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A discussion on circular dichroism: electronic and structural principles - Circular dichroism of helical polynucleotide chains

Identifieur interne : 000C28 ( Istex/Corpus ); précédent : 000C27; suivant : 000C29

A discussion on circular dichroism: electronic and structural principles - Circular dichroism of helical polynucleotide chains

Auteurs : J. Brahms ; Ronald Sydney Nyholm

Source :

RBID : ISTEX:3076FB209D69332C0AC268D8C2FE6E2DCAD66CE8

Abstract

In contrast to relatively well developed experimental and theoretical studies on polypeptides and proteins (see Gratzer 1967 and McLachlan 1967, this volume) the investigation of optical activity of polynucleotides and nucleic acids were very restricted. The optical rotatory dispersion curves of polynucleotides examined in the visible and near u. v. fit one-term Drude equation regardless of the conformation (Fresco 1961; Levedahl & James 1957; Ts’o, Helmkamp & Sander 1962). Recent circular dichroism (c. d.) measurements of several polynucleotides and nucleic acids (figure 1) indicated clearly the presence of dichroic bands in the u. v. region of base absorption which can be related to the dissymmetrical helical conformation (Brahms 1963). The intensity of circular dichroic bands decreases strongly under the conditions in which the helical structure is unstable and goes to random coil form (Brahms 1964; Brahms & Mommaerts 1964). Thus polyadenylic acid (poly A) is known according to X-ray data to exist at acid pH in a helical two strand and right handed conformation (Rich, Davies, Crick & Watson 1961). In acid solution the same polyadenylic acid exhibits strong circular dichroic bands which disappear at high temperature (figure 2).

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DOI: 10.1098/rspa.1967.0058

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<div type="abstract" xml:lang="en">In contrast to relatively well developed experimental and theoretical studies on polypeptides and proteins (see Gratzer 1967 and McLachlan 1967, this volume) the investigation of optical activity of polynucleotides and nucleic acids were very restricted. The optical rotatory dispersion curves of polynucleotides examined in the visible and near u. v. fit one-term Drude equation regardless of the conformation (Fresco 1961; Levedahl & James 1957; Ts’o, Helmkamp & Sander 1962). Recent circular dichroism (c. d.) measurements of several polynucleotides and nucleic acids (figure 1) indicated clearly the presence of dichroic bands in the u. v. region of base absorption which can be related to the dissymmetrical helical conformation (Brahms 1963). The intensity of circular dichroic bands decreases strongly under the conditions in which the helical structure is unstable and goes to random coil form (Brahms 1964; Brahms & Mommaerts 1964). Thus polyadenylic acid (poly A) is known according to X-ray data to exist at acid pH in a helical two strand and right handed conformation (Rich, Davies, Crick & Watson 1961). In acid solution the same polyadenylic acid exhibits strong circular dichroic bands which disappear at high temperature (figure 2).</div>
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<p> In contrast to relatively well developed experimental and theoretical studies on polypeptides and proteins (see Gratzer 1967 and McLachlan 1967, this volume) the investigation of optical activity of polynucleotides and nucleic acids were very restricted. The optical rotatory dispersion curves of polynucleotides examined in the visible and near u. v. fit one-term Drude equation regardless of the conformation (Fresco 1961; Levedahl & James 1957; Ts’o, Helmkamp & Sander 1962). Recent circular dichroism (c. d.) measurements of several polynucleotides and nucleic acids (figure 1) indicated clearly the presence of dichroic bands in the u. v. region of base absorption which can be related to the dissymmetrical helical conformation (Brahms 1963). The intensity of circular dichroic bands decreases strongly under the conditions in which the helical structure is unstable and goes to random coil form (Brahms 1964; Brahms & Mommaerts 1964). Thus polyadenylic acid (poly A) is known according to X-ray data to exist at acid pH in a helical two strand and right handed conformation (Rich, Davies, Crick & Watson 1961). In acid solution the same polyadenylic acid exhibits strong circular dichroic bands which disappear at high temperature (figure 2).</p>
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<p> ]> </p>
<p>Circular dichroism of helical polynucleotide chains</p>
<p>BY J. BRAHMS</p>
<p>
<italic>Centre</italic>
<italic>de</italic>
<italic>Recherches</italic>
<italic>sur</italic>
<italic>les</italic>
<italic>Nacromolécules</italic>
,
<italic>Strasbourg</italic>
,
<italic>France</italic>
</p>
<p>INTRODUCTION</p>
<p>In contrast to relatively well developed experimental and theoretical studies on</p>
<p>polypeptides and proteins (see Gratzer 1967 and McLachlan 1967, this volume)</p>
<p>the investigation of optical activity of polynucleotides and nucleic acids were very</p>
<p>restricted. The optical rotatory dispersion curves of polynucleotides examined in</p>
<p>the visible and near
<mml:math>
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</mml:math>
. fit one&hyphen;term Drude equation regardless ofthe conformation</p>
<p>(Fresco 1961; Levedahl &James 1957; Ts'o, Helmkamp & Sander 1962).</p>
<p>
<mml:math>
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<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">4</mml:mn>
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<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mn mathvariant="normal">2</mml:mn>
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<mml:mn mathvariant="normal">0</mml:mn>
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</mml:math>
</p>
<p>
<mml:math>
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(nm)</p>
<p>FIGURE 1. Circular dichroic and absorption spectra (
<italic>e</italic>
)
<italic>ofDNA</italic>
in</p>
<p>aqueous solutions containing
<mml:math>
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<mml:mn mathvariant="normal">1</mml:mn>
<mml:mi mathvariant="normal">m</mml:mi>
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<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:math>
at neutral
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>Recent circular dichroism (c.d.) measurements of several polynucleotides and</p>
<p>nucleic acids (figure 1) indicated clearly the presence of dichroic bands in the
<mml:math>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>region of base absorption which can be related to the dissymmetrical helical con&hyphen;</p>
<p>formation (Brahms 1963). The intensity of circular dichroic hands decreases</p>
<p>strongly under the conditions in which the hehcal structure is unstable and goes</p>
<p>to random coil form (Brahms 1964; Brahms & Mommaerts 1964). Thus poly&hyphen;</p>
<p>adenylic acid (poly
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<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
) is known according to
<mml:math>
<mml:mi mathvariant="normal">X</mml:mi>
</mml:math>
&hyphen;ray data to exist at acid
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
</p>
<p>in a helical two strand and right handed conformation (Rich, Davies, Crick &</p>
<p>Watson 1961). In acid solution the same polyadenylic acid exhibits strong circular</p>
<p>dichroic bands which disappear at high temperature (figure 2).</p>
<p>Another
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectrum is observed when poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
is exposed to neutral solutions,</p>
<p>indicating a different conformation from the double strand hehx (figure 2).</p>
<p>At present it seems accepted that the exciton theory may explain satisfactorily</p>
<p>the optical rotatory power of helical polymers. The exciton theory was applied to a</p>
<p>[150]</p>
<p>
<italic>Circular</italic>
<italic>dichroism</italic>
<italic>of</italic>
<italic>helical</italic>
<italic>polynucleotide</italic>
<italic>chains</italic>
151</p>
<p>polymeric array by Moffitt (1956), Moffitt, Fitts & Kirkwood (1957) and largely</p>
<p>developed by Tinoco, Woody &Bradley (1963), Bradley, Tinoco &Woody (1963)</p>
<p>and Tinoco (1962).</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">λ</mml:mi>
</mml:math>
(nm)</p>
<p>FIGURE 2. Circular dichroic spectra of poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
in aqueous solutions</p>
<p>at
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
</mml:math>
and at
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">9</mml:mn>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>In order to relate the optical activity to the helical structure of polynucleotides</p>
<p>we will make a comparison between the theory and experimental results obtained</p>
<p>on models that is dimers or oligomers.</p>
<p>(
<italic>a</italic>
)
<italic>Simple</italic>
<italic>dimer</italic>
:
<italic>diadenylic</italic>
<italic>acid</italic>
</p>
<p>The exciton theory predicts that in a dimer composed of two identical residues</p>
<p>an interaction will occur between them. As a result in the excited state the dimer</p>
<p>will have two states
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="normal">+</mml:mi>
</mml:math>
<mml:math>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
and
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
of different energies due to the interaction of the</p>
<p>electrons on residue one with residue two. The general assumption is that the in&hyphen;</p>
<p>dividual residues are not too distant and behave as separate non overlapping elec&hyphen;</p>
<p>tronic system. The energies of the split states will be characterized by
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">E</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mi mathvariant="italic">E</mml:mi>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
</p>
<p>where
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
is the potential energy of interaction between groups and
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">E</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
is the energy</p>
<p>of the monomer excited state. Thqsplitting into two energy levels will be reflected</p>
<p>in the absorption spectra of the dimer where the absorption band of the monomer</p>
<p>will be split into two bands with frequencies</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">/</mml:mo>
<mml:mi mathvariant="italic">h</mml:mi>
</mml:math>
</p>
<p>(
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
frequency of the monomer band).</p>
<p>
<italic>This</italic>
<italic>sphtting</italic>
<italic>energy</italic>
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
can be evaluated by theoretical computation of transition</p>
<p>monopoles placed at the carbon and nitrogen nuclei in each adenine (Bush 1965;</p>
<p>Warshaw, Bush & Tinoco 1965). Another way of calculating
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
is by applying</p>
<p>152</p>
<p>dipole&hyphen;dipole approximation where the dipoles involved are simply the dipole</p>
<p>transition</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
<mml:mo mathvariant="normal">[</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:mo mathvariant="normal">]</mml:mo>
</mml:math>
. (1)</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
is the vector distance between the two dipoles point
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
,
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
</mml:math>
is its</p>
<p>magnitude, and
<mml:math>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:math>
the electric transition dipole moment. Alternatively, one can cal&hyphen;</p>
<p>culate the splitting by a semi&hyphen;empirical scheme (Van Holde, Brahms & Michelson</p>
<p>1965; Brahms, Michelson & Van Holde 1966). If we assume that the diadenylic</p>
<p>acid
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
represent the beginning of a single stranded helix therefore the inter&hyphen;</p>
<p>action energy
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
should be approximately the same in the dimer and in the polymer.</p>
<p>According to the nearest neighbour theory (Bradley
<italic>et</italic>
<mml:math>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mi mathvariant="italic">l</mml:mi>
</mml:math>
. 1963) the position of the</p>
<p>maximum of the perpendicularly polarized band of a polynucleotide helix can be</p>
<p>given as</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal"></mml:mo>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">+</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">h</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi class="unknown_entity" mathvariant="normal">cos</mml:mi>
<mml:mi mathvariant="italic">γ</mml:mi>
</mml:math>
, (2)</p>
<p>where
<mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
</mml:math>
is the angle of rotation of successive bases about the helix axis, and
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
</p>
<p>monomer frequency. Since the shift of the polymer spectrum is experimentally</p>
<p>determined we can eliminate
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
and calculate the splitting for the dimer and for the</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:math>
&hyphen;mer the position of
<mml:math>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:math>
&hyphen;bands. The absorption frequencies of these bands are re&hyphen;</p>
<p>lated
<italic>to</italic>
the monomer frequency
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
by</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">K</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">+</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mi mathvariant="italic">V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">h</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi class="unknown_entity" mathvariant="normal">cos</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mi mathvariant="italic">K</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="normal">+</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="italic">K</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
. (3)</p>
<p>The position ofthese bands can be calculated using the observed shift in the polymer</p>
<p>spectra (Brahms
<italic>et</italic>
<italic>al</italic>
. 1966):</p>
<p>
<mml:math>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal"></mml:mo>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi class="unknown_entity" mathvariant="normal">cos</mml:mi>
<mml:mo mathvariant="normal">{</mml:mo>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mi mathvariant="italic">K</mml:mi>
<mml:mo mathvariant="normal">/</mml:mo>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="normal">+</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:mo mathvariant="normal">}</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi class="unknown_entity" mathvariant="normal">cos</mml:mi>
<mml:mi mathvariant="italic">γ</mml:mi>
</mml:mrow>
</mml:mfrac>
</mml:math>
. (4)</p>
<p>
<italic>The</italic>
<italic>rotational</italic>
<italic>strength</italic>
,
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">k</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
of these bands in the dimer may be calculated from the</p>
<p>general equation given by Bradley
<italic>et</italic>
<italic>al</italic>
. (1963) or expressed by a simplified expres&hyphen;</p>
<p>sion (Van Holde
<italic>et</italic>
<italic>al</italic>
. 1965)</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mo mathvariant="normal">&MinusPlus;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mi mathvariant="italic">Z</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:msub>
<mml:mi mathvariant="italic">λ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:msup>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi class="unknown_entity" mathvariant="normal">sin</mml:mi>
<mml:mi mathvariant="italic">γ</mml:mi>
</mml:math>
, (5)</p>
<p>where
<mml:math>
<mml:mi mathvariant="italic">Z</mml:mi>
</mml:math>
is the vertical distance between the base planes and
<mml:math>
<mml:mi mathvariant="italic">μ</mml:mi>
</mml:math>
is the magnitude</p>
<p>of the electric transition dipole moment. We are simply considering tbe
<mml:math>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">*</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
</p>
<p>electric transition polarized in the plane of tffi base. The nitrogen non&hyphen;bonding</p>
<p>electrons of the bases can give rise to
<mml:math>
<mml:mi mathvariant="italic">n</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">*</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
transition (Mason 1955; Brahms</p>
<p>1964) but they are weak and difficult to uncover in an unambiguous way in the</p>
<p>presence of strong
<mml:math>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">*</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
absorption bands. This indicates that the rotational</p>
<p>strength
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
</mml:math>
of a dimer composed of identical residues like
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
will appear in</p>
<p>pairs of positive and negative bands separated by the ineraction energy
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
. The</p>
<p>sum of
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">+</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
and
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
</mml:mrow>
</mml:msub>
</mml:math>
is equal zero. The rotational strength is proportional to
<mml:math>
<mml:msup>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
and to</p>
<p>the distance between the residues. However, one should notice that the splitting in</p>
<p>energy between the two states
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="normal">+</mml:mi>
</mml:math>
<mml:math>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
and
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
will decrease with increasing distance</p>
<p>
<italic>Circular</italic>
<italic>dichroism</italic>
<italic>of</italic>
<italic>helical</italic>
<italic>polynucleotide</italic>
<italic>chains</italic>
</p>
<p>153</p>
<p>like
<mml:math>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mo mathvariant="normal">/</mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">3</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
according to equation (1). The mononucleotide
<italic>AMP</italic>
has very small</p>
<p>optical activity. The
<mml:math>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">*</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
electric transitions are polarized in the plane of</p>
<p>purine and
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:msup>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">ι</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">e</mml:mi>
</mml:math>
bases. The magnetic transition moment must be perpen&hyphen;</p>
<p>dicular to the base plane and therefore to the electric transition moment. The</p>
<p>small optical activity observed in some mononucleotides is probably caused by</p>
<p>the perturbation by asymmetric ribose, otherwise the monomer will be inactive.</p>
<p>In the dimer, all of the observed circular dichroism is due to the formation of the</p>
<p>dissymmetrical structure.</p>
<p>The same nearest neighbour theory can be extended to a series of oligomers. The</p>
<p>rotational strengths are given by Bradley
<italic>et</italic>
<italic>al</italic>
. (1963); the equation can be com&hyphen;</p>
<p>pressed to a more compact form (see Brahms
<italic>et</italic>
<italic>al</italic>
. 1966).</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">λ</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>FIGUBE 3. Circular dichroic spectra of diadenylic acid
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">5</mml:mn>
</mml:math>
curve 1 at
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
</mml:math>
and curve 2</p>
<p>at
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">9</mml:mn>
</mml:math>
; the absorption spectra at these two
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
values are shown as curves 3 and 4</p>
<p>respectively. The points
<mml:math>
<mml:mo mathvariant="normal"></mml:mo>
</mml:math>
correspond to the theoretical curve (the data are taken from</p>
<p>Van Holde
<italic>et</italic>
<italic>al</italic>
. 1965).</p>
<p>Figure 3 shows the circular dichroic spectra of the dimer
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
at two
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
</mml:math>
and</p>
<p>
<mml:math>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">9</mml:mn>
</mml:math>
(curve 1 and 2) and the absorption spectra (curve 3 and 4).</p>
<p>The experimental curve of
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
indicates clearly that a pair of bands of opposite</p>
<p>sign are present in the region of adenine absorption.</p>
<p>The two bands of
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
are spaced above and below the position of the monomer</p>
<p>absorption band which confirms the splitting in perfect agreement with the theory.</p>
<p>Thus while the difference in sign allows resolution in the circular dichroism spectrum,</p>
<p>the bands cannot be resolved in the absorption spectrum. We conclude that the</p>
<p>dichroism arises from the dissymmetric conformation of two adenylic residues.</p>
<p>154</p>
<p>Some conclusion can be drawn about the conformation of
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
. The two bases</p>
<p>cannot be parallel, that is the angle between the transitions moments on base one</p>
<p>and two cannot be any multiple of
<mml:math>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">8</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
since this will lead to
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:math>
and no optical</p>
<p>activity. An extended configuration in which the bases are not coplanar but perpen&hyphen;</p>
<p>dicular (see Kuhn & Rometsch 1944) will lead to
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">&PlusMinus;</mml:mo>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:math>
but there will. be no splitting</p>
<p>and therefore no
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. In
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
the distance between two oscillators is too great</p>
<p>
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
to allow an effective coupling. Furthermore, intermolecular hydrogen&hyphen;</p>
<p>bonded structure or any associative forms cannot be accepted since the circular</p>
<p>dichroism spectrum is insensitive to concentration of the samples.</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">λ</mml:mi>
</mml:math>
(nm)</p>
<p>FIGURE 4. Schematic distribution of rotational strength predicted for the first adenylate</p>
<p>oligomers for chain length
<mml:math>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:math>
to 5. Relative
<mml:math>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">l</mml:mi>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mi mathvariant="normal">Θ</mml:mi>
<mml:mn mathvariant="normal">8</mml:mn>
</mml:math>
of rotational strength are given on</p>
<p>a mole of oligomer basis (see Brahms
<italic>et</italic>
<italic>al</italic>
. 1965).</p>
<p>The examination of models of the dimer
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
led to the conclusion that the dis&hyphen;</p>
<p>symmetric conformation involves a parallel stacking of the bases rotated by an</p>
<p>angle of about 30 to
<mml:math>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">5</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
. This can represent the start of a single&hyphen;strand helix quite</p>
<p>similar in dimension to half of a double&hyphen;strand
<italic>DNA</italic>
helix.</p>
<p>Using equation (5) with
<mml:math>
<mml:mi mathvariant="italic">Z</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
<mml:math>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">8</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
, one can calculate the rota&hyphen;</p>
<p>tional strength which corrected for the cancellation yield the value of
<mml:math>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">5</mml:mn>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
</p>
<p>or
<mml:math>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
for angle
<mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
or
<mml:math>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">5</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
respectively, which is in good agreement with</p>
<p>experimental value of about
<mml:math>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
. (Van Holde
<italic>et</italic>
<italic>al</italic>
. 1965). For the trimer we</p>
<p>obtain
<mml:math>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
if
<mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">5</mml:mn>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
and
<mml:math>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">9</mml:mn>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
if
<mml:math>
<mml:mi mathvariant="italic">γ</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
. This agreement in absolute</p>
<p>value between theory and experiment is reassuring and confirms both the model and</p>
<p>the theory.</p>
<p>
<italic>Circular</italic>
<italic>dichroism</italic>
<italic>of</italic>
<italic>helical</italic>
<italic>polynucleotide</italic>
<italic>chains</italic>
</p>
<p>155</p>
<p>For higher adenylate oligomers such calculations are more difficult because of</p>
<p>large number of bands to be taken into account with resulting overlapping and</p>
<p>cancellation. Assuming that the conformation of the dimer
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
represents the</p>
<p>element of structure which will develop with increasing number of residues into a</p>
<p>single strand helix, one can make some predictions for small oligomers with a number</p>
<p>of residues
<mml:math>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:math>
ranging from 1 to 6. The distribution of rotational strength for small</p>
<p>adenylate oligomers, shown in figure 4, indicates that the higher wavelength compon&hyphen;</p>
<p>ent is always of positive rotational strength, whereas lowest wavelength always of</p>
<p>negative rotational strength (see Brahms
<italic>et</italic>
<italic>al</italic>
. 1966). The good agreement between</p>
<p>the predicted and observed characteristics (figure 4) support the model and the</p>
<p>theory of the band splitting.</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">λ</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>FIGURE 6. Circular dichroic spectra of adenylate oligonucleotides at
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
</mml:math>
. On the left are</p>
<p>shown data for the trimer at various temperatures between
<mml:math>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:math>
and
<mml:math>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:math>
; in the centre</p>
<p>for the heptomer at temperatures
<mml:math>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:math>
and
<mml:math>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
, and on the right for the high polymer be&hyphen;</p>
<p>tween
<mml:math>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:math>
and
<mml:math>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:math>
. Curve 7 is for the quaternary ammonium salt of poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
in 98&percnt;</p>
<p>ethanol, and curve 8 for the monomer
<italic>AMP</italic>
in aqueous solution.</p>
<p>Figure 5 indicates the observed circular dichroism curves for some adenylate</p>
<p>oligomers at neutral
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
. Qualitatively the general shape for all the oligomers is the</p>
<p>same for the dimer and for the high polymer. One may describe the structure of</p>
<p>poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
in neutral aqueous solution and at low temperatures as a single&hyphen;chain stacked&hyphen;</p>
<p>base helix. This is also demonstrated in figure 6 where the rotational strength</p>
<p>per mole of residues increases smoothly with the chain length from the dimer. In</p>
<p>contrast at acid
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
the rotational strength exhibit a sudden increase at about the</p>
<p>level of heptamer. The changes in the circular dichroism spectra of oligo adenylics</p>
<p>at acidpH are typical ofthe double strand formation. Thus the same molecule, poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
</p>
<p>can exist in two conformations.</p>
<p>156</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:math>
</p>
<p>FIGURE 6. Rotational strength of the positive dichroic band as a function of chain length
<mml:math>
<mml:mi mathvariant="italic">N</mml:mi>
</mml:math>
</p>
<p>for adenylate oligomers at
<mml:math>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mo mathvariant="normal">;</mml:mo>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">5</mml:mn>
</mml:math>
;
<mml:math>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>(
<italic>b</italic>
)
<italic>Rotational</italic>
<italic>strength</italic>
<italic>of</italic>
<italic>different</italic>
<italic>dimers</italic>
</p>
<p>The described method of calculating
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
</mml:math>
will be adequate for dimers composed of</p>
<p>identical residues like
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
with a single absorption band in the region under in&hyphen;</p>
<p>vestigation
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
</mml:math>
320 to
<mml:math>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
. However, we shall consider more
<mml:math>
<mml:mover accent="true">
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
<mml:mo mathvariant="normal">´</mml:mo>
</mml:mover>
</mml:math>
omplex cases of</p>
<p>dimers composed of different nucleotides. Furthermore, such bases like guanine</p>
<p>and cytosine exhibit two distinct bands near each other in the same spectral region,</p>
<p>at neutral
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
. One is led to consider not only the contribution of degenerate effects</p>
<p>or resonant interactions but also non&hyphen;degenerate or non&hyphen;resonant interactions.</p>
<p>Let us consider a dimer with stacked parallel bases characterized by a ground</p>
<p>state and two excited states
<mml:math>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:math>
and
<mml:math>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:math>
. The rotational strength will be expressed</p>
<p>by the following equation (Bush 1965) in Tinoco's notation
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">9</mml:mn>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">z</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
:</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">O</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">π</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mi mathvariant="italic">c</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo mathvariant="normal">[</mml:mo>
<mml:mo mathvariant="normal">&MinusPlus;</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>
<mml:math>
<mml:mi mathvariant="normal">+</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo mathvariant="normal">:</mml:mo>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">h</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>
<mml:math>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mo mathvariant="normal">:</mml:mo>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">h</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">]</mml:mo>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>The first equation
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
describes degenerate interaction between identical mono&hyphen;</p>
<p>mers andis the same as that given by Tinoco (1963). The contribution to the rotational</p>
<p>strength in a dimer in which subunit one absorbs at
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
and subunit two absorbs at</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
is given by equation
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
and the equation
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
refers to the contribution to the</p>
<p>
<mml:math>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">t</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">c</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="italic">η</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:math>
strength for the dimer in which monomer one absorbs at
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
and monomer</p>
<p>
<italic>Circular</italic>
<italic>dichroism</italic>
<italic>of</italic>
<italic>helical</italic>
<italic>polynucleotide</italic>
<italic>chains</italic>
</p>
<p>157</p>
<p>two absorbs at
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
. The interaction potential
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
between degenerate groups refers</p>
<p>to the splitting of the degenerate bands into
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="normal">+</mml:mi>
</mml:math>
<mml:math>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
and
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
levels, while for non&hyphen;</p>
<p>degenerate interactions the
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
is included explicitly. The equation (6) will allow</p>
<p>also the calculation of
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
</mml:math>
oftwo sequence isomers where monomer one is 3' linked and</p>
<p>monomer two 5' linked. In contrast to the diadenylic acid where only one absorption</p>
<p>band is observed, dimers containing cytosine and guanine with two bands will</p>
<p>request the calculation of
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">O</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
and
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">O</mml:mi>
<mml:mi mathvariant="italic">B</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
. If all the bands are considered the sum ofthe</p>
<p>rotational strength will be zero in the region under consideration that is 220
<italic>to</italic>
</p>
<p>300
<mml:math>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>In other words the equation (6) predicts that the circular dichroism spectra will</p>
<p>be composed of pairs of positive and negative bands. This is confirmed by experi&hyphen;</p>
<p>mentally obtained
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. curves of some heterodimers
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">U</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">C</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
<mml:math>
<mml:mi mathvariant="italic">G</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">U</mml:mi>
</mml:math>
(Brahms,</p>
<p>Maurizot & Michelson 1966).</p>
<p>(
<italic>c</italic>
)
<italic>Case</italic>
<italic>of</italic>
<italic>non</italic>
&hyphen;
<italic>conservative</italic>
<mml:math>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="italic">d</mml:mi>
</mml:math>
.
<italic>spectra</italic>
</p>
<p>All previously examined circular dichroic spectra of oligonucleotides were in</p>
<p>good agreement with the exciton theory. Therefore, one may expect that in general</p>
<p>the
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectra of all oligonucleotides in a single strand conformation will be com&hyphen;</p>
<p>posed of about equal positive and negative band for which the local sum rule will</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">λ</mml:mi>
</mml:math>
(nm)</p>
<p>FIGURE 7. Circular dichroic spectrum of
<mml:math>
<mml:mi mathvariant="italic">C</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">C</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">5</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
at neutral pH in
<mml:math>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="italic">K</mml:mi>
<mml:mi mathvariant="italic">F</mml:mi>
</mml:math>
and at about</p>
<p>
<mml:math>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:math>
. Dashed line corresponds to the
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectrum of the monomer
<italic>CMP</italic>
.</p>
<p>be obeyed. Figure 7 shows
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectra of a dinucleotide
<mml:math>
<mml:mi mathvariant="italic">C</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">C</mml:mi>
</mml:math>
which indicates</p>
<p>clearly the presence of one or two hands of positive sign in the region of 300 to</p>
<p>
<mml:math>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:math>
(see Bush & Brahms 1966). One cannot observe the presence of a band of</p>
<p>equal amplitude and opposite sign. In general this compound exhibits
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectra</p>
<p>completely different in shape of that of
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">p</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
. Thus the sum of the rotational</p>
<p>158</p>
<p>strengths of oligomer shown in figure 7 is not equal zero in the spectral region under</p>
<p>consideration. This does not represent any violation of the general optical activity</p>
<p>sum rule since the far ultraviolet region was not investigated.</p>
<p>The understanding of this more complex situation requires to examine a very</p>
<p>general theory of Tinoco (1962) of polymer optical activity, in order to find terms</p>
<p>which will contribute to the rotational strength not as equal positive and negative</p>
<p>pairs.</p>
<p>Tinoco's treatment is based on Kirkwood theory (1937) and describes the rota&hyphen;</p>
<p>tional strength of the polymer by the following expression:</p>
<p>
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<mml:mi mathvariant="normal">=</mml:mi>
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</mml:mrow>
<mml:mrow>
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</mml:mrow>
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</mml:mrow>
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<mml:msub>
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</mml:mrow>
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</mml:math>
</p>
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<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">e</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>
<mml:math>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mo mathvariant="normal">/</mml:mo>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:munder>
<mml:mstyle displaystyle="true" mathvariant="normal">
<mml:mo></mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi mathvariant="italic">J</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:munder>
<mml:munder>
<mml:mstyle displaystyle="true" mathvariant="normal">
<mml:mo></mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:munder>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mo mathvariant="normal">:</mml:mo>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mo mathvariant="normal">}</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">k</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">h</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo mathvariant="normal">]</mml:mo>
</mml:math>
:
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>In this equation term
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
represents the contribution of the monomer which is</p>
<p>very small for mononucleotides, as previously indicated. Terms
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
,
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
,
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">e</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
,</p>
<p>will be zero in the planar bases for the
<mml:math>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mo mathvariant="normal"></mml:mo>
<mml:msup>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">*</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
transitions which we are considering</p>
<p>only. This is because all the electric transition moments are in the plane of the bases</p>
<p>and the magnetic moments
<mml:math>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:math>
are perpendicular. Furthermore, the coefficient</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="normal">y</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mo mathvariant="normal">;</mml:mo>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
is small since it involves the ground state of group
<mml:math>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:math>
; according to the dipole</p>
<p>approximation</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">V</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mo mathvariant="normal">,</mml:mo>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mi mathvariant="italic">b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
. T.
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">j</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
. (8)</p>
<p>In conclusion, the contribution of the terms
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
and
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
is expected to provide</p>
<p>the explanation for the observed non&hyphen;conservative
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectra of oligonucleotides,</p>
<p>in the region of 320 to 200
<mml:math>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>The calculation of these two terms (Bush & Brahms 1966) leads to the division</p>
<p>of the summation over the excited states into two groups.</p>
<p>1. One must consider the interaction among transitions in the region of 200 to</p>
<p>
<mml:math>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:math>
, so called 'near
<mml:math>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
' transitions. However, term
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
yields the rotational</p>
<p>strength which give rise to positive and negative values like exciton terms (see</p>
<p>§(
<italic>b</italic>
)) and cannot explain the observed effects.</p>
<p>2. The interaction with the' far
<mml:math>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
' transitions giving rise to rotational strength</p>
<p>in the' near
<mml:math>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">v</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mo mathvariant="normal">'</mml:mo>
</mml:math>
. These transitions to higher energy states are not known in nucleo&hyphen;</p>
<p>tides; they will be taken together into one term using Kirkwood polarizability</p>
<p>
<italic>Circular</italic>
<mml:math>
<mml:mi mathvariant="italic">d</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">c</mml:mi>
<mml:mi mathvariant="italic">h</mml:mi>
<mml:mi mathvariant="italic">r</mml:mi>
<mml:mi mathvariant="italic">o</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">S</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:math>
<italic>of</italic>
<italic>helical</italic>
<italic>polynucleotile</italic>
<italic>chains</italic>
</p>
<p>159</p>
<p>approximation. The evaluation of terms
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">b</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
and
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mi mathvariant="italic">f</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
include the approximation</p>
<p>of
<mml:math>
<mml:mi mathvariant="italic">y</mml:mi>
<mml:mo mathvariant="normal">&Backslash;</mml:mo>
</mml:math>
by equation (8) where
<mml:math>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:math>
is the ordinary dipole interaction tensor</p>
<p>
<mml:math>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:msubsup>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">8</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo mathvariant="normal">[</mml:mo>
<mml:mi mathvariant="normal">I</mml:mi>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">3</mml:mn>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:mo mathvariant="normal">]</mml:mo>
</mml:math>
. (9)</p>
<p>The following equation gives the rotational strength at
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
arising from the inter&hyphen;</p>
<p>action ofthe transition
<mml:math>
<mml:mn mathvariant="italic">0</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mi mathvariant="italic">α</mml:mi>
</mml:math>
with all the far
<mml:math>
<mml:mi mathvariant="normal">u</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">v</mml:mi>
</mml:math>
. transitions above a certain energy</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">ω</mml:mi>
</mml:math>
which will be taken as about 50000
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:msup>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:math>
<mml:math>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="normal">o</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
<mml:mi mathvariant="normal">&MediumSpace;</mml:mi>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">A</mml:mi>
<mml:mi mathvariant="italic">ω</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mn mathvariant="normal">2</mml:mn>
<mml:munder>
<mml:mstyle displaystyle="true" mathvariant="normal">
<mml:mo></mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:munder>
<mml:munder>
<mml:mstyle displaystyle="true" mathvariant="normal">
<mml:mo></mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
</mml:munder>
<mml:mfrac>
<mml:mrow>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">h</mml:mi>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="italic">J</mml:mi>
<mml:mo mathvariant="normal">[</mml:mo>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="italic">π</mml:mi>
<mml:mi mathvariant="italic">i</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">C</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
. T.
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">ω</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mo mathvariant="normal">|</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">ι</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">×</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">+</mml:mi>
<mml:msubsup>
<mml:mi mathvariant="italic">ν</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn mathvariant="normal">2</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:msub>
<mml:mi mathvariant="italic">μ</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mi mathvariant="italic">a</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
. T.
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">ω</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">m</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">i</mml:mi>
<mml:mi mathvariant="italic">a</mml:mi>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
<mml:mo mathvariant="normal">]</mml:mo>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
</p>
<p>where
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">α</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">ω</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
is the polarizability tensor arising from all transition of energy greater</p>
<p>than
<mml:math>
<mml:mi mathvariant="italic">ω</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>This equation yields a contribution of a non&hyphen;conservative character. The first</p>
<p>term is the Kirkwood polarizability term and depends on the polarizability dif&hyphen;</p>
<p>ferences in plane and out of plane. The second term contains the magnetic moment</p>
<p>and the polarizability. Both terms depend on the direction of the electric dipole</p>
<p>transition moment. This emphasizes the importance of the geometric factor.</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">λ</mml:mi>
</mml:math>
(nm)</p>
<p>FIGURE 8. Circular dichroic curves of
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
from tobacco mosaic virus, in
<mml:math>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:math>
</p>
<p>
<mml:math>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mn mathvariant="normal">1</mml:mn>
</mml:math>
at neutral temperature: 22, 46,
<mml:math>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>It is possible that through this dependence the non&hyphen;conservative effect is promi&hyphen;</p>
<p>nent in the
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectra of
<italic>single</italic>
<italic>strand</italic>
oligonucleotides containing cytosine, but is</p>
<p>not in the
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. of diadenylic acid. This is probably of importance for the under&hyphen;</p>
<p>standing ofthe differences between the
<mml:math>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mo mathvariant="normal">.</mml:mo>
<mml:mi mathvariant="normal">d</mml:mi>
</mml:math>
. spectra of
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
which is ofnon&hyphen;conserva&hyphen;</p>
<p>tive type (figure 8) and of
<italic>DNA</italic>
which conservative (figure 1).</p>
<p>(
<italic>d</italic>
)
<italic>Stability</italic>
<italic>of</italic>
<italic>polynucleotide</italic>
<italic>hebices</italic>
</p>
<p>Further informations about the helical conformations of polynucleotide chains</p>
<p>are obtained from the studies of relative stability. We will take as an example a</p>
<p>series of adenylate oligomers of various chain lengths from the dimer to the high</p>
<p>polymer at neutral
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
. The circular dichroism which is characteristic of these</p>
<p>160</p>
<p>single&hyphen;strand helices disappears gradually as the temperature is raised (figure 5).</p>
<p>This process is reversible and presumably reflects the loss of the ordered helical</p>
<p>structure. This gradual change depicted in figure 9 where the rotational strength of</p>
<p>the positive band (
<italic>R</italic>
) is plotted against temperature. One can suppose a low</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">T</mml:mi>
<mml:msup>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">&compfn;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>FIGURE 9. The change in rotational strength of the positive dichroic band with</p>
<p>temperature for some adenylate oligomers at
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mn mathvariant="normal">7</mml:mn>
<mml:mo mathvariant="normal"></mml:mo>
<mml:mn mathvariant="normal">4</mml:mn>
<mml:mo mathvariant="normal">.</mml:mo>
</mml:math>
</p>
<p>enthalpy value of the process which may be largely of non&hyphen;conServative type. This</p>
<p>allows to define an. apparent equilibrium constant
<mml:math>
<mml:mi mathvariant="italic">K</mml:mi>
</mml:math>
, by</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">K</mml:mi>
<mml:mi mathvariant="normal">=</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mo mathvariant="normal">-</mml:mo>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo mathvariant="normal">,</mml:mo>
</mml:math>
</p>
<p>where
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
</mml:math>
represents the rotational strength at a given temperature and
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mn mathvariant="normal">0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:math>
and
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
</p>
<p>are the limiting values of
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
</mml:math>
at low and high temperatures, respectively. The value</p>
<p>of
<mml:math>
<mml:msub>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mrow>
<mml:mi mathvariant="italic">n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
at high temperature approaches zero which is expected for a random chain of</p>
<p>optically inactive subunits. The low temperature limit was never reached in our</p>
<p>experiments and was estimated by extrapolation of curves shown in figure 9.</p>
<p>Having obtained the value ofequilibrium constants, one can construct the
<mml:math>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mo mathvariant="normal">'</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:math>
</p>
<p>Hoff plot and calculate
<mml:math>
<mml:mi mathvariant="normal">Δ</mml:mi>
<mml:msup>
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
for the thermal denaturation process.</p>
<p>Figure 10 shows that the lines obtained for several adenylate oligomers are</p>
<p>parallel indicating that
<mml:math>
<mml:mi mathvariant="normal">Δ</mml:mi>
<mml:msup>
<mml:mi mathvariant="italic">H</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
must be the same for all oligomers. We may conclude</p>
<p>that the thermodynamic properties are not dependent upon the chain length which</p>
<p>is typical of a non&hyphen;cooperative process (see Brahms
<italic>et</italic>
<italic>al</italic>
. 1966). This means that</p>
<p>essentially the same elementary process characterizes the 'melting' of the ordered</p>
<p>structure of the polymer and of the dimer. One may describe this process as un&hyphen;</p>
<p>stacking of a pair of bases. The structure of a single strand polynucleotide chain</p>
<p>may be represented as a collection of stacked dimerswhich may break independently</p>
<p>
<mml:math>
<mml:msup>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mrow>
<mml:mi mathvariant="normal">n</mml:mi>
</mml:mrow>
</mml:msup>
</mml:math>
a non&hyphen;cooperative fashion.</p>
<p>At temperatures well below
<mml:math>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mi mathvariant="normal">o</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:math>
poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
at neutral
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
adopt a rigid conforma&hyphen;</p>
<p>tion of single strand and right&hyphen;handed helix with the stacked bases.</p>
<p>
<italic>Circular</italic>
<italic>dichroism</italic>
<italic>of</italic>
<italic>helical</italic>
<italic>polynucleotide</italic>
<italic>chains</italic>
</p>
<p>161</p>
<p>
<mml:math>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:msup>
<mml:mn mathvariant="normal">0</mml:mn>
<mml:mrow>
<mml:mi mathvariant="italic">θ</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo mathvariant="normal">/</mml:mo>
<mml:mi mathvariant="italic">T</mml:mi>
</mml:math>
</p>
<p>FIGURE 10. Van't Hoff plot corresponding to the data shown in figure 8</p>
<p>(for explanation see the text).</p>
<p>In contrast in the double stranded structure of poly
<mml:math>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
at acid
<mml:math>
<mml:mi mathvariant="normal">p</mml:mi>
<mml:mi mathvariant="normal">H</mml:mi>
</mml:math>
the state of any</p>
<p>residue is dependent of that of its neighbours. The melting process' is cooperative</p>
<p>and chain length dependent (figure 11).</p>
<p>
<mml:math>
<mml:mi mathvariant="italic">T</mml:mi>
<mml:msup>
<mml:mi mathvariant="normal">(</mml:mi>
<mml:mrow>
<mml:mo mathvariant="normal">&compfn;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mi mathvariant="normal">)</mml:mi>
</mml:math>
</p>
<p>FIGURE 11. The change in rotational strength for some adenylate oligomers in</p>
<p>aoidic solutions as a function of temperature.</p>
<p>I I</p>
<p>Vol. 297 A.</p>
<p>162</p>
<p>The double stranded structures are stabilized by the stacking of the bases and</p>
<p>by hydrogen and ionic bonds between the two chains. These single and double</p>
<p>stranded conformations provide good models for the understanding of
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mi mathvariant="italic">N</mml:mi>
<mml:mi mathvariant="italic">A</mml:mi>
</mml:math>
and</p>
<p>
<italic>DNA</italic>
structure.</p>
<p>REFHlRHiNcEs (Brahms)</p>
<p>Bradley, D. F., Tinoco, J. Jr. & Woody, R. W. 1963
<italic>Biopolymers</italic>
1, 239.</p>
<p>Brahms, J. 1963
<italic>J</italic>
.
<italic>Am</italic>
.
<italic>Chem</italic>
.
<italic>Soc</italic>
. 85, 3298.</p>
<p>Brahms, J. 1964
<italic>Nature</italic>
,
<italic>Lond</italic>
. 202, 797.</p>
<p>Brahms, J., Maurizot, J. C. & Michelson, A. M. 1966 (in preparation).</p>
<p>Brahms, J. & Mommaerts, W. F. H. M. 1964
<italic>J</italic>
.
<italic>Mol</italic>
.
<italic>Biol</italic>
.</p>
<p>Brahms, J., Michelson, A. NI. & Van Holde, K. E. 1966
<italic>J</italic>
.
<italic>Molec</italic>
.
<italic>Biol</italic>
15, 467.</p>
<p>Bush, C. A. 1965 Thesis, University of California, Berkeley.</p>
<p>Bush, C. A. & Brahms, J. 1966
<italic>J</italic>
.
<italic>Chem</italic>
.
<italic>Phys</italic>
. (in the Press).</p>
<p>Fresco, J. R. 1961
<italic>Tetrahedron</italic>
13, 185.</p>
<p>Gratzer, W. B. 1967
<italic>Proc</italic>
.
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mi mathvariant="italic">o</mml:mi>
<mml:mi mathvariant="italic">y</mml:mi>
</mml:math>
.
<italic>Soc</italic>
. A 297, 163 (this Discussion).</p>
<p>Kirkwood, J. G. 1937
<italic>J</italic>
.
<italic>Chem</italic>
.
<italic>Phys</italic>
. 5, 479.</p>
<p>Kuhn, W. & Rometsch, M. 1944
<italic>Helv</italic>
.
<italic>Chem</italic>
.
<italic>Acta</italic>
27, 1090.</p>
<p>Levedahl, B. H. & James, T. W. 1957
<italic>Biochim</italic>
.
<italic>biophys</italic>
.
<italic>Acta</italic>
26, 89.</p>
<p>Mason, S. F. 1955
<italic>Spec</italic>
.
<italic>Publ</italic>
. no. 3
<italic>Chem</italic>
.
<italic>Soc</italic>
. p. 139.</p>
<p>McLachlan, A. D. 1967
<italic>Proc</italic>
.
<mml:math>
<mml:mi mathvariant="italic">R</mml:mi>
<mml:mi mathvariant="italic">o</mml:mi>
<mml:mi mathvariant="italic">y</mml:mi>
</mml:math>
.
<italic>Soc</italic>
. A 297, 141 (this Discussion).</p>
<p>Moffitt, W. 1956
<italic>J</italic>
.
<italic>Chem</italic>
.
<italic>Phys</italic>
. 25, 467.</p>
<p>Moffitt, W., Fitts, D. D. & Kirkwood, J. G. 1957
<italic>Proc</italic>
.
<italic>Natn</italic>
.
<italic>Acad</italic>
.
<italic>Sci</italic>
.
<italic>U</italic>
.
<italic>S</italic>
.
<italic>A</italic>
. 43, 723.</p>
<p>Rich, A., Davies, D. R., Crick, F. H. C. & Watson, J. D. 1961
<italic>J</italic>
.
<italic>molec</italic>
.
<italic>Biol</italic>
. 3, 71.</p>
<p>Tinoco, I. Jr. 1962
<italic>Adv</italic>
.
<italic>chem</italic>
.
<italic>Phys</italic>
. 4, 113.</p>
<p>Tinoco, I. Jr. 1963
<italic>Rod</italic>
.
<italic>Res</italic>
. 20, 133.</p>
<p>Tinoco, I. Jr., Woody, R. W. & Bradley, D. F. 1963
<italic>J</italic>
.
<italic>Chem</italic>
.
<italic>Phys</italic>
. 38, 1317.</p>
<p>Ts'o, P. O. P., Helmkamp, G. K. & Sander, C.
<mml:math>
<mml:mn mathvariant="normal">1</mml:mn>
<mml:mn mathvariant="normal">9</mml:mn>
<mml:mn mathvariant="normal">6</mml:mn>
<mml:mi mathvariant="normal">z</mml:mi>
</mml:math>
<italic>Biochim</italic>
.
<italic>biophys</italic>
.
<italic>Acta</italic>
55, 584.</p>
<p>Van Holde, K. E., Brahms, J. & Michelson, A. M. 1965
<italic>J</italic>
.
<italic>molec</italic>
.
<italic>Biol</italic>
. 12, 726.</p>
<p>Warshaw, M. M., Bush, C. A. & Tinoco, J. Jr. 1965
<italic>Biochem</italic>
.
<italic>Biophys</italic>
.
<italic>Res</italic>
.
<italic>Commun</italic>
. 18, 633.</p>
</body>
</article>
</istex:document>
</istex:metadataXml>
<mods version="3.6">
<titleInfo lang="en">
<title>A discussion on circular dichroism: electronic and structural principles - Circular dichroism of helical polynucleotide chains</title>
</titleInfo>
<titleInfo type="alternative" lang="en" contentType="CDATA">
<title>A discussion on circular dichroism: electronic and structural principles - Circular dichroism of helical polynucleotide chains</title>
</titleInfo>
<name type="personal">
<namePart type="given">J.</namePart>
<namePart type="family">Brahms</namePart>
<namePart>J. Brahms</namePart>
<affiliation>Centre de Recherches sur les Macromolécules, Strasbourg, France</affiliation>
<role>
<roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Ronald Sydney</namePart>
<namePart type="family">Nyholm</namePart>
<namePart>R. S. Nyholm, F. R. S.</namePart>
<nameIdentifier type="royal society fellow">NA1866</nameIdentifier>
<role>
<roleTerm type="text">organiser</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre>
<originInfo>
<publisher>The Royal Society</publisher>
<place>
<placeTerm type="text">London</placeTerm>
</place>
<dateIssued encoding="w3cdtf">1967-02-27</dateIssued>
<copyrightDate encoding="w3cdtf">2017</copyrightDate>
</originInfo>
<language>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
<languageTerm type="code" authority="rfc3066">en</languageTerm>
</language>
<physicalDescription>
<extent unit="words">3793</extent>
</physicalDescription>
<abstract type="extract" lang="en">In contrast to relatively well developed experimental and theoretical studies on polypeptides and proteins (see Gratzer 1967 and McLachlan 1967, this volume) the investigation of optical activity of polynucleotides and nucleic acids were very restricted. The optical rotatory dispersion curves of polynucleotides examined in the visible and near u. v. fit one-term Drude equation regardless of the conformation (Fresco 1961; Levedahl & James 1957; Ts’o, Helmkamp & Sander 1962). Recent circular dichroism (c. d.) measurements of several polynucleotides and nucleic acids (figure 1) indicated clearly the presence of dichroic bands in the u. v. region of base absorption which can be related to the dissymmetrical helical conformation (Brahms 1963). The intensity of circular dichroic bands decreases strongly under the conditions in which the helical structure is unstable and goes to random coil form (Brahms 1964; Brahms & Mommaerts 1964). Thus polyadenylic acid (poly A) is known according to X-ray data to exist at acid pH in a helical two strand and right handed conformation (Rich, Davies, Crick & Watson 1961). In acid solution the same polyadenylic acid exhibits strong circular dichroic bands which disappear at high temperature (figure 2).</abstract>
<note type="footnotes">This text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR.</note>
<relatedItem type="host">
<titleInfo>
<title>Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences</title>
</titleInfo>
<titleInfo type="abbreviated">
<title>Proc. R. Soc. Lond. A</title>
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