An Accelerated ISAF Algorithm with the Fast Mapping Strategy

Transcription

1 528 JOURNAL OF COMPUTERS, VOL. 7, NO. 2, FEBRUARY 202 An Acceleraed ISAF Algorihm wih he Fas Mapping Sraegy Gongming Wang Insiue of Compuing Technology, Chinese Academy of Sciences, Beijing, China Graduae Universiy of Chinese Academy of Sciences, Beijing, China Fa Zhang (Corresponding auhor) Insiue of Compuing Technology, Chinese Academy of Sciences, Beijing, China Fei Sun Insiue of Biophysics, Chinese Academy of Science, Beijing, China, Zhiyong Liu (Corresponding auhor) Insiue of Compuing Technology, Chinese Academy of Sciences, Beijing, China Absrac ISAF (icosahedral symmery-adaped funcions) is a new approach used for 3D reconsrucion of icosahedral macromolecules, which can achieve beer resoluions compared wih he commonly used Fourier-Bessel algorihm. However, ISAF is significanly slow. Among all reasons, he operaion ha roaing each image sixy imes coss los of running ime. By analyzing he sixy symmerical characerisics of icosahedrons in Fourier space, we proved ha he posiions of sixy mapped poins derived from one sampling poin are all he same in asymmeric uni. Thus, he sixy symmerical roaing of each image can be removed and he reconsrucion speed is increased. This acceleraing sraegy was validaed by means of experimens wih simulaed daa and experimenal Cryo-EM daa. The resuls showed ha he speedup of his sraegy was up o 4 imes and i could grow up wih he increase of he maximum Fourier radius and he number of images a he premise of mainenance of accuracy. Is running speed is abou 9 imes as grea as ha of Fourier-Bessel algorihm and is abou 3 imes han ha of recisafs algorihm. Index Terms 3D reconsrucion, mapping, asymmeric uni, ISAF, speedup I. INTRODUCTION Crowher and Klug e.al proposed he heories of 3D reconsrucion for proein molecules based on EM (elecron microscopy) images in lae 9s []. Afer abou 50 years developmen, he EM reconsrucion mehods have formed hree main kinds: elecron crysallography, elecron omography, single paricle echnology. Currenly, single paricle echnology based Cryo-EM (cryo-elecron microscopy) has played an increasingly imporan role for deermining srucures of frozen and non-crysalline sae macromolecules [2,3]. Among all kinds of molecules, he icosahedral molecule has been widely sudied [4]. The icosahedral single paricle reconsrucion mehods are divided ino wo kinds [5]. One is called direc Fourier inversion mehod which is he mos compuaionally efficien, bu may have large memory requiremen and is generally more sensiive o noise. The oher is called he synhesis mehod which is less sensiive o image noise and has less memory requiremen, bu less compuaionally efficien. Two represenaives of synhesis mehod are he Fourier-Bessel algorihm [] and he ISAF algorihm [6, 7]. The difference beween hem is he basis funcion and inerpolaion coordinae sysem. The Fourier-Bessel algorihm uses he cylindrical coordinae sysem and exponenial funcion, while he ISAF algorihm uses spherical coordinae sysem and symmery-adaped funcions. Because icosahedral molecules have sixy symmerical characerisics in Fourier space [,5, 6], one FFT image is roaed sixy imes o ge he sixy equivalen FFT images in ISAF algorihm. Subsequenly, he sampling poins in he sixy FFT images mus be mapped ono he asymmeric uni. The purpose of his roaing operaion is increasing SNR (Signal o Noise Raio). Then he resoluion of reconsruced map is improved [6]. However, since he number of processed images has o be increased sixy imes, significanly more compuing resources are required. Some previous sudies have shown an exponenial relaionship beween he number of Cryo-EM images and he resoluion [9,0]. Therefore, roaing each image sixy imes would become a bole-neck in 3D reconsrucion. So, i is very imporan o reduce he complexiy from his roaing operaion. For ISAF algorihm, he sixy equivalen poins generaed from sixy symmery operaions mus be doi:0.4304/jcp

2 JOURNAL OF COMPUTERS, VOL. 7, NO. 2, FEBRUARY mapped ono asymmeric uni in Fourier space. Wih he help of sixy symmerical characerisics of icosahedral molecules in Fourier space, we proved ha he posiions of sixy mapped poins in asymmeric uni are all he same. Tha is o say, afer roaing sixy imes, he srucure informaion in asymmeric uni is similar o ha wihou roaing sixy imes. Thus, his complex roaing operaion can be removed a he premise of mainenance of accuracy. The acceleraed ISAF algorihm is proposed according o his poin. Wih his mehod, he speed of mapping sampling poins ono asymmeric uni can be improved imes. The speed of he whole 3D reconsrucion could be enhanced o a cerain exen. To verify his poin, he experimens were carried ou wih simulaed daa and experimenal Cryo-EM daa. The Fourier-Bessel algorihm and recisafs [6] algorihm were used for comparison wih our acceleraed ISAF algorihm. The experimenal resuls show ha he reconsruced map wihou roaing sixy imes is idenical wih he one wih roaing sixy imes. The speedup in he sage of mapping molecular images is imes and he whole speedup is up o 4 imes. Is running speed is abou 9 imes as grea as ha of Fourier-Bessel algorihm and is abou 3 imes han ha of recisafs algorihm.. In addiion, he speedup of his mehod is increasing wih he increase of he maximum Fourier radius and he number of images. This mehod can also be exended for 3D reconsrucion of oher polyhedral molecules. II. METHODS The processing seps of synhesis mehod include hree sages: mapping molecular images, solving fiing coefficiens and calculaing densiy funcion. The main operaion in mapping molecular images is roaing each FFT images sixy imes and hen mapping sampling poins in he sixy FFT images ono asymmeric uni. I is known ha his operaion seriously affec he speed of ISAF algorihm. If he roaing operaion is simplified, he speed of ISAF algorihm can be acceleraed significanly. In his secion, his acceleraed ISAF algorihm and is mahemaical proof are proposed. A. Uniqueness Mapping Analysis In he course of 3D reconsrucion based on synhesis algorihm, he above roaing operaion is common used boh in he cylindrical coordinae and in he spherical coordinae sysems. The purpose of his operaion is enhancing SNR by averaging a number of images [,6]. However, wih he help of heories of crysal symmery group, i is found ha his operaion is redundan in spherical coordinae sysem as follows. In real space, icosahedral molecule has 5-2 symmerical characerisics in he cylindrical coordinae sysem and has symmerical characerisics in he spherical coordinae sysem. In Fourier space, icosahedral molecule has he idenical symmerical characerisics in he cylindrical coordinae and in he spherical coordinae sysems because Fourier ransform has he roaional invariance. In he cylindrical coordinae sysem, he sixy symmerical poins ( Ri, Φ i,zi )( i ) are mapped ono he 5-2 symmerical uni {( R, Φ,Z )( R > 0,0 Φ 72) }. The posiions of hem in 5-2 symmerical uni are differen according o he difference beween symmerical characerisics and he 5-2 symmerical characerisics of icosahedral molecule. Thus, he SNR is enhanced because he srucure informaion in 5-2 symmerical uni increases sixy imes. On he conrary, for one sampling poin in spherical coordinae sysem, i is found ha he posiions of he sixy mapped poins are all he same in he symmerical uni (commonly referred o as 'asymmeric uni') {( R, Θ, Φ )( R 0,69.09 Θ 90, 3.72 Φ 3.72) }. The brief analysis is as follows. The spherical surface whose radius is R can be divided ino idenical regions U i ( i ). The area of each region is he same as he area of he asymmerical riangle: U = {( R, Θ, Φ )( R 0,69.09 Θ 90, 3.72 Φ 3.72) } Here, U is one of he sixy regions and is denoed as U. The poin from one region can be mapped ono anoher and he number of mapped poins in he corresponding region is only one. A = ( R,Θ,Φ ) denoes one poin in he region U i. Is 59 symmerical poins A2,A3 A is disribued o he res of he 59 regions and one poin belongs o one region. A k denoes he symmerical poins of A in region U. According o he sixy symmerical characerisics, he sixy symmerical poins A,A2 A can be all mapped ono he region. U. From he uniqueness mapping propery, i is found ha he mapped poins are all A k. Tha is o say, he posiions of mapped poins are all he same. B. The Acceleraing Sraegy Based on Uniqueness Mapping As describe above, all posiions of he sixy mapped poins are idenical in he asymmeric uni. Therefore, he equivalen poin of he sixy mapped poins by averaging is equal o one of hem. So, he SNR has no increased as shown in (). P F i i i= i= P = = Pi F = = Fi ( i ) () The formula equaion () is used for calculaing he equivalen posiion () and srucure facor value ( F ) of he sixy mapped poins in asymmerical uni. In his formula, P i ( i ) and F i ( i ) denoe posiions and srucure facor values of he sixy mapped poins respecively. All F i ( i ) are all he same because he sixy poins derive from he same sampling poin in he original image. Similarly, all

3 530 JOURNAL OF COMPUTERS, VOL. 7, NO. 2, FEBRUARY 202 P i ( i ) are he same due o he proof of above secion. Under his condiion, formula is hold. The posiions and srucure facor values of mapped poins are used for consrucing fiing coefficiens equaion se. From he above saemen, i is known ha geing rid of his operaion has no effec on consrucing fiing coefficiens equaion se. Thus, wheher carrying ou he sixy symmerical operaions or no has no effec on he following sep. Besides, removing his redundan operaion can speed up he compuaion process. For he purpose of expression briefly, he ISAF algorihm wih sixy symmerical operaions is called original ISAF algorihm and he one wihou sixy symmerical operaions is called acceleraed ISAF algorihm for shor. III. RESULTS The heorem of uniqueness mapping is proved and he acceleraed ISAF algorihm is proposed in he previous secion. In his secion, he 3D reconsrucion experimens are carried ou wih simulaed daa and experimenal Cryo-EM daa, respecively. The goal is o validae acceleraed ISAF algorihm. The recisafs algorihm proposed by Hongrong liu [6] is seleced for comparison because i can achieve he resoluion of 3.88 Å [8]. The Fourier-Bessel algorihm is seleced for comparison also. The experimenal resuls are analyzed in erms of accuracy and speed. Besides, he Fourier-Bessel algorihm is compared wih our new algorihm o demonsrae he advanages of 3D reconsrucion for icosahedral molecular in spherical coordinae sysem. The following experimens are all implemened on one PC whose CPU is AMD Dual-Core 2.6G Hz, wih DDR 2G.Bye memory. A. The reconsrucion experimen wih simulaed daa (a) (b) Figure. Simulaed projecion images of he melon necroic spo virus. (a) Wihou noise. (b) wih an SNR of 0.. The simulaed daa are he projecions of he map generaed from he melon necroic spo virus srucure (PDB ID 2ZAH), which is solved by X-ray crysallography o 2.8 Å [] and has icosahedral symmerical characerisics. Firsly, his model was generaed a a resoluion of 4 angsrom by using pdb2mrc [2] from EMAN's procedure library. The key parameers were apix=.4 and res=4. The size of model is pixels. Secondly, 2000 projecions wih random orienaions were generaed by using prjecicosfile [3] from he EMAN's package. Finally, he random noise whose SNR was equal o 0. is added o each of he projecions. The images wih and wihou noises were shown in Fig. respecively. In he following experimens, original ISAF algorihm, acceleraed ISAF algorihm, Fourier-Bessel algorihm and recisafs algorihm were all esed. The maximum Fourier radius was /33.6Å -,/8.48Å -,/9.24Å - and /4.2Å -, respecively. For he purpose of comparison, he Fourier ransform was applied o he original srucure of melon necroic spo virus. Afer ha, he Fourier coefficiens were disposed if he corresponding Fourier radius was greaer han /33.6Å -,/8.48Å -,/9.24Å - and /4.2Å -, respecively. Finally, he Fourier inverse ransform was performed on he runcaed Fourier coefficiens. Thus, he original maps a a resoluion of 33.6Å, 8.48Å, 9.24Å and 4.2Å were generaed. (a) (b) (c) (d) Figure 2. The reconsruced maps a differen maximum Fourier radiuses. From lef o righ, he firs column is he original map. The oher columns are he reconsruced maps wih original ISAF algorihm, acceleraed ISAF algorihm, Fourier-Bessel algorihm and recisafs algorihm respecively. From op o boom, he corresponding maximum Fourier radiuses are /33.6Å -,/8.48Å -, /9.24Å - and /4.2Å - Fig. 2 show he comparison of reconsruced maps by he original ISAF algorihm (he second column), he acceleraed ISAF algorihm (he hird column), he Fourier-Bessel algorihm (he fourh column) and he recisafs algorihm (he las column), and he maximum Fourier radius used in esing equals o /33.6Å -,/8.48Å -,/9.24Å - and /4.2Å -, respecively. From his picure, i is found ha he reconsrucion resuls wih and wihou sixy symmerical operaions are boh he same. I can be seen clearly now ha he accuracy of reconsrucion in spherical coordinae sysem is beer han ha of reconsrucion in he cylindrical coordinae sysem.

4 JOURNAL OF COMPUTERS, VOL. 7, NO. 2, FEBRUARY FSC Original ISAF algorihm Acceleraed ISAF algorihm Fourier-Bessel algorihm recisafs algorihm Spaial Frequency(/angsrom) Figure 3. The FSC curves of he reconsruced maps wih four mehods a he maximum Fourier radius of /4.2Å - The FSC (Fourier Shell Correlaion) [4] curves a he maximum Fourier radius of /4.2Å - were used for calculaing he resoluion of maps generaed using original ISAF algorihm, acceleraed ISAF algorihm, Fourier-Bessel algorihm and recisafs algorihm, which are shown in Fig. 3. The FSC curves using original ISAF algorihm and acceleraed ISAF algorihm are coinciden wih each oher and hey are drop o 0.5 a /4.23Å -.The FSC curve using Fourier-Bessel algorihm is below hem and i drops o 0.5 a /4.66Å -. The FSC curve using recisafs algorihm is beween hem and i drops o 0.5 a /4.28Å -. I indicaes ha he effecive resoluion using original ISAF algorihm and acceleraed ISAF algorihm are boh 4.23Å, he one using Fourier-Bessel algorihm is 4.66Å and he one using recisafs algorihm is 4.28Å. In ligh of his, he maps generaed using original ISAF algorihm and acceleraed ISAF algorihm are idenical, which are beer han ha using Fourier-Bessel algorihm and recisafs algorihm. Equaion (2) is used for compuing he speedup of our acceleraion sraegy. In his formula, i cos is he ime spen calculaing he srucure facors wih roaing sixy imes and noni cos is he ime spen on anyhing else (e.g. reading and wriing images). icos + nonicos A = (2) icos / + nonicos The reconsrucion speedups wih differen number of projecions a he maximum Fourier radius of /4.2Å - are shown in Tab.. The reconsrucion speedups wih 2000 projecions a he differen maximum Fourier radius are shown in Tab. 2. In Tab. and Tab. 2, he meanings of he column iems are as follows: No is he number of projecions, i cos, nonicos and A are he meanings in equaion (2), A, F and R are he running imes wih acceleraed ISAF algorihm, Fourier-Bessel algorihm, recisafs algorihm respecively. The uni in Tab. and Tab. 2 is second. From he wo ables, i is found ha he speedup of acceleraed ISAF algorihm is increasing wih he increase of he maximum Fourier radius and he number of projecions. Under he circumsance of high resoluion (less han 0Å), he speedup is ofen over 20 imes and up o 26 imes. Is running speed is 6 imes as fas as Fourier-Bessel algorihm and is abou 2.5 imes han ha of recisafs algorihm. TABLE THE SPEEDUP WITH DIFFERENT NUMBERS OF PROJECTIONS AT THE MAXIMUM FOURIER RADIUS OF /4.2Å - No. i cos noni cos A A F TABLE 2 THE SPEEDUP AT THE DIFFERENT MAXIMUM FOURIER RADIUS WITH 2000 PROJECTIONS Res i cos noni cos A A F R /33.6Å /8.48Å /9.24Å /4..2Å B. The reconsrucion experimen wih experimenal Cryo-EM daa In his secion, he experimenal daa are he Cryo-EM images of HBV (Human Hepaiis B Virus) from R.A.Crowher, which are consis of 4588 HBV paricles recorded on elecron micrographs. The riangulaion is T=4 and he diameer is abou 3Å. Fig.4 shows 2 images a he differen defocus. The imaging parameers are as follows: he size of each paricle is pixels, he sep of sampling is 2.5Å/pixel, he ype of elecron microscopy is FEI F30, he speed volage is 300kV, he spherical-aberraion coefficien is 2mm, he defocus is beween.3µm and 2.4µm. These parameers are used for CTF correcion [5]. Figure 4. 2 CryoEM images of HBV a differen defocus. Like he previous secion, he 3D reconsrucion experimens are carried ou by using four algorihms (he original ISAF algorihm, he acceleraed ISAF algorihm, he Fourier-Bessel algorihm and he recisafs algorihm) a he differen maximum Fourier radius (/30.36Å -, /2.25Å -, /2.5Å -, and /7.5Å - ). The experimenal resuls are shown in Fig. 5. I is found ha he reconsruced maps wih and wihou sixy symmerical operaions are boh idenical and are beer han ha using Fourier-Bessel algorihm and recisafs algorihm. R

5 532 JOURNAL OF COMPUTERS, VOL. 7, NO. 2, FEBRUARY 202 (a) (b) (c) (d) Figure 5. The reconsruced maps a differen maximum Fourier radiuses. From lef o righ, hey are he reconsruced maps wih original ISAF algorihm, acceleraed ISAF algorihm, Fourier-Bessel algorihm, and recisafs algorihm respecively. From above o below, he corresponding maximum Fourier radiuses are /30.36Å -, /2.25Å -, /2.5Å -, /7.5Å -. FSC original ISAF algorihm acceleraed ISAF algorihm Fourier-Bessel algorihm recisafs algorihm Spaial Frequency(/angsrom) Figure 6. The FSC curves of he reconsruced maps wih four mehods a he maximum Fourier radius of /7.5Å - TABLE 3 THE SPEEDUP WITH DIFFERENT NUMBERS OF CRYO-EM IMAGES AT THE MAXIMUM FOURIER RADIUS OF /7.5Å - No. i cos noni cos A A F R The FSC curves of maps generaed from hese algorihms are shown in Fig. 6 a he maximum Fourier radius of /7.5Å -. The effecive resoluion using original ISAF algorihm and acceleraed ISAF algorihm are boh 7.97Å, he one using Fourier-Bessel algorihm is 8.38Å, and he one using recisafs algorihm is 8.27Å. So, removing roaion sixy imes has no influence on reconsrucion and he reconsrucion algorihm in he spherical coordinae sysem is beer han ha in he cylindrical coordinae sysem. Like he previous secion, he equaion (2) is used for compuing he speedups of his acceleraing sraegy. The compuing resuls are shown in Tab. 3 and Tab. 4. Tab. 3 illusraes he speedups wih differen number of projecions a he maximum Fourier radius of /7.5Å -. Tab. 4 shows speedups wih 4588 projecions a he differen maximum Fourier radius. The meanings of column iems in Tab. 3 and Tab. 4 are equivalen o ha in in Tab. and Tab. 2. The uni in Tab. 3 and Tab. 4 is second. From Tab. 3 and Tab. 4, i is found ha he speedup is increasing wih he increase of he maximum Fourier radius and he number of images. Under he circumsance of high resoluion, he speedup is ofen over 35 imes and up o 4 imes. Is running speed is abou 9 imes as grea as ha of Fourier-Bessel algorihm and is abou 3 imes han ha of recisafs algorihm. In summary, removing sixy symmerical operaions of 3D reconsrucion of icosahedral molecule in spherical coordinae sysem has no effec on accuracy. Thus removing his sep can enhance he speed of reconsrucion grealy. In addiion, his acceleraed ISAF algorihm is beer han he Fourier-Bessel algorihm in erms of boh speed and accuracy. TABLE 4 THE SPEEDUP AT THE DIFFERENT MAXIMUM FOURIER RADIUS WITH 4588 CRYO-EM IMAGES Res i cos noni cos A A F R /30.36Å /2.25Å /2.5Å /7.5Å IV. CONCLUSIONS In he field of 3D reconsrucion of proein srucures, he ISAF algorihm can achieve beer resoluions bu wih a low running speed. The sudy had revealed roaing each image sixy imes is a mos ime-consuming operaion among all operaions. Thus, simplifying his operaion is can increase he running speed of ISAF algorihm. The sixy symmerical characerisics of icosahedrons in Fourier space is very useful for his poin. I is found he posiions of sixy mapped poins in 5-2 symmerical uni aren all he same, bu he posiions of hem in symmerical uni are idenical. So, he informaion conen in 5-2 symmerical uni is increasing bu he one in symmerical uni is invariable. Tha is o say, he sixy symmerical operaions is necessary for Fourier-Bessel algorihm in cylindrical coordinae sysem because he SNR in 5-2 symmerical uni is enhancing. Bu his operaion is no use for ISAF algorihm in spherical coordiane sysem because he SNR in symmerical uni is consan. This phenomenon is proved heoreically and is called heorem of uniqueness mapping. Based on his heorem, his complex operaion can be removed and he acceleraed ISAF algorihm is proposed subsequenly. The simulaed daa of melon necroic spo virus and he

6 JOURNAL OF COMPUTERS, VOL. 7, NO. 2, FEBRUARY experimenal Cryo-EM daa of HBV are used for validaing our acceleraed ISAF algorihm. The resuls show ha his acceleraed ISAF algorihm can speed up significanly a he premise of mainenance of accuracy. Is running speed is abou 9 imes as grea as ha of Fourier-Bessel algorihm and is abou 3 imes han ha of recisafs algorihm. More imporanly, he speedup of his sraegy is increasing wih he increase of he maximum Fourier radius and he number of images. In addiion, he reconsrucion process of oher polyhedrons molecule -- such as erahedral molecule, hexahedral molecule, ocahedral molecule and so on is similar.o ha of icosahedral molecule. In his sense, our acceleraing sraegy can be exened o hese new circumsances. Therefore, we will sudy is applicaion o oher-hedron symmerical molecules. ACKNOWLEDGEMENT The auhors are graeful o Zhongjun Hu, Lingpeng Cheng, ec. for solving relaive problems occured in he course of sofware developmen, o RA Crowher for providing he HBV daa. In addiion, his work is he basic research, so none of he auhors have a financial ineres relaed o his paper. Furhermore, his research is suppored by knowledge innovaion projec of CAS (Gran No. KGCX-YW-3), and Naional Science Fundaion of China (Gran No. 7029, 0364). spo virus deermined a 2.8 A resoluion. Aca Crysallogr, Sec.F 2008, 64:8-3. [2] Ludke, S.J., Baldwin, P.R., Chiu, W., 999. EMAN: semi-auomaed sofware for high resoluion single paricle reconsrucions. J. Sruc. Biol. 28, [3] Liang, Y., Ke, E.Y., Zhou, Z.H., IMIRS: a high-resoluion 3D reconsrucion package inegraed wih a relaional image daabase. J. Sruc. Biol. 37, [4] Harauz G., Van Heel M:Exac filers for general geomery hree dimensional reconsrucion. Opik 986, 73: [5] Penczek P A, Zhu J, Schroder R, Frank J. Three-dimensional reconsrucion wih conras ransfer compensaion from defocus series. Scanning Microscopy 997, : Gongming Wang: was born in 98. He is a Ph. D candidae of Insiue of Compuing Technology, Chinese Academy of Sciences. His research ineress include compuer graphics, digial image processing and visualizaion. Fa Zhang: was born in 974. He is an associae professor of Insiue of Compuing Technology, Chinese Academy of Sciences. His research ineress include high performance algorihms and bioinformaics. REFERENCES [] De Rosier D J, Klug A: Reconsrucion of hree-dimensional srucures from elecron micrographs. Naure (London)968, 27: [2] Bocher B, Wynne S A, Crowher R A: Deerminaion of he fold of he core proein of hepaiis B virus by elecron cryomicroscopy. Naure 997, 386:88-9. [3] Conway J F, Cheng N, Zlonick A, Wingfield P T, Sahl S J, Seven A C: Visualizaion of a 4-helix bundle in he hepaiis B virus capsid by cryo-elecron microscopy. Naure 997, 386:9-94. [4] Caspar D L D, Klug A: Physical Principles in he Consrucion of Regular Viruses. Cold Spring Harbor Symposia on Quaniaive Biology 962, 27:-24. [5] Z Hong Zhou: Towards aomic resoluion srucural deerminaion by single paricle cryo-elecron microscopy. Curren Opinion in Srucural Biology 2008, 8(2): [6] Hongrong Liu, Lingpeng Cheng, e al: Symmery-adaped spherical harmonics mehod for high-resoluion 3D single-paricle reconsrucions. Journal of Srucural Biology 2008, 6(): [7] Gongming Wang, Fa Zhang, Qi Chu, Liya Fan, Fei Sun, Zhiyong Liu. A Fas Calculaion Sraegy of Densiy Funcion in ISAF Reconsrucion Algorihm. SCIENCE CHINA, F Series. (Acceped) [8] Xuekui Yu, Lei Jin, Z. Hong Zhou; 3.88 Å srucure of cyoplasmic polyhedrosis virus by cryo-elecron microscopy; Naure 453, (5 May 2008) [9] Zhou Z H, Doughery M, Jakana J, He J, Rixon F J, Chiu W Seeing he herpesvirus capsid a 8.5 Å. Science 2000, 288(5467): [0] Gabashvili I S, Agrawal R K, Spahn C M, Grassucci R A, Svergun D I, Frank J, Penczek P. Soluion srucure of he E. coli 70S ribosome a.5 Å. Cell 2000, 00(5): [] Wada Y, Tanaka H, e al. The srucure of melon necroic Fei Sun: was born in 979. He is a professor in he Insiue of Biophysics, Chinese Academy of Sciences. His research ineress include combining cryo-elecron microscopy, 3D reconsrucion, crysallography and oher biophysical echnology o invesigae he srucure and funcion of membrane proeins and supra bio-macromolecular complexes. Zhiyong Liu: was born in 946. He is a professor of Insiue of Compuing Technology, Chinese Academy of Sciences. His research ineress include high performance algorihm and archiecure, and parallel processing.