59)Spence,J.C.H.HighResolutionMicroscopy,3rded.;OxfordUniversityPress:Cary,NC,2003.(60)Reimer,L.;Kohl,H.TransmissionElectronMicroscopyofImageFormation;Springer:New-York,2008.(61)Kirkland,A.;Chang,L.-Y.;Haigh,S.;Hetherington,C.Appl.Phys.,425.(62)Chiu,W.;Glaeser,R.M.,207.(63)Erickson,H.P.;Klug,A.Philos.Trans.R.Soc.,B,105.(64)Thon,F.InPhaseContrastElectronMicroscopy.ElectronMicro-scopyinMaterialsScience;Valdre,U.,Ed.;AcademicPress:NewYork,1971;p570.(65)Toyoshima,C.;Unwin,N.,279.(66)Zernike,F.,686.(67)Nagayama,K.;Danev,R.Philos.Trans.R.Soc.,B2008,2153.(68)Boersch,H.Z.Naturforsch.,615.(69)Unwin,P.N.Philos.Trans.R.Soc.,B,95.(70)Majorovits,E.;Barton,B.;Schultheiss,K.;Perez-Willard,F.;Gerthsen,D.;Schroder,R.R.,213.(71)Cambie,R.;Downing,K.H.;Typke,D.;Glaeser,R.M.;Jin,J.,329.(72)Danev,R.;Nagayama,K.MethodsEnzymol.,343.(73)Danev,R.;Kanamaru,S.;Marko,M.;Nagayama,K.J.Struct.,174.(74)Trinick,J.;Berriman,J.,393.(75)Schroder,R.R.;Hofmann,W.;Menetret,J.-F.J.Struct.Biol.,28.(76)Fujii,T.;Iwane,A.H.;Yanagida,T.;Namba,K.,724.(77)Bozzola,J.J.;Russell,L.D.ElectronMicroscopy:PrinciplesandTechniquesforBiologists,2nded.;Jones&BartlettPublishers:Sudbury,MA,1998;pp240(78)Roseman,A.M.;Neumann,K.,207.(79)Typke,D.;Nordmeyer,R.A.;Jones,A.;Lee,J.;Avila-Sakar,A.;Downing,K.H.;Glaeser,R.M.J.Struct.Biol.,17.(80)Henderson,R.;Cattermole,D.;McMullan,G.;Scotcher,S.;Fordham,M.;Amos,W.B.;Faruqi,A.R.,73.(81)Boyle,W.S.;Smith,G.E.BellSystemsTech.J.,587(82)Chen,D.H.;Jakana,J.;Liu,X.;Schmid,M.F.;Chiu,W.J.Struct.,45.(83)Clare,D.K.;Orlova,E.V.J.Struct.Biol.,303.(84)Faruqi,A.R.J.Phys.:Condens.Matter,314004.(85)Faruqi,A.R.;Henderson,R.Curr.Opin.Struct.Biol.,549.(86)Milazzo,A.C.;Leblanc,P.;Duttweiler,F.;Jin,L.;Bouwer,J.C.;Peltier,S.;Ellisman,M.;Bieser,F.;Matis,H.S.;Wieman,H.;Denes,P.;Kleinfelder,S.;Xuong,N.H.,152.(87)Milazzo,A.C;Moldovan,G.;Lanman,J.;Jin,L.;Bouwer,J.C.;Klienfelder,S.;Peltier,S.T.;Ellisman,M.H.;Kirkland,A.I.;Xuong,N.H.,744.(88)McMullan,G.;Chen,S.;Henderson,R.;Faruqi,A.R.,1126.(89)Tietz,H.R.Microsc.Microanal.,804.(90)Suloway,C.;Pulokas,J.;Fellmann,D.;Cheng,A.;Guerra,F.;Quispe,J.;Stagg,S.;Potter,C.S.;Carragher,B.J.Struct.Biol.2005151,41.(91)Zhang,J.;Nakamura,N.;Shimizu,Y.;Liang,N.;Liu,X.;Jakana,J.;Marsh,M.P.;Booth,C.R.;Shinkawa,T.;Nakata,M.;Chiu,W.J.Struct.Biol.,1.(92)Lander,G.C.;Stagg,S.M.;Voss,N.R.;Cheng,A.;Fellmann,D.;Pulokas,J.;Yoshioka,C.;Irving,C.;Mulder,A.;Lau,P.W.;Lyumkis,D.;Potter,C.S.;Carragher,B.J.Struct.Biol.,95.(93)Mastronarde,D.Microsc.Microanal.,1182.(94)Smith,J.M.J.Struct.Biol.,223.(95)Ludtke,S.J.;Baldwin,P.R.;Chiu,W.J.Struct.Biol.,82.(96)Zhu,Y.;Carragher,B.;Potter,C.S.IEEETrans.Medical,1053.(97)Zhu,Y.;Carragher,B.;Glaeser,R.M.;Fellmann,D.;Bajaj,C.;Bern,M.;Mouche,F.;deHaas,F.;Hall,R.J.;Kriegman,D.J.;Ludtke,S.J.;Mallick,S.P.;Penczek,P.A.;Roseman,A.M.;Sigworth,F.J.;Volkmann,N.;Potter,C.S.J.Struct.Biol.,3.(98)Chen,J.Z.;Grigorie,N.J.Struct.Biol.,168.(99)Boisset,N.;Penczek,P.;Taveau,J.C.;You,V.;DeHaas,F.;Lamy,J.,201.(100)Barcena,M;Koster,A.J.Semin.CellDev.Biol.,920.(101)Zheng,S.Q.;Keszthelyi,B.;Branlund,E.;Lyle,J.M.;Braunfeld,M.B.;Sedat,J.W.;Agard,D.A.J.Struct.Biol.2007,138.(102)Winkler,H.J.Struct.Biol.,126.(103)Nickell,S.;Forster,F.;Linaroudis,A.;Net,W.D.;Beck,F.;Hegerl,R.;Baumeister,W.;Plitzko,J.M.J.Struct.Biol.,227.(104)Schoenmakers,R.H.M.;Perquin,R.A.;Fliervoet,T.F.;Voorhout,W.;Schirmacher,H.Microsc.Anal.,5.(105)Kremer,J.R.;Mastronarde,D.N.;McIntosh,J.R.J.Struct.,71.(106)Mastronarde,D.N.J.Microsc.,212.(107)Suloway,C.;Shi,J.;Cheng,A.;Pulokas,J.;Carragher,B.;Potter,C.S.;Zheng,S.Q.;Agard,D.A.;Jensen,G.J.J.Struct.Biol.,11.(108)Zhou,Z.H.;Hardt,S.;Wang,B.;Sherman,M.B.;Jakana,J.;Chiu,W.J.Struct.Biol.,216.(109)Mindell,J.A.;Grigorie,N.J.Struct.Biol.,334.(110)Sander,B.;Golas,M.M.;Stark,H.J.Struct.Biol.2003,392.(111)Huang,Z.;Baldwin,P.R.;Mullapudi,S.;Penczek,P.A.J.Struct.Biol.,79.(112)Fernandez,J.J.;Sanjurjo,J.;Carazo,J.M.,267.(113)Mallick,S.P.;Carragher,B.;Potter,C.S.;Kriegman,D.J.,8.(114)Wiener,N.Extrapolation,Interpolation,andSmoothingofStationaryTimeSeries;Wiley:NewYork,1964.(115)Mancini,E.J.;Fuller,S.D.ActaCrystallogr.,Sect.D:Biol.,1278. CollegeLondon,whereshepresentlyholdstheBernalChairofStruc-turalBiology.ShehasbeenelectedasaFellowoftheRoyalSocietyandamemberoftheEuropeanMolecularBiologyOrganization.Herresearchinterestscovertheactionsofmacromolecularmachinessuchasmolecularchaperones,involvedinproteinfoldingandmisfolding,aswellasproteinrefoldingduringmembraneporeformation.Shehasbuiltupacryo-electronmicroscopylaboratoryatBirkbeck,tostudymacromolecularcomplexesaswellascellularstructuresusingsingleparticleandtomographyapproaches. ElenaOrlovareceivedherB.Sc.andM.Sc.inPhysicsfromMoscowPhysical-TechnicalUniversity,andherPh.D.degreeinPhysicsandMathematicsfromtheInstituteofCrystallographyinMoscow.AfterworkinginthelaboratoriesofProfessorsB.K.VainshtainandN.A.KiselevinMoscow,sheworkedinthelaboratoriesofW.Chiu(Houston)andM.vanHeel(BerlinandLondon).Presently,sheisaprofessoratBirkbeckCollege(London).Herresearchinterestsareinstructuralanalysisofbiomacromolecularcomplexesusingcryoelectronmicroscopyimagingandinmethodsdevelopment.Hergrouphasanalyzedarangeofdierentmolecularcomplexesstartingfromsymme-tricalandasymmetricalhugeviralassembliestoverysmallregulatoryproteinssuchasthetumoursuppressorp53.WethankJoachimFrank,RichardHenderson,RonaldMilligan,andPeterRosenthalforhelpfulcommentsonthemanuscript,DanClare,MaudDumoux,RichardHayward,MayaTopf,NeilRanson,UliGohlke,andStephenFullerforprovidinggures,andAndrewServiceandAnne-CecileMaatforhelpwithmanuscriptpreparation.WearegratefultotheWellcomeTrust,BBSRC,EU3DEMNoEforfunding.ThisreviewgrewoutofmaterialspreparedforaseriesofcoursesfundedbytheEuropeanMolecularBiologyOrganization.(1)Dubochet,J.;Adrian,M.;Chang,J.J.;Homo,J.C.;Lepault,J.;McDowall,A.W.;Schultz,P.Q.Rev.Biophys.,129.(2)Al-Amoudi,A.;Chang,J.J.;Leforestier,A.;McDowall,A.;Salamin,L.M.;Norlen,L.P.;Richter,K.;Blanc,N.S.;Studer,D.;Dubochet,J.EMBOJ.,3583.(3)Huang,B.;Bates,M.;Zhuang,X.Annu.Rev.Biochem.2009,993.(4)McDermott,G.;LeGros,M.A.;Knoechel,C.G.;Uchida,M.;Larabell,C.A.TrendsCellBiol.,587.(5)Lucic,V.;Leis,A.;Baumeister,W.Histochem.CellBiol.,185.(6)Koster,A.J.;Grimm,R.;Typke,D.;Hegerl,R.;Stoschek,A.;Walz,J.;Baumeister,W.J.Struct.Biol.,276.(7)McIntosh,R.;Nicastro,D.;Mastronarde,D.TrendsCellBiol.,43.(8)Al-Amoudi,A.;Studer,D.;Dubochet,J.J.Struct.Biol.2005,109.(9)Hsieh,C.E.;Marko,M.;Frank,J.;Mannella,C.A.J.Struct.Biol.,63.(10)Henderson,R.Q.Rev.Biophys.,171.(11)Frank,J.Annu.Rev.Biophys.Biomol.Struct.,303.(12)vanHeel,M.;Gowen,B.;Matadeen,R.;Orlova,E.V.;Finn,R.;Pape,T.;Cohen,D.;Stark,H.;Schmidt,R.;Schatz,M.;Patwardhan,A.Q.Rev.Biophys.,307.(13)Verkleij,A.;Orlova,E.V.ElectronMicroscopyinLifeScience,3D-EMNetworkofExcellence;EuropeanCommission:London,2009.(14)Jensen,G.J.,Ed.MethodsinEnzymology:Cryo-EM,PartB,3-D;AcademicPress,Elsevier:SanDiego,CA,2010;Vol.482(15)Zhang,X.;Jin,L.;Fang,Q.;Hui,W.H.;Zhou,Z.H.,472.(16)Bhushan,S.;Homann,T.;Seidelt,B.;Frauenfeld,J.;Mielke,T.;Berninghausen,O.;Wilson,D.N.;Beckmann,R.PLoSBiol.,e1000581.(17)Henderson,R.;Baldwin,J.M.;Ceska,T.A.;Zemlin,F.;Beckmann,E.;Downing,K.H.J.Mol.Biol.,899.(18)Miyazawa,A.;Fujiyoshi,Y.;Stowell,M.;Unwin,N.J.Mol.Biol.,765.(19)Moody,M.F.StructuralBiologyUsingElectronsandX-rays.AnIntroductionforBiologists;AcademicPress,Elsevier:Amsterdam,2011.(20)Beck,M.;Lucic,V.;Forster,F.;Baumeister,W.;Medalia,O.,611.(21)Heuser,T.;Raytchev,M.;Krell,J.;Porter,M.E.;Nicastro,D.J.CellBiol.,921.(22)Jensen,G.J.,Ed.MethodsinEnzymology:Cryo-EM,PartA,SamplePreparationandDataCollection;AcademicPress,Elsevier:SanDiego,CA,2010;Vol.481(23)Harris,J.R.NegativeStainingandCryoelectronMicroscopy:TheThinFilmTechniques;BIOSScienticPublishers:Oxford,UK,1997.(24)Saibil,H.R.ActaCrystallogr.,Sect.D:Biol.Crystallogr.,1215.(25)Harris,J.R.;Scheer,D.,461.(26)Sherman,M.B.;Orlova,E.V.;Terzyan,S.S.;Kleine,R.;Kiselev,N.A.,131.(27)Dobro,M.J.;Melanson,L.A.;Jensen,G.J.;McDowall,A.W.MethodsEnzymol.,63.(28)Rhinow,D.;Kuhlbrandt,W.,698.(29)Yoshioka,C.;Carragher,B.;Potter,C.S.Microsc.Microanal.,43.(30)Tilley,S.J.;Orlova,E.V.;Gilbert,R.J.;Andrew,P.W.;Saibil,H.R.,247.(31)Wang,L.;Sigworth,F.J.,292.(32)Adrian,M.;Dubochet,J.;Fuller,S.D.;Harris,J.R.,145.(33)Golas,M.M.;Sander,B.;Will,C.L.;Luhrmann,R.;Stark,H.,980.(34)Kastner,B.;Fischer,N.;Golas,M.M.;Sander,B.;Dube,P.;Boehringer,D.;Hartmuth,K.;Deckert,J.;Hauer,F.;Wolf,E.;Uchten-hagen,H.;Urlaub,H.;Herzog,F.;Peters,J.M.;Poerschke,D.;Luhrmann,R.;Stark,H.Nat.Methods,53.(35)Golas,M.M.;Bohm,C.;Sander,B.;Eenberger,K.;Brecht,M.;Stark,H.;Goringer,H.U.EMBOJ.,766.(36)Cavalier,A.;Spehner,D.;Humbel,B.M.HandbookofCryoPreparationMethodsforElectronMicroscopy.MethodsinVisualization;CRCPress:London,2009.(37)Studer,D.;Graber,W.;Al-Amoudi,A.;Eggli,P.J.Microsc.,285.(38)Studer,D.;Humbel,B.M.;Chiquet,M.Histochem.CellBiol.,877. conjunctionwithotherbiochemicalandbiophysicaldataonthesample.Themapshouldbeexaminedatacontourlevelthatenclosestheapproximatemolecularmass.MassmeasurementsbyscanningtransmissionEMcanbeveryusefulforinterpreta-tion,althoughaccesstospecializedscanningtransmissionEMfacilitiesislimited.Themap,normallycontouredat1shouldshowcontinuousdensitywellabovebackgroundnoise(obviouslycheckedbeforemasking)becausedisconnectedpiecesofdensitywouldnotmakesenseforasinglecomplex.Densitysectionsofthemapshouldbeviewedingrayscalerepresentation,tocheckforinconsistenciessuchasregionsofanomalouslyhighdensity,whichwouldnotbenoticedinanisosurfacerepresentation.Withamapat4Åresolutionorbetter,itmaybepossibletobuildanatomicmodelwiththemethodsusedinX-raycrystallography(Figure33).InthecaseofEM,thedensityisfullydetermined(assumingsucientangularsampling)fromtherecordedimages,whichcontainbothamplitudeandphaseinformation.Therefore,animportantdierencebetweenmodelbuildingincrystallographyandinEMisthattheatomicmodelisnotrequiredtorenetheEMmap.Fortomogramsofcellsorsubcellularstructures,segmentationisusedtoidentifysubstructuressuchasmembranesandcytos-keletalelements.10.2.AtomicStructureFittingDockingofknownorrelatedatomicstructuresofcomponentsintotheEMmapofanassemblyisthemaintoolforinterpreta-234236Mostsingle-particlemapsareinthe730Åresolutionrange,sothattheycannotbeindependentlyinterpretedintermsofmolecularstructure.Inthisresolutionrange,itisnotpossibletobuildatomicstructures,norisitalwayspossibletounambiguouslyidentifythepositionsofknowndomains.Inthelowresolutionrange(2030Å),largedomainsmayberecognizablebytheirshapes.Inthe9Åresolutionrange,-helicalsecondarystructuresareresolved.Theindividual-strandsareseenwitharesolutionbeyond4.5Å.Side-chaindetailisonlypresentinexceptionallyhigh-resolutionstructures,suchastheaquareovirusparticleshowninFigure33,butdockingintolowerresolutiondensitymapsoftenprovidesgoodpredictivevalueforprobingmechanismsanddesigningmutants.Overthewholeresolutionrange,mapinterpretationisalmostalwaysfacilitatedbytheavailabilityofknownorrelatedatomicstructuresforcomponentsthatcanbeusedfortting(Figure34).Thebasicprincipleofttingisdensitycorrelation.Atargetdensitymapiscalculatedfromtheatomicstructure,atthesameresolutionastheEMmap,andacrosscorrelationsearchin3Disusedtoalignthetwodensities.Thesearchcanbedoneineitherrealorreciprocalspace.Forasmallobjectbeingdockedintoalargermap,themethodoflocalcorrelationwasdeveloped(section4.3),givingamoresensitivemeasureoft.Evenatmodestresolution,ifthesubregionhasanasymmetricshape,itmaybepossibletopositionthestructurewithanaccuracyofafewangstroms.Fittingasetofsmall,separatesubunitsintoalargemapatlowresolutionisverydicult,unlessinformationonsubunitinterfacesisavailable.Labelingexperimentsareveryhelpfulifanaccessiblepositioncanbeidentiedforinsertionofabindingsite,forexample,auniquecysteineforbindingaderivatizedgoldparticle,orfusionofaproteindomainsuchasGFP.However,goldlabelscanbindnonspecicallyordisassemblefragilecomplexes.Oftentherearehingemovementswhenmoleculesassembleintolargercomplexes,sothattheoriginalsearchobjectdoesnotmatchthedensityasarigidbody.Forthiscase,ttingapproachesareused(Figure34).235,237241Themoleculesareallowedtobendindesignatedhingeregions,ormultipleconformationsaregener-atedbynormal-modeanalysisandthenusedfortting.Forthesemethods,thereisadangerofoverinterpretationwithunjustidetails,especiallywithlowresolutionmaps.Ifmajorrefoldingoftheatomicstructureissuggested,itisimportanttousebiochemicalorbiophysicalexperimentstoprovidesupportingdata,forexample,interatomicdistancemeasuresbyspectroscopyorcross-linking.Themoreconstraintsareavailable,themorereliableisthenalresult.10.3.BiologicalImplicationsUltimately,themostimportantquestionsare:Doesthestructuremakesense?Whatnewbiologicalinsightdoesitprovide?Withcientresolution,thestructurecanbeusedtopredicteectsofmutationsorsitesofpotentialcross-links,andthesepredictionscanbetestedinmolecularbiologicalexperiments.3DEManalysisincreasinglyformsapartofmolecularandcellbiologystudies.Thefutureprospectistocombine3Dinformationoverthewholerange,tounderstandtheoperationofmacromolecularmachinesincellsandtissues.Anexampleofacryo-tomogramofasectionofskintissue,fromwhichtheintercellulardesmosomejunctionswereextracted,aligned,andaveragedtorevealthe3DdensitycorrespondingtocadherinmoleculesthatcouldbettedwithanatomicmodelisshowninFigure35.242Withtheconcurrentprogressinmacromolecularcrystallo-graphy,itisoftenpossibletoderiveapseudoatomicmodeloflargeassembliesbydockingatomicstructuresofcomponentsintoEMmaps.Advancesresultingfromthesehardwareandsoftwareimprovementsarehelpingtorevealthemechanismsofoperationofmacromolecularmachinesbyprovidingsnapshotsoftheirdierentfunctionalstates.The3DEMeld,followingmacromolecularcrystallography,ismaturing,withaninternationaldatabaseofEMdensitymaps(EMDatabank.org)linkedtothePDB,currentlycontainingover1000entriesandgrowingsteadily.AUTHORINFORMATIONCorrespondingAuthors*E-mail:e.orlova@mail.cryst.bbk.ac.ukandh.saibil@mail.cryst.bbk.ac.uk. HelenSaibilobtainedherB.Sc.inBiophysicsfromMcGillUniversityinMontrealandPh.D.atKingsCollegeLondon.AfterpostdoctoralgrantsatKingsCollegeandattheCentredEtudesNucleaires,Grenoble,followedbyanacademicpostatOxfordUniversity,shejoinedtheCrystallographyDepartmentatBirkbeck orientationvariationwithinclasses,andasaresultfacilitatesrecognitionofconformationalvariations.Theapproachhasbeenappliedtothereconstructionofheterogeneousribosomecomplexesandtoicosahedralviruseswithsymmetrymis-matchesorpartialoccupancyofsomecomponents.Thethirdcategoryisbasedonaposteriorianalysisof3Dreconstructionsbyconsideringapopulation(asmanyaspossi-ble)of3Dreconstructionstodeterminethevariancein3D.Many3Dmapsarereconstructedforthevarianceanalysis;themostrepresentativeonesarethenusedasinitialmodelsfornement.Intheso-calledbootstraptechnique,mapsarecalculatedfromrandomlyselectedsubsetsofimageswhosespatialorientationsweredeterminedbyprojectionmatchingtoaninitial3Dmap.Theevaluationofvarianceintheresulting3Dmapsandlocalizationofregionswithhighvarianceallowsassessmentoftheheterogeneity,andestimationofcovarianceinthepopulationenablesclassicationof3Dmaps.Oncetheregionofmajorvariationislocalizedinthe3Dmapsandinthecorresponding2Dprojections,imagesaresortedintosubgroupsaccordingtoaveragepixeldensityinthehighvarianceregion.Anotherideaisthemaximumlikelihood-basedclassicationof3Dmapsthatidentiesconformationalvariabilitywithinthemapsandthenseparatesthedierentmolecularstates.10.MAPINTERPRETATION10.1.AnalysisofMapFeaturesOncethemapofanewstructureisobtained,itshouldbepossibletoestimatethemolecularmassandoligomericstate,in Figure34.ttingofthecrystalstructureoftheN-terminalpartofthehumanapopotosome(domainsNBD,HD1,WHD,andHD2)intothecorrespondingsegmentedcryoEMmapat9.5Åresolution(ref239).(a)Initialtbeforeadjustmentofthestructure.(b)Resultoftting.FigurecourtesyofShujunYuan. Figure35.Fromasectionofskintissuetomolecularshapeofcadherin.(a)Segmented,renderedimageshowingthedierentcellularcomponentsinthereconstructedtissuesection.(b)Tomogramslice.D,desmosome;IF,intermediatelaments;Nu,nucleus;ER,endoplasmicreticulum;NE,nuclearenvelope;Mi,mitochondrion.(c)Desmosomeextractedfromtheareainthereddashedboxin(b),withaninsetoftheaveragedimage.(d)Subtomogramaveragewithttedcadherins.Reproducedwithpermissionfromref242.Copyright2007MacmillanPress. Inthesecondcategoryofsortingmethods,aninitial3Dmapisrequiredtoseparatetheimagesintosubsetscontainingimagesofamolecularcomplexinsimilarorientations.Analysisofhetero-geneityisthendonein2Dforeachimagesubset.Thisminimizes Figure32.Statisticalanalysistodetectvariableligandoccupancy.Amodeldatasetwithvariableligandoccupancy,simpliedtoshowonlyoneorientation(a),andthecorrespondingeigenimages(b).Thersteigenimageisthesumofallimages.Theareacorrespondingtotheligandhasdensityproportionaltotheoccupancy(50%)oftheligandinthecomplex.Thesecondeigenimageshowsaverydarkspotlocatedintheareaoftheligand.Thisfeaturereectsthemajorvariationpresentinthedataset.Theremainingeigenimagesreectvariationsrelatedtonoiseintheimages.(c)RealeigenimagesfromadatasetofGroELwithvariablebindingofnon-nativemalatedehydrogenase.Eigenimages2and3showvariationsmainlyrelatedtoderentorientationsaroundtherotationaxis.Eigenimage4indicatessmallvariationsintiltaroundahorizontalaxis.Eigenimages58mainlyrevealvariationsrelatedtooccupancyandlocationoftheligandinthecomplex(arrows).Reproducedwithpermissionfromref229.Copyright2007ElsevierInc. Figure33.High-resolutionsingle-particleEMofAquarheovirus.(a)Rawimagesofvirusesinvitreousice.(b)3Dreconstructioncoloredaccordingtoradius.(c)StructureofsubunitVP5withthebackbonemodelandenlargementtoshowside-chaindetail.Reproducedwithpermissionfromref15.Copyright2010ElsevierInc. 8.3.TemperatureFactorandAmplitudeScaling(Sharpening)Advancesinsingle-particleanalysismeanthatcryoEMstructuresincreasinglyreachsubnanometerresolutions,re-vealingnotonlydomainorganizationofmolecularcomplexesbutalsotheirsecondarystructuralelements.ItisthereforeimportantthatcryoEMmapsshowthefeaturesnecessaryforinterpretationofthesestructuralelements.Methodsofalign-ment,averaging,andreconstructionusuallyresultinover-weightingofthelow-resolutioninformation.Consequently,nedetailsinthemapareobscured.Thelossofdetailscanbedescribedbythetemperaturefactor,or-factor,whichrepresentsthelossofsignalwithresolutionasthesmearingoutofatomsbythermalvibrations.Thefalloofsignalwithreciprocalspacingcanbedescribedbyaplotofln,whereisthesphericallyaveragedscatteringamplitudeandistherealspacecoordinate.208Thecurveislinearatlowspatialfrequencies,anditsslopeisproportionaltotheradiusofgyrationofthescatteringobject(theGuinierregioninsmallanglescattering).Itisastandardproceduretomakethehigh-frequencydetailsmorevisiblebyscalingtheexperimentalmapseitherbyapplyingaltertoreducethecontributionoflowfrequencycomponentsorbyrescalingtheamplitudedecayaccordingtotheamplitudespectrumofareferenceatomicstructure,eectivelysharpeningthemap.ThiscorrectionhasbeendonebyusingX-raysolutionscatteringcurvestoscaletheFourieramplitudescomputedfromtheEMrecon-struction.218,219Amplitudescalingcanthereforeuncoverdetailsinthestructure.ThischangeinscalingoftheFTamplitudesdoesnotaectthemeasuredresolutionofthestructure,butitseectscanbeobservedbyexaminingtherotationallyaveragedpowerspectrumofthemap.Figure30showsanexamplecomparinganEMmapofTMVbeforeandafteramplitudescalingandsharpening.9.HETEROGENEITYIN2DAND3D9.1.SourcesofHeterogeneityTheresolutionofmacromolecularstructuredeterminationbycryoEMismoreoftenlimitedbyconformationalvariationofthestructurethanbyproblemswithmicroscopyorimageprocessing.Imagesofabiologicalcomplexinsolutionwillreectthedistatesofthecomplexcapturedduringvitrication.Samplehetero-geneitycanarisefromseveralsources:(i)partialoccupancyofaligandinamolecularcomplex,221(ii)structuraldynamicsthatisectedinafewdistinctreactionstatesorbyagradualtransforma-tionthroughintermediatestates,and(iii)multipleoligo-mericstatesofdierentsymmetryand/orsize.30,226Ideally,distinctconformationsshouldbetrappedbiochemicallybeforeEMima-ging(e.g.,ref223),butinmanycasesthisisnotpossible.9.2.MethodsforComputationalSortingofMixedStructuresThreemainapproacheshavebeendevelopedforcomputa-tionalseparationofmixedstructures(Figure31).Inthecategory,recognitionofheterogeneityandinitialsortingaredonein2Donly,priortoany3Dreconstruction.ThisapriorigroupofmethodsisbasedprimarilyonMSAoffeaturesinthe2Dimagestodetectstructuralvariationsanddiscriminatethemfromorientationdierences.Theimagesaresortedaccordingtotheirmajorvariations,whicharereectedinthelowordereigenimages.Toseparateimageswithvariableoccupancyofasubstrate,twostagesofMSAandclassicationcanbeused.Intherststep,imagesareseparatedaccordingtofeaturesshowingglobalvarianceduetoorientationdierences,whilethesecondclassicationisbasedonlocalizeddierencesinducedbysubstratebinding.Thesestepsdonotrequireangularorientationdetermination,sothetechniqueisindependentofanyinitial3Dmodel.Thetechniquewasshowntodiscriminateoverallsizevariationsassmallas5%.226,227ThisapproachhasbeenusedtoseparateribosomeEF-Gcomplexesandchaperoninsubstratecomplexes228,229(Figure32). Figure31.Threemainapproachescurrentlyusedtoidentifyandsortmolecularheterogeneity.Therstapproach(leftpanel)isbasedonstatisticalanalysisof2Dimages(apriorianalysis)todetecttheheterogeneityofthesampleinitsimages.Theinitialsortingisdonepriortoany3DreconstrucThesecondapproach(middlepanel)requiresaninitial3Dmaptoseparatetheimagesintosubsetsaccordingtotheirorientation.Analysisofstructuheterogeneityisdonein2Dforeachorientationsubset.Thethirdmethod(aposteriorianalysis)isbasedonexaminationofvariationsinmultiple3Dmaps(rightpanel).Reproducedwithpermissionfromref220.Copyright2010ElsevierInc. tothenoiselevel,or0.143havebeenproposedonthebasisofSNRestimates.208,211SystematicerrorsthataectbothhalvesofthedatasetequallywillnotbedetectedintheFSC,whichwillthereforebeoveroptimistic.Ifasharp-edgedmaskisusedaroundthemaps,orifnoisebecomescorrelatedwiththesignalduringnement,spurioushigh-resolutioncorrelationcanbegen-erated,sothatthecorrelationfallstoaminimumandthenrisesagainathighresolution,reectinggoodcorrelationbetweenthemasksappliedtothereconstructions.TheFSCcanbederivedfromtheSNRfromtherelationshipbetweenSNRandthecrosscorrelation(CC). Anothermethod,rstproposedfor2Daveragesandsubse-quentlyextendedto3Dstructures,isthespectralsignal-to-noiseratio(SSNR).Inthiscase,thesignalisestimatedtobethereprojectionsofthemap,andthenoiseisestimatedbytakingtheerencebetweeninputimagesandthecorrespondingrepro-jections.Thisapproachdoesnotrequirethedatasettobedividedintohalves.LiketheFSC,theSSNRrequiresthealignedinputimages.Itshouldbenotedthatagoodresolutionvaluedoesnotguaranteethatthemapiscorrect.Forresolutionassessmentoftomograms,Cardoneetal.pro-posedtwomethods.Thesimplermethodisdirectlyequivalenttothesingle-particleFSC,usingtomogramscalculatedfromevenandoddprojections.Amoreaccuratemethodthatiscomputa-tionallymoreexpensiveisbasedonaveragingaseriesofFourierringcorrelationsbetweenagivenprojectionandthecorrespond-ingreprojectionofthetomogramcalculatedfromalloftheotherprojections.Afurthermethodhasbeenproposed,-measure.Itdoesnotrequiretheinputdata,butusesthenalmapitself,alongwiththesurroundingregionofthereconstructionoutsidetheparticle,fortheresolutionestimation.Thismethodexaminesthecorrela-tionsbetweenadjacentpixelsintheFTofthereconstruction.Foramapcontainingpurenoise,adjacenttransformpixelsareuncorrelated.Backgroundmaskingintroducessuchcorrelations,whichcanbepredicted,andthestructureitselfintroducesfurthercorrelations.Fromthesecorrelationsandfromanestimateofthenoisemeasuredontheregionsurroundingtheparticle,theFSCcurvecanbepredictedwithoutaccesstotheinputdata.Thisisclearlyanadvantage,butrequiresthemaptobeprovidedwithouttightmaskingofthestructure.Althoughthesevariouscriteriaareavailable,mostworkcurrentlyusesthe0.5FSCcriterion.Whatmattersisnotanumber,smallorlarge,givingtheresolution.Theimportantthingiswhatthemapshows.If-helicesareresolved,theresolutionmustbebetterthan9Å.-Strandsrequireittobebetterthan4.5Å.Moreover,therearemanyexamplesintheliteratureofmuchlowerresolutionmapsthatgiveimportantbiologicalinsights. Figure30.ectsoffullCTFcorrectionandamplitudescalingontheappearanceandresolutionofanEMmapofTMV.(a)SurfaceviewandtwoorthogonalcentralsectionsofanEMmapofTMV,withthettedatomicstructureshownonthesections(ref23).(b)Enlargementoftheboxedregionin(a),ofamapobtainedonlywithphasecorrectionbutnotamplitudecorrectionorscaling.(c)Thesamemapregionafterfullamplitudecorrection.(d)Themapregionafterfullamplitudecorrectionand-factorscaling.(e)Rotationallyaveragedpowerspectraofthemapswithphasecorrection(blue),amplitudeandphasecorrection(red),ofamapcalculatedfromtheatomicstructuret(green),andofthefullycorrectedand-factorscaledmap(purple).(f)FSCcurvesforthephaseandamplitudecorrectedmaps,coloredasin(e).Reproducedwithpermissionfromref83.Copyright2010ElsevierInc. volume,subtomogramaveraging(describedinsection4.4.2)canbeusedtoimproveSNRand,ifthestructureispresentinerentorientations,tollinthemissingwedge,thusimprovingtheresolutionoftheaveragedvolumes.CTFcorrectionisdicultintomograms,becausetheverylowdoseineachtiltviewdoesnotgivesucientsignaltomeasuretheThonrings,andalsobecausethedefocusvariesacrosstiltedimages.Nevertheless,severalapproacheshavebeendeveloped,suchascorrectinginbandsparalleltothetiltaxis,wherethewidthofthebanddecreaseswithincreasingtiltangle,102,151,206,207andtwoapproacheshavebeencomparedforestimatingthedefocusinatiltseries:correctingbytheaveragedefocusofthewholetiltseries,ordeterminingdefocusfromtheverysmallchangesinmagnicausedbychangesindefocus.8.EVALUATIONOFRECONSTRUCTIONQUALITYANDItisnotstraightforwardtoverifythatasingle-particlerecon-structioniscorrectandthentoevaluateitsresolution.Thereareexamplesintheliteratureofdierentmapsofthesameobject.Thematchbetweeninputimagesandreprojectionsisnecessarybutnotsucienttoensurethatthemapiscorrect.Itisalsoessentialthattheclassmembersresembletheclassaveragesandthatthecharacteristicviewsarerecognizableintherawdata.Notethatresolutioncanbeveryanisotropic,especiallywithtiltdata,andthatitcanvarybetweendierentregionsofastructure.Forexample,rigidregionswillbemoreaccuratelyrepresentedexibleones,andperipheralregionswillbemoreaectedbyorientationerrorsthancentralones.Toevaluatemapreliability,anapproachsomewhatequivalenttothefreefactorincrystallographyhasbeenproposed.Theideaistocollectsometiltpairs,withrelativelylowtilt(10andtodeterminetheparticleorientationsbyprojectionmatch-ingtothenalmap.Thisprocedureprovidesacheckontheconsistencyofthemapwithindependentdata,andallowsforhanddetermination,butcanbeverydicultatlowresolutionifthestructuredoesnothavestronglyasymmetricfeatures.Thepoint-to-pointresolutionofanimageisdenedbythemini-mumdistancebetweentwodistinguishabledensitymaxima.However,theaccuracyoflocatingthecenterofmassofadensitymaximumis5timesbetterthanthepointtopointresolution(Figure29).Ifthemapshowsfeaturesofsecondarystructure,itscorrectnesscanbeveriedbyttingofcomponentswithknownatomicstructures.8.1.CausesofResolutionLossStructureinformationcanbelostordistortedatallstagesofthedatacollectionandanalysis,dependingoninstrumentation,experimental,andcomputationalskills.Poorelectronopticalalignment,drift,detectornoise,magnicationvariations,inaccuratedefocusdetermination,errorsinalignment,sam-pleheterogeneity,exibility,incompleteangularcoverage,andradiationdamagecanallcombinetogivedramaticfalloofthehigh-resolutioninformation.10,208,209Inaccuracyofalignmentleadstotheblurringofeachpointintheimage,whichcanbedescribedbyasapointspreadfunction(PSF)withaGaussiandistribution.BetteralignmentleadstoasharperPSF.Conversely,abroadPSFleadstoerrorsindeterminationofangularorientationsandslowstherene-mentprocedure,increasingthenumberofiterationsinthealignmentreconstructionloop.8.2.ResolutionMeasuresThemeasurementofresolutionshouldquantifythelevelofreliabledetaildetectableinthenalmap.Inpractice,thedetectabilityoffeaturesatagivenresolutionisdeterminedbytheSNRinthatfrequencyrangeofthedata.Toquantifyresolution,theSNRmustbeestimatedasafunctionofspatialfrequency.Withcrystallographicdata,thesignalisconcentratedindiractionpeaks,whereasthenoiseisdistributedcontinu-ouslyoverreciprocalspace.Therefore,theSNRinanygivenfrequencyrangeisreadilyestimatedbycomparingtheditionpeaktothesurroundingregion,andtheresolutionisdeterminedbythespatialfrequencyofthehighestresolutionractionpeaksclearlydetectable(typically3higher)overbackgroundnoise.Insingle-particleandtomographydata,bothsignalandnoisearedistributedoverthewholespectrum,andthereisnosimplewaytoestimatetheresolution.Themostwidelyusedmethodfordeterminingtheresolutionofasingle-particlereconstructionisFourierring(in2D)orFouriershellcorrelation(FSC).Thedatasetissplitintotwoequivalenthalves,usuallybyseparatingodd-andeven-numberedimagesfromthedatastack.Separatereconstructionsarecalculatedfromthetwohalves,andtheir3DFTs()arecomparedbycross-correlationinspatialfrequencyshells().Theaveragecorrelationforeachshellisplottedandtypicallyshowsafallofromacorrelationof1atlowresolutiondownto0athighresolution. Thespatialfrequencyat0.5correlationiscommonlytakenastheresolutionestimate,butothercriteria,forexample,comparison Figure29.Resolutiondenitionbyseparationoffeatures.(a)Whentwopointsarefarapart,thereisadeeptroughofdensitybetweenthem.(b)Twopointsareregardedasjustresolvedwhenthepeakofonepointspreadfunctionoverlapstherstminimumoftheother(Rayleighcriterion),seeref60.(c)Thepointspreadfunctionsoftwodotsclosetogetheroverlaptoformonemaximum,sothatthepointsarenotresolved. missingwedgeofinformationresultsinananisotropicPSFthatiselongatedinthedirection.Theresulting3DdensitymapisdistortedbyconvolutionoftheoriginalstructurewiththePSF.Ifthetiltdataarecollectedfromcrystalsinarbitraryorientationsonthegrid,themissingwedgeisreducedtoamissingcone.TheuenceoftheanisotropicPSF(missingcone)dependsontheindividualstructuralfeaturesandorientationoftheproteininthecrystal.Inbacteriorhodopsinandmostother-helicalmem-braneproteins,thehelicesaremainlyparalleltothe(vertical)axis,sotheyarenotgreatlydistortedbythePSF.However,structuralelementswithorientationsparalleltotheplaneofthecrystalwillbemorepoorlyresolved.TherearesomeproblemsincommonwithX-raycrystal-lography,notablythatcrystaldisorderreducestheresolutionoftheelectrondensitymap.Becausethecrystalsaretwo-dimen-sional,theyareeasilybentanddistortedduringEMspecimenpreparation.Smalldistortionscanbecomputationallycorrectedunbendingbasedonthecorrelationmapbetweenasmallcrystallinepatchandthewholecrystal.Deviationsofthecorre-lationpeakpositionsfromthoseofaperfectcrystallographiclatticeshowhowtheunitcellsmustbemovedbacktorecreatetheperfectlattice.TheFTofthecorrectedlatticeprovidesbetternedreectionswithmoreaccuratephases.CombinationofreectionamplitudesfromelectronditionandphasesfromtheimagespermitsrestorationoftheFTofthecrystalin3D.TheinverseFTgeneratesthe3Dstructureoftheunitcell.Thetechniqueisbenetingfromsoftwaredevel-opmentandautomateddatacollection.Oneofthebestresultsobtainedbyelectrondiractionofabiologicalspecimenisthe1.9Åresolutionstructureoflens-specicaquaporin-0(AQP0),awaterchannelformingjunctionsbetweenlensThestructurerevealsdetailsofthedistributionoflipidsaroundtheaquaporintetramers.7.5.TomographicReconstructionElectrontomographyisusedfor3Danalysisofindividual,largestructuressuchassinglecellsortheircomponents.7,20principleisthesameasinmedicaltomography,inwhichthesectionsofapatientsbodyarereconstructedslicebyslicefromimagescollectedatdierentangles.Accordingly,thewordtomographyoriginatesfromtwoGreekwords:tomosmean-toslice,andgraphmeaningimage.Electrontomographyalsohassomefeaturesincommonwithelectroncrystallography,inwhichthesamplesaretiltedaroundaxesperpendiculartotheelectronbeam.Forspecimenswiththetypicalslabgeometry,thelongerpathlengthofthebeamthroughthesampleathightiltandtechnicalconstraintsintiltingrangeofspecimenholdersimposesalimitationonmaximumtiltangle,sothatpartofspaceisnotsampled.Consequently,thereisamissingwedgeinthedata.Thiswedge(orpyramidfordual-tilttomography)resultsinworseresolutionin(incidentelectronbeam)direction(Figure17).Theresolutionachievableincryo-tomographicreconstructionislimitedbyradiationdamage.Thetotaldoseisthemainfactorningthequalityofthereconstruction,butthedoseperimageinatiltseriesmustbesucientlyhightoallowaccuratealign-mentofimagesintheseries.52,205Anotherlimitationinelectrontomographyisthedeteriorationofimagequalityathightilt,duetotheincreasedelectronpathlengthmentionedabove.Thisincreaseselectronscatteringbythesample,inparticularinelasticscattering,whichreducesimageintensityandcontrast.Longerexposuretimescancompensateforlowercontrastathightilt,butthisincreasesthedoseperimageandconsequentlytheradiationdamage.Althoughthereareseveralprogramsforautomatedtiltseriesdatacollection,therawimagescollectedarenotperfectlyalignedrelativetoeachother.Therefore,asinsingle-particleimageprocessing,theseimagesmustbeaccuratelyalignedbeforeproceedingto3Dreconstruction.Imagealignmentintomogra-phyisperformedinrealspaceusingcross-correlationandducialmarkers.Projectionmatchingcanbeusedforrenement.Theimagesareusuallyalignedstartingfromlowtiltangles,andthealignmentprogressivelyincludeshighertilts.BecauseEMimagescorrespondessentiallyto2Dprojectionsoftheobjectalongtheelectronbeam,theimagescollectedfromthesameareaatdierenttiltanglescorrespondtothesetofobjectprojectionsatdierentbutknownorientations.Oncetheimagesarealignedwithinatiltseries,a3Dreconstructionoftheobjectcanbereadilyobtainedusingbackprojectionoralgebraictechniques.6,7,102Recentdevelopmentshaveextendedtheapplicabilityofcryo-electrontomographyandhaveledtoimprovementsindataprocessing.Inadditiontolarge,irregularassembliessuchasHerpessimplexvirusandsubcellularorganelles,cellandtissuesectionscanbeimagedinthevitreousstate(seesection2.1.3).Ifmultiplecopiesofastructurearepresentinthereconstructed Figure28.Electroncrystallography.(a)Schematicdiagramoflatticelinesfroma2Dcrystalandtheirintersectionwithatiltedplaneofdata.Adaptedfromref198.Copyright1982PergamonPress.(b)3Delectrondiractionpatternofatubulincrystal.PlaneAshowstheuntiltedelectrondipattern,andplanesBandCrestorethelatticelinesfromthetiltseries.ThemissingwedgecanbeseenonplaneC(dashedlines).Unitvectorsindicatethepositionoftheorigin.Part(b)isreproducedwithpermissionfromref202.Copyright2010ElsevierInc. importantduetothelargenumberofhelicalpolymersfoundinbiology.Unfortunately,inrealitymosthelicalassembliesareexibleanddistorted,whichrestrictstheapplicationofFourierBesselmethods.Earlyapproachestoovercomethisprobleminvolvedthestraighteningofbenthelices,butamoreectivesolutionwassubsequentlysuggestedusingthesingle-particleapproach.Theimageofthehelicalobjectisdividedintoshort,overlappingsegments,whicharealignedasseparateimagesrelativetoreferenceprojectionscalculatedfromamodel,fol-lowedbyreconstruction.InanapproachdevelopedbyEgelman,194thehelicalparametersandthequalityofthereconstructionareassessedbyminimizationofdierencesbetweensymmetry-relatedelementsinthereconstruction.Thedensitydierencesareassessedforarangeofaxialriseandazimuthalrotationvalues.Thebestparametersareusedtocreateamodelforfurtheriterationsofprojectionmatching.Inadditiontolocaldisorder,somehelicalstructuressuchasmicrotubuleshaveabreak(seam)inthepackingoftheirconstituentprotolaments,leadingtobreakdowninhelicalsymmetry.Ruby-HelixsoftwaredevelopedbyKikkawaenablestheanalysisofsuchasymmetrichelicesbyassessmentofdistortionsinthediractionphasescausedbythe(Figure26c).Successfulapplicationofthenewmethodsinstudiesofhelicalviruses,actinlaments,pili,andotherbiologicalpolymersrevealedavarietyofpossibledistor-tionspresentinthesestructures,highlightingtheneedforfurtherdevelopmentofthetechniquestoimprovetheresolution.7.3.DistributionofProjectionsThequalityofthereconstructiondependsnotonlyontheimagequalityandimplementationofthealgorithms,butalsoontheangulardistributionofprojections.Inprinciple,reconstruc-tionmethodsassumethatthereareaninnitenumberofprojectionsthatareevenlydistributedaroundtheEulersphere.TheEulersphereisanimaginaryspherewhoseoriginisatthecenterofmassoftheobject.Theintersectionofaprojectiondirectionwiththespheredenesapointonitssurfacethatdenotestheprojectionorientation(Figure27a).Thedistributionofthesepointsdemonstratesthedistributioninangularspaceofprojectionsoftheobjectunderstudy(Figure27b).OrlovdemonstratedthatareconstructionofanobjectcanbeobtainedwithisotropicresolutionifthesetofprojectionsisdistributedalonganycurveconnectingoppositepolesoftheEulersphere.Nonetheless,thisconditionassumesaninnitenumberofprojectionsalongsuchcurves.Unfortunately,evenundercryoconditions,biomolecularcomplexesoftendisplaypreferredorientations,sothattheprojectionsareunevenlydistributedinspaceandtheconditionrequiredforcompletereconstructionisnotsatised.Inthiscase,theresolutionbecomesanisotropicduetotheabsenceofinformationincertaindirections.Examplesarecomplexeswithstronglychargedorhydrophobicsurfaceregionsthatadsorbtotheairwaterinterface,oratcomplexesadsorbedtoasupportlm,resultinginpreferredorientationincryo-EM.7.4.ElectronCrystallographyImportantworkinthedevelopmentofhigh-resolutionEMofbiologicalsamplesusedelectroncrystallographyof2Dcrystals.198ThismethodwaspioneeredbyUnwinandHendersonintherstdirectdemonstrationof-helicaldensitiesinamembraneprotein.Thestructureofbacteriorhodopsinwassubsequentlydeterminedbyelectroncrystallographyto3.5Åandthen3Åresolution.TheseresultsstimulatedthedevelopmentofmolecularstructuredeterminationmethodsinEM.ThebasicideaofelectroncrystallographyisverysimilartoX-raycrystal-lographybuthastheadvantagesthatthephasesaredeterminedfromtheimagesofcrystalsandthatlatticedistortionscanbecorrectedintheimages.Becausethecrystallatticehasonlyoneortwolayers,itsscatteringiscontinuousalongthedirectionper-pendiculartothecrystalplane.Therefore,thediractionspotsareextendedintolatticelines.Eitherimagesorelectronditionpatternscanbecollectedfrom2Dcrystals.Tollinthe3Dinformation,thelatticelinesaresampledatdierentheightsbycollectingdataatdierenttiltangles55,202(Figure28).TheelectrondiractionpatternintensitiesarenotaectedbytheCTFofthemicroscope,butCTF-correctedimagesprovidethephasesofthereTypicallybothelectrondiractionpatternsandimagesfrom2Dcrystalsarecollectedfromcrystalstiltedrelativetotheincidentelectronbeam.However,theEMgridcannotbetiltedmorethanbecausethebarsofthesupportgridobstructthebeamandalsobecausethesamplebecomestoothickalongthebeamdirection.Restrictiontomeansthatinformationismissingalongthe-axis,normaltotheplaneofthecrystal.This Figure27.Eulersphereanddistributionofprojections.(a)TheEulersphereisanimaginarysphereofunitradiuswiththeobjectlocatedatitscenter.Thepointsonitssurfacerepresentviewdirectionsoftheobject.Aprojectiondirectionisshownbythevectorfromthecentertotheviewpointonthespheresurface,sotheanglesoftheprojectionaredescribedbythevectordirection.Inthisgure,theangleconventionisasinIMAGIC,andcorrespondingtoSPIDERangles,and,with=90.(b)Anexampleoftheangledistributionofasingle-particledatasetontheEulersphereshowninelliptical(Mollweide)projection.Thisrepresentationshowstheangleofprojectiondirectionsrelativetotheaxis(angle)andaroundit(angle),buttherotationintheimageplaneisnotshown.Theseguresarenormallyusedtoexaminetheangulardistributionofimagesusedforreconstruction,toassesstheuniformityofspatialcoverageinthedataset. 7.1.3.3.SimultaneousAlgebraicReconstruction.Thisap-proachcombinesthebestfeaturesofARTandSIRT.Thetechnique,introducedbyAndersenandKak,usesbilinearinterpolationforthereconstructionandprojectionstepsandrestrictstheareaofreconstructiontoacircle(spherein3D).Thisrestrictionsimplifiestheweightingschemeofprojections:partialweightsareassignedonlytotheindividualRSpointsthatintersectwiththecirclecoveringtheareaofreconstruction;insidethecircle,theRSsareusedwithfullweight,whileweightsaresettozerooutsideofthatarea.Tofurtherreducethenoiseresultingfromunavoidableinconsistencieswithrealprojectiondata,thecorrectiontermsaresimultaneouslyappliedforalloftheraysinoneprojectionasinSIRT.InSART,reconstructionsareobtainedbybilinearinterpolation. calculatedAnotherimplementationofthealgebraictechniqueisRMLE,orrelaxationmethodsforlinearequations.Thismethodappliesadditionalconstraintsdependingontheobjectdatatypesandusesanyaprioriinformationontheobject,suchaspositivedensityintheobject,densitythresholds,andlocationoftheobject.Suchadditionalconstraintsimprovetheconvergenceofiterativeapproaches(seedetailsinref170).7.2.FourierMethods7.2.1.FourierInversion.Intuitively,FouriermethodsareveryclosetoX-rayorelectroncrystallography,wheredataarecollectedtofillFourierspacesothattheinverseFouriertrans-formgeneratesthe3Dmapoftheobjectinrealspace.single-particleanalysis,theinverseFourierapproachisbasedonthetheoremthataprojectionofanobjectcorrespondstothecentralsectionoftheFTofthatobject(centralsectiontheorem,Figure21).FTsofparticleimagesyieldasetofcentralsectionsinthecorrespondingdirections.Thesesectionsarepartofthe3DobjectFT,buttheinformationisincompleteandmustberebuiltbyinterpolationbetweenthesections.Theinversetransformwillthenreproducetheelectrondensitydistributionoftheobject.SymmetryoftheobjectallowsforbetterandmoreevensamplingoftheobjectFTwithfewerimages.InverseFouriertechniqueswerethefirstmethodsusedfor3Dreconstruction.7.2.2.FourierBesselReconstruction.AmodifiedversionoftheinverseFourierapproachhasbeenextensivelyusedintheanalysisofcomplexeswithhelicaloricosahedralsymmetry.Theadvantageofhelicaloricosahedralparticlesisintheirhighsymmetry,whichmeansthateachimageisequivalenttomanysymmetry-relatedprojections.Thenumberofrelatedprojectionsdependsonthesymmetryofthecomplex.Thus,oneimageofanicosahedralstructurecorrespondsto59othersymmetry-relatedviews,whileforhelicalsymmetrythenumberofequivalentviewsisdefinedbythenumberofparticlesperhelicalrepeatandthelengthofthehelix.Intheidealsituation,asingleimageofahelixprovidessufficientviewsoftheasymmetricunittoobtaina3Dreconstruction.145,189,190Ifthemolecularcomplexhasrotationalorhelicalsymmetry,itsdensitydistributionisconvenientlydescribedincylindricalpolarcoordinates.Inthiscase,theFouriertransformoftheobjectcanbeexpressedasaFourierBesseltransform.TheadvantageofusingpolarcoordinatesinFourierspace(Besselfunctions)isthatthedimensionalityofthetransformcanbereducedtoasetofZ-planes(normaltothehelicalaxis)eachcontainingconcentricringsofdierentradii,thusreducingtheinterpolationtojustonedimension(Figure26aandb;fordetailsseeref145).EMimagesofhelicalstructuresprovideonlyrestrictedsamplingoftheamplitudesandphasesalongtheseringsbecauseofthelimitednumberofprojections,andhelicalsymmetryisusedtodeterminecylindricalfunctionsthatdene3DFTofthecomplex.Oncethe3DFTislled,theinversecanbecomputedtoobtainthe3Dreconstructionofthecomplex.Helicalbacteriophagetailsweretherststructurestobereconstructedin3DfromEMimages.Themethodsremain Figure26.FourierBesselreconstruction.(a)Ahelicalstructurewithasinusoidaldensityproleofpitch.(b)TheFouriertransformofthehelix(a)constitutestwoplanesonwhichtheamplitudesarerepresentedasconcentricringswithphasesalternatingbetween0and180.TheamplitudesoftheringsaredescribedbyBesselfunctions.(c)Reconstructionofamicrotubulecomplexedwiththekinesin-5motorataresolution9Å.EnlargementofthboxedareashowsthetoftheX-raystructureintotheEMmap.Parts(a)and(b)arebasedonearlierguresbyMoody.Part(c)isreproducedwithpermissionfromref197.Copyright2010ElsevierInc. ofvariablestobedeterminedis2500inthe2Dcaseandgrowsto625000in3Dspace.Inpractice,theimagesarebiggerthanthis,sothatdirectsolutionoftheequationsetbecomesunfeasible.Therefore,alternativeapproachesareneeded,basedonreason-ableapproximationoftheobjectratherthanonexactsolution.Inalgebraictechniques,thevalueofcanbeestimatedasthesumofallRSsfromMprojectionsthatintersectatthepoint),multipliedbyaweightingfactor,whereeachRSisonepixelwide.wherepassesthrough()thpixel.Theweightfactorrepresentsthecontributionofthe()thpixeltothethRS.Thewholeproblemcanbedescribedasminimizationofthediencesbetweenoriginal(measured)andcalculatedprojections:,calculated,measuredVariousalgebraictechniquesusedierentcriteriatoestimatetheseerrorsandtoapplycorrections.Theycanbesubdividedintofourgroups:ART,algebraicreconstructiontechnique;SIRT,177simultaneousiterativereconstructiontechnique;SART,simultaneousalgebraicreconstructiontechnique;andRMLE,relaxationmethodsforlinearequations.7.1.3.1.AlgebraicReconstructionTechnique.InART,theinitialarray(thefirstapproximation)isblank:=0,andeq24issolvediteratively:measuredwheredenotesthethapproximation(=0);measuredthemeasuredthprojection,andisthecalculatedprojectioninthesamedirection;andistheweightmatrix.Correctionsaremadeafteraddingeachsuccessiveprojection.Thisisasimplemethod,buttheresultdependsonthestartingprojection.Theprocessmaybecomeunstablebecauseofampli-cationofinconsistenciesinnoisyprojections.Dierentimple-mentationsofARTvaryinweightingmatrixspecicationandusingadditionalconstraintssuchasdensitythresholdingandzerodensityoutsideoftheobject.Thereisaversionofmulti-plicativeARTinwhichtheinitialapproximationisdenedas=1,andcalculated7.1.3.2.SimultaneousIterativeReconstruction.Asinaddi-tiveART,onecanstartwithablank(zero)reconstruction,orwith=1ifthemultiplicativecorrectionapproachisused.ThemaindistinctionbetweenARTandSIRTtechniquesisinhowthereconstructioncorrectionisperformedinaniterationstep:inART,differencesbetweenthecurrentlyusedprojectionandcorrespondingreprojectionarecalculated,andthecurrentrecon-struction(calculatedonthebasisofthelimitedsetofprojec-tionsusedsofar)isimmediatelymodified;inSIRT,allprojectionsareusedtocreatethecurrentreconstructionbeforecalculatingreprojectionsandcorrespondingdifferencesareusedtocalculateanoverallcorrectivematrixforthenextiteration:maxmeasuredwhereandareweightingparameters.181ResultsofSIRTdonotdependonthestartingprojection.AlthoughSIRTconvergesmoreslowlythanART,itproducesbetterresults.182 Figure25.Filteredbackprojection.Theoriginalobjectcontainstwodotsofdierentdensities.Theupperpanelrepresentsreconstructionsbybackprojectionofthesedotsusing7,15,45,and180projections,respectively.Althoughtheradialstreaksareeliminatedbyusingmoreprojections,thmethodleavesahaloaroundthereconstructeddots.Thebottompanelsshowreconstructionsfromthesameprojectionsusingltering.Reductionofthehaloismostpronouncedonthereconstructionswithmoreprojections. arecalledraysums(RS).AnestimateofthedensityinagivenpixelofthereconstructionwithcoordinatesisthesumofallRSsthatpassthroughthatpixel(Figure24b).However,thissimpletechniquedoesnotaccuratelyreconstructtheoriginalobject;detailsaresmearedoversomedistanceorsurroundedbyahalo(Figure24CandD).ThesedistortionsarisebecausethereconstructionisconvolutedwithabroadPSF,whichhasafalloffof1/in2Dand1/in3Dspace: in2Dspace in3Dspaceorwhereistheconvolutionoperatorandistherealspace7.1.2.FilteredBack-ProjectionorConvolutionMethods.Filteredback-projectionisamodifiedversionoftheback-projectionalgorithm,whichcorrectsfortheblurringintroducedbythePSFfunctionmentionedinsection7.1.1(Figure25).TheoperationcanbeperformedineitherrealorFourierspace.InFourierspace,thecorrectionisachievedbyapplyingafiltercorrespondingtotheinverseofthePSF.For1/,thisfunctionisproportionaltothespatialfrequencyandiscalledarampfilter.Avarietyoflterscanbeusedinrealspace.OnetypeofusedforcorrectingbackprojectionistheLaplaceoperator,whichisappliedtotheprojectionsforpreltering.ThesereconstructionalgorithmsarebasedonfunctionsthatapproximatetheinverseRadontransform;theyperformback-projectionreconstructiononthepreprocessedprojections.Thepreprocessingmodiestheprojectionsusingwindow(apodizing)functions(Hammingwindow),whichareequaltozerooutsideachosendistanceintervalandenhancethesignalwithintheinterval.somepackages,thelteringisperformedin3Dspaceonthereconstructionobtainedbyback-projection.Filtercharacteristicsinadditiontothe1/termdependonthedistributionofprojectionsandtheirnoiselevel,aswellasthesymmetryoftheobject.149,174,175Mostpublishedlterfunctionshavebeenderivedanalyticallyfromtheoretical170,1737.1.3.AlgebraicMethods.Thedevelopmentofalgebraicmethodshasbeenstimulatedbymedicaltomography.Inthiscase,reconstructionofthe3Dobjectisbasedondeterminationofsuccessiveplanarslicesoftheobject(patient),sothattheproblemisreducedtoasetof2Dreconstructionsfrom1Dprojections.Wewillexplainthemethodsin2Dspace,becausetheconceptofreconstructioncanbeeasilyextendedto3Dspace.Thistechniquerequiresthattheobjectisdescribedbyapositivefunctionoveraniteregion(theobjectisoflimitedsize)andcanberepresentedasadigitalarrayofdensities.Anelementofthearraywithcoordinatesisthepixel.Theprojectionisdenedasineq20:where=1,2,...,,2,...,=1,2,...,Equation22islinear,withunknowns.Forprojections,therewillbelinearequations.Solutionofthecompletesetofequationswouldgivethereconstructionoftheobject.Theproblemarisesfromthefactthatanumberofunknowns(thesizeofthearray)canbelargerthannumberofequationsintheset(),andthatthenumberofunknownsincreasesdramaticallywithimagedimensions.Ifthesetofequationscanhavemorethanonesolution.Moreover,inreality,projectionsmaynotbeconsistentwitheachotherbecauseofnoise.Evenforanimageof5050pixels,thenumber Figure24.Back-projectionalgorithm.(a)Projections,andareobtainedexperimentallyfromanobjectcontainingtwodotsofdi2,and3aretheanglesofthedierentprojectiondirections,and,andaretheunitvectorsofthecorrespondingprojectiondirections(eq20).(b)Backprojectionisdonebystretchingprojectionsbackthroughtheareatobereconstructedalongtheoriginalprojectiondirections,orinotherwordsbycreatingraysofpixelswiththedensityofthecorrespondingprojectionpixel.Thisisshownaslightanddarkgraylinfromprojections1,2,and3.Theraysaresummedinthereconstructedarea,providinginformationonthedotpositions.(c)Themoreprojectionsthatareused,thebetterdenedarethedots.(d)Anartifactofthetechniqueisthateachpointissurroundedbyabackgroundhalo.Theintensityofthehaloisproportionaltothedensityofthedot. determinethestructureofacomplexwithaligandorwithlocalizedconformationalchanges.Ifthestructureoftheinitialcomplexisknown,itcanbeusedtogeneratereprojectionsthatcanbeusedforprojectionmatchingorcommonlinessearchinrealorreciprocalspace.Theresultingnewmodelcanbeusedforsubsequentrenement.Theinitialresultofprojectionmatchingusuallyresemblesthestartingmodel,butafterafewroundsofnementthenewfeaturesofthedatasetshouldbecomestronger.However,iftherelationshipbetweenmodelstructureanddataisnotwellestablished,thepossibilityofreferencebiasneedstobecarefullychecked.Conversely,EMmapscanbeusedasmolecularreplacementmodelstophaseX-raystructures.Forthisapproach,theremustbeoverlapinresolutionrangesbetweentheEMandX-raydata.Sofar,phasingfromEMhasmainlybeenusedwithlargecomplexesorvirusesforwhichitisdiculttoobtainheavy-metalderivatives.7.3DRECONSTRUCTIONInEM,wearedealingwith2Dimagesthatcanbeconsideredas2Dprojectionsofthe3Delectronpotentialofthespecimen,afterrestorationoftheimageinformationbyCTFcorrection.Severalalternativeapproacheshavebeendevelopedforreconstructionofa3Dobjectfromitsprojections.166Thesemethodsfallintotwomajorgroups.Methodsthatperformthereconstructioninrealspaceincludeback-projectionandalgebraicmethods.Intheothergroup,thereconstructionisdoneinFourierspace.Thecurrenttrendistowardautomationofalloftheimageprocessingsteps,fromparticlepickingto3Dreconstruction.167Foricosahedralparticles,whichareeasiertoprocessbecauseoftheirshapeandtheirhighsymmetry,thereconstructionstepsaremorereadilyautomated.168,1697.1.Real-SpaceMethodsTheAustrianmathematicianJohannRadondemonstratedin1917thatan-dimensionalfunctioncanberestoredfromitsintegralsoverthecontinuumofstraightlines,whichrepresentitsone-dimensionalprojections.ThecontinuoussetoflineprojectionsisknownastheRadontransformofthesionalfunction.2DsectionsofRadontransforms(sinograms)areusedinorientationdetermination(seesection5).Theinverseofthecomplete(-dimensional)Radontransformnesthedistributionofdensitiesoftheobject.However,therearedicultiesinnumericalimplementationoftheinverseRadontransformforstructuralanalysis,andseveralotherimplementa-tionsareusedtoapproximatethistransform.7.1.1.BackProjection.Thedigitalprojectionatangleofatwo-dimensionalfunctionisthesumofdensitiesalongonepixelwideparallelrays(Figure24a):wherearetheobjectpixelindices,istheprojectionpixelindex,and)isaline(orplane)overwhichthesummationisperformed,isaunitvectorthatdefinestheprojectiondirectionatangle,andistheprojectioncoordi-nate.Back-projectionworksbystretchingtheprojectionbackoverthevolume(array)tobereconstructedalongtheprojectiondirection.Pixelsofaprojectionbeingstretchedformlinesthat Figure23.Projectionmatchingprocedure.Asetofimagesiscomparedtoasetofreferencesfromaninitialmodel(lowresolution).Oncethebestmatchisfoundbetweentheimageandoneofthereferences(reprojections),basedontheheightofthecorrelationpeak,theshiftrelativetothematchreferenceandanglesofthatreferenceareassignedtotheimage.Images1and6havethebestcorrelationwithmodelprojectiona(redarrows),whileimages2and5matchimagee(bluearrows).Image3correspondstothetiltedviewc(yellowarrow).Anew3Dmapiscalculatedusingimageswiththeassignedangles.Therened3Dreconstructionisthenreprojectedwithasmallerangularincrementtogeneratenewreferencesforthenextiterationof fewerindependentvaluesofthetransformarecompared.AtlowSNR,thisdierenceinthenumberofcomparisonsmeansthattheprobabilityofndingviewsnearsymmetryaxesmustbedownweighted.6.3.CommonLinesinRealSpaceTheRadontransform(discussedinsection7)isthesetofall1D(line)projectionsofan-dimensionalfunction.Thiscon-ceptisusefulinconsideringtherelationshipsbetweena3Dobjectanditsprojections.Inparticular,a2DsectionoftheRadontransformofa3Dfunctioncorrespondstothesetof1Dprojectionsofthe2Dprojection.Onthebasisofthisconcept,acommonlinesapproachinrealspaceforarbitrarysymmetrywasdevelopedbyvanHeelandcolleaguesandimplementedinIMAGIC.12,154,157,158Foreach2Dimage,asetof1Dprojectionsiscalculatedandpresentedasanimage(sinogram)whoselinesareformedoftheseriesof1Dprojectionsfrom0to360.Itisimportanttonotethatcenteringofimagesisessentialforangleassignmentbycommonlines,becauseshiftingthe2Dimageshiftsthe1Dprojections.InthesearchforcommonlinesinFourierspace,theimagesarecenteredbythephaseminimizationprocedure,becausethecommonlinesmustbecentrosymmetric.Thetaskistondthebestmatchinglinesforeachpairofimagesbeingcompared,bycrosscorrelationbetweentheirsinograms(Figure22).Especiallywithlowsymmetrystructures,thelowSNRmakesthiscomparisonverydicultwithsinogramsobtaineddirectlyfromtherawimages.Animportantinnovationmakingitpossibletoworkwithlowersymmetrieswasuseofclassaverages(seesection5)ratherthanindividualrawimagesforthecommonlinessearch.Itisadvisibletomakeseveraltrialstogetaninitial3Dreconstructionbyangularreconstitutionandtochecktheconsistencyoftheresults,especiallywithasymmetricstruc-tures.Onceaconsistentinitial3Dmaphasbeenobtained,thestructurecanberenedbyfurthercyclesofalignment,classition,andcommonlinesearching.6.4.ProjectionMatchingTheprocedureofprojectionmatchingismucheasiertounderstandinprinciple,butitneedsaninitialmodel.Oncea3Dstructureisavailable,evenatverylowresolution,itcanbeusedtogeneratereprojectionsatallpossibleorientations.Thesetofreprojectionscanthenserveasreferenceimages,inasystematiccomparisonofeachimageinthedataset(orsetofclassaverages)withallofthereferenceimages(Figure23).projectionmatching,foreachimageinturn,theEuleranglesofthereferenceimagethatgivesthebestcrosscorrelationareassignedtotherawimageorclassaverage.Foreachcomparison,allpossiblein-planealignmentsmustbetested,sothatthisisaverylengthycalculation.OncetheEuleranglesareassigned,anew3Dmapcanbecalculatedandtheprocedureiteratedwiththenewsetofreprojections(Figure23).Real-spaceprojec-tionmatchingisimplementedinEMAN,117TheprogramFREALIGNdoestheprojectionmatchingsearchinreciprocalspace,givingsomeadvantagesinspeedandprovidinganoptionforreningdefocusofeachparticle.Anotherprojectionmatchingmethod,PFT(polarFouriertransforms),wasdevelopedbyBakerandcolleaguesfornementoficosahedralstructures146,161(BakerandCheng,1996,SinkovitsandBaker,2009).Analternativeapproachuseswaveletexpansionstocompareimagesandreprojections,de-monstratingimprovementsinspeedandrobustnesstonoise.6.5.MolecularReplacementAsinproteincrystallography,itisusuallymuchquickerandeasiertodetermineastructureifasucientlysimilarstartingmodelisalreadyavailable.Inmanycases,theobjectiveisto Figure22.Sinogramsandsinogramcorrelationfunctionsforamodelstructure.Threeprojections(numbered13)areshownofamodelcomposedofthreeGaussiandotswithdierentdensities.S1,S2,andS3aresinogramsorsetsof1Dprojectionsofthecorresponding2Dprojections.CSC12andCSC32representcross-sinogramcorrelationfunctionsbetweenprojections1and2andprojections3and2,respectively.Eachpointofthesinogramcorrelationfunctioncontainsthecorrelationcoecientofapairoflinesfromthetwosinograms.Solidlinesindicatethecommonlinesbetweenprojections2and1,whilethedashedlinesindicatethecommonlinesbetweenprojections2and3.EachCSChastwopeaksbecauseprojectionsfrom180to360mirrorthosefrom0to180.Theangulardistancebetweenthecommonlines(solidanddashed)givestheanglebetweenprojections1and3. rotationaxescoincide,atiltofoneparticlewillcorrespondtoa+45tiltoftheother.Theproblemistondequivalentviewsintiltimagesarisingfromparticlesthatareorthogonalat0tilt.Combiningsuchtiltviewsfromparticleswithdierentin-planeorientationswillgenerateatomographicseriesaroundthecommonaxisandcanbeusedtogeneratea3Dreconstructionwithnomissingcone(seeFigure1ofLeschzinerandNogales1526.2.AngleAssignmentbyCommonLinesinReciprocalSpaceForanysetof2Dprojectionsofagiven3Dstructure,therearerelationshipsbetweentheprojectionsthatcanbeusedtodeterminetheirrelativeorientations(Figure20).Eachpairof2Dprojectionshasatleastone1D(line)projectionincommon.153,154InFourierspace,2DprojectionscorrespondtoplanespassingthroughtheoriginofFourierspace,and1Dlineprojectionsbecomeradiallinesinthetransform.ThecommonlinebetweentwoprojectionsinFourierspaceisthelineofintersectionofthecorrespondingtwoplanesinFourierspace(Figure21).Withonlytwoimages,theanglebetweenthetwointersectingplanescannotbedeterminedbecauseonlyonecommonlineexists,butwiththreeimagestherearethreecommonlines,andanglesbetweenanytwocommonlinescanbefoundwithrespecttothethirdone,sothatalloftheorientationsarexed.Determinationofcommonlinesfromindividualrawimagesiscult,butthepresenceofsymmetryprovidesmanymoreconstraintsandresultsinmultiplecommonlines,bothfromthesameimage(self-commonlines)andbetweenimagepairs(crosscommonlines).Icosahedralvirusesprovidethemostfavorablecase,andCrowtherdevelopedtheapplicationofcommonlinesfordeterminingtherelativeorientationsofvirusparticlesinFourierspace.Usingtheiricosahedralsymmetry,hewasabletondthecommonlinesandtodeterminetheparticleorientations.Becausethesearchingisdoneinreciprocalspace,theradiallinesoftheimagetransformsarecomparedandthecommonlinesidentiedbyminimizingthesumofphaseresidualsbetweenpairsofcommonlines.FullerintroducedaweightingschemetomakethecommonlinesmethodmoreeectiveforusewithcryoEMimagesoficosahedralparticles.Thephaseresidualcomparisondependsonparticleorientation:thecommonlinesarelesswellseparatedinviewsaroundthesymmetryaxes,and Figure21.Surfacerenderedviews,projections,andtransformsectionsofastructure,withacommonlineintersectionillustratedinreciprocalspace.Thestructurehasrotationalsymmetry,andthereareseveralsymmetry-relatedcommonlines.Fromtheanglesbetweencommonlineprojectionsoferentviews,therelativeEuler-angleorientationsofasetofprojectionscanbedetermined.Adaptedwithpermissionfromref24.Copyright2000InternationalUnionofCrystallography. assemblieswithoutusingsymmetry(50SribosomeandRyRchannel.Imagesaretakeninpairs,sothatthesameeldofparticlesisrecordedrstathightilt(45)andthenuntilted(Figure19).Theimagepairsaretrackedbyaligningthetwoeldsviarecognizablepointfeatures.ThemethodhasmainlybeenusedwithnegativestainEM,becausecryo-EMismorecultathightiltangles.Itismoststraightforwardiftheparticleshaveapreferredorientationonthecarbonsupportlm.Inthatcase,alloftheuntiltedimageswillbethesame,exceptforin-planerotation,andthetiltedimageswillcorrespondtoprojectionslyingonaconeoforientations.Thepositionontheconeforeachtiltedviewisdeterminedbythein-planeorientation(azimuthalangle)ofthecorrespondinguntiltedview.Iftheparticlesdonotallhavethesamein-planeview,theuntiltedimagesmustrstbesortedoutintogroupsofsimilarviewsbycation,sothetiltedviewscanbegroupedaccordingtotheircorrespondingin-planeorientations.Thisinformationiscienttodenetheorientationsofthetiltedparticles,andarst3Dmap,orsetofmapsfordierentin-planeorientationclasses,canbecalculated.Inprinciple,themethodissimpleandreliable,andindeeditiswidelyusedforgettingastartingmodel.However,theconicaltiltapproachhassomelimitations.Itistechnicallydiculttogetgoodqualityimagesathightilt,becauseofspecimenthicknessandmicroscopestagestability,especiallyforcryo-EM.Thetiltedimageswillhaveagradientofdefocus,althoughwithcontinuouscarbonlmitispossibletodeterminethedefocusandcorrectforit.Amoredicultproblemisincompletestaining,inwhichparticlesarenotfullyembeddedinstainandthehighestregionsofthestructurearemissingfromtheimages.Partialstainingcanbeavoidedbyplacingthestainedparticlesbetweentwocarbonlms,butthistaskisexperimentallymoredicult,andverythincarbonlmsareneededtoavoidexcessivelossofcontrast.Currentmicroscopesmakeitmorefeasibletoavoidtheseproblemsbyusingcryo-EMforconicaltilt.Finally,thelimitonmaximumtiltangleimposedbythespecimenholderandthicknessofthetiltedspecimenresultsinamissingconeofdata,limitingtheresolutionin.Thisproblemcanbeediftherearedierentparticleorientationsintheuntiltedimage,sothatdierentconicaltiltreconstructionscanbemergedtocompensateformissingcones.Theorthogonaltiltstrategyprovidesanelegantapproachto3Dreconstructionfromtiltedviews.Unlikeconicaltilt,thismethodrequireswelldistributedout-of-planeorientations.Pairsofimagesarecollectedatand45tilts.Supposetherearetwoparticleswithout-of-planeorientations90apart.Ifthe Figure19.Conicaltiltgeometry.(a)Theoriginalobject,witharrowsindicatingtheangulardirectionsofthedataprojections.(b)RepresentationofthesectionsinFourierspacecorrespondingtodataprojectionscollectedwithinthisconeofangles.AcentralcrosssectionoftheplanesinFourierspaceisshownin(c).(d)Asurfaceviewoftheresultingconicaltiltreconstruction,surroundedbytheeightprojectionscorrespondingtotheoriginalviewdirections.Reproducedwithpermissionfromref99.Copyright1998ElsevierInc. Figure20.RelationshipsbetweenimagesandprojectionsinrealandFourierspace.The3Dstructurecanbeprojectedontoplanestogive2Dprojections,whichcaninturnbeprojectedindierentdirectionstoyield1D(line)projections,indicatedbytheoperatorofsummation.ThecompletesetoflineprojectionsisknownastheRadontransform.Asinogramisasetoflineprojectionsofthe2Dprojectionorasectionofthe3DRadontransform.Inthereversedirection,thesetoflineprojectionscanbecombinedtoreconstructthe2Dimageandthesetof2Dprojectionscombinedtoreconstructthe3Dobject,indicatedbytheoperatorofstretching.Theimageinformationcanbeequivalentlyrepresentedinreciprocalspace,intheformofFourieramplitudesandphases(rightcolumn).Fouriertransforms()ofthe2Dprojectionscorrespondtocentralsectionsofthe3Dtransform(extraction),andthelineprojectionscorrespondtolinespassingthroughtheoriginofFourierspace(centrallines).Therefore,theobjectcanalsobereconstructedbycombining(lling)thesetofcentralsectionsintothe3Dtransformfollowedbyinverse3DFouriertransformation.Adaptedwithpermis-sionfromref12.Copyright2000CambridgeUniversityPress. Evaluationoftheimagesimilaritiesthencanbecarriedoutasacomparisonofvectorswithareducednumberofcomponents.5.2.HierarchicalClusteringTheprincipalcomponentsofthedatacloudcanbeusedtosorttheimagesintogroupsbyaclusteringprocedure.Todecidehowtogrouptheimages(orelementsofthedataset),thedistancebetweenthem,ortheirsimilarity,mustbeestimated.Therearetwomainapproachesforclusteringthatdierintheirstartingpoint:Intheagglomerative,orascendant,hierarchicalcation,eachpointinthedatahyperspaceisinitiallyconsideredasagroup(class)followedbymergingthemostsimilar(closelyspaced)pointsintotherequestednumberofclusters.Thedivisiveapproachinitiallyplacesallofthedatainonecluster,whichmustbeseparatedintosmallergroupsaccordingtotheirdissimilarity.Dependingonthedistanceofeachdatapointfromtheexistingclusters,thatelementwilleitherjointhenearestclusterorformtheseedofanewcluster.Theprincipaldierencebetweenthecurrentlyusedalgo-rithmsisthedenitionofthedistancesbetweenelements(metric)inthehyperspace.ThemetricstypicallyusedareEuclidiandistances,chi-squaremetrics(),ormodulationdistances.Thesmalleristhedistancebetweenthepoints,thegreateristhecorrelation(similarity)betweenthecorrespondingimages.ThesimpleEuclideandistancemeasureissensitivetodierencesinscaling(normalization)betweentheimages.Thus,twoimageswithdensitiesthatareproportionaltoeachothercouldincor-rectlyendupindierentclustersusingthismetric.Therefore,themeasureincorporatesnormalizationbytheaverageofallimages,andthemodulationmeasurescalestheimagesbytheirstandarddeviations,allowingformorerobustclassischemes.ThealgorithmimplementedinIMAGICisbasedonmini-mizationoftheintraclassvarianceinacluster(betweenthemembersofthecluster)andmaximizationoftheinterclassvariancebetweenthecentersofmassoftheclusters.SPIDER,thereareoptionstouseeithercorrespondenceanalysisbasedonchi-squaremetrics(),whichrequiresalldatatobepositive,orPCA,whichdoesnothavethatrequirement.5.3.K-MeansClusteringandtheMaximumLikelihoodMethodK-meansisaclustering(partition)method,whichstartswithanednumber()ofpointsrandomlyselectedfromthedataasseeds.Eachdatapointisassignedtoaclusternearesttooneofthepoints,andthecenterofthecreatedclusterisredened.Asfurtherpointsareadded,thealgorithmiterativelyreorganizestheclustersuntilthesumofintraclusterdistancesisminimized.TheresultsofclassicationbyK-meansusuallydependontheinitialcenterassignment.Thisapproachworksbestwithasmallnumberofclusters.ThemaximumlikelihoodmethodcanbeusedtoclusterimageswithlowSNR.Thisapproachisbasedonrandomselectionofsubsetsofthedatafromwhichseedsofclustersarecreated,followedbytheoptimizationoftheclusters.Seedpositionsarereassessedduringformationoftheclusters.ThemaximumlikelihoodmethodalongwithK-meansclusteringhasbeenimplementedinXmipp.Theuseofstatisticalanalysisandclassicationofimagesisimportantfordiscriminatingvariationsfromanysource,dierencesindefocus,dierentparticleorientationsthatreectdierent2Dprojectionsofa3Dstructure,structuralvariationswithinanorienta-tiongroup,andeventuallyconformationalchangesofthecomplexes.6.ORIENTATIONDETERMINATIONTocalculatethe3Dmapfromasetofprojectionviews,therelativeorientationsofthe2Dprojectionsmustbedetermined.Therearetwogeneralapproachestothisproblem.Anexperi-mentallybasedapproachinvolvesthecollectionofimagesofthesameparticlesatdierenttiltangles.Thismethodisparticu-larlyapplicableforparticlesthatadoptapreferredorientationonthesupportgrid.Theotherapproachiscomputationallybased,inwhichuntiltedimagesarecollected.Forthesecondapproach,itisessentialtocollectarangeofviewsdistributedoverdiorientations.Thebiggestchallengeinorientationdeter-minationistogettherstsetofassignmentsforadatasetcorrespondingtoanunknown3Dstructure,especiallyifitisasymmetric.Onceaninitialmodel(startingmodel)isavailable,theorientationscanberened.Asignicantprobleminsingle-particleanalysisisthatanincorrectstartingmodelcanbiastheresultorevencompletelyinvalidateit,andthereareexamplesintheliteratureofdissimilarorcompletelydierentEMstructuresforthesamebiologicalcomplex.Insuchcases,furtherinforma-tionisneededfrombiochemical,biophysical,orgeneticexperi-mentstohelpvalidatetheresultingstructure.6.1.RandomConicalTiltRadermacherdevelopedthemethodofrandomconicaltiltthatprovidedtherstreconstructionsofmacromolecular Figure18.Schematicofadatacloudillustratingtheprinciplesofmultivariatestatisticalanalysisandclassication.(a)Eachimageisrepresentedbyacolor-codeddotinamultidimensionaldatacloud,whichhasbeensubjectedtoMSA.(b)Thedotsaresortedintothreeclassesaccordingtocolorandposition.Severaloutlyingdots(representedbyinconsistencybetweencolorandposition)arenotassignedtomajorclassesandrepresentclassescomposedonlybyonedot,andarenotconsideredasrepresentativeclasses. differentdirection,dependingontheorientationoftheobjectintheoriginaltomogram.Toavoidbiastotheorientationofthemissingwedge,eachpairwisecorrelationmustincludeonlytheregionsofFourierspacecommontobothimages(Figure17).Subtomogramaveraginghasbeenusedtostudyparacrystalsoffilaments,viralparticles,andtheirsubstructuressuchassurfacespikes.5.STATISTICALANALYSISOFIMAGESAsdiscussedinsection4,thestructuralfeaturesoftheobjectofinterestinanEMimagearetypicallycorruptedbynoiseresult-ingfromcountingnoiseinthenumberofelectronsperimageelement,sensitivityofindividualchannelsintheimagesensor,radiationdamagetothespecimen,anductuationsinlocalconcentrationsofbuerchemicalcomponents.Inaddition,rapidfreezingcantrapbiologicalcomplexesindierentstructuralstatesthatmustbeseparated.Howcanalargeimagedatasetbetransformedintoasystemwithfewerparametersthatadequatelyrepresentsdierentprojectionsofthesamemoleculesaswellastheirdierentbiologicalstates?Assumingthatthenoiseisnotcorrelatedtothestructure,itcanbesuppressedbyaveragingmanyimagesoftheparticles,therebyenhancingthestructuralinformation.Foraveraging,itisessentialthattheparticleimagesarebroughtintoregistersothatsimilarfeaturessuperimposeintheiraverage.Ingeneral,thealignmentisaniterativeprocessbeginningwithcoarsefeaturesofthedataset,forexample,centerofmassofeachparticleimage,followedbygroupingandaveragingofindividualimages.Aver-agingimprovestheSNRbyafactorof,whereisthenumberofaveragedimages.Thisinturnfacilitatesthedetermi-nationofrelativeorientationsofthedierentgroupaveragescharacteristicviews).Analysisofimagesfollowedbyclassitionintodierentgroups(clusters)accordingtotheirfeaturesisthebasisofthestatisticalapproach.StatisticalanalysiswasintroducedintoEMimageanalysisaround1980.methodsareusedforanalysisofvariations,suchasprincipalcomponent,multivariate,orcovarianceanalysis.ClassicandonebyhierarchicalorK-meansclustering.5.1.PrincipalComponentAnalysisEachimageofpixelscanberepresentedasavectorindimensionalhyperspacewithcoordinatesdenedbythedensityvaluesoftheimagepixels.Soasetofimagescanbeconsideredassetofvectorsor,equivalently,asacloudofpoints(endsofthevectors)inthehyperspace(Figure18).Similarimageswillcorrespondtopointsthatareclosetoeachotherwithinthecloud.However,apairwisecomparisonofallimageswouldbeveryslowbecauseitrequirespixel-by-pixelevaluationofthedierencesforallpossibleshiftsandrotations.Theessenceofthestatisticalapproachistoreducethenumberofvariablesdescribingthedatasetandtondasmallersetofuncorrelatedvariables,calledprincipalcomponents.Multivariatestatisticalanalysis(MSA)identiesthelargestvariationsinabigdatasetandchangesthecoordinatesysteminthehyperspaceusingthesemajorcomponentsasnewaxes.Theaxesareorientedalongthedirectionsofthesevariationsandareorthogonal(andthereforeuncorrelated)toeachother.Principalcomponentanalysis(PCA)usestheeigenvectorsofthecovariancematrix(pairwisecomparisonofallimages)asprincipalcomponents(forexplanation,seeref139).Typically,onlyasubsetofnewcoordinatesisusedwithdirectionscorrespondingtolargestvariationsinthedataset.Inimageanalysis,eigenvectorsarepre-sentedaseigenimages,whichshowtheregionsofmajordensityvariationsintheimagedataset.Thesmallervariationsareusuallyattributedtonoisecomponentsofthedata.Thereductionofdimensionalityofthespaceleadstoacompressedrepresentationofthedatasetwithoutmuchlossofinformation.Thiscompres-sionisachievedbyrepresentingeachimageasalinearcom-binationoftheprincipalcomponents(seedetailsinref140). Figure17.Diagramsofangularcoverageandthecorrespondingimages,toillustratealignmentofsubtomogramstakingaccountofthemissingwedge.(a)Theoriginalimagewithnomissingdata.(b)Theeectofamissingwedgealongtheaxisontheimage.Onlyprojectionswithinthegraysectorareusedtoproducetheimage.Somefeaturesoftheface(wrinklesandeyes)arenotresolved.(c)Anothersetofprojectionswiththemissingwedgeinadierentorientationcausesdierentfeaturestobelost.(d)Ifonlythedatacommontothetwoimages(b)and(c)arepresent(),theimageismoredistorted.Nevertheless,alignmentofthetwoimages(bandc)canbebasedonthisoverlappinginformation.Otherwise,thealignmentwouldbebiasedbythemissingwedge.(e)Afteralignment,thetwodatasets(b)and(c)canbecombinedtogiveabetterangularcoverage,sothatthereconstructionmorecloselyresemblestheoriginalobject.Modiedwithpermissionfromref134.Copyright2008ElsevierInc. orientationandtoseparatedierentout-of-planeviews.Afewiterationsofthesealignmentandclassicationstepsprovidegoodaveragesrepresentingthecharacteristicviewsinthedataset.Variousprotocolshavebeendevelopedfortranslationalandrotationalalignmentofimagedatasets.Testsonmodeldatasuggestthat,afterinitialcentering,iterationsofrotationalfollowedbytrans-lationalalignmenttothereferenceimagesareeective12,123,124(Figure15).Thequalityoftheresultalsodependsontheaccuracyoftheinterpolationprocedures,becausethedigitalimagesmustberotatedandshiftedbynonintegralpixelvaluesduringalignment.125Theprogressofanalignmentcanbeevaluatedbyexaminingtheaverageandvarianceimages(Figure16).Theaverageofanalignedsetofsimilarimagesshouldimproveincontrastandvisibledetailduringrenement,andthevarianceshouldde-crease.Inaddition,thecross-correlation(CC;maximumvalueofthenormalizedCCF)betweenreferencesandrawimagesshouldincreaseduringrenement.4.2.1.MaximumLikelihoodMethods.Foralignmentofanimagedatasettoasetofreferences,eachimageisassignedthealignmentparametersofthesinglereferenceimagewithwhichithasthehighestCC.ThemaximumlikelihoodapproachusesthewholesetofCCvaluesbetweeneachimageandallofthereferencestodefineaprobabilitydistributionoforientationparametersfortheimagebeingaligned.126,127ForclustersofreferencesgivingsimilarCCvalues,thisapproachislikelytoprovidemorereliablealignmentparametersthanwouldbeobtainedjusttakingaccountofthehighestCC,butitiscomputationallyveryexpensive.4.3.TemplateMatchingin2Dand3DSofar,wehaveconsideredalignmentof2Dimagestorefer-ences,butthereisalsoaneedtodetectknownfeatures(motifs)innoisyanddistortedimagedatainboth2Dand3D.In2D,motifdetectionisusedforautomatedparticlepickinginrawmicrographs.In3D,thetaskistosearchforoccurrencesofknownmolecularcomplexesintomograms.Thesetasksrepre-sent2Dand3Dversionsofasearchforaknown,orapproxi-matelyknown,structuralmotifinimagedata.Inautomatedparticlepickingfrommicrographs,individualparticleswithlowSNRarelocatedbyacross-correlationsearchofthewholemicrographwithoneormoretemplateimages,referencesderivedfromthedata,amodel,orarelatedstructure.In3D,ifaknownstructuralmotifisexpectedtobepresentinthereconstructedvolume,the3Dmapofthatmotifcanbeusedtosearchforoccurrencesofrelatedfeaturesinthetomogram.Themainproblemisreliableidenticationofmotifsinnoisydata.Inthecaseoftemplatematching,asmallregionofthewholemicrographor3Dstructureissearchedbycross-correlationwiththetemplate.Iftheimageorstructureisnormalizedasawhole(globalnormalization),thecross-correlationbetweenthetem-plateandeachsmall,localregionwillbeinuencedbymanyfeaturesoutsidetheregionofinterest.Ontheotherhand,iftheimageorstructureisnormalizedjustinthelocalregionateachstepofthesearch,theresultingcorrelationvalueswillgivemorereliableresultsreectingthelocalmatchwiththetemplate.AlocallynormalizedcorrelationapproachwasdevelopedbyRosemanandiswidelyused.124,128,1294.4.AlignmentinTomography4.4.1.AlignmentwithandwithoutFiducialMarkers.Theaccuracyoftomographicreconstructiondependsonthealignmentofsuccessivetiltviews.Alignmentisdonebytrackingthedisplacementsofmarkerparticles(fiducialmarkers)acrosstheimageasafunctionoftiltangle.Denseparticlessuchascolloidalgoldbeadsorquantumdots(semiconductorparticlesthatarebothfluorescentandelectrondense)areusedforthispurpose.Forplasticsections,thesemarkersareappliedtothesurfaces.Withagooddistributionoffiducialmarkersandastablespecimen,itispossibletoobtainaccuratealignmentandeventocorrectforlocaldistortions.Alignmentcansometimesbeimprovedbyrestrictingittosubregionsofinterest,whichmovecoherentlythroughthetiltseries.Forcryo-tomography,ducialmarkerscanbemixedintocellsuspensionsbeforefreezing.Alternatively,amethodfordeposit-ducialmarkersontosectionsatcryo-temperatureshasbeenpublished.Incryo-tomography,therequirementtolimitthetotaldosemeansthattheSNRineachviewisverylow.addition,cumulativeradiationdamageandtiltingchangetheimagefromoneviewtothenext.Theseproblemsreducethesuccessrateofalignment,especiallyforvitreoussections.Withsucientcontrastofimagefeatures,markerlessalign-mentcanbeused.Amethodhasbeendevelopedinwhichalargearrayofrandomlychosenpointsistrackedbycross-correlation.Becauseofthecontinuallychangingimages,track-ingisdonethroughmanyoverlappingshorttrails.Themarkersarecheckedforconsistencytosearchforusefulones.4.4.2.AlignmentofSubregionsExtractedfromTomo-grams.Tomographicreconstructionsofirregularobjectssuchassubcellularregionsoftencontainmultiplecopiesofmolecularcomplexes.Ifthesecomplexescanberecognizedandextractedfromthetomogram,theycanbealignedandclassifiedassingleparticlesin3D,givingsubstantialimprovementsinSNR.Themaindifferencewithsingle-particleanalysisin2Disthatthetomogramhasawedgeofmissingdata(section3.4).Foreachoccurrenceoftheobject,thiswedgeofmissingdatawillbeina Figure16.Averageandvarianceforanimagesetofparticleswhoseorientationsaredistributedbyrotationaroundthesymmetryaxis(a,b)andforanimagesetofparticlesinasingleorientation(c,d).Theaveragein(a)containsimagesofparticlesindierentorientations,resultingincantvariationofimagefeatures(b).Panel(d)isfeatureless,becausealloftheparticlesintheaverage(c)havethesameorientation,sothattheprojectionsonlydierinthenoisebackground.FigurecourtesyofNeilRanson. alignmentofpreprocessedimagesistocentertheparticlesintheirselectedboxes.Particlescanbecenteredeitherbyshiftingthecenterofmassoftheimagetothecenteroftheimageframeorbyafewiterationsoftranslationalalignmenttotherotationallyaveragedsumofallimages.Inanotherversionofreference-freealignment,aseriesofarbitrarilyselectedimagesareusedinturnasreferencestoalignalloftheotherimages.Ifthesignalisweak,orthereferenceimagedoesnotmatchthedata,noisecanbecorrelatedtothereferenceimageduringalignment.Therefore,toavoidbias,itisimportanttostartanewanalysiswithreference-freealignment.Theproblemofreferencebiasisillustratedbytestsinwhichpurenoisedatasetsarealignedtoareferenceimage.BecausethecorrelationissensitivetotheSNRintheimagedata,theaccuracyofthecorrelationmeasurecanbeimprovedbyweightingthecorrelationofFouriercomponentsaccordingtotheirSNR.Alignmentofasingle-particledatasetisaccomplishedbyaseriesofcomparisonsinwhichalignmentparametersaredeter-minedonthebasisofcorrelationsofeachrawimagewithoneorasetofreferenceimages.Themajorinformationforalignmentcomesfromthestronger,low-frequencycomponentsoftheimages.BecauseofthelowSNRincryo-images,itisimportanttomaximizethecontributionofthesignaltothecorrelationmeasurementbyreducingnoise.Therearetwowaystoreducenoiseintheimages.Inrealspace,amaskaroundtheparticleservestoexcludebackgroundregionsoutsidetheparticle.Inreciprocalspace,aband-passltercanbeappliedtoexcludelow-frequencycomponentsrelatedtobackgroundvariationsoverdistancesgreaterthanthemaximumextentoftheparticleandhigh-frequencycomponentsbeyondtheresolutionoftheanal-ysis.Inlateriterationsofalignment,itisusefultoincreasethecontributionofhigher-frequencycomponents.Inadditiontotheirarbitrarypositionsandorientationsintheplaneoftheimageprojection,theparticlesmayhavediout-of-planeorientations,whichwillgiverisetodierentprojec-tions.Tosorttheimagesintogroupswithcommonorientations,statisticalanalysisandclassicationareessentialtools(seenextsection)inalignmentbyclassiInitialclassaveragesselectedfromarstroundofclassicationcanserveasrefer-encestobringsimilarimagestothesamein-planepositionand Figure15.Alignmentusingtranslationalandrotationalcrosscorrelationsandautocorrelation.(a)Twoimagestobealigned,withthesecondshiftedocenter.Therightpanelshowsthecross-correlationfunction(CCF)ofthesecondimagewiththerst.Thecrossesindicatetheimagecenters.Thearrowindicatestheshiftthatmustbeappliedtoimage2tobringitintoalignmentwithimage1,accordingtotheCCFmaximum.(b)Twoimages,relatedbyarotation,showninCartesian(left)andpolarcoordinates(right).ThecurvedarrowshowstherotationintheCartesiancoordinateview,andthedashedlineshowsthecorrespondingshiftofafeatureinthepolarcoordinaterepresentation.(c)Plotoftherotationalcorrelationbetweenthetwoimagesin(b).Thearrowshowstheangularshiftrequiredtoalignimage2toimage1.(d)Imagesandtheircorrespondingautocorrelationfunctions(ACF).Whentheimageisshifted(secondpanel),theACFisunchanged(translationallyinvariant).Thereferenceimage(ref)has3-foldsymmetry,buitsACFis6-foldbecauseofthecentrosymmetricpropertyofACFs.RotationoftheimagecausesthesamerotationoftheACF,buthasanambiguityof.ApossiblealignmentstrategyistousetheACFrstforrotationalalignment,usingthepropertyoftranslationalinvariance.TheCCFthencanbeusedfortranslationalalignment,checkingboth0and180rotationalpositions. noise.Thesignal-to-noiseratio(SNR)isdenedaswhereistheenergy(theintegralofthepowerspectrumafternormalization)ofthesignalspectrum,andnoiseistheenergyofthenoise.Manyviewsoftheparticlearerecordedindierentorienta-tions,buteachindividualimagehasalowSNR.Themaintaskinextractingthe3Dstructuralinformationistodeterminetherelativepositionsandorientationsoftheseparticleimagessothattheycanbepreciselysuperimposed.Alignmentisdonebyshiftsandrotationsthatbringeachimageintoregisterwithareferenceimage.Crosscorrelationisthemaintoolformeasuringsimilarityofimages,butitisnotveryreliableatlowSNR.Inpractice,alignmentsareiteratedsothatsuccessiveaveragescontainnerdetails,whichinturnimprovethereferenceimage,forsubsequentroundsofrenement.4.1.TheCross-CorrelationFunctionThecorrelationfunctioniswidelyusedasameasureofconsistencyordependencybetweentwovaluesorfunctions.Inimageanalysisitisusedforassessmentofsimilaritybetweenimages.Crosscorrelationcomparestwodierentimages. Equation18denesthenormalizedcrosscorrelationfunction(CCF)betweentwofunctions,)and),whereisavectorinspace,andistheshiftbetweenimages.Inourcase,imagesarethe2Dfunctionsbeingcompared,andvectorsintheimageplane.Theimagesarenormalizedtoameanvalueofzero,toavoidinuenceofthebackgroundlevel.Withoutnormalizationoftheimages,theCCFwouldbeosetbyaconstantproportionaltotheproductofthemeanvaluesoftheimages.Thenormalizedcross-correlationfunctionismaximalwhenthetwoimagesareidenticalandperfectlyaligned,andthedisplacementofthecorrelationpeakfromtheorigingivesthedisplacementofimagewithrespecttoimage.ItisquickertocalculatetheCCFinFourierspace,becausetheFTofthecorrelationintegralistheproductofthecomplexconjugateofrstimageFTwiththesecondimageFT. whereisavectorinFourierspace,andGandGareFTsofgandgThecross-correlationofanimagewithitselfistheautocorrela-tionfunction(ACF).Incrystallography,theACFisknownasthePattersonfunction,whichisobtainedbyFouriertransformationofintensitiesindiractionpatternsandgivesamapofinteratomicdistances(correlationpeaksbetweenpairsofatoms).4.2.AlignmentPrinciplesandStrategiesFacedwithadatasetofimagesofanunknownstructure,wedonothaveanapriorireferenceforalignment.Asuitablerefer-encecanbegeneratedfromthedatabyapproachesknownasreference-freealignment.Inonesuchapproach,therststepin Figure14.(a)CTFcurvefromuncorrecteddata,(b)afterphasecorrection,and(c)overlayoforiginal(black),thesquareofthecurveafterrescaling(red),andamplitudecorrection(green).Panel(c)courtesyofStephenFuller. denominatorisnecessarytoavoiddivisionbyvaluescloseto(Figure14).Amplitudecorrectionhasbeenimplemen-tedinEMAN,SPIDER,andothersoftwarepackages.Tovisualizehigh-resolutiondetails,itisalsoimportanttocorrecttheenvelopedecayofimageamplitudesathighspatialfrequencies(seesection8.3).3.4.3.ImageNormalization.AfterCTFcorrection,theimageofaweakphaseobjectcanbeconsideredasareasonableapproximationofthe2Dprojectionofthe3Dobject,exceptfortheregionsaffectedbyCTFzeros,wherethesignalislow.Thisallowstheprocessofimageanalysistoprogresstowarddetermi-nationofthe3Ddensitydistributionfortheobject.Nonetheless,someimportantstepsofpreprocessingarenecessary.EvenwiththesameEMsettingsduringdataacquisition,variationsinspecimenparticleorientation,supportlmthick-ness,andlmprocessingconditionsleadtodierencesinimagecontrast.Inaddition,structuralanalysisrequiresthemergingofimagedatacollectedduringmultipleEMsessions.Optimizationofdataprocessingrequiresstandardizationofimagesknownasnormalization.ItisconventionalinEMimageprocessingtosetthemeandensityofallparticleimagestothesamelevel,usuallyzero,andtoscalethestandarddeviationofthedensitiestothesamevalueforallimages,whichisimportantforthealignmentprocedure.Imagesarenormalizedusingtheformula: Fi,j
isthestandarddeviationoftheoriginalimage,andisthetargetstandarddeviationinthedata.Themeandensityoftheimagesisdenedas F¼ wherearedimensionsoftheimagearray,andthedensityintheimagepixelwithcoordinatesnedas
I,Ji,j¼1ðFi,j
Thenormalizationsetsallimagestothesamestandarddeviationandameandensityofzero.4.IMAGEALIGNMENTTheinformationwewishtoextractfromEMimages,thesignal,istheprojecteddensityofthestructureofinterest.Therecordedimagescontain,inadditiontothesignal,uctuationsinintensitycausedbynoisefrommanydierentsources.Sourcesofnoiseincludebackgroundvariationsiniceorstain,damagetothemoleculefrompreparationproceduresorradiation,anddetector Figure13.CTFcurves,forasingledefocus(a),overlaidfortwodierentdefocusvalues(b).Theredcurvecorrespondstoaclosertofocusimage,andoscillatesmoreslowly.Image(c)showsmultipledefocusvalues.Thecyan/greencurvescorrespondtotheimageswiththehighestdefocus,andtheredcurveisclosesttofocus.(d)Thesumofamplitudeabsolutevaluesofallcurvesin(c),showingtheoveralltransferofspatialfrequencycomponentsidatasetwiththedefocusdistributionshown.ImagescourtesyofNeilRanson. complicatestheinterpretationoftheimagebecausefeaturesinsomesizerangeswillhavereversedcontrast.Imagingofbiolo-gicalobjectsrequiresacompromisebetweencontrastenhance-mentandminimizationofimagedistortions.TheintensitydistributionintheEMimageplaneisrelatedtotheprojectedelectronpotentialbywheresinisthephasecontrasttransferfunctionandisdebyeq9.nestheshapeoftheimageofapointintheobjectplaneformedbythemicroscopeoptics,thepointspreadfunction(PSF)ofthemicroscope.Therefore,therealimageisdistorted,becausetheidealobjectimageisconvolutedwiththePSF,andisnotdirectlyrelatedtothedensitydistributionintheoriginalobject.Torestoretheimage,sothatitcorrespondstotheprojectedelectronpotentialofthesample,theimagemustbecorrectedfortheeectofcontrastmodulationbysin,themicroscopephasecontrasttransferfunction(CTF).TheCTF,modiedbyanenvelopedecay,andthePSFofamicroscopearerelatedbyFouriertransformation.Forweakphaseobjects,deconvolutionwiththePSFofthemicroscopeisnecessaryforcompleterestorationofimagedata.TheprocedureofeliminatingtheeectsoftheCTFiscalledCTFcorrection.3.4.1.DeterminationoftheCTF.Foragivenmicroscopesetup,thevoltageandsphericalaberrationareconstant,butthedefocusvariesfromimagetoimagebecauseofvariationsinlenssettings,sampleheight,andthickness.TherearetwomainapproachesfordeterminationandcorrectionoftheCTF.Inthefirstone,theimagesareCTF-correctedbeforestructuralanalysis.Inthesecondapproach,structuralanalysisisdoneseparatelyoneachmicrograph,anddeterminationandcorrec-tionoftheCTFareperformedonthestructuresobtained.Eachapproachhasitsownadvantagesanddisadvantages.IfCTFcorrectionisdonerst,datacanbecombinedfrommanydierentmicrographsandsubsequentlyprocessedto-gether.Thesecondmethodisapplicableifeachmicrographhasasucientnumberofparticlestocalculatea3Dreconstruc-tion.ThismethodworkswellforparticlesathighconcentrationandhastheadvantagethatCTFdeterminationismoreaccuratebecauseofthehighSNRinthereconstruction,inwhichtheimageshavebeencombined.However,withfewerparticlesandlowersymmetry,itwillnotbepossibletogetagoodreconstruc-tionoftheobjectfromasinglemicrograph,sothattheapproachismorepractical.ManualCTFdeterminationinvolvescalculationoftherotationallyaveragedpowerspectrum(diractionintensity)ofasetof2Dimages,whichcanonlybedoneintheabsenceofastigmatism.Theamplitudeprole(squarerootoftheinten-sities)iscomparedtoamodelCTF.Themodeldefocusisvariedndthebestmatchbetweenthetwoproles.Thevaluecorrespondingtothematchisthenusedasthedefocusforthatparticularsetofimages.Itisalsopossibletoincludeadditionalprocessingstepssuchasband-passlteringtoremoveback-groundandprovidesmoothingformoreaccuratedetectionofthepositionsoftheCTFminima.Therotationalaveragingusedintheabovemethodassumesgoodastigmatismcorrection.SoftwaredevelopedbyMindellandGrigorie(CTFFIND3)searchesforthebestmatchofex-perimentalwiththeoreticalCTFfunctionscalculatedatdidefoci.Thissoftwareincludesthedeterminationofastigmatismintheimages,assumingthatitseectontheCTFcanbeapproximatedbyanellipse(validforsmallastigmatism),withaveragingoftheprolesoversectorsoftheellipse.Scriptscanbeusedtoautomatethesearchandcorrection.Insomestudies,statisticalanalysishasbeenemployedtosortpowerspectraofparticleimages(squaredamplitudesoftheimageFouriertransform)intogroupswithsimilarCTF.ClassaveragesofthespectraprovideahigherSNRforCTFdeter-mination.Other,moresophisticatedapproachesthattakeintoaccountbackgroundandnoisearedescribedbyHuangandezandcoauthors.Afullyautomatedprogram,ACE,implementedinMatlab,incorporatesamodelforbackgroundnoiseandusesedgedetectiontodenetheellipticalshapeoftheThonrings.3.4.2.CTFCorrection.TherepresentationoftheobjectofinterestisconsideredasfaithfuliftheEMimagescorrespondingtoitsprojectionsarecorrectedfortheeffectsofthemicroscopeCTF.Afullrestorationofthespecimenspectrumrequiresdivisionofthe(eq7)bytheCTF,sin.However,thisoperationisnotpossiblebecauseoftheCTFzeroes,andthespectrumcannotberestoredfromimagestakenatasingledefocus.Tofullyrestoretheinformation,itisnecessarytouseimagestakenatdifferentdefocusvalues,sothatzeroesofeachparticularCTFwillbefilledbymergingdatafromimageswithdifferentdefoci(Figure13).3.4.2.1.PhaseCorrection.ThesimplestmethodofCTFcorrectionistofliptheimagephasesinregionsofthespectrawheresinreversesitssign.Inmanycases,thisproducesreliablereconstructionsbecausealargenumberofimageswithdifferentdefociaremergedtogether,leadingtorestorationofinformationlostinindividualimagesinthevicinityofCTFzeroes.PracticallyallEMimageanalysissoftwarepackageshaveoptionsforthistypeofCTFcorrection.3.4.2.2.AmplitudeCorrectionandWienerFiltration.moreadvancedmethodofinformationrestorationiscorrectionofbothamplitudedistortionsandphasesoftheimagespectra.ThiscorrectionusuallytakesintoaccountnotonlyCTFoscilla-tionsbutalsocompensatesfortheamplitudedecayathighspatialfrequencies.Intheory,thefollowingoperationshouldbesuffi-cient:gg¼whereImistherecordedimage,PSFisthepointspreadfunctionofthemicroscope,theFouriertransformofwhichisCTF,andisthecorrectedimage.Iftherewerenonoiseintheimagespectra,reliablecorrectioncouldbedoneeverywhereexceptforpointswheretheCTFiszero.Inpractice,smallCTFvaluessuppresssignaltransferintheseregions,andnoiseunaffectedbytheCTFdominatesthespectrathere.Thus,simplydividingtheimagespectrabytheCTFwouldleadtopreferentialamplifica-tionofnoise.Toavoidthis,aWienerfilterisusedtotakeaccountoftheSNRandperformanoptimalfiltrationtocorrectlyrestorethespectra: whereisafunctionofSNR:=1/(SNR).MultiplicationoftheFouriertransformoftheimagebytheCTFcorrectstheimagephases,whiledivisionbyCTF+1/(SNR)providestheamplitudecorrection.Additionof1/(SNR)tothe regionatdierentmagnicationscales,sothatobjectsselectedinalowermagnicationoverviewcanbelocatedfordatacollection,inparticularafterstagemovements.Thesoftwaremustcompen-sateforinaccuraciesinmechanicalstagepositioning.Thiscompensationisdonebycollectingoverviewimagesandtheareasofinterestbycross-correlationwithpreviouslyrecordedimages,sothattheselectedareacanbepositionedwithsuprecisionforhigh-magnicationrecording.Foralloftheseopera-tions,electronicimagerecordingisessential,andtheavailabilityofhigh-resolutionCCDcamerashasenabledthedevelopmentofautomation.Severalautomationsystemshavebeendeveloped,bothbyacademicusers(e.g.,Leginon;JADAS)andbyEMsuppliers(FEI,JEOLsystems).Someofthemarecoupledtodataprocessingpipelinesthatextendtheautomationthroughthestagesofparticlepickingandimageprocessing(e.g.,AppionSerialEMisawidelyusedsystemthatprovidessemiautomatedproceduresformanuallyselectingaseriesoftargetsforsubse-quentunsupervisedcollectionoftomogramsandcanalsobeusedforsingle-particledata.Insingle-particleEM,dataprocessingbeginswithparticleselection.Conventionally,theparticlesareidentiedbyshapeandcharacteristicfeaturesthatareoftendiculttorecognizeforanewcomplex.Evenforknowncomplexes,manualselectionof100000single-particleimagesisprohibitivelytime-consumingandtedious.Notsurprisingly,theideaofautomatingparticleselectionhasbeenafocusofresearcheorts.Therstcomputa-tionalmethodswerebasedontemplatematching,andmoresophisticatedapproachesweresubsequentlybasedonpatternrecognition.AcomparativeevaluationofdierentprogramscanbefoundinthereviewbyZhuandcoauthors,andotherprogramshavebeendevelopedmorerecently.3.3.TomographicDataCollectionThepurposeofelectrontomographyistoobtaina3Dreconstructionofauniqueobject,suchasacellsection,isolatedsubcellularstructure,ormacromolecularcomplex,thatcantakeupavarietyofdierentstructures.Aseriesofimagesofthesameregionisrecordedoverthelargestpossiblerangeoftiltangles,upto70.Thelimitationontiltisultimatelyduetotheincreasedpathlengthofthebeamthroughthesample,althoughthespecimenholdermayalsolimitthetilt.Electrontomogramswillthereforebemissinginformationfroma40wedgeofspace,resultinginsomedistortiontothe3Dmap(Figure12Thehightilt,especiallyofthickerspecimens,increasestheinelasticscatteringandmultipleelasticscattering,thereforereducingthefractionofcoherentelectronsusefulinimageformation,inthescatteredbeam.Theenergy-losselectronscanberemovedfromtheimagebyanenergylter,whichisparticularlyimportantforimprovingcontrastintomography.Forplasticsections,theinitialexposuretothebeamcausesthinningofthesections,butsubsequentlythesamplechangeslittleduringdatacollection.Therefore,datacollectionwithangularstepsispossible.Roomtemperaturetomographyalsofacilitatesdual-axisdatacollection,inwhichasecondtiltseriesiscollectedafter90rotationofthespecimenintheplaneofthestage,sothatthemissingwedgeisreducedtoamissingpyramid.Therefore,datacollectioncanbeoptimizedforplasticsections,butdehydrationandstainingdonotpreservemoleculardetail.However,asmentionedabove,sectionsupto300nmthickcanbeusedtogivea3Doverviewoflargerstructures.Ontheotherhand,inelectroncryo-tomography,themolec-ularstructureispreservedinthefrozen-hydratedsample,butitishardtogetbeyond34nmresolution.Theresolutionofcryo-tomographyisseverelylimitedbyradiationdamage,becauseatleast50100imagesmustbecollectedofthesameareaforthetiltseries.TheseconictingrequirementsforlowdoseandmanyexposuresmeanthattheimagesarerecordedwithextremelylowelectrondoseandthereforeverylowSNR,andtheaccumulateddamagechangesthestructureduringthetiltseries.Thethickeristhesample,themoreviewsareneededtoreachagivenresolu-tion.Inaddition,thelimitationonmaximumtiltangleleavesamissingwedgeofdata.Theseproblemsmakeprocessingofcryo-tomogramsmoredicult.Thebestresolutionisobtainedbyaveragingsubregionsofcryo-tomogramscontainingmultipleoccurrencesofthesameobject,forexample,viralspikes(seesection4.4).Thismethodiscalledsubtomogramaveraging.Automationisindispensableforelectrontomography.Well-developedtomographysoftwareisavailablefrombothacademicandcommercialsources(SerialEM;UCSFTomo;Protomo;103105,106).Leginonincorporatestomographicandothertiltdatacollectionprotocolssuchasconicaltilt(section6.1).3.4.PreprocessingofSingle-ParticleImagesAlthoughtheoreticalandtechnicalprogressinelectronmicro-scopyhasimprovedtheimagingofweakphaseobjects,defocusing Figure12.Distortionscausedbythemissingwedge.(a)Amodelobject.(b)Setofimageplanesatdierentanglesfromatiltseries.Thelimitationonmaximumtiltangleresultsinamissingwedgeofdata.(c)Reconstructionoftheobjectshowingelongatedfeaturesduetothemissingwedge.Reproducedwithpermissionfromref99.Copyright1998ElsevierInc. frequenciesindicatesthelossofnedetailsinthedigitizedimages.Densitometercharacteristicsandassessmentshavebeendescribedinseveralarticles.3.1.3.DigitalDetectors.DigitalimaginghaspracticallyreplacedrecordingonfilmsinphotographyandiswidelyusedinEMduetodevelopmentsinautomateddatacollectionandtomographymethods.Themostpopularcamerasarebasedoncharge-coupleddevice(CCD)sensorsthatconverttheanalogueopticalsignalintodigitalformat.TheCCDwasinventedin1969byW.S.BoyleandG.E.SmithatBellTelephoneLaboratories(Nobelprize,2009).Thephysicalprincipleofthisdeviceisanalogtransformationofphotonenergy(light)intoasmallelectricalchargeinaphotosensoranditsconversionintoanelectronicsignal.CCDchipsconsistofanarrayoramatrixofphotosensitiveelements(wells)thatconvertslightintoelectricchargeaccumulatedinthewells(Figure11).Charge-coupledreferstothereadoutmechanism,inwhichchargesareseriallytransferredbetweenneighboringpixelstoareadoutregister,amplified,andconvertedtoadigitalsignal.Thereadoutisdonethroughoneorseveralports,whichdeterminesthespeedofCCDimagerecording.Becausehigh-energyelectronsirreversiblydamagethephoto-sensitivewellsinCCDs,currentlyavailabledevicesemploymono-orpolycrystallinescintillatorstoconverttheelectronstophotons,whicharethenrelayedtotheCCDchip(Figure11).Althoughthegraininessofthescintillatorandelectron-to-photonconversionaddnoisetotheimages,theuseofascintillatorgreatlyextendstheusablelifeofaCCDchip.Thisdetectionschemeworksquitewellforacceleratingvoltagesupto120kV.Athighervoltages,thecamerasensitivitydecreases,and,tocompensate,thickerscintillatorlayersareneededtoimprovetheelectrondetectioneciency.Inaddition,imagequalityisdegradedbecausethehigher-energyelectronsarescatteredinthescintillator,reducingimageresolution.TheCCDisaverysensitiveandeectiveelectrondetectorwithremarkablylinearresponseandverylargedynamicrange(16bitresolution).Thisallowsrecordingofbothlowcontrastimagesandelectrondiractionpatternsinwhichdiractionintensitiescanrangeoverseveralordersofmagnitude.Thedisadvantageofthistypeofcameraisthehighcostandlimitedsensorsize.CCDchipsof55cm4kpixels)arenowwidelyused,anddigitalcameraswith8k8ksensorsand12cmindiameterareavailable.ThetypicalsizeofcurrentCCDpixelsism,whichimposesadditionalrestrictionsontheminimalmagnicationusedtorecordimages,becausetheimagesamplingbytheCCDshouldbenerthanthetargetresolutionbyaboutafactorof4(seesection8).ExamplesofsuccessfuluseofCCDimagingforhigh-resolutioncryo-EMat300kVareshownbyChenwithcoauthorsandClareandOrlova.Thecurrentgenerationofdigitaldetectorsforelectronmicro-scopyincludesadirectdetectiondevice(DDD),whichcanbeexposeddirectlytothehighenergyelectronbeam.HybridpixeldetectorssuchasMedipix2aredirectelectrondetectorsthatcountindividualelectrons,ratherthanproducingasignalpro-portionaltotheaccumulatedcharge.AnothertypeofnewDDDisthemonolithicactivepixelsensor(MAPS),inwhichthesignalisproportionaltotheenergydepositedinthesensitiveelement.TheDDDusesaradiation-hardenedmonolithicactive-pixelsensordevelopedforchargedparticletrackingandimagingandsmallerpixelsize(5ThesedetectorsarebeingcombinedwiththeCMOS(complementarymetaloxidesemiconductor)design,inwhichtheampliersarebuiltintoeachpixel,enablinglocalconversionfromchargetovoltageandthusfasterreadout.Directexposuretotheincidentelectronbeamcantlyimprovesthesignal-to-noiseratioincomparisontoaCCD.Thistypeofsensorhashighradiationtoleranceandallowsforcaptureofelectronimagesat200and300keV.AcomparisonofdigitaldetectorsdemonstratedthatDDDincombinationwithCMOScanprovidegoodDQE,MTF,andimprovedsignal-to-noiseratioatlowdose.DesignofdigitalcamerasinEMcontinuestoimprove:thelatestcamerasareabletoregisterelectronsoverabroadenergyrangeandcoverlargeareaswithsmallerpixelssothatthedetectorarea(16k16kpixels)becomescomparabletoorbiggerthan84,87,893.2.Computer-ControlledDataCollectionandParticlePickingThegoalofautomateddatacollectionistoreplacethehumanoperatorintime-consuming,repetitiveoperationssuchassearch-ingforsuitablespecimenareasandrecordingverylargedatasets,includinglow-doseoperation,particleselection,andobtainingtiltdata.MostEMsnowhavecomputer-controlledoperationforlenssettingsandstagemovement,alongwithbasicimageanalysisoperationssuchasFTs.Essentialstepstocontrolaresettingsforillumination,stageposition,magnication,tilt,andfocus.Theautomationsystemmustbeabletorecognizethesame Figure11.DiagramofaCCDdetectorforEM.Theincidentelectronsareconvertedtophotonsbythescintillator.FiberopticstransmittheimagetotheCCD(chargecoupleddevice)sensorwherethephotonsgenerateelectricalcharge(CCDelectrons).ThechargeisaccumulatedinparallelregisterDuringreadout,thischargeisshiftedlinebylinetotheserialregisterfromwhereitistransferredpixelbypixeltotheoutputanalog-to-digitalcImagereproducedwithpermissionfromH.Tietz. electronsofdierentwavelengthcanbedeectedalongdipaths,andtheltercanbeeitherinthecolumn(lter)orpostcolumn(GIF).TheuseofenergylteringtoimprovethecontrastofcryoEMimageswasintroducedbyTrinickandBerrimanandSchrEnergylteringismostimportantfortomography,becauseofthelongpathlengthofthebeamthroughthetiltedsample.Anin-columnlterhasrecentlybeenusedtoobtainveryhigh-qualityimagesofactinlaments,theauthorsattributeasignicantpartofthecontrastimprove-menttothe3.IMAGERECORDINGANDPREPROCESSING3.1.ElectronDetectors3.1.1.PhotographicFilm.Untilrecently,theconventionalimagedetectorwasphotographicemulsion.Thelight-sensitivecomponentsinfilmsaremicroscopicsilverhalidecrystalsembeddedinagelatinmatrix.Absorptionofincidentradiationbythecrystalsinducestheirtransitionintoametastablestate,thusrecordingtheimage.Theimageremainshiddenuntilphotographicdevelopertransformssilverhalideintovisiblesilvergrains.TheopticaldensityOD=log(1/),whereisthetransmissionofthefilm.TheODofthefilminresponsetoilluminationdose,thenumberofphotons/electronsperunitarea,initiallyincreaseslinearlywithdose,thenstartstosaturateandeventuallyreachesaplateauathighdose,althoughitisS-shapedforlight.Atlowenergy80keV),opticaldensityisdirectlyproportionaltoelectronenergy,andthepeaksensitivityisaround80100keV.Withinthecurrentworkingrangeofelectronenergy(100300keV),thespeedofEMfilmsisinverselyrelatedtotheelectronenergy:higher-energyelectronsinteractlesswiththesilverhalidecrystals,leadingtolowerODforthesameirradiationdose.Therefore,emulsionsproducedforelectronmicroscopyareoptimizedforsensitivityto100300keVelectrons,withlargegrainsizeandhighsilverhalidecontent.ThefilmmainlyusedforTEMisKodakSO-163,whichprovidesgoodcontrastatlowdose.Theadvantageofphotographicfilmistheextremelyfineandthelargeimagedetectionarea.Photographicfilmisstillthemosteffectiveelectrondetector,intermsofspatialresolutionoveralargearea(numberofeffectivepixels)andcost.Theinconveniencesofusingfilmsarethattheyintroduceanadditionalloadonthemicroscopevacuumsystemduetothepresenceofadsorbedwaterandtheyneedchemicalprocessing,drying,anddigitization.3.1.2.DigitizationofFilms.Filmsmustbedigitizedforcomputeranalysis.Toconverttheopticaldensitiesofthefilmintodigitalformat,thefilmisscannedwithafocusedbrightbeamoflight.Thetransmittedlightisfocusedonaphotodiodeconnectedtoaphotoamplifierthatproducesanelectricalsignal.Theintensityofthecurrentisconvertedintoanumberrelatedtotheopticaldensityofthefilm.Thedensitometermeasurestheaveragedensitywithinsquareelements(pixels)whosesizeisdeterminedbythesamplingresolution.LinearCCDdetectorsareusedtomeasurealineofpixelsinparallel.Digitisationdoesnotprovideafaultlesstransferofopticaldensityintodigitalformat.Theaccuracyisdeterminedbythequalityoftheopticalsystemandthesensitivityofthephotodetectorsandampliers.Densitometerperformancecanbedescribedintermsofthemodulationtransferfunction(MTF),whichisdenedasthemodulusofthedensitometerstransferfunction.Theoutputimageisconsideredastheconvolutionoftheinputimagewiththepointspreadfunctionofthedensit-ometer.ThedependenceofMTFonspatialfrequencydescribesthequalityofsignaltransfer.AstrongfallooftheMTFathigh Figure10.Phasecontrastinopticalandelectronmicroscopy.(a)Brighteld(upperpanel)andphasecontrast(lowerpanel)imagesofaeldofcells.Thecellsareapproximately50minlength.Panel(a)wasprovidedbyMaudDumouxandRichardHayward.(b)Schematicrepresentationofthelightmicroscope.(c)Schematicrepresentationoftheelectronmicroscopeforcomparison,showingthemajorlenses.Thepositionsofphaseplatesareindicated.(d)ImagesofGroELtakenwithout(upperpanel)andwiththephaseplate(lowerpanel).Scalebars,20nm.Image(d)isreproducedwithpermissionfromref67.Copyright2008RoyalSocietyPublishing. Thediractionpatternoftheimage(imageplaneofthemicroscope)isgivenbywhere)istheDiracdeltafunction.Intheplaneoftheimage,theamplitudecontrastisdescribedby2cosandthephasecontrastby2sin(foramoredetaileddescriptionofimageformation,seerefs60and63).Forphaseobjects,thesinetermofeq10hasthemajorinuence.Itdescribesanadditionalphaseshiftduetosphericalaberrationandchangesintheimagecontrastdependingondefocus.ThemajoreectoftheCTFonimagesofweakphaseobjectsarisesfromoscillationsofthesintermthatreversethephasesofalternateThonringsintheFouriertransformoftheimage(Figure9).Forthincryospecimens,theamplitudecontrastfor120keVelectronshasbeenestimatedat7%,whereasfornegativelystainedsamplestheamplitudecontrastcanrisetoFor300keVcryoimages,itdropsto2.5.PhasePlatesandEnergyFiltersTheverysmallphaseshiftsinducedbybiologicalsamplesinthescatteredelectronsresultinpoorimagecontrast.Inphasecontrastlightmicroscopy,theimagingofphaseobjectsisenabledbytheuseofaquarter-wavephaseplate,whichproducesvisiblecontrastbyshiftingthephaseofthescatteredlightrelativetothatofthetransmittedbeamby90,leadingtoconstructiveinter-ference(Figure10a,b).AnequivalentsolutionforelectronmicroscopywaspioneeredbyBoersch.AnearlyattempttocreateadevicetochangethephaseofthecentralbeamrelativetothescatteredrayswasdonebyUnwin,whodevisedasimpleelectrostaticphaseplatethatwasinsertedintotheopticalsystem.Heusedathinpoorlyconductingcylinder(aspidersthread)overacircularapertureinsertedinthebackfocalplaneoftheobjectivelens(wheretheelectronractionpatternisformed).Thiscylinderpartlyobstructedthecentralbeamandbecamechargedwhenilluminatedbytheelectronbeam,thuscreatinganelectrostaticphaseplate.Theexperimentswithnegativelystainedsamplesclearlydemon-stratedincreasedcontrast.Thepracticalrealizationofthisideahasonlyrecentlybecomefeasible.Microfabricationhasallowedtheconstructionoftheminiaturephaseplates,whicharepositionedinthebackfocalplaneoftheobjectivelens(Figure10c,d).Thephaseplatefunctionsasanelectrostaticlensandisplacedinthepathofthescatteredelectrons,shiftingtheirphaseby90sothatcontrastisimprovedwhentheyrecombinewiththeunscatteredelectronsintheimageplaneoftheTEM.Theresultinglargeincreaseincontrastoverawideresolutionrange,especiallyatlowresolution,isparticularlyusefulforelectroncryo-tomography.Anadditionalapproachtoimprovingimagecontrastisenergyltering.Afractionoftheelectronsreachingtheobjectivelensareinelasticallyscattered,havinglostenergybyinteractionwiththesampleatoms.Thelowerenergy(correspondingtolongerwavelength)oftheseelectronscausesthemtobefocusedinerentplanesfromtheelasticallyscatteredelectrons,inotherwords,chromaticaberration.Therefore,inelasticelectronsdegradetherecordedimagewithadditionalbackgroundandblurring,inadditiontodamagingthesample.Energylterscanbeusedtostoptheseelectronsfromcontributingtotheimageaftertheirinteractionwiththespecimen.Filteringworksonthebasisthat Figure9.Imagesofcarbonlmandtheirdiractionpatterns,showingThonringsandcorrespondingCTFcurves.Theleftimagewasobtainedat0.5defocus,andthemiddleimagewasat1mdefocus.TheThonringsofthesecondimagearelocatedclosertotheoriginandoscillatemorerapidly.Theringsalternatebetweenpositiveandnegativecontrast,asseenintheplottedcurves.Anexampleofanastigmaticimageanditsdiractionpatternisshownintherightpanel.Thelargestdefocusisalongaxis,andthesmallestisalongaxis phaseofthescatteredbeam)by90(Figure8candd),whichchangestheexitwaveasfollows:Theintensityintheimageplanethencanbeapproximatedbythefollowingexpression:Here,theintensitybecomesproportionaltotheprojectionoftheelectronpotentialofthesample,andthemagnitudeof2willbemuchgreaterthan(.Therefore,thephaseshiftofthescatteredbeamtransferstheinvisiblephasecontrastintoamplitudecontrastthatcanberecorded.Howinpracticecanthecontrastbeincreased?Onemethodistousesubstancesthatincreasethescattering,suchasnegativestains.Anotherpossibi-lityistoutilizeimperfectionsofthemicroscopesuchassphericalaberration.Inpractice,theimagecontrastobtaineddependsontheoperatingconditionsofthemicroscopesuchastheleveloffocusandaberrations.Multiplescatteringofelectronswithinthickspecimensobscurestherelationbetweenobjectandimage.ThereareseveralfactorsthataecttheappearanceandcontrastofanEMimageincludinglensaberrations,limitedincidentbeamcoherence,quantumnoisebecauseofthediscretenatureofelectrons(shotnoise),radiationstabilityofthesample,instabil-itiesinthemicroscope,andenvironment,forexample,vibrations,strayelectromagneticelds,temperaturechanges,andimperfectmechanicalstabilityoftheEMcolumn.Instabilitiesandlimitedcoherenceoftheelectronbeamcausefalloofthesignaltransferbythemicroscopeforneimagedetails,leadingtoblurringofsmallfeatures.Insimpleterms,asharpdotwillnotbeimagedasadotbutasablur.Thelinkbetweentheoriginaldotanditsimageisdescribedbythepointspreadfunction(PSF)oftheimag-ingdevice,inourcaseoftheelectronmicroscope.ThePSFisafunctionthatdescribestheimperfectionsoftheimagingsysteminrealspace.However,aconvenientwaytodescribetheinuenceofthesefactorsontheimageistouseFourier(diraction)space:Þg¼CTFwhereistheFouriertransformoftheobservedimage;isspatialfrequency(Fourierspacecoordinate);istheFouriertransformofthespecimen;CTF()isthecontrasttransferfunctionofthemicroscope;and)isanenvelopefunction.)describestheinuenceofvariousinstabilitiesandspecimendecayunderthebeam.Theenvelopedecaycanbepartlycompensatedbyweighting,forexample,withsmallanglescatteringcurves(seesection8.3).Theopticaldistortionsareusuallyapproximatedasaproductoffunctionsattributedtoindividualdampingfactors(e.g.,lenscurrentinstability).ThelinktothePSFisgivenbythefollowingequation:Þg¼CTFTheamplitudeandphasechangesarisingfromobjectivelensaberration,orCTF(),areusuallydescribedbythefunctionexp(),wheredescribesthephaseshiftarisingfromsphericalaberrationandimagedefocus:Þ¼
12RB2
whereisthephaseshiftcausedbyaberrations,isspatialfrequency,avectorinthefocalplaneoftheobjectivelens,thecoecientofsphericalaberration,isthewavelengthoftheelectronbeam,andisthedefocus,thedistanceoftheimageplanefromthetruefocalplane.Itwasfoundthattheimagecontrastofbiologicalobjectscouldbeimprovedbythecombinedeectsofsphericalaberrationandimagedefocus,movingtheimageplaneawayfromexactfocus.Thebasisforthecontrastenhancementisthatsphericalaberrationcombinedwithdefocusinducesaphaseshiftbetweenscatteredandunscatteredelectrons.Thegreaterphaseshiftbetweenscatteredandunscatteredraysleadstostrongerimagecontrast. Figure8.Graphicalrepresentationofphasecontrast.(a)Complexplanerepresentationofawavevectorwithphase.(b)Vectorrepresentationofthescatteredwave,unscatteredwave,andresultantwave.Amplitudes(vectorlengths)ofareverysimilar,resultinginlowimagecontrast.(c)/2phaseshiftofthescatteredwaveleadstoanoticeabledecreaseintheresultantwaveamplituderelativetotheunscatteredwave(negativephasecontrast).(d)/2phaseshiftofthescatteredwaveincreasestheamplitudeoftheresultantwaverelativetotheunscatteredwave(positivephasecontrast). Oneofthedicultiesofbiologicalelectronmicroscopyisthatbiologicalmoleculesproduceverylittleamplitudecontrast.Theyconsistoflightatoms(H,O,N,andC)anddonotabsorbelectronsfromtheincidentbeambutratherdeectthem,sothatthetotalnumberofelectronsintheexitwaveimmediatelyafterthespecimenremainsthesame.Thatmeansthatthespecimensdonotproduceanyintensitymodulationoftheincidentbeamandtheimagefeaturesarenotvisible.Yetthesespecimensstillchangetheexitwavebecauseelectronsinteractwiththematerial.Electronsundergoscatteringatvaryinganglessotheyhaveerentpathlengthsthroughthespecimen,givingphasecon-trast(Figure7).Onecansaythattheyexperiencealocation-dependentphaseshift.Thesephasevariationsencodedintheexitwavearemadevisiblebybeingconvertedintoamplitudevaria-tionsthataredirectlydetectablebyasensor.Inpractice,thisisachievedbyintroducinga90phaseshiftbetweenincidentandscatteredwaves.2.4.1.FormationofProjectionImages.Inthecaseofelasticscattering,thescatteringangleisproportionaltotheelectronpotentialoftheatom(thehigheristheatomicnumber,thehigherisitselectronpotential).TheexitwavethathaspassedthroughthesamplecanbedescribedasÞÞðwhereistheexitwaveemergingfromthespecimen;theincidentwave;iselectronmass;electronwavelength;isPlancksconstant;andisthespecimenpotentialprojectedalongdirection,whichcoincideswiththeopticalaxisofthemicroscope,isavectorintheimageplane,andcorrespondstothethicknessofthesample.Becausebiologicalspecimensingeneralareweakelectronscatters,thephaseshiftintroducedbythesampleissmall;thatis,theexponenttermineq2isclosetounity,whichmakesitpossibletodescribetheexitwavebythefollowingapproximation:ÞÞðThetransmittedwave)consistsoftwoparts:thetermcorrespondstotheunscatteredwave,andthesecondterm,correspondingtothedeected(scattered)electrons,islinearlyproportionaltothespecimenpotential.Thesecondterm)hasaphaseshiftof90,becauseitcorrespondstotheimaginarypartoftheexpressionindicatedbythefactor(Figure8aandb).Inthefollowingdiscussion,weassumethattheamplitudeoftheincidentwave=1.2.4.2.ContrastforThinSamples.Theimageisformedbyallelectrons,bothscatteredandunscattered,givingverylittlecontrastforthin,unstainedbiologicalspecimens.Thisisknownasphasecontrast,whichresultsfrominterferenceoftheunscat-teredbeamwiththeelasticallyscatteredelectrons(Figures7and8).Thintransparentsamplesscatterelectronsthroughsmallanglesandaredescribedasweakphaseobjects.Theintensitydis-tributionobservedintheimageplanewillbegivenbywheredenotesthecomplexconjugate.However,themagni-tudeof(1,sotheimagewillhavepracticallynocontrast.Toincreasethecontrast,itisnecessarytochangethe Figure7.Phasecontrast.(a)Aphaseobjectilluminatedbyaparallelbeam.(b)Theresultingimageshowsonlyweakfeatures.(c)Acrosssectionoftheobjectoutlinedbydashedlinesin(A).Arrowsshowthechangesinthewavefront(parallellines)afterinteractionwiththesample.Theintensityisnotchanged,butthewavefrontbecomescurved.(D)Intensityoftherayscreatingtheimageintheregionofthecrosssection.Notethattheintensitydierencesaresmall. Figure6.Amplitudecontrast.(a)Anamplitudeobjectilluminatedbyaparallelbeam.(b)Theimageresultingfrominteractionofthebeamwiththesample.(c)Acrosssectionoftheobjectoutlinedbythedashedlinesin(a);someoftheraysareabsorbedinthesample.Arrowsshowthechangesinthewavefrontafterinteractionwiththesample.(d)Intensityoftherayscreatingtheimageintheregionofthecrosssection.Blackdotsintheimagecorrespondtoareasofbeamabsorption(c). crystaltungstensharpenedtogiveatipradius25nm,ascomparedto5mforLaBcrystals.Thetipiscoatedwith,whichlowerstheworkfunctionforelectrons.Thermallyemittedelectronsareextractedfromthecrystaltipbyastrongpotentialgradientattheemittersurface(fieldemission),andthenacceleratedthroughvoltagesof100300kV.2.3.2.TheElectronMicroscopeLensSystem.Asinlightmicroscopy,condenserlensesconvertthedivergingelectronbeamintoaparalleloneilluminatingthespecimen(Figure4).Thespecimeninmodernelectronmicroscopesislocatedinthemiddleoftheobjectivelens,fullyimmersedinthemagneticfield.Anobjectiveapertureisplacedinthebackfocalplaneofthislens;theaperturepreventselectronsscatteredathighanglesfromreachingtheimageplane,thusimprovingtheimagecontrast.Theobjectivelensprovidestheprimarymagnification(20andisthemostimportantopticalelementoftheelectronmicroscope.Itsaberrationsplayakeyroleinimaging.Theimageisfurthermagnifiedbyintermediateandprojectorlensesbeforetheelectronsarriveatthedetector.Alternatively,theelectrondiffractionpatternatthebackfocalplaneoftheobjectivecanberecordedafterbeingmagnified.2.3.3.ElectronMicroscopeAberrations.Electromagneticlenseshavethesametypesofdefectsasopticallenses,sphericalandchromaticaberrations,curvatureofthefield,astigmatism,andcoma,ofwhichthemostsignificantarespherical,chro-matic,andastigmaticaberrations(Figure5).Thequalityofthebeamsourceisessentialforcoherenceoftheelectronbeamneededforhigh-resolutionimaging.Sphericalaberrationisanimagedistortionduetothedependenceoftherayfocusonthedistancefromtheopticalaxis(Figure5b).Rayspassingthroughtheperipheryofthelensarerefractedmorestronglythanparaxialrays.Chromaticaberrationiscausedbythelensfocusingrayswithlongerwavelengthsmorestronglysothatpartoftheimageisformedinaplaneclosertotheobject,resultingincoloredaroundedgesintheimages(Figure5c).Chromaticaberrationinelectronmicroscopesresultsfromvariationsinelectronenergycausedbyvoltagevariationintheelectronsource,electronenergyspreadintheprimarybeam,andenergylossinelasticeventsinthesample,andblursthefinedetailsinimages.Astigmaticaberrationisproducedbydeviationfromaxialsymmetryinthelens,sothatthelensisslightlystrongerinonedirectionthanintheperpendiculardirection.Astigmatisminelectronmicroscopesiscausedbyanasymmetricmagneticfieldinthelensesandcanbecompensatedbystigmatorcoils.Itresultsintwodifferentimageplanescorrespondingtothesedirectionssothattheimageofapointbecomesanellipse(Figure5d).Theaberrationsdescribedherearethemajoronesthataffecttheimages,althoughtherearealsoother,higherorderaberrations,whichmustbeconsideredforhigh-resolutionanalysis.2.4.ContrastTransferNormally,imagesrepresentintensityvariationscausedbyregionalvariationsinspecimentransmission.Thesevariationsarerecordedbyadetectorsystem;theimagecontrastContnedastheratioofthedierencebetweenbrightestdarkestpointsintheimageandtheaverageintensityofthewholeimage: Fmax
Fmin Theimagecontrastresultingfromabsorptionofpartoftheincidentbeamisknownasamplitudecontrast(Figure6).Becauseonlyasmallfractionoftheelectronsisactuallyabsorbedbythebiologicalspecimenininelasticinteractions,theamplitudecontrastcanalsobeincreasedbyusingtheobjectivelensaperturetoeliminateelectronsscatteredathighangles. Figure5.Raydiagramsoflensaberrations:(a)perfectlens,(b)spherical,(c)chromatic,and(d)astigmaticaberration.isthefocallengthofthelens. exposuresof10eorless.Therefore,radiationdamagedictatestheexperimentalconditionsandlimitstheresolutionofbiologicalstructuredetermination,especiallyforcryo-tomogra-phy.Toreduceradiationdamageduringareaselection,align-ment,andfocusing,speciallowdosesystemsareusedtodethebeamuntilthenalstepofimagerecording.AnexampleofelectronbeamdamageisshowninFigure3b.Lowerelectrondosescanbeusedfortwo-dimensional(2D)crystalsthanforsingleparticles,becausethesignalfromallunitcellsisaveragedineachdiractionspot.Therefore,thediractionspotsarevisibleevenwhentheunitcellsarenotvisibleintheimage.2.3.ImageFormationThebasicprincipleofelectronopticallensesisthedeofelectrons,negativelychargedparticlesofsmallmass,byanelectro-magneticeld.Similartoaconventionallightmicro-scope,theEMconsistsofanelectronsource,aseriesoflenses,andanimagedetectingsystem,whichcanbeaviewingscreen,aphotographiclm,oradigitalcamera.Electronmicroscopyhasmadeitpossibletoobtainimagesataresolutionof0.8Åforradiation-insensitivematerialssciencesamples,1.9Åforelec-troncrystallographyofwell-ordered2Dproteincrystals,3.3Åforsymmetricalbiologicalsingle-particlemacromolecularand5.5Åfortheribosome.16,172.3.1.ElectronSources.Thestandardelectronsourceisatungstenfilamentheatedto2000C.Atthistemperature,theelectronenergyisgreaterthantheworkfunctionoftungsten.Thethermallyemittedelectronsareacceleratedbyanelectricfieldbetweentheanodeandfilament.AnothercommonelectronsourceisaLaBcrystal,whichproduceselectronsfromasmallereffectiveareaofthecrystalvertexwhoseemittingsurfaceisatalowertemperaturebecauseofalowerworkfunction.Thisbeamhashighercoherenceandcurrentdensity.Atpresent,themostadvancedelectronsource,usedinhighperformancemicro-scopes,isthefieldemissiongun(FEG).TheFEGbeamisstillsmallerindiameter,morecoherent,andbrighter,withaverysmallspreadofenergies.Thisisachievedbyusingsingle Figure4.Simpliedschematicrepresentationofanelectronmicroscope. Figure3.Interactionoftheelectronbeamwiththesample.(a)Schematicofelasticandinelasticelectronscattering.Collisionofbeamelectronswithatomicelectronsornucleileadstoenergyloss(inelasticscattering),whiledeectionbytheelectronclouddoesnotchangetheenergyoftheelectron(elasticscattering).(b)Eectofelectronbeamdamageonacryoimageofacell.Theelectrondoseisshownontheimages.Increasingdosecausesdamagetocellularstructures,butdierentcellregionsandmaterialsshowtheeectsofdamageatdierentlevelsofradiation.Inthiscase,damageappearsontheWeibelPaladebodies.Reproducedwithpermissionfromref54.Copyright2009NationalAcademyofSciences. Importantly,antigenicityisoftenconservedinFSmaterial,sothatimmunolabelingorotherchemicallabelingcanbedoneonthesections.Thisisamajoradvantageovervitreoussectioning,forwhichantibodylabelingisimpossible.FSisanimportantadjuncttocryo-sectioningfortomographyofcellstructures,becauselargevolumesarefarmorereadilyimagedandstructuresofinteresttrackedinthe200300nmthicksectionsthatcanbeexaminedwithFS.Inaddition,theuorescenceofGFPisretainedinthefreeze-substitutedsections,facilitatingcorrelativeuorescence/EM.AchemicalreactionoftheGFPchromo-phorewithdiaminobenzidineproducesanelectrondensepro-duct,allowingGFPtagstobepreciselylocalizedinEMsections.Therefore,thecombinationofcryo-sectioningandfreeze-sub-stitutiononthesamesamplecanprovideanoverviewofthe3Dstructure,chemicallabeling,anddetailedstructuralinformationonregionsofinterest.2.1.4.3.Cryo-SectioningofFrozen-HydratedSpecimens.SectioningremovestherestrictionofcryoEMtoexaminationofonlythethinnestbacterialcellsorcellextensions.Afteralongperiodofdevelopment,vitreoussectioninghasstartedtobecomegenerallyaccessible.Thevitrifiedblockissectionedat140toCwithadiamondknife.Compressionofthesectionsalongthecuttingdirectionandcrevassesonthesurfaceofthickersectionspresentmechanicalartifacts.Nevertheless,HPFandcryo-sectioningcurrentlyprovidethebestviewintothenativestructuresofcellsandtissues(Figure2b).Becausethenativestructuresarepreserved,macromolecularstructurescanbeimagedinvitrifiedsections.Therefore,cryo-ETisanimportantsteptowardtheultimategoalofunderstandingtheatomicstructureofthecell.Cryo-sectionsmustbearound50150nmthick,tondthebestcompromisebetweenformationofcrevasses(thicker)andsectioncompression(thinner).Becauseofthelowcontrastandthetinyfractionofcellvolumesampledinsuchthinsections,itcanbeveryhardtolocatetheobjectofinterest,unlessthestructureislargeandveryabundant,orassociatedwithlarge-scalelandmarks,suchasmembranesorlargeorganelles.Forthisreason,andalsoforbiochemicalidentication,averyimportantrecentdevelopmentiscorrelativecryo-uorescenceandEM.Cryostagesarebeingdevelopedforuorescencemicroscopes,andifthesignalisstrong,theuorescencecanberstmappedoutonthecryosectionorcellcultureonanindexed(ndergrid,andthenthesamegridcanbeexaminedbycryoEM.2.1.4.4.FocusedIonBeamMilling.Analternativetocryo-sectioningcurrentlybeingexploredisfocusedionbeammilling,inwhichmaterialisremovedfromthesurfaceofafrozenspecimenbyirradiationwithabeamofgalliumions,untilthesampleisthinenoughforTEM.Millingisdoneundervisualcontrolinacryo-scanningEM,followedbycryo-transfertotheTEMfortomography.Preliminaryworksuggeststhatthethinnedlayerremainsvitrified,withoutnoticeableeffectsoftheionbeamexposure.Themethodproducesasmoothsurface,importantly,withoutsectioncompressionorcrevasses,thusavoidingthemechanicalartifactsofcryo-sectioning.2.2.InteractionofElectronswiththeSpecimenImagingwithelectronsprovidestheadvantageofhighresolu-tion,duetotheirshortwavelength.However,thestronginter-actionofelectronsfromtheprimaryelectronbeamwiththesamplecausesradiationdamageinthesample.Thenatureoftheinteractionoftheelectronswiththesampledependsontheelectronenergyandsamplecomposition.Someelectronspassthroughthesamplewithoutanyinteractions,othersaredebytheelectrostaticeldofthenucleus,screenedbytheouterorbitalelectronsofspecimenatoms,andsomeelectronsmaycollideornearlycollidewiththeatomicnuclei,sueringhighangleectionsorevenbackscattering.Oftheinteractingelectrons,somearescatteredwithoutenergyloss(elasticscattering),butotherstransferenergytothespecimen(inelasticscattering)(Figure3a).Energytransferfromincidentelectronscanionizeatomsinthespecimen,induceX-rayemission,chemicalbondrearrangement,andfreeradicals,orinducesecondaryelectronscattering,allofwhichchangethespecimenstructure.Radiationdamageofspecimensisasignicantlimitationinhigh-resolutionimagingofbiologicalmolecules.ProlongedexposuretoanintenseelectronbeaminanEMproducesalevelofdamagecomparabletothatcausedtolivingorganismsexposedtoanatomicexplosion.Typicalvaluesofelectronexposureusedforbiologicalsamplesrangefrom1to20electron/Å.Althoughbiologicalspecimenscantolerateanexposureof100500e,dependingonspeci-mentemperatureandchemicalcomposition,thehighestresolu-tionfeaturesofthespecimenarealreadyaectedatelectron Figure2.Slicesofsingleaxistomogramsofyeastcellsectionspreparedbyfreeze-substitution(a)andcryo-sectioningofvitriedsamples(b).Theblackdotsaremainlyribosomes.R,ribosomes;N,nucleus;V,vacuole;MT,microtubules(ringshapedcrosssections);M,mitochondrion;ER,endoplasmicreticulum.Panel(b)wasproducedbyDanClare. thermalstability.Rapidfreezingisusedtobringthesampletothesolidstatewithoutdehydrationoricecrystallization,andthesampleismaintainedatlowtemperatureduringtransferandobservationintheEM.Themethodwidelyusedforfreezingaqueoussolutionsistoblotthemtoathinlayerandimmediatelyplungeintoliquidethaneorpropane(C)cooledbyliquidnitrogenforrapidheattransferfromthespecimen1,27(Figure1bCoolingbyplungingintoliquidethaneismuchfasterthanplungingdirectlyintoliquidnitrogenbecauseliquidethaneisusedneartoitsfreezingpointratherthanatitsboilingpoint,soitdoesnotevaporateandproduceaninsulatinggaslayer.Rapidcoolingtrapsthebiologicalmoleculesintheirnative,hydratedstateembeddedinglass-like,solidwater,vitrifiedice,andpreventstheformationoficecrystals,whichwouldbeverydamagingtothespecimen.TherearetwotremendousadvantagesofcryoEM:thesample,whichiskeptaroundC,nearliquidnitrogentemperature(C),istrappedinanative-like,hydratedstateinthehighvacuumofthemicroscopecolumn,andthelowtemperaturegreatlyslowstheeffectsofelectronbeamdamage.AnimportantconsiderationincryoEMsamplepreparationisthetypeofsupportlm.Somesamplesadheretothecarbonsupportlm,butcontinuouscarbonlmscontributeadditionalbackgroundscatteringandreducetheimagecontrast.Therefore,perforatedlmsareoftenused,inwhichthesampleisimagedinregionsoficesuspendedoverholesinthesupportlm.Home-madeholeylmsprovidearandomdistributionofholes.Nanofabricatedgrids(e.g.,Quantifoilgrids,QuantifoilMicroToolsGmbH;C-atgrids,Protochips,Inc.)withregularlyarrangedholesareusedforautomatedandmanualdatacollec-tion.Asignicantlyhighersampleconcentrationisusuallyneededforgoodparticledistributioninholes.Theicethicknessisextremelycriticalforachievinggoodcontrastwhilepreservingtheintegrityofthestructure.Ittakessomeexperiencetoadjusttheblottingsothattheiceisanoptimalthicknessforeachsample.Thegeneralruleistohavetheiceasthinaspossiblewithoutsquashingthemoleculesofinterest.Inadditiontothermalstability,amajorissueissampleconductance;iceunsupportedbycarbonlmisaninsulator,andchargingeectscausedbytheelectronbeamcanseriouslydegradetheimage,especiallyathightilt.Thisproblemislessenedbyincludinganadjacentcarbonlayerintheilluminatedarea.Newsupportmaterialswithhigherconductivitythancarbonarebeinginvestigated.Thesingle-particleapproachcanbeappliedtopreparationsofisolatedobjectssuchasparticlesinaqueoussolutionormem-branecomplexesindetergentsolution.EMisexperimentallymoredicultindetergent,whichmaygiveextrabackgroundandchangethepropertiesoftheice.Membranecomplexescanalsobeimagedinlipidvesicles,inavariantofsingle-particleanalysisinwhichtheparticleimagesareexcisedfromlargerassemblies.Thereisalowersizelimitforsingle-particleanalysis,becausetheobjectmustgenerateenoughcontrasttobedetectedandforitsorientationtobedetermined.Single-particlecryo-EMbecomesverydicultwhentheparticleislessthanafewhundredkDainmass.Thesizelimitisaectedbytheshapeoftheparticle;anextendedstructurewithdistinctprojectionsinerentdirectionswillbemucheasiertoalignthanacompactsphericalparticleofsimilarmass.Forsmallparticles,negativestainEMisused.Ahybridapproachtosamplepreparation,cryo-negativestaining,hasbeendeveloped.Thesampleisembeddedinstainsolutionandthenvitried,afterpartialdrying.ThismethodallowssmallercomplexestobestudiedbycryoEM,buthasthedisadvantagethatthesampleisinahighconcentra-tionofheavymetalsalt,farfromphysiologicalconditions.2.1.3.StabilizationofDynamicAssemblies.Asmolecularbiologymovestowardstudiesofmorecomplexsystems,thefocusofinteresthasmovedtowardmorebiochemicallyhetero-geneoussamples.Althoughtherearecomputationalmethodsforsortingparticleswithstructuralvariations(section9),thesuccessoftheexperimentdependscriticallyonthequalityofthebio-chemicalpreparation.Oneapproachfordealingwithunstable,heterogeneousassembliesistouseproteincross-linkerssuchasglutaraldehydetostabilizecomplexesduringdensitygradientseparation,aproceduretermedGraFix.PromisingresultshavebeenobtainedwithverydifficultsamplessuchascomplexesinRNAediting,butitshouldbenotedthatcross-linkersmayalsointroduceartifactsinflexibleassemblies.2.1.4.EMPreparationofCellsandTissues.2.1.4.1.HighPressureFreezing.MostcellularstructuresaretoothickforTEMimaging,andsamplesarepreparedasthinsections.Standardchemicalfixationhasprovidedtheclassicalviewofcellstructure,inwhichthesampleiscross-linkedwithfixativesandthendehydratedandembeddedinplasticresinsothatitcanbereadilysectionedforEMexamination.Plastic-embeddedsec-tionsarecontrastedwithheavymetalstaining.Althoughthistreatmentcanleadtoextensiverearrangementandextractionofcellandtissuecontents,thegreatmajorityofcellstructureinformationattheEMlevelhasbeenderivedfromsuchmaterial.High-pressurefreezinghasmadeitpossibletoavoidchemicalxationsothatcellandtissuesectionscanbeimagedinthevitreousstate.Tovitrifyspecimensthickerthanafewmicrometers,itisnecessarytodotherapidfreezingathighpressures,around2000bar,becausethefreezingrateinthickersamplesatambientpressureisnothighenoughtopreventicecrystalgrowth.Instrumentsforhigh-pressurefreezing(HPF)wererstdevelopedinthe1960sandarewidelyusedincellpreparation,incombinationwithfreeze-substitution(seesection2.1.4.2).Thespecimenisintroducedintoapressurechamberatroomtemperatureandrapidlypressurized,withcoolingprovidedbyliquidNowthroughthemetalsampleholder.Samplessuchasyeastorbacterialcellsin100mthickpelletsorpastescanreadilybevitriedbyHPF.Sampleswithhigherwatercontent,suchasembryonicorbraintissue,aremorediculttovitrifyinthismanner,becausewaterisapoorthermalconductor,andthinnertissueslices(m)mustbeused.Forthesamereason,aqueousmediasurroundingthesamplemustbesupple-mentedbyantifreezeagentssuchas1-hexadeceneor20%dextranbeforevitricationbyHPF.2.1.4.2.Freeze-Substitution.Freeze-substitution(FS)elim-inatessomeoftheartifactsofchemicalfixationanddehydrationandprovidesgreatlyimprovedstructuralpreservation,whileretainingtheeaseofworkingwithplasticsectionsandroomtemperaturemicroscopy.Thesampleisinitiallyvitrifiedasforcryo-sectioning,butthengraduallywarmedforsubstitutionofthewaterwithacetone,followedbystainingandresinembedding90toC(see,forexample,ref42).SomeresinscanbepolymerizedbyUVilluminationatlowtemperature,sothatallprocessingiscompletedatlowtemperature.Withthistreat-ment,cytoplasmiccontentssuchasribosomesareretainedandrearrangementofcellstructuresisreduced(Figure2a).However,smallicecrystalsformduringFSprocessing,andstainingisnotuniform,sothattheresultsarenotreliableonthemolecularscale. underhighvacuumtoavoidunwantedscatteringbygasmole-culesintheelectronpath.Consequently,theEMspecimenmustbeinthesolidstateforimaging,andspecialpreparationtechniquesarenecessarytoeitherdehydrateorstabilizehydratedbiologicalsamplesundervacuum.2.1.1.NegativeStainingofIsolatedAssemblies.simplestmethodforexaminingasolutionorsuspensionofisolatedparticlessuchasvirusesorothermacromoleculesisnegativestaining,inwhichadropletofthesuspensionisspreadonanEMsupportfilmandthenembeddedinaheavymetalsaltsolution,typicallyuranylacetate,blottedtoathinfilmandallowedtodry(Figure1a).Althoughuranylacetateisthemostwidelyusedstainandgivesthehighestcontrast,somestructuresarebetterpreservedinotherstainssuchastungstenormolybdenumsalts.Theheavymetalstainisdepositedasadensecoatoutliningthesurfacesofthebiologicalassembly,givinginformationaboutthesize,shape,andsymmetryoftheparticle,aswellasanoverviewofthehomogeneityofthepreparation.Themethodiscallednegativestainingbecausethemacromolecularshapeisseenbyexclusionratherthanbindingofstain.Themethodisquickandsimple,althoughnotfoolproof.Somemoleculesarewellpreservedinnegativestain,butfragileassembliescancollapseordisintegrateduringstaininganddrying.Ingeneral,the3Dstructurebecomesflattenedtoagreaterorlesserdegree,andthestainmaynotcovertheentiremolecule,sothatpartsofthestructuremaybedistortedorabsentfromtheimagedata.Therefore,itisnormallypreferabletousecryo-methodsfor3Dstructuredetermination.Theexceptionisforsmallstructures,below200kDa,forwhichthesignalincryo-EMmaybetooweakforaccuratedetectionandorienta-tiondetermination.Forsuchstructures,3Dreconstructionisdonefromnegativestainimagesandcanprovidemuchusefulinformation.2.1.2.CryoEMofIsolatedandSubcellularAssemblies.Macromoleculesandcellsarenormallyinaqueoussolution,andhydrationisnecessaryfortheirstructuralintegrity.CryoEMmakesitpossibletostabilizesamplesinthenative,hydratedstate,evenunderhighvacuum.ThemaintechnicaleffortofcryoEMistokeepthespecimencoldandfreeofsurfacecontaminationinanotherwisewarmmicroscopewhileretainingmechanicaland Figure1.NegativestainandcryoEMsamplepreparation.(a)Schematicviewofsampledeposition,staining,anddrying,withanexamplenegativestainimage.(b)Schematicofplungefreezingandofavitriedlayer,andanexamplecryoEMimage.Panel(b)isadaptedwithpermissionfromref24.Copyright2000InternationalUnionofCrystallography. 10.2.AtomicStructureFitting774410.3.BiologicalImplications7744AuthorInformation7744Biographies7744Acknowledgment7745References77451.INTRODUCTION1.1.LightandElectronMicroscopyandTheirImpactinTofullyunderstandbiologicalprocessesfromthemetabolismofabacteriumtotheoperationofahumanbrain,itisnecessarytoknowthethree-dimensional(3D)spatialarrangementanddynamicsoftheconstituentmolecules,howtheyassembleintocomplexmolecularmachines,andhowtheyformfunctionalorganelles,cells,andtissues.ThemethodsofX-raycrystal-lographyandNMRspectroscopycanprovidedetailedinforma-tiononmolecularstructureanddynamics.Atthecellularlevel,opticalmicroscopyrevealsthespatialdistributionanddynamicsofmoleculestaggedwithuorophores.Electronmicroscopy(EM)overlapswiththeseapproaches,coveringabroadrangefromatomictocellularstructures.ThedevelopmentofcryogenicmethodshasenabledEMimagingtoprovidesnapshotsofbiologicalmoleculesandcellstrappedinaclosetonative,hydratedstate.1,2BecauseoftheimportanceofmacromolecularassembliesinthemachineryoflivingcellsandprogressintheEMandimageprocessingmethods,EMhasbecomeamajortoolforstructuralbiologyoverthemoleculartocellularsizerange.Therehavebeentremendousadvancesinunderstandingthe3Dspatialorganiza-tionofmacromoleculesandtheirassembliesincellsandtissues,duetodevelopmentsinbothopticalandelectronmicroscopy.Inlightmicroscopy,super-resolutionandsinglemoleculemethodshavepushedtheresolutionofuorescenceimagesto50nm,usingthepowerofmolecularbiologytofusemoleculesofinterestwithuorescentmarkerproteins.X-raycryo-tomogra-phyisdevelopingasamethodfor3Dreconstructionofthickerm)hydratedsamples,withresolutionreachingthe15nmresolutionrange.InEM,majordevelopmentsininstrumenta-tionandmethodshaveadvancedthestudyofsingleparticles(isolatedmacromolecularcomplexes)invitriedsolutionaswellasin3Dreconstructionbytomographyofirregularobjectssuchascellsorsubcellularstructures.Cryo-sectioningcanbeusedtopreparevitriedsectionsofcellsandtissuesthatwouldotherwisebetoothicktoimagebytransmissionEM(TEM).Inparallel,softwareimprovementshavefacilitated3Dstruc-turedeterminationfromthelowcontrast,lowsignal-to-noiseratio(SNR)imagesofprojecteddensitiesprovidedbyTEMofbiologicalmolecules.Alignmentandclassicationofimagesinboth2Dand3DarekeymethodsforimprovingSNRanddetectionandsortingofheterogeneityinEMdatasets.resolutionofsingle-particlereconstructionsissteadilyimprovingandhasgonebeyond4Åforsomeicosahedralvirusesand5.5Åforasymmetriccomplexessuchasribosomes,givingaclearviewofproteinsecondarystructureelementsand,inthebestcases,resolvingtheproteinornucleicacidfold.1.2.EMofMacromolecularAssemblies,IsolatedandinSituAvarietyofmolecularassembliesofdierentshapes,sizes,andbiochemicalstatescanbestudiedbyTEM,providedthesamplethicknessiswellbelow1000nm.Thereisarangeofsampletypesedbytwoextremecases:biochemicallypuried,isolatedcomplexes(singleparticlesororderedassembliessuchas2Dcrystals)andunique,individualobjectssuchastissuesections,cells,ororganelles.FrompreparationsofisolatedcomplexeswithmanyidenticalsingleparticlespresentonanEMgrid,manyviewsofthesamemoleculecanbeobtained,sothattheir3Dstructurecanbecalculated.Near-atomicresolutionmapswererstobtainedfromsamplesinorderedarrayssuchas2Dcrystalsandhelices.Membraneproteinscanbeinducedtoform2Dcrystalsinlipidbilayers,althoughexamplesofhighlyorderedcrystalsleadingtohigh-resolution3Dstructuresarestillrare.Ifmembrane-boundcomplexesarelargeenough,theycanalsobepreparedassingleparticlesusingdetergentsorinliposomes.Ingeneral,thesingle-particleapproachiswidelyapplicableandhascaughtupwiththecrystallographicone.Thisapproachisapplicabletohomogeneouspreparationsofsingleparticleswithanysymmetryandmolecularmassesintherangeof0.5100MDa(e.g.,viruses,ribosomes)andcanrevealnedetailsofthe3Dstructure.Thestudyofsingleparticlesbycryo-EMinthe0.10.5MDasizerangestillneedsgreatcaretoavoidproducingfalsebutself-consistentdensitymaps.Inaddition,thesingle-particleapproachcanbeusedtocorrectforlocaldisorderinorderedarrays,improvingtheyieldofstructuralinformation.Regardingthequalityofthisstructuralinformation,theresolutionofcryo-EMissteadilyimproving,andcomparisonsofcryo-EMresultswithX-raycrystallographyorNMRofthesamemoleculesindicatethatcryo-EMoftenprovidesfaithfulsnapshotsofthenativestructureinsolution.Adetailedaccountofthebasicprinciplesofimaginganddiractioncanbefoundinref19.Forcells,organelles,andtissuesections,electrontomographyprovidesawealthof3Dinformation,andmethodsforharvestingthisinformationareinanactivestateofdevelopment.Auto-matedtomographicdatacollectioniswellestablishedonmodernmicroscopes.Amajorfactorlimitingresolutionincryo-electrontomographyisradiationdamageofthespecimenbytheelectronbeamduringacquisitionofatiltseries.Attheforefrontofthiseldareeortstooptimizecontrastatlowelectrondose,inordertolocateandcharacterizemacromolecularcomplexeswithintomogramsofcellsandtissues.Atpresent,complexesmustbewellover1MDatobeclearlyidentiableinanEMtomographicreconstruction.Examplesofimportantbiologicalstructureschar-acterizedbyelectrontomographyincludethenuclearporecomplexandtheagellaraxoneme.Forthicker,cellularsamples,X-raymicroscopy(tomography)providesinformationinthe15100nmresolutionrange,bridgingEMtomographyuorescencemethods.Theabovedevelopmentshaveledtoaourishingeldenablingmultiscaleimagingtolinkatomicstructuretocellularfunctionanddynamics.InthisReview,weaimtocoverthetheoreticalbackgroundandtechnicaladvancesininstrumentation,software,andexperimentalmethodsunderlyingthemajordevelopmentsin3DstructuredeterminationofmacromolecularassembliesbyEMandtoreviewthecurrentstateoftheartinthe2.EMIMAGING2.1.SamplePreparationElectronimagingisapowerfultechniqueforvisualizing3Dstructuraldetails.However,becauseelectronsinteractstronglywithmatter,theelectronpathofthemicroscopemustbekept StructuralAnalysisofMacromolecularAssembliesbyElectronMicroscopyE.V.Orlova*andH.R.Saibil*CrystallographyandInstituteofStructuralandMolecularBiology,BirkbeckCollege,MaletStreet,LondonWC1E7HX,UnitedKingdom1.Introduction77111.1.LightandElectronMicroscopyandTheirImpactinBiology1.2.EMofMacromolecularAssemblies,IsolatedandinSitu2.EMImaging77112.1.SamplePreparation77112.1.1.NegativeStainingofIsolated2.1.2.CryoEMofIsolatedandSubcellular2.1.3.StabilizationofDynamicAssemblies77132.1.4.EMPreparationofCellsandTissues77132.2.InteractionofElectronswiththeSpecimen77142.3.ImageFormation77152.3.1.ElectronSources77152.3.2.TheElectronMicroscopeLensSystem77162.3.3.ElectronMicroscopeAberrations77162.4.ContrastTransfer77162.4.1.FormationofProjectionImages77172.4.2.ContrastforThinSamples77172.5.PhasePlatesandEnergyFilters77193.ImageRecordingandPreprocessing77203.1.ElectronDetectors77203.1.1.PhotographicFilm77203.1.2.DigitizationofFilms77203.1.3.DigitalDetectors77213.2.Computer-ControlledDataCollectionandParticlePicking3.3.TomographicDataCollection77223.4.PreprocessingofSingle-ParticleImages77223.4.1.DeterminationoftheCTF77233.4.2.CTFCorrection77233.4.3.ImageNormalization77244.ImageAlignment77244.1.TheCross-CorrelationFunction77254.2.AlignmentPrinciplesandStrategies77254.2.1.MaximumLikelihoodMethods77274.3.TemplateMatchingin2Dand3D77274.4.AlignmentinTomography77274.4.1.AlignmentwithandwithoutFiducial4.4.2.AlignmentofSubregionsExtractedfrom5.StatisticalAnalysisofImages77285.1.PrincipalComponentAnalysis77285.2.HierarchicalClustering77295.3.K-MeansClusteringandtheMaximumLikeli-hoodMethod6.OrientationDetermination77296.1.RandomConicalTilt77296.2.AngleAssignmentbyCommonLinesinReci-procalSpace6.3.CommonLinesinRealSpace77326.4.ProjectionMatching77326.5.MolecularReplacement77327.3DReconstruction77337.1.Real-SpaceMethods77337.1.1.BackProjection77337.1.2.FilteredBack-ProjectionorConvolution7.1.3.AlgebraicMethods77347.2.FourierMethods77367.2.1.FourierInversion77367.2.2.FourierBesselReconstruction77367.3.DistributionofProjections77377.4.ElectronCrystallography77377.5.TomographicReconstruction77388.EvaluationofReconstructionQualityandReliability77398.1.CausesofResolutionLoss77398.2.ResolutionMeasures77398.3.TemperatureFactorandAmplitudeScaling9.Heterogeneityin2Dand3D77419.1.SourcesofHeterogeneity77419.2.MethodsforComputationalSortingofMixed10.MapInterpretation774310.1.AnalysisofMapFeatures7743 October21,2010