跳到主要內容

臺灣博碩士論文加值系統

(100.24.118.144) 您好!臺灣時間:2022/12/06 05:41
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:保羅
研究生(外文):Paul Antonio Cardenas Lizana
論文名稱:利用分子動力學研究沉澱DNA分子的拉伸行為
論文名稱(外文):Stretching a Single Condensed DNA Molecule Studied by Molecular Dynamics Simulation
指導教授:蕭百沂
指導教授(外文):Pai-Yi Hsiao
學位類別:碩士
校院名稱:國立清華大學
系所名稱:工程與系統科學系
學門:工程學門
學類:核子工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:98
中文關鍵詞:DNA拉伸
外文關鍵詞:Condensed DNA toroidreentrant condensationforce-extension curve (FEC)extensible worm-like chain (EWLC)“stick-release patterns”entropic elasticitymolecular dynamics simulationnon-viral gene therapybioengineering
相關次數:
  • 被引用被引用:0
  • 點閱點閱:114
  • 評分評分:
  • 下載下載:15
  • 收藏至我的研究室書目清單書目收藏:0
Experiments have shown that a semiflexible polyelectrolyte, such as a DNA,
can be condensed by multivalent counterions and the preferred form is toroid. By
using molecular dynamics simulations, a single DNA molecule is condensed into
a compact toroid-like structure. DNA is treated as a bead-spring chain, using
parameters of dsDNA. The influence of the counterion size and DNA monomer
size on the DNA structure is studied. We found that for a DNA monomer size
of ¾ and counterion size of 0.5¾, the complex (DNA plus condensed counterions)
forms a well-defined toroidal structure. The dependence of the structure of the
condensed DNA on the initial configuration is investigated. We observed that the
final conformation does not depend on the initial state. The condensed DNA toroid
is then stretched by pulling one end of the chain at various constant velocities to
investigate the effects of the pulling velocity on the force-extension curve (FEC).
We found that the pulling velocity influences the force profile and the internal
structure of the condensed DNA molecule. Moreover, the responses at both DNA
ends are different if the pulling velocity is larger than the reference Rouse velocity,
Vo. For velocities larger than Vo, the FEC’s dependence over the pulling velocity
is linear at the DNA end which is moving at constant velocity; nevertheless, these
FECs oscillate around a constant force (¼ 2.5KBT/¾) at the other end. We
found that a pulling velocity equals to 5×10−4¾/¿ does not perturb the complex.
Moreover, the influence of the pulling velocity on the bond length is linear. We
observed that the entropic behavior of the DNA molecule is strongly affected by
the condensed counterions. The FEC shows a series of “stick-release patterns”.
It gradually increases with increasing extension and then abruptly decreases; this
behavior appears repeatedly and becomes stronger and stronger as the condensed
DNA molecule is losing its turns. We showed that these ”stick-release patterns”
are a consequence of turn-by-turn unfolding of the condensed DNA toroid. The extensible worm-like chain (EWLC) model is found able to describe qualitatively
the behavior of the DNA molecule when its extention is close to the overall contour
length. We presented a clear evidence and described the mechanism of why the
condensed DNA molecule forms a “stick-release patterns”. Our results provide
new microscopic information about the internal structure of a single condensed
DNA toroid being stretched and are in qualitative agreement with experiments.
Experiments have shown that a semiflexible polyelectrolyte, such as a DNA,
can be condensed by multivalent counterions and the preferred form is toroid. By
using molecular dynamics simulations, a single DNA molecule is condensed into
a compact toroid-like structure. DNA is treated as a bead-spring chain, using
parameters of dsDNA. The influence of the counterion size and DNA monomer
size on the DNA structure is studied. We found that for a DNA monomer size
of ¾ and counterion size of 0.5¾, the complex (DNA plus condensed counterions)
forms a well-defined toroidal structure. The dependence of the structure of the
condensed DNA on the initial configuration is investigated. We observed that the
final conformation does not depend on the initial state. The condensed DNA toroid
is then stretched by pulling one end of the chain at various constant velocities to
investigate the effects of the pulling velocity on the force-extension curve (FEC).
We found that the pulling velocity influences the force profile and the internal
structure of the condensed DNA molecule. Moreover, the responses at both DNA
ends are different if the pulling velocity is larger than the reference Rouse velocity,
Vo. For velocities larger than Vo, the FEC’s dependence over the pulling velocity
is linear at the DNA end which is moving at constant velocity; nevertheless, these
FECs oscillate around a constant force (¼ 2.5KBT/¾) at the other end. We
found that a pulling velocity equals to 5×10−4¾/¿ does not perturb the complex.
Moreover, the influence of the pulling velocity on the bond length is linear. We
observed that the entropic behavior of the DNA molecule is strongly affected by
the condensed counterions. The FEC shows a series of “stick-release patterns”.
It gradually increases with increasing extension and then abruptly decreases; this
behavior appears repeatedly and becomes stronger and stronger as the condensed
DNA molecule is losing its turns. We showed that these ”stick-release patterns”
are a consequence of turn-by-turn unfolding of the condensed DNA toroid. The extensible worm-like chain (EWLC) model is found able to describe qualitatively
the behavior of the DNA molecule when its extention is close to the overall contour
length. We presented a clear evidence and described the mechanism of why the
condensed DNA molecule forms a “stick-release patterns”. Our results provide
new microscopic information about the internal structure of a single condensed
DNA toroid being stretched and are in qualitative agreement with experiments.
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Agradecimientos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1 Introduction 15
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Reentrant condensation of DNA molecule . . . . . . . . . . . . . . . 20
1.3 Morphology of a condensed DNA molecule . . . . . . . . . . . . . . 22
1.4 Present research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Simulation Method and Setup 27
2.1 DNA structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Coarse-grained model . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 Molecular dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Force fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.1 Non-bonded interactions . . . . . . . . . . . . . . . . . . . . 33
2.4.2 Bonded interactions . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Integration algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.6 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Results and Discussions 39
3.1 Toroidal structure of a single condensed DNA molecule . . . . . . . 39
3.1.1 Gyration tensor . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.2 Asphericity . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Counterion size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 Size and shape of a condensed DNA molecule . . . . . . . . . . . . 45
3.3.1 Gyration tensor . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 The winding number . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Stretching process and pulling velocity . . . . . . . . . . . . . . . . 49
3.4.1 Stretching process . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.2 Pulling velocity . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 Force-extension curve (FEC) . . . . . . . . . . . . . . . . . . . . . . 58
3.5.1 NL and NR . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5.2 Stick-release behavior . . . . . . . . . . . . . . . . . . . . . . 61
3.5.3 Asphericity . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.4 Minor radius, ro, and major radius, R . . . . . . . . . . . . . 72
3.5.5 Effective fractional extension, x/Leff . . . . . . . . . . . . . 74
3.6 How do our results depend on different initial configuration? . . . . 76
3.7 Snapshots of our condensed DNA toroid during the stretching process 77
4 Conclusion 79
Appendix 83
A The Worm-Like Chain 84
A.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
A.2 Experimental results and their models . . . . . . . . . . . . . . . . 86
Bibliography 89
[1] F. Miescher. Ueber die chemische Zusammensetzung der Eiterzellen. Hoppe-
Seyler’s medicinisch-chemische Untersuchungen, 4:441, 1871.
[2] J. Watson, and F. Crick. A structure for Deoxyribose Nucleic Acid. Nature,
171:737, 1953.
[3] V. Vijayanathan, T. Thomas, and T. J. Thomas. DNA Nanoparticles and
Development of DNA Delivery Vehicles for Gene Therapy. Biochemistry,
41:14085, 2002.
[4] T. Nakamura, R. Moriguchi, K. Kogure, A. Minoura, T. Masuda, H. Akita, K.
Kato, H. Hamada, M. Ueno, S. Futaki, and H. Harashima. DNA Nanoparticles
and Development of DNA Delivery Vehicles for Gene Therapy. Biol Pharm
Bull., 29:1290, 2006.
[5] CG. Baumann, V. Bloomfield , SB Smith , C Bustamante , MD Wang , SM
Block. Stretching of single collapsed DNA molecules. Biophys J., 78:1965,
2000.
[6] Y. Murayama, and M Sano. Force Measurements of a Single DNA Molecule
in the Collapsing Phase Transition. J. Phys. Soc. Jpn., 70:345, 2000.
[7] Y. Murayama, Y. Sakamaki, and M Sano. Elastic Response of Single DNA
Molecules Exhibits a Reentrant Collapsing Transition. Phys. Rev. Lett.,
90:018102, 2003.
[8] H. Wada, Y. Murayama, and M Sano. Model of Elastic Responses of Single
DNA molecules in the Collapsing Transition. Phys. Rev. Lett., 66:061912,
2002.
[9] M. Ueda and K. Yoshikawa. Phase Transition and Phase Segregation in a
Single Double-Stranded DNA Molecule. Phys. Rev. Lett., 77:2133, 1996.
[10] Y. Burak,G. Ariel, and D. Andelman. Onset of DNA Aggregation in Presence
of Monovalent and Multivalent Counterions. Biophys. J., 85:2100, 2003.
[11] H. Wada, Y. Murayama, and M Sano. Model of Elastic Responses of Single
DNA molecules in the Collapsing Transition. Phys. Rev. Lett., 72:041803,
2005.
[12] I. Kulic and H. Schiessel. DNA Spools under Tension. Phys. Rev. Lett.,
92:228101, 2004.
[13] F. Solis and M. Olvera de la Cruz. Collapse of Flexible Polyelectrolytes in
Multivalent Salt Solutions. J. Chem. Phys., 112:2030, 2000.
[14] T. Nguyen, I. Rouzina, and B. Shklovskii. Reentrant condensation of DNA
indeuced by multivalent cations. J. Chem. Phys., 112:2562, 2000.
[15] F. Solis and M. Olvera de la Cruz. Flexible Linear Polyelectrolytes in Mul-
tivalent Salt Solutions: Solubility Conditions. European Physics J. E, 4:143,
2001.
[16] V. Bloomfield. DNA condensation by multivalent cations. Biopolymers,
354:269, 1997.
[17] V. Bloomfield. DNA condensation. Curr. Opinion Struct. Biol., 6:334, 1996.
[18] W. Earnshaw, and S. Harrison. DNA arrangement in isometric phage heads.
Nature (London), 268:598, 1977.
[19] L. Black, W. Newcomb, J. Boring, and J. Brown. Ion Etching of Bacteriophage
T4: Support for a Spiral-Fold Model of Packaged DNA. Proc. Natl. Acad. Sci
USA, 82:7960, 1985.
[20] N Hud. Double-stranded DNA organization in bacteriophage heads: an al-
ternative toroid-based model. Biophys. J., 69:1355, 1995.
[21] I. Kulic, D. Andrienko, and M. Deserno. Twist-bend instability for toroidal
DNA condensates. Europhys. Lett., 67:418, 2004.
[22] J.Widom, and RL Baldwin. Cation-induced toroidal condensation of DNA
studies with Co3+(NH3)6. J Mol Biol., 144:431, 1980.
[23] AZ. Li, TY. Fan, and M. Ding. Formation study of toroidal condensation of
DNA. Sci China B., 35:169, 1992.
[24] V. Bloomfield. Condensation of DNA by multivalent cations: Considerations
on mechanism. Biopolymers, 31:1471, 1991.
[25] V. Vijayanathan, T. Thomas, A. Shirahata, and T. J. Thomas. DNA Conden-
sation by Polyamines: A Laser Light Scattering Study of Structural Effects.
Biochemistry, 40:13644, 2001.
[26] T. Kral, M. Hof, and M. Langner. The Effect of Spermine on Plasmid Conden-
sation and Dye Release Observed by Fluorescence Correlation Spectroscopy.
Biol. Chem., 40:331, 2002.
[27] D. Porschke. Dynamics of DNA Condensation. Biochemistry, 23:4821, 1984.
[28] D. Chattoraj , L. Gosule, and J. Schellman. DNA condensation with
polyamines. 2. Electron microscopic studies. J. Mol. Biol., 121:327, 1978.
[29] S. Hamilton and D. Pettijohn. Properties of condensed bacteriophage T4
DNA isolated from Escherichia coli infected with bacteriophage T4. J Virol.,
19:1012, 1976.
[30] L. Gosule and J. Schellman. Compact form of DNA induced by spermidine.
Nature., 29:259, 1976.
[31] Z. Lin, C. Wang, X. Feng, M. Liu, J. Li, and C. Bai. The observation of
the local ordering characteristics of spermidine-condensed DNA: atomic force
microscopy and polarizing microscopy studies. Nucleic Acids Res., 26:3228,
1998.
[32] P. Arscott , A. Li, and V. Bloomfield. Condensation of DNA by trivalent
cations. 1. Effects of DNA length and topology on the size and shape of
condensed particles. Biopolymers, 30:619, 1990.
[33] M. Haynes, R. Garrett, and W. Gratzer. Structure of nucleic acid-poly base
complexes. Biochemistry, 9:4410, 1970.
[34] M. Hsiang, and R. Cole. Structure of histone H1-DNA complex: effect of
histone H1 on DNA condensation. Proc. Natl. Acad. Sci. USA, 74:4852,
1977.
[35] N. Hud, M. Allen, K. Downing, J. Lee, and R. Balhorn. Identification of the
elemental packing unit of DNA in mammalian sperm cells by atomic-force
microscopy. Biochem. Biophys. Res. Commun., 193:1347, 1993.
[36] U. Laemmli. Characterization of DNA condensates induced by poly(ethylene
oxide) and polylysine. Proc. Natl. Acad. Sci. USA, 72:4288, 1975.
[37] M. Cerritelli, N. Cheng, A. Rosenberg, C. McPherson, F. Booy, and A. Steven.
Encapsidated conformation of bacteriophage T7 DNA. Cell. Proc. Natl. Acad.
Sci. USA, 91:271, 1997.
[38] http://www.fda.gov/cber/gene.htm
[39] Y. Yoshikawa, K. Yoshikawa, and T. Kanbe. Formation of a Giant Toroid
from Long Duplex DNA. Langmuir., 15:4085, 1999.
[40] M. Frank-Kamenetskii, V. Anshelevich, and A. Lukashin. Polyelectrolyte
Model of DNA. Sov. Phys. Uspekhi, 30:317, 1987.
[41] E. Rajasekaran and B. Jayaram. Counterion condensation in DNA systems:
The cylindrical Poisson-Boltzmann model revisited. Biopolymers, 34:443,
2004.
[42] M. Manning. Limiting Laws and Counterion Condensation in Polyelectrolyte
Solutions I. Colligative Properties. J. Chem. Phys., 51:924, 1969. 1969.
[43] M. Manning. Limiting laws and counterion condensation in polyelectrolyte
solutions. IV. The approach to the limit and the extraordinary stability of the
charge fraction. Biophys Chem., 7:95, 1977.
[44] C. Anderson, M. Record. Polyelectrolyte Theories and their Applications to
DNA. Jr. Annu. Rev. Phys. Chem., 33:191, 1982.
[45] E. Kramarenko, A. Khokhlov, and K. Yoshikawa. Collapse of Polyelectrolyte
Macromolecules Revisited Macromolecules., 30:3383, 1997.
[46] R. Winkler, M. Gold, and P. Reineker. Collapse of Polyelectrolyte Macro-
molecules by Counterion Condensation and Ion Pair Formation: A Molecular
Dynamics Simulation Study. Phys. Rev. Lett., 80:3731, 1998.
[47] M. Stevens, K. Kremer. The nature of flexible linear polyelectrolytes in salt
free solution: A molecular dynamics study. J. Chem. Phys., 103:1669, 1995.
[48] R. Dias, A. Pais, B. Lindman, and M. Miguel. Modeling of DNA Compaction
by Polycations. J. Chem. Phys., 119:8150, 2003.
[49] P. Crozier and M. Stevens. Simulations of single grafted polyelectrolyte chains:
ssDNA and dsDNA. J. Chem. Phys., 118:3855, 2003.
[50] M. Stevens, K. Kremer. Structure of salt-free linear polyelectrolytes. Phys.
Rev. Lett., 71:2228, 1993.
[51] M. Stevens, K. Kremer. Structure of salt-free linear polyelectrolytes. J. Chem.
Phys., 103:1669, 1995.
[52] M. Jonsson, and P. Linse. Polyelectrolyteˆamacroion complexation. II. Effect
of chain flexibility. J. Chem. Phys., 115:10975, 2001.
[53] A. Pais, M. Miguel, P. Linse, and B. Lindman. Polyelectrolytes confined to
spherical cavities. J. Chem. Phys., 117:1385, 2002.
[54] PY. Hsiao. Linear polyelectrolytes in tetravalent salt solutions. J. Chem.
Phys., 124:044904, 2006.
[55] PY. Hsiao. Chain morphology, swelling exponent, persistence length, like-
charge attraction, and charge distribution around a chain in polyelectrolyte
solutions: effects of salt concentration and ion size studied by molecular dy-
namics simulations. Macromolecules., 39:7125, 2006.
[56] Stevens M. Simple simulation of DNA condensation. Biophys J., 80:130,
2001.
[57] Ou Zhaoyang and M. Muthukumar. Langevin dynamics of semiflexible poly-
electrolytes: Rod-toroid-globule-coil structures and counterion distribution.
J. Chem. Phys., 123:074905, 2005.
[58] I. Miller, M. Keentok, G. Pereira, D. Williams. Semiflexible polymer con-
densates in poor solvents: Toroid versus spherical geometries. Phys. Rev. E,
71:031802, 2005.
[59] Y. Takenaka, K. Yoshikawa, Y. Yoshikawa, Y. Koyama, T. Kanbe. Morpho-
logical variation in a toroid generated from a single polymer chain. J. Chem.
Phys., 123:014902, 2005.
[60] SB. Smith , L Finzi , C. Bustamante. Direct mechanical measurement of
the elasticity of single DNA molecules by using magnetic beads. Science,
258:1122, 1992.
[61] SB. Smith , Y. Cui , C. Bustamante. Overstretching B-DNA: the elastic
response of individual double-stranded and single-stranded DNA molecules.
Science, 271:795, 1996.
[62] HG. Hansma. Properties of biomolecules measured from atomic-force micro-
scope images: a review. J. Struct. Biol., 119:99, 1997.
[63] C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith. Entropic elasticity
of ¸-phage DNA. Science., 265:1599, 1994.
[64] M D Wang, H Yin, R Landick, J Gelles, and S M Block. Stretching DNA
with optical tweezers. Biophys J., 72:1335, 1997.
[65] Q. Liao, A. Dobrynin, and M. Rubinstein. Molecular Dynamics Simulations
of Polyelectrolyte Solutions: Nonuniform Stretching of Chains and Scaling
Behavior. Macromolecules., 36:3386, 2003.
[66] R. Zhang and B. Shklovskii. The pulling force of a single DNA molecule
condensed by spermidine. Physica A, 349:563, 2005.
[67] F. Ritort, S. Mihardja, S. B. Smith, and C. Bustamante. Condensation transi-
tion in DNA-Polyaminoamide dendrimer fibers studied using optical tweezers.
Phys. Rev. Lett., 96:118301, 2006.
[68] R. Franklin and R. Gosling. Molecular Configuration in Sodium Thymonu-
cleate. Nature, 171:740, 1953.
[69] D. Elson and E. Chargaff. On the desoxyribonucleic acid content of sea urchin
gametes. Experientia, 8:143, 1952.
[70] E. Chargaff, R. Lipshitz, and C. Green. Composition of the desoxypentose
nucleic acids of four genera of sea-urchin. J Biol Chem., 195:155, 1952.
[71] E. Chargaff, R. Lipshitz, C. Green, and M. Hodes. The composition of the
deoxyribonucleic acid of salmon sperm. J Biol Chem., 192:223, 1951.
[72] E. Chargaff, R. Lipshitz, C. Green, and M. Hodes. Some recent studies on
the composition and structure of nucleic acids. J Cell Physiol Suppl., 38:41,
1951.
[73] B. Magasanik, E. Vischer, R. Doniger, D. Elson, and E. Chargaff. The sepa-
ration and estimation of ribonucleotides in minute quantities. J Biol Chem.,
186:37, 1950.
[74] E. Chargaff. Chemical specificity of nucleic acids and mechanism of their
enzymatic degradation. Experientia, 6:201, 1950.
[75] R. Hockney, and J. Eastwood. Computer simulation using particles. McGraw-
Hill, New York, 1981.
[76] Oppenheim, A. V. and R.W. Schafer. Discrete-Time Signal Processing. En-
glewood Cliffs, NJ: Prentice-Hall, 1989.
[77] Kenneth Barbalace http://klbprouctions.com/ Periodic Table of Elements,
Sorted by Ionic Radius. EnvironmentalChemistry.com. 1995 - 2007. Accessed
on-line: http://EnvironmentalChemistry.com/yogi/periodic/ionicradius.html
[78] E. Clementi and D. L. Raimondi. Atomic Screening Constants from SCF
Functions. J. Chem. Phys., 39:2686, 1963.
[79] J. Slater. Atomic Radii in Crystals. J. Chem. Phys., 41:3199, 1964.
[80] J. Widom and R. L. Baldwin. Cation-indunced toroidal condensation of DNA:
Studies with Co3+(NH3)6 J. Mol. Biol., 144:431, 1980.
[81] Y. Murayama, H.Wada, and M. Sano. Internal Fricition of a Single Condensed
DNA: Dynamic Force Measurements Using Optical Tweezers. Unpublished
paper.
[82] N. K. Lee and D. Thirumalai. Pulling-Speed-Dependent Force-Extension Por-
files for Semiflexible chains Biophys J., 86:2641, 2004.
[83] M. Saminathan, T. Antony, A. Shirahata, L. H. Sigal, T. Thomas, and T.
J. Thomas. Ionic and Structural Specificity Effects of Natural and Synthetic
Polyamines on the Aggregation and Resolubilization of Single-, Double-, and
Triple-Stranded DNA. Macromolecules., 28:8759, 1995.
[84] O. Kratky, and G. Porod. R¨ontgenuntersuchung gel¨oster Fadenmolek¨ule Rec.
Trav. Chim. Pays-Bas., 68:1106, 1949.
[85] J. Marko and E. Siggia. Stretching DNA. Macromolecules., 28:8759, 1995.
[86] T. Odijk. Stiff chains and filaments under tension. Macromolecules., 28:7016,
1995.
[87] C. Bouchiat, M. Wang, J. Allemand, T. Strick, S. Block, and V. Croquette.
Estimating the persistence length of a worm-like chain molecule from force-
extension measurements. Biophys J., 76:409, 1999.
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top