Biopolymer Biopolymer － － DNADNA

BiophysicsBiophysicsDept. Phys. Tunghai Univ.Dept. Phys. Tunghai Univ.

C. T. ShihC. T. Shih

A Brief History of the A Brief History of the Discovery of DNADiscovery of DNA

A Brief History of the Discovery of DNAA Brief History of the Discovery of DNA

18601860 年代，奧地利年代，奧地利神父孟德爾（神父孟德爾（ GregoGregor Mendel, 1822-188r Mendel, 1822-18844 ）發現豌豆中有某）發現豌豆中有某種成對的「因子」可種成對的「因子」可以決定遺傳性狀。以決定遺傳性狀。

““Quantum” in EvolutionQuantum” in Evolution

達爾文學說所遇到的挑戰：當時流行的遺傳學觀點是，遺傳因子由血液所攜帶，兒女的性狀是由雙親的性狀（血液）混合而成。然而由前述「熵」的統計意義可知，經過許多世代的繁殖後，最後的性狀特徵會「均一化」：融合成一種中間態，就好像把不同溫度的水逐漸混合，最後會變成全部均一溫度。這樣一來，物種只會被消滅而不會有演化。 Charles Darwin1809~1886

““Quantum” in EvolutionQuantum” in Evolution

孟德爾的豌豆實驗（ 1857~1865 ）：選取了「莖的高矮」、「豆莢綠黃」、「種子圓皺」等幾組相對的性狀的豌豆作雜交研究。統計的結果顯示，「高：矮」、「綠：黃」、「圓：皺」的比例大致都 3:1 。這個簡單整數比的」結果類似化學中的定比定律及倍比定律（ Dalton 因此得到了「不可分割的原子」的概念），而孟德爾則因此領悟了「遺傳因子為不可分割的單位」的概念。 Gregor Mendel(1823~1884)

The Structure of a GeneThe Structure of a Gene““We shall assume the structure of a gene to be that We shall assume the structure of a gene to be that of a huge molecule, capable of only of a huge molecule, capable of only discontinuoudiscontinuouss change, which consists in the rearrangement of t change, which consists in the rearrangement of the atoms and leads to an isomeric molecule. The rhe atoms and leads to an isomeric molecule. The rearrangement may affect only a small region of the earrangement may affect only a small region of the gene, and a gene, and a vast numbervast number of different rearrangeme of different rearrangements may be possible.”nts may be possible.” － － What is Life? E. ScWhat is Life? E. Schrhröödingerdinger

1869: Miescher1869: Miescher

18691869 年，瑞士生物學年，瑞士生物學家 家 Johann Miescher (18Johann Miescher (1844~ 1895) 44~ 1895) 在病患繃帶的在病患繃帶的膿汁中發現一種新物質，膿汁中發現一種新物質，由於是在細胞核中，他將由於是在細胞核中，他將之取名為「核素」之取名為「核素」 (nucle(nuclein)in) ，此即為，此即為 DNADNA （去氧（去氧核糖核酸）。核糖核酸）。

1890: Discovery of Chromosome1890: Discovery of Chromosome

18901890 年代，科學家在年代，科學家在細胞分裂的過程中觀察細胞分裂的過程中觀察到，成對的染色體在細到，成對的染色體在細胞分裂時會先複製出另胞分裂時會先複製出另一份，然後平均分配給一份，然後平均分配給兩個子細胞，因此開始兩個子細胞，因此開始有學者認為染色體可能有學者認為染色體可能是遺傳物質的攜帶者。是遺傳物質的攜帶者。

1908: Morgan1908: MorganThomas Morgan (186Thomas Morgan (186

6 ~1945) 6 ~1945) 首先利用果首先利用果蠅來研究遺傳學，他發蠅來研究遺傳學，他發現有許多基因是一起遺現有許多基因是一起遺傳的，因此推測有些基傳的，因此推測有些基因在染色體上的位置是因在染色體上的位置是相連的，並且訂出了果相連的，並且訂出了果蠅的基因圖譜。蠅的基因圖譜。 MorgaMorgann 於於 19331933 年獲得諾貝年獲得諾貝爾生理及醫學獎。爾生理及醫學獎。

Drosophila MelanogasterDrosophila Melanogaster

果蠅是遺傳學研究中極為重要的研究對象，果蠅是遺傳學研究中極為重要的研究對象，牠的優點是：生命史短（每十二天繁殖一牠的優點是：生命史短（每十二天繁殖一代）、多產（平均一隻雌果蠅產一千個卵）、代）、多產（平均一隻雌果蠅產一千個卵）、飼養容易、成本低廉。飼養容易、成本低廉。

1909: Garrod1909: Garrod

英國遺傳學家 英國遺傳學家 ArchibArchibald Garrod (1857~193ald Garrod (1857~1936) 6) 指出，當一些特殊的指出，當一些特殊的蛋白質無法執行正常功蛋白質無法執行正常功能時，會引起某些遺傳能時，會引起某些遺傳疾病。這個假說可說是疾病。這個假說可說是日後「一基因、一蛋日後「一基因、一蛋白」之前身。白」之前身。

1928: Griffith1928: Griffith19281928 年，英國軍醫年，英國軍醫

Frederick Griffith (18Frederick Griffith (1881~1941) 81~1941) 以老鼠實驗發現，以老鼠實驗發現，將活的良性肺炎雙球將活的良性肺炎雙球菌與死的惡性肺炎雙菌與死的惡性肺炎雙球菌混合，可以引起球菌混合，可以引起轉型，得到活的惡性轉型，得到活的惡性菌，使老鼠死亡。菌，使老鼠死亡。為什麼細胞會發生為什麼細胞會發生轉化？轉化？

1942: Beadle & Tatum1942: Beadle & Tatum19421942 年，年， George BeaGeorge Bea

dle (1903~1989) dle (1903~1989) 與 與 EdEdward Tatum (1909~197ward Tatum (1909~1975) 5) 以麵包上的紅黴菌以麵包上的紅黴菌（（ Neurospora Neurospora ）實驗）實驗證實，證實， DNADNA 上所帶的遺上所帶的遺傳訊息，其功能是製造傳訊息，其功能是製造特定的酵素。他們獲得特定的酵素。他們獲得了了 19581958 年的諾貝爾生理年的諾貝爾生理與醫學獎。與醫學獎。

Beadle & Tatum’s ExperimentBeadle & Tatum’s Experiment以 以 X X 光照射黴菌光照射黴菌將黴菌分類：有突變（在最低條件的培養皿中仍將黴菌分類：有突變（在最低條件的培養皿中仍可繁殖）以及沒有突變（不會繁殖）可繁殖）以及沒有突變（不會繁殖）在有突變的族群中加入不同的酵素後，又會開始在有突變的族群中加入不同的酵素後，又會開始繁殖，由觀察知，有三種突變種：繁殖，由觀察知，有三種突變種：無法合成維生素 無法合成維生素 B6B6無法合成維生素 無法合成維生素 B1B1無法合成 無法合成 para-aminobenzoic acidpara-aminobenzoic acid每個突變都是一個基因遭破壞，而缺少對應的酵每個突變都是一個基因遭破壞，而缺少對應的酵素來合成繁殖所需之營養素素來合成繁殖所需之營養素一基因 – 一酵素理論一基因 – 一酵素理論

1944: Avery1944: Avery

美國微生物學家 美國微生物學家 OswOswald Avery (1877~1955) ald Avery (1877~1955) 實驗發現，實驗發現， GriffithGriffith 所觀所觀察到的細菌轉型現象，察到的細菌轉型現象，是由是由 DNADNA 所造成，確所造成，確認了攜帶遺傳因子的物認了攜帶遺傳因子的物質是質是 DNADNA 。。

1949: Chargaff1949: Chargaff

19491949 年，年， Irwin CharIrwin Chargaff (1905~) gaff (1905~) 提出了所提出了所謂的 謂的 Chargaff Chargaff 法則：法則：DNADNA 中的四種核甘酸：中的四種核甘酸：AA 與與 TT 的含量相同，的含量相同， CC與與 GG 的含量相同，推的含量相同，推翻了過去翻了過去 ATCGATCG 含量含量均勻的假說。均勻的假說。

The Discovery of Double HelixThe Discovery of Double Helix

19511951 年，年， Rosalind Franklin Rosalind Franklin 得到得到 DNADNA 分分子的子的 X-rayX-ray 繞射照片，繞射照片， 19531953 年，年， WatsonWatson 與與CrickCrick 解出了解出了 DNADNA 的雙螺旋結構，此為分子的雙螺旋結構，此為分子生物學的大躍進。生物學的大躍進。

We wish to suggest a structure for the salt of deoxyribose nucleic acid (D.N.A.). This structure has novel features which are of considerable biological interest. A structure for nucleic acid has already been proposed by Pauling and Corey (1). They kindly made their manuscript available to us in advance of publication. Their model consists of three intertwined chains, with the phosphates near the fibre axis, and the bases on the outside. In our opinion, this structure is unsatisfactory for two reasons: (1) We believe that the material which gives the X-ray diagrams is the salt, not the free acid. Without the acidic hydrogen atoms it is not clear what forces would hold the structure together, especially as the negatively charged phosphates near the axis will repel each other. (2) Some of the van der Waals distances appear to be too small.Another three-chain structure has also been suggested by Fraser (in the press). In his model the phosphates are on the outside and the bases on the inside, linked together by hydrogen bonds. This structure as described is rather ill-defined, and for this reason we shall not comment on it.We wish to put forward a radically different structure for the salt of deoxyribose nucleic acid. This structure has two helical chains each coiled round the same axis (see diagram). We have made the usual chemical assumptions, namely, that each chain consists of phosphate diester groups joining ß-D-deoxyribofuranose residues with 3',5' linkages. The two chains (but not their bases) are related by a dyad perpendicular to the fibre axis. Both chains follow right- handed helices, but owing to the dyad the sequences of the atoms in the two chains run in opposite directions. Each chain loosely resembles Furberg's2 model No. 1; that is, the bases are on the inside of the helix and the phosphates on the outside. The configuration of the sugar and the atoms near it is close to Furberg's 'standard configuration', the sugar being roughly perpendicular to the attached base. There is a residue on each every 3.4 A. in the z-direction. We have assumed an angle of 36° between adjacent residues in the same chain, so that the structure repeats after 10 residues on each chain, that is, after 34 A. The distance of a phosphorus atom from the fibre axis is 10 A. As the phosphates are on the outside, cations have easy access to them.The structure is an open one, and its water content is rather high. At lower water contents we would expect the bases to tilt so that the structure could become more compact.The novel feature of the structure is the manner in which the two chains are held together by the purine and pyrimidine bases. The planes of the bases are perpendicular to the fibre axis. The are joined together in pairs, a single base from the other chain, so that the two lie side by side with identical z-co-ordinates. One of the pair must be a purine and the other a pyrimidine for bonding to occur. The hydrogen bonds are made as follows : purine position 1 to pyrimidine position 1 ; purine position 6 to pyrimidine position 6.If it is assumed that the bases only occur in the structure in the most plausible tautomeric forms (that is, with the keto rather than the enol configurations) it is found that only specific pairs of bases can bond together. These pairs are : adenine (purine) with thymine (pyrimidine), and guanine (purine) with cytosine (pyrimidine).In other words, if an adenine forms one member of a pair, on either chain, then on these assumptions the other member must be thymine ; similarly for guanine and cytosine. The sequence of bases on a single chain does not appear to be restricted in any way. However, if only specific pairs of bases can be formed, it follows that if the sequence of bases on one chain is given, then the sequence on the other chain is automatically determined.It has been found experimentally (3,4) that the ratio of the amounts of adenine to thymine, and the ration of guanine to cytosine, are always bery close to unity for deoxyribose nucleic acid.It is probably impossible to build this structure with a ribose sugar in place of the deoxyribose, as the extra oxygen atom would make too close a van der Waals contact. The previously published X-ray data (5,6) on deoxyribose nucleic acid are insufficient for a rigorous test of our structure. So far as we can tell, it is roughly compatible with the experimental data, but it must be regarded as unproved until it has been checked against more exact results. Some of these are given in the following communications. We were not aware of the details of the results presented there when we devised our structure, which rests mainly though not entirely on published experimental data and stereochemical arguments.It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.Full details of the structure, including the conditions assumed in building it, together with a set of co-ordinates for the atoms, will be published elsewhere.We are much indebted to Dr. Jerry Donohue for constant advice and criticism, especially on interatomic distances. We have also been stimulated by a knowledge of the general nature of the unpublished experimental results and ideas of Dr. M. H. F. Wilkins, Dr. R. E. Franklin and their co-workers at King's College, London. One of us (J. D. W.) has been aided by a fellowship from the National Foundation for Infantile Paralysis.J. D. WATSON F. H. C. CRICK Medical Research Council Unit for the Study of Molecular Structure of Biological Systems, Cavendish Laboratory, Cambridge. April 2.1. Pauling, L., and Corey, R. B., Nature, 171, 346 (1953); Proc. U.S. Nat. Acad. Sci., 39, 84 (1953). 2. Furberg, S., Acta Chem. Scand., 6, 634 (1952). 3. Chargaff, E., for references see Zamenhof, S., Brawerman, G., and Chargaff, E., Biochim. et Biophys. Acta, 9, 402 (1952). 4. Wyatt, G. R., J. Gen. Physiol., 36, 201 (1952). 5. Astbury, W. T., Symp. Soc. Exp. Biol. 1, Nucleic Acid, 66 (Camb. Univ. Press, 1947). 6. Wilkins, M. H. F., and Randall, J. T., Biochim. et Biophys. Acta, 10, 192 (1953).

A structure for Deoxyribose Nucleic Acid

1966: Genetic Code1966: Genetic CodeMarshall Nirenberg Marshall Nirenberg 與 與

H. Gobind Khorana H. Gobind Khorana 研研究小組找到了遺傳碼（究小組找到了遺傳碼（ gegenetic codenetic code ）。在）。在 DNADNA序列中每三個核甘酸鹼基序列中每三個核甘酸鹼基代表一個氨基酸，稱為一代表一個氨基酸，稱為一個「編碼子」（個「編碼子」（ codoncodon ）。）。他們因此獲得了他們因此獲得了 19681968 年年諾貝爾獎。諾貝爾獎。

Structure of DNAStructure of DNA

ComponentComponentDeoxyribose (a pentosDeoxyribose (a pentose = sugar with 5 carboe = sugar with 5 carbons) ns) Phosphoric Acid Phosphoric Acid Organic (nitrogenous) Organic (nitrogenous) basesbases

Purines - Adenine and Purines - Adenine and GuanineGuaninePyrimidines -Cytosine aPyrimidines -Cytosine and Thymine) nd Thymine)

Base+

Sugar=

Nucleoside

Nucleoside+

phosphate=

Nucleotide

Nucleotide – OH = Deoxy Nucleotide

DNA Backbone (Single DNA Backbone (Single Strand)Strand)

Polarity

Features of the 5’- StructureFeatures of the 5’- StructureAlternating backbone of deoxyribose and pAlternating backbone of deoxyribose and phosphodiester groups hosphodiester groups Chain has a direction (known as polarity), Chain has a direction (known as polarity), 5'- to 3'- from top to bottom 5'- to 3'- from top to bottom Oxygens (red atoms) of phosphates are pOxygens (red atoms) of phosphates are polar and negatively charged olar and negatively charged A, G, C, and T bases can extend away froA, G, C, and T bases can extend away from chain, and stack atop each other m chain, and stack atop each other Bases are hydrophobic Bases are hydrophobic

DNA Double HelixDNA Double Helix

Features of the DNA Double HelixFeatures of the DNA Double Helix

Two DNA strands form a helical spiral, winding Two DNA strands form a helical spiral, winding around a helix axis in a right-handed spiral around a helix axis in a right-handed spiral The two polynucleotide chains run in opposite The two polynucleotide chains run in opposite directions directions The sugar-phosphate backbones of the two DNA The sugar-phosphate backbones of the two DNA strands wind around the helix axis like the railing strands wind around the helix axis like the railing of a spiral staircase of a spiral staircase The bases of the individual nucleotides are on The bases of the individual nucleotides are on the inside of the helix, stacked on top of each the inside of the helix, stacked on top of each other like the steps of a spiral staircaseother like the steps of a spiral staircase

Base PairsBase Pairs

Chargaff’s Law: A—T, C—G by H-bondsChargaff’s Law: A—T, C—G by H-bonds

Spatial Geometry and Secondary StructureSpatial Geometry and Secondary Structure

Two polynucleotide chains are Two polynucleotide chains are wound around a common axis to wound around a common axis to produce a double helixproduce a double helixDiameter = 20Diameter = 20ÅÅDistance of adjacent bases = 3.4ÅDistance of adjacent bases = 3.4ÅRotation of adjacent bases = 36°Rotation of adjacent bases = 36°

Forces Stabilizing DNA Forces Stabilizing DNA Secondary Structure: H-BondsSecondary Structure: H-BondsH-Bond strength of the base pairs:H-Bond strength of the base pairs:

A—T ~ 7 kcal/moleA—T ~ 7 kcal/moleC—G ~ 17 kcal/moleC—G ~ 17 kcal/moleComparison: Covalent bond EComparison: Covalent bond EC—CC—C =83.1 =83.1 kcal/molekcal/mole

Rigidity of bonds: to lengthen the bonds by Rigidity of bonds: to lengthen the bonds by 0.10.1Å, we need the energyÅ, we need the energy

0.1 kcal/mole for H-bonds0.1 kcal/mole for H-bonds3.25 kcal/mole for C—C covalent bond3.25 kcal/mole for C—C covalent bond

Forces Stabilizing DNA Secondary Forces Stabilizing DNA Secondary Structure: Stacking InteractionsStructure: Stacking Interactions

Polymorphism of DNAPolymorphism of DNA

B-DNA: B-DNA: 正常條件下的結構正常條件下的結構A-DNA: A-DNA: 低濕度下可能由低濕度下可能由 B-DNAB-DNA 變為變為 A-DNAA-DNAZ-DNA: Z-DNA: 某些特殊序列在特殊條件下，如某些特殊序列在特殊條件下，如 GCGCGCGCGCGC 在高在高濃度的食鹽水中可能變成這種結構濃度的食鹽水中可能變成這種結構

Tertiary Structure: SupercoilTertiary Structure: Supercoil

This is a famous electron micrograph of an E. coli cell that has been carefully lysed, then all the proteins were removed, and it was spread on an EM grid to  reveal all of its DNA.

Relaxed － inactive

Supercoiled － active

Energetics of DNA SpercoilEnergetics of DNA SpercoilL (Link): number of times that one ribbon edge wL (Link): number of times that one ribbon edge winds around the other (integer for closed loop)inds around the other (integer for closed loop)T (Twist): number of times either edge winds aroT (Twist): number of times either edge winds around the helix axisund the helix axisW (Writhe): number of turns that the helix makes W (Writhe): number of turns that the helix makes around the supercoil axis (can be positive or negaround the supercoil axis (can be positive or negative)ative)L=T+WL=T+WEnergis for the three parts:Energis for the three parts:

EELL=a=aLL(L-L(L-L00))22

EETT=a=aTT(T-T(T-T00))22

EEWW is complicated is complicated

Chen, J. and Seeman, N.C. (1991), Nature (London) 350, 631-633. Zhang, Y. and Seeman, N.C. (1994), J. Am. Chem. Soc. 116, 1661-1669.

Approximate Models for DNA Approximate Models for DNA Structure – Coarse GrainingStructure – Coarse Graining

DNA DNA 是很複雜的生物大分子，要直接以原子尺度是很複雜的生物大分子，要直接以原子尺度研究非常困難，因此必須做許多層次的近似研究非常困難，因此必須做許多層次的近似首先掌握主要的結構特性與交互作用首先掌握主要的結構特性與交互作用

Backbone Backbone 上的糖以及磷酸原子團是週期性的上的糖以及磷酸原子團是週期性的DNA DNA 分子結構具有某種程度的規則性 – 其「骨架」分子結構具有某種程度的規則性 – 其「骨架」可能可以用固態物理的方法近似可能可以用固態物理的方法近似但又不似晶體完美，較具彈性，需引入聚合體物理方但又不似晶體完美，較具彈性，需引入聚合體物理方法研究法研究鹼基的排列沒有規則性（？）鹼基的排列沒有規則性（？）

First Level of HierarchyFirst Level of Hierarchy

Linear Rod-Like ModelLinear Rod-Like Model

H=HH=Hss+H+Htt+H+Hbb+H+Hs-ts-t+H+Hs-bs-b+H+Ht-bt-b

Stretch: Stretch: 拉長或壓縮；拉長或壓縮； Twist: Twist: 扭轉；扭轉； Bend:Bend: 彎曲，後三項為交叉作用項彎曲，後三項為交叉作用項各能量大小比較：各能量大小比較： HHss, H, Htt較大，較大， HHbb小小 1~2 1~2 ordersorders ，， HHs-bs-b 與與 HHt-bt-b 可以忽略可以忽略用用 discrete model discrete model 更簡單：更簡單：

nnnnt

nnnns

kIH

uuKuMH

}2/)(2/{

}2/)(2/{

21

2

21

2

Linear Rod-Like Model (ContLinear Rod-Like Model (Conti.)i.)

HHs-ts-t comes from the interaction between longitudi comes from the interaction between longitudinal and torsional motions → k and K are not connal and torsional motions → k and K are not constants:stants:

If we restricted ourselves to terms up to 2nd ordIf we restricted ourselves to terms up to 2nd order (small deviations from the relaxed state), we fier (small deviations from the relaxed state), we find that Hs-t only makes a constant contribution nd that Hs-t only makes a constant contribution and can be neglected (as zero energy shift) → thand can be neglected (as zero energy shift) → the two types of motion are decouplede two types of motion are decoupled

)()(~),()()(~),(

1211011

1211011

nnnnnnnn

nnnnnnnn

KuuKKuuKKkuukkuukk

Linear Rod-Like Model (ContLinear Rod-Like Model (Conti.)i.)

Now the problem becomes a standard coupled oscillatioNow the problem becomes a standard coupled oscillation onen oneThe equation of motion:The equation of motion:

Use the periodic boundary condition: uUse the periodic boundary condition: unn=u=un+Nn+N and and φφnn= = φφn+n+

NN, the solution is (q=2, the solution is (q=2m/Na, m is an integer):m/Na, m is an integer):

)2()2(

110

110

nnnn

nnnn

kIuuuKuM

2/10

2/10

0

0

}/)]cos(1[2{

}/)]cos(1[2{

)}(exp{)}(exp{

Iqakw

MqaKw

twqnaitwqnaiuu

t

s

tnn

snn

Second Level of HierarchySecond Level of Hierarchy

Third Level of HierarchyThird Level of Hierarchy

Fourth Level of HierarchyFourth Level of Hierarchy

A

A

T

T

C

C

G

G

Fifth Level of HierarchyFifth Level of Hierarchy

Full-Atom