The analysis of circular dichroism of biomolecules

1 THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES P . M . BAYLEY

National Institute for Medical Research, Mill Hill, London, NW7 CONTENTS 1. INTRODUCTION

3

2. BASIC DEFINITIONS

4

3. THE ELECTRONIC ORIGINS OF ROTATIONAL STRENGTH

8

4. MODELS FOR OPTICAL ACTIVITY AND ITS CONFORMATIONALDEPENDENCE 4.1. The Mixing of States 4.2. The Coupling of Transitions

10 12 14

5. THE OPTICAL PROPERTIES OF PEPTIDES 5.1. Dipeptides 5.2. Extensions to Polymers 5.3. Summary of the Position

17 17 28 28

6. Tim DERIVATION OF ROTATIONAL STRENGTH FROM O R D AND CD SPECTRA 6.1. Resolution of Overlapping Effects of the Same Sign 6.2. Overlapping Effects of Opposite Signs--Equal Effects (Couplets and Conservative Systems) 6.3. Overlapping Effects of Opposite Signs--Unequal Effects (Non-conservative Systems)

29 31 32 35

7. FACTORS OTHER THAN CONFORMATIONAFFECTING EXPERIMENTAL SPECTRA 7.1. Chemical Constitution 7.2. p H 7.3. Keto-Enol Tautamerisms: Cis-Trans Isomerization 7.4. Redox State: Liganding 7.5. Solvent 7.6. Temperature 7.7. The Attachment of Small Molecules 7.8. Summary

39 39 40 40 41 41 42 42 43

8. THE STANDARD STRUCTURES; POLYPEPTIDES 8.1. The a Helix 8.2. The fl Structure 8.3. The Random Coil

43 43 45 46

9. MULTI-COMPONENT ANALYSIS 9.1. Analytical Methods 9.2. Limitations 9.3. Further Developments

47 48 50 50

10. QUESTIONS SUSCEPTIBLE TO TH]K)RETICAL TREATMENT: SOME RESULTS 10.1 Irregular Structures: Lysozyme 10.2. Small Peptide Systems 10.2.1. Gramicidin S 10.2.2. Gramicidin A 10.3. Detection of Conformational Changes in Proteins by Peptide CD

51 52 55 55 58 60

11. EXPERIMENTALAPPLICATIONS 11.1. Small Molecules: Nueleotide Coenzymes and Analogues 11.2. Extrinsic Chromophores as Conformational Probes 11.3. Membranes and Related Systems 11.4. Fast Kinetic Observations: Instrumental Developments

61 61 64 68 69

1

2

CONTENTS

12. CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

70 72 72

1 THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES P. M. BAYLEY National Institute for Medical Research, Mill Hill, London, NW7

1. INTRODUCTION Optical rotatory dispersion (ORD) and circular dichroism (CD) properties of molecules are determined by their conformation, i.e., their specific three-dimensional organization. The importance of conformation in the function of biological molecules is now an accepted fact, and measurement of ORD and CD spectra has become a routine means of studying molecular conformation in solution. The interpretation of these spectra is often complicated. The aim of this article is to give a simple but functional description of some of the less familiar spectroscopic principles involved, and to show how an understanding of the origins of optical activity in biomolecules can help in deriving structural information from CD spectra. Two broad approaches to the analysis of CD are discussed. (i) In the phenomenological approach, the spectra of complex molecules are analysed in terms of the sum of contributions from specific structures such as helices, coils, and sheets. This multicomponent analysis depends upon comparison of experimental spectra with those of the well-characterized structures taken alone and in simple combinations. This procedure is partially successful, but is limited by the variability of the reference states and by the degree of correspondence of these with the actual conformations present. An understanding of the origins of optical activity helps to set the limits to the interpretation of these analyses. (ii) In the theoretical approach, optical rotation theory is used to predict the properties of proposed structures. For well-characterized chromophores, such as peptide, aromatic, and nucleotide, the optical properties may be computed for a variety of systems, e.g. for dimers as a function of the conformational variables; for small specific structures with a limited number of chromophores; and for large, effectively infinite, polymeric systems of regular structure, embodying the elements of helical symmetry. In addition, the irregular, yet fully specified regions of biological macromolecules can be treated, and the limitations of the multicomponent analysis can be assessed quantitatively. The second approach with which this article is mainly concerned emphasizes that it is the total conformation which determines the optical properties. Rotational strength is, ideally, the parameter by which theory and experiment are to be compared. This quantity, which is the factor common to ORD and CD, is in general readily obtained from CD spectra, and may be derived theoretically. In all the theoretical mechanisms involved, the sign and magnitude of the rotational strength are dependent upon conformation. The methods apply to assemblies of all chromophores; particular examples will be taken from proteins and polypeptides. Finally, applications of the theoretical ideas are discussed and examples from current experimental work are presented.

4

P . M . BAYLEY

2. B A S I C

DEFINITIONS

Details of the basic principles may be found in the articles by Moscowitz (1960), Schellman and Schellman (1964), and Fasman (1963) and the books of Velluz and Legrand (1965) and Crabb6 (1965). Principles of electronic absorption spectroscopy are treated at an intermediate level in the books by Sandorfy (1964) and Murrell (1963). Only a brief survey of principles is given here. (i) Absorption. In the visible and ultraviolet regions of the electromagnetic spectrum (600-180 nm), the interaction of radiation with the polarizable electrons of the molecule causes a redistribution of the electron density, and a reduction of the velocity of the radiation (relative to velocity in vacuo) by the factor n, the refractive index. At certain frequencies v, the energy of the incident radiation will satisfy the condition AE -----by, where AE is the enorgy difference between the ground state and an electronic excited state, and the electron will undergo a transition into the excited state. This transition is characterized by the frequency, or wavelength at which it occurs, and the magnitude of the electronic displacement involved. In the vapour state, absorption spectra approximate to a collection of discrete

1.40

1.20 1.00-

y MO

•

~

~t(0

0.80. 0.60 0.40.

f,,,\

0.20. 0'00

1

1

),

1

~1~ Xo X,+Ao --0.20 -0.40.

-0"6-0.5.00--4:00-.3:00_2:00-1:00 0:00 1-'00 2"00 3:00 4:00 5.00 Uo units delta

F I o . 1. p ~ r s

o f a Gaussian curve. The~curve y = Yo exp -- uo~ w

erooo =

the area is given in terms of Ao, the half-width:at Yo/e by area = ~/(~) × yo × Ao or, in l~rms o f h, the width at yo/2 by area ~ 1.06 × Yo × h Ao and h are related by Ao = 0.598 h.

THE ANALYSISOF CIRCULARDICHROISM OF BIOMOLECULES

5

lines corresponding to such transitions, with fine structure deriving from different vibrational levels of the two electronic states. In solution, the spectra are broadened by interaction of the chromophore with the solvent, vibrational structure may be lost entirely, and smooth curves are observed with defined band shape, e.g. Gaussian, log-normal (Siano and Metzler, 1969), etc. The parameters of a Gaussian curve are given in Fig. 1 and all derivations will be made for this band shape. The integrated area under the absorption band of the Kth transition yields the quantityfr, the oscillator strength of classical theory, or its quantummechanical analogue, the dipole strength Dr. This quantity can be calculated from the computed electron densities of ground and excited states. The absorption spectrum may be expressed as the sum of a series of transitions, characterized by intensity Dr, located at ~r and with Ar (Gaussian) bandwidth. For practical purposes it is more convenient to use the maximum absorption ~max, ~r and At, where E is molar absorptivity (molecular extinction coefficient). Useful relationships a r e f r ----4.6 x 10 -9 X ~max X h (cm -1) and f =

1.085 x 102 x Dx/Ax (nm)

(ii) Optical activity comprises the phenomena of optical rotation and circular dichroism both of which derive from the unequal interaction of the right- and left-handed circularly polarized components of plane polarized light with asymmetric molecules. Optical activity is characterized by the rotational strength of a transition Rx, which may be positive or negative. ORD and CD spectra may therefore be represented as the sum of a series of transitions, characterized by intensity Rr, located at Ax, and with Ax (Gaussian) bandwidth. (iii) Circularly polarized light may be thought of as an electrical vector rotating with the appropriate handedness while simultaneously propagating linearly towards an observer. The sense of hand is that seen by the observer. (iv) Optical rotation. The rotation of the plane of polarization of plane polarized light was formerly known as circular birefringence. This more descriptive title indicated the origin of the effect as the difference in nL and nR, the refractive indices for left- and righthanded circularly polarized light. The rotation is given by a = ~r/A (nL -- nR), with units radians per centimetre of path. [a], the specific rotation of a solution, concentration C g m l - ~ is given by [a] = a1800/Crr, with units degree/deeimetre path for 1 g/cc: it is this quantity which is measured experimentally. For a solution C g m l - 1, path length L decimotres, observed rotation in degrees (aobs), M =

(%bs) CL

[ff], the molecular rotation of this solution, solute molecular weight M is given by [~] ---[,~]M/100, with units degree cm 2 decimole -x. For polymers, a mean residue molecular weight is generally taken for M, giving [m] the mean residue rotation. Correction for solvent refractive index gives [m'] = [m] 3/(n 2 + 2). (v) Circular dichroism is the difference in extinction coefficient for left- and right-handed circularly polarized light. A~ = (% -- ER) where all ~ refer to molecular extinctions and units, as for ¢, are mole- 1 cm 2 or r,l-~ cm -~, i.e. 1 cm path of 1 molar solution. (vi) Ellipticity is an alternative means of expressing circular diehroism: the differential absorptivity for left- and right-handed circularly polarized light causes the transmitted light to be elliptieally polarized to a degree directly proportional to the circular dichroism. Molecular ellipticity is given by [0] == 3299. A~; units are degree cm 2 deeimole-t

6

P.M. BAY~y

Rotational strength is given as the integrated intensity beneath a single band in CD spectra: AE RK Gc | d If the band is Gaussian, go

Ae~ = Ae~. exp -- \(A - - --~K ! A~t2 and then R K --

1

Ae~ A K

2.28

~K

The units are Debye magnetons (I DM = 0.927 × 10 -38 c.g.s, units). The derivation of R~ from optical rotation data is discussed later (§ 6). (vii) Tke relationship o f O R D and CD. The concept of plane-polarized light as the sum of left- and right-handed circularly polarized light and the interrelationship of ORD and CD are clearly illustrated in Moscowitz (1960), Velluz and Legrand (1965), and Crabb6 (1965). It is important to emphasize that there is only one physical process involved, namely the interaction of the components of the plane-polarized electromagnetic radiation (light) with the electrons of the molecule. Either a refractive property (ORD) or an absorptive property (CD) may be observed, depending upon the experimental arrangement. The optical rotation varies non-linearly (i.e. disperses) throughout the spectrum; by contrast CD occurs only in the region of absorption bands, and will be closely related to the absorption spectrum, to which reference is generally made in assigning the optically active electronic transitions of the chromophore. The analogy of [a] and Ae to refractive index and absorption coefficient for unpolarized light is close. Differences are that in the case of ORD and CD the spectra may take on both positive and negative values and that optical activity may be associated with bands which are only weak in absorption. The relationships between absorptive and refractive properties are governed by the Kr6nig-Kramers transform which allows either property to be computed from the other. Details are given in Lowry (1935), Moscowitz (1961), and Emeis et al. (1967). The general relations between intensive and extensive properties of this kind are discussed by Schellman and Schellman (1964) and qualitatively by Foss (1963). (viii) Conformation, configuration, and asymmetry. Optical activity is shown by molecules which do not possess either a centre of symmetry or a mirror plane: a simple test is that the molecule is not superposable upon its mirror image. Although different usages exist, for this article the term configuration will be restricted to the spatial distribution about a single point, e.g. an asymmetric tetrahedral carbon atom (cf. IUPAC, 19 "0). Thus proteins are in general made up of L-amino acids; polynucleotides are based on the D-sugars. The polymers must themselves be asymmetric, being based on asymmetric units, and in addition they are capable of a variety of spatial arrangements of the constituent units. The term conformation is used to cover the full three-dimensional organization. This may involve a regular geometric transformation between units leading to a helical structure. Alternatively, if successive transformations are unrelated, a fully specified but irregular structure is generated. It may now be seen why asymmetric molecules show differential properties to left- and right-handed circularly polarized light. These polarizations have helical symmetry and an asymmetric molecule, e.g. a helical molecule of defined handedness presents a differently

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

7

polarizable medium to right- and left-handed circularly polarized light. It may be noted that a helix maintains its handedness when viewed from either end. The properties in question are therefore due to the intrinsic asymmetry of the molecular structure and persist in solution. In non-helical asymmetric molecules, the polarizability similarly but less obviously has a defined handedness. (ix) Chromophores. Reference will frequently be made to the properties of individual chromophores: these are groups identifiable both structurally and spectroscopically, e.g. peptide, aromatic, purine, and pyrimidine. The macromolecule exhibits properties related to its constituent chromophores. To a first approximation, a principle of additivity holds in absorption properties allowing identification of component chromophores, e.g. aromatic groups in proteins, purines, and pyrimidines in nucleic acids. Additivity clearly does not hold when electron interchange occurs, e.g. a conjugated polyene is not the sum of its constituent ethylenic groups, see, for example, Murrell (1963), but would be treated as a new chromophore itself. (x) Non-additivity of chromophores. Strong interactions between component chromophores may lead to non-additive properties where the non-additivity is dependent upon conformation. The property of the assembly may be less than or greater than the sum of its pans. In absorption, hypochromism, and hyperehromism of the Kth transition, taken over n groups in the assembly, may be defined in terms of the oscillator strengths as: tl

< ~ f K . ~ : hypochromism; l=l n

hyperchromism. 1=1

Since, for any single group, the Kuhn-Thomas sum rule (see Kauzmann, 1957) requires conservation of total oscillator strength, i.e.

2 ~fK

t=l

= constant,

K=I

where the sum is over all transitions, it follows that hypochromism in one part of the spectrum must be balanced by hyperchromism elsewhere, and vice versa. It may also be noted that hyper- and hypochromism may occur in situations of high symmetry and are therefore not necessarily related to optical activity. (xi) Optically active chromophores. For single chromophores a useful distinction has been made by Moffit and Moscowitz (1959) and Moscowitz (1961) in terms of (a) chromophores which are intrinsically symmetrical (e.g. a planar ketone) but disymmetrically perturbed by the environment, and (b) chromophores which are intrinsically disymmetric (e.g. the isomers of the screw type of molecule hexahelicene, in which the identifiable chromophore itself has a helical sense) and in which the optical activity is larger by several orders of magnitude. In macromolecules containing many chromophores, such mechanisms for the generation of optical activity rarely occur in isolation. The occurrence of chromophore-chromophore interactions in an asymmetric conformation gives rise to optical activity by mechanisms distinct from those above. In order to establish the common ground between these mechanisms, the electronic origins of rotational strength must be examined.

8

P . M . BAYLEY 3. T H E

ELECTRONIC

ORIGINS

OF ROTATIONAL

STRENGTH

The rotational strength of a transition is given by the Rosenfeld equation RK ---- Im(#e" ~m)This equation says that the rotational strength of the Kth transition is given by the imaginary part of the dot or scalar product of the electric and magnetic transition dipoles, ~e and respectively. "Imaginary" refers to the presence of the quantity i = V'--1. Thus in order to show optical activity the transition must have both electric and magnetic transition dipole properties, and since these quantities are vectors, they must have directional components in common. The properties of electric and magnetic transition dipole derive from the nature of the redistribution of electron density between ground and excited state associated with the electronic transition. Where these two states can be accurately represented by wavefunctions for the molecule (e.g. by combination of simpler atomic orbitals) a variety of properties of the states themselves and for transitions between the states can be evaluated theoretically. Two particularly notable transition properties may be distinguished: the transition may involve the linear displacement of electronic charge, or it may involve the rotation of electronic charge about an axis. The linear translation of charge generates an electric dipole: in polyatomic systems the redistribution of charge over many centres may be represented as the vector sum of the individual dipoles, and the net effect is again a single electric dipole. The rotation of charge about an axis generates a magnetic moment in the direction of the axis, predicted by the right-hand rule and represented by a magnetic dipole. These properties are generated by the electronic transition, and are consequently known as the electric and magnetic transition dipoles. They constitute the basis of the selection rules for absorption spectroscopy: #e ~ 0;

~m -"- 0

electrically allowed transition (magnetically forbidden);

~e ~ 0;

~,~ ~ 0

magnetically allowed transition (electrically forbidden).

The dipole strength (the integrated intensity beneath an absorption band) is given by D K ~ He'He;

p u t t i n g / t e = er, where e ( = 4.8 × 10 -1° e.s.u.) is taken as unit charge and DK is then expressed as A_2. It is the electrically allowed transitions which are readily observed in absorption 'spectroscopy, e.g. adenine for which emax = 1.5 × 104 at '~max = 260 nm and ;~, = 280 nm; h e n c e f = 0.37, D = 0.89 A 2, and ~//e 4.52 Debyes. This is equivalent to the translation of one electron over approximately 1 A. The most common source of bands of this type are transitions of rr electrons into the lowest unoccupied rr* orbital. An example of the allowed ~r--rr*transitions is the 190 nm transition of the peptide chromophore. Electronically this transition is mainly accounted for as the displacement ofrr electron density from the region of the nitrogen atom into the ~r* orbital when it is located mainly on the carbon and oxygen atoms (Schellman and Nielsen, 1967a). Consequently,/re-"-3 Debyes, and the direction is found experimentally to be in plane at + 9 ° towards the carbon atom from the O - N line (Peterson and Simpson, 1957). The principal bands of purines and pyrimidines in the region of 260 nm have intensities of the order of 5 × 103-104. The electronic character of these bands has been correlated with rr---tr* transitions of benzene (Clark and Tinoco, 1965): the ~--"

THE ANALYSISOF CIRCULARDICItROISM OF BIOMOLECULES

(a)

(b)

(c) FIG. 2. The carbonyl chromophore. (a) n orbitals: np, is the optical electron, no is the (linear) H-bonding electron. (b) ~rorbital: molecular orbital formed from C2r, and O2e, atomic orbitals in bonding combination. (c) ~r* orbital, (dotted): (2P, atomic orbitals in antibonding combination). The transition from np, to ~r* is magnetically allowed, generating/tin axially. greatly increased intensity, relative to benzene, is due to the lower symmetry of these heterocycles, and the substitution by N and O functions. Not all ~r--rr* transitions are necessarily electrically allowed: for the 260 nm transition of benzene itself, the symmetries of the ground state ~r and excited state rr* orbitals are such that #e ~ 0. The transition is effectively forbidden, the relatively low intensity (Em,x ---- 102) deriving from vibrational modes which violate the strict symmetry considerations (see, for example, Murrell, 1963). The classic example of the magnetically allowed transition is the n--rr* transition o f ketones (e.g. acetone ~278 = 15) (Stern and Timmons, 1970) and peptides (e.g. the amide of acetamide derivatives e21o = 100) (Nielsen and ScheUman, 1967). The transition involves the displacement of an n electron (non-bonding, or inert-pair electron) into an orbital o f ~r* symmetry. Transitions of non-bonding electrons have been discussed in detail by Kasha (1961). O f the two non-bonding orbitals associated with C-----O, it is the axial no orbital which acts as hydrogen-bond accepter, and the ne, orbital which contains the optical electron (Fig. 2a). The transition from Py symmetry to the Pz symmetry of the ~r* orbital constitutes a rotation of charge about the carbonyl axis and consequently generates a magnetic transition dipole axially along the C,------Obond (Fig. 2b, c). The lack of translation is reflected in /re ,,~ 0, and the band is very weak in absorption: in the case of peptides it is observed only as a tail to the strong ~r--~* transition.

I0

P.M. BAYLEY

AS described here, the electrically allowed and magnetically allowed transitions constitute mutually exclusive groups. Yet the Rosenfeld equation requires the simultaneous existence of non-zero/z e and/~m for the generation of optical activity. This is achieved by the breakdown of the above exclusion under suitable conditions of asymmetry and is the feature common to the examples of optically active chromophores cited in the previous section. Thus while the phenomenon of optical activity is relatively commonplace, its electronic origins depend upon rather subtle effects, involving the principle of non-superposition of asymmetric isomers. This will be illustrated in § 4 with reference to specific models. On a purely theoretical basis, if ~bc and ~s are wavefunctions for the ground and excited states of a molecule, transition properties/t~ and/t m may be evaluated using the quantummechanical operators for electric or magnetic dipole (see Kauzmann, 1957)./t~ and #m are then given by integrals between the states of the type p~= < ~a I E[ ~s >, equivalent to J'~G E ~s d~ and #m = ~bGI M [ ~s equivalent to j" ~c M ~s dr. For (p,)~, the electric dipole in the x direction, the electric dipole operator [EI is given by texl: this is an odd-function of x, i.e.f(x) = - - f ( - - x ) and for (Pe)~ ~ 0 the transition from ~bGto ~s must involve a change from odd to even function (or vice versa). For (/tin)x, the magnetic dipole in the x direction, the magnetic dipole operator IMI includes the term

which operates on y to give --z and on z to give y: thus for (/lm)~ ¢ 0, ~C as a function o f y with ~s as a function of z (or vice versa) is a suitable combination (Fig. 2). The selection rules for a transition may be obtained relatively simply: the validity of quantitative predictions, however, depends on the quality of the functions taken for ~c and ~s- Such ab initio calculations are possibly only for the simplest systems, and consequently all calculations of rotational strength represent approximate treatments. Assumptions may be inherent at all levels, e.g. wavefunctions, the basis states or the properties of individual chromophores. Nevertheless, certain mechanisms have become well established and subjected to experimental test. It is instructive to see how individual models can account for rotational strength before considering in detail the results of a more general model. 4. MODELS FOR OPTICAL ACTIVITY AND ITS CONFORMATIONAL DEPENDENCE Optical activity requires a transition to have both electric and magnetic transition dipoles associated with it. The mechanism for the simultaneous generation of/t, and/t,, for a helix is shown in Fig. 3. An electron travelling in a right-handed helical path generates #m along the axis (q-z) by the right-hand rule; the translational component also along ÷ z generates #~. In this case, R is positive. For the mirror-image situation (Fig. 3b), the sign of/tin is reversed and R would be negative. Helical systems are therefore amongst the simplest prototypes for optical activity. Only in certain rare disymmetric molecules are both the ground and excited states extended over a helical pathway as in Fig. 3a and b, when enormous values for RK are found. Examples of this sort are hexahelicene, urobilin, an asymmetric dipyrrylmethene, and skewed conjugated dienes (Moscowitz et al., 1964; Lightner et al., 1970). Bilirubin bound to albumin (Blauer and King, 1970) and certain cyclic polyene antibiotics (§ 11.3, Bayley and Calam, 1972) are even more intense (cf. R~: N 1.5 DM for L-urobilin, ~ 20 DM for bilirubin-BSA, and ~ 70

THE ANALYSIS OF CIRCULA-~ DICHROISM OF BIOMOLECULES

l1

(a)

(b)

(c)

FIG. 3. Helical excitations. The generation of/re and p= by an electron travelling in (a) righthanded, (b) left-handed helical p a t h : / t = derives from application of the "right-hand rule": /re by the translation along the axis: R = pc.p= is (a) positive, (b) negative; (c) the sense of handedness of the structural helix is right-handed: the relative orientation of the (coupled) monomer p, (solid arrows) gives a polymer/t~ in -- z and/~,~ in + z , for the fully in-phase transition. Hence R = p~" Pm is negative.

DM for amphotericin B). These examples of disymmetry, though illuminating, are clearly exceptional. The more general case of helical structures involves chromophores which are not conjugated but are arranged in a helical array. The interaction of chromophores in the excited states generates a set of exciton states (McRae and Kasha, 1964) in which the excitation is effectively delocalized through the array. Consequently the helical geometry confers simultaneous non-zero values for the/~e and/tr~ of certain exciton states. This concept is further discussed in § 8.1. It may be noted that the handedness of the structure and the handedness of the electron path on excitation are not necessarily identical (Fig. 3c). In simpler systems involving a small finite number of symmetric (generally planar) chromophores oriented in a structure which is itself asymmetric, two principle means of generating/re and p,~ simultaneously will be distinguished: (i) the mixing of transitions within a chromophore, and (ii) the coupling of transitions between chromophores. These mechanisms involve the interaction of the excited states of chromophores; groundstate electron exchange (e.g. conjugation) between chromophores is not involved. The formulation used is the matrix formulation introduced by Schellman (ScheUman and Nielsen,

12

P.M. BAYLEY

1967b; Bayley et aL, 1969) and Woody (1968) which has the advantage of relative simplicity of notation. There is a close formal resemblance to the secular matrix method for deriving molecular orbitals by linear combination of atomic orbitals (see, for example, Streitweiser, 1961). In this case, it is electronic states which are being combined and hence may be described as configuration interaction. The results are in accord with the general perturbation theory described by Tinoco (1962). 4.1. The Mixing of States For the peptide chromophore, the n-=* transition (210 nm) and the =-=* transition (190 nm) correspond to transitions from ground state 10> to excited states Is> and lfl > respectively (Schellman and Nielsen, 1967a). The wavefunctions corresponding to these basis states are ¢o, ¢,, and ~bB respectively. The orientation of#m of the n-=* and #e of the =--zr* transitions are shown in Fig. 4a and the relative energies in Fig. 4b. IP>

2"

/J'..

,.>

/~,.

(a]

(hi

Fro. 4. The peptide chromophore. (a) The relative orientations (in plane) of #,, (n-~r*) and /re (~r--~r*)of the monomer. (b) relative energiesof the states [0>, [a> and [/3>, where 10> [a> is the n-=* and [0> ~ 113> the rr-=* transition. In the quantum-mechanical representation of electronic states, where some mechanism of interaction exists between two states, a better representation of physical reality is given by a linear combination of the two (cf. the LCAO method). Condon et al. (1937) showed that mixing of certain states can occur in the presence of an asymmetric electrostatic field. Thus for the peptide, in the presence of an asymmetric distribution of the bonding, nonbonding electrons, formal charges, and ionized groups, the excited states [e> and [fl> undergo mixing. New transitions 1¢> -- 1¢i > and 1¢> [¢2 > are produced, where -

-

I¢1 > = C . ~= + Cl~ ¢B, 1¢5 > = C2, ¢~ + C~2 ¢~. The coefficients derive from the diagonalization of the matrix E~

V~[

and

V~a

E a [ and

C l l = C22=C1 -- C12=6'21 = - -

equivalent to the solution of the simultaneous equations CI(E,-- A) + C2 V , , = O , -

c~ v=, +

c,(E,

-

a) = o.

(72

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

13

In these expressions, E , and E# are the energies of states I s > , I/3> relative to 10>. V,# is the term representing the interaction between states Is > and ]/3> in the asymmetric electrostatic field. It may be evaluated explicitly in terms of the electronic formulation of the basis states. In general, V~# ~ E~, E#, and C2 is small. The eigenvalues are ~i ~ E~ and A2 ~ EB. 141 > is predominantly Is> and I42> predominantly I/3>. The non-zero values of C1 and C2 indicate that 41 also contains some I/3> character and 42 some Is> character. Since la> and I/3> have/tm and/re associated with them respectively, the states 14i > and [42 > satisfy the conditions for optical activity. These results are summarized in Table 1. TABLE1. GENERATION OF ROTATIONAL STRENGTH BY THE MIXING State

Eigenfunction

Transition dipole Magnetic Electric

~2

It is seen that

Cll~m

Rotational strength R1 = C2pe"Cllt,.

C2/te

Magnetic -- Cz/~m Electric C,/~e R 2 ---~ --R1

OF I a > AND Ifl>

R2 = C1/~e"--C2.u,. = --C, C2#.'#m

and hence 2

E RI =

0.

1=1

This is implicit in the unitary nature of the secular matrix. The conservation rule ~R~ ---=0 is obeyed over this limited set of two transitions. The unique feature of this mechanism involves the transition of an n electron in the presence of an asymmetric field. It is known as the "one-electron" mechanism. Two points are notable. (i) The development of rotational strength R1 in the state 141 > (which is principally the n-Tr* transition since C1 ~ 1) is accompanied by the simultaneous development of R2 ( = --RI) in 142 >, the state from which electric dipole moment is "'borrowed" (which is principally the 7r-~r* transition); thus more than one state is involved, and consequently the name is not to be taken too literally. (It will be referred to as the CAE mechanism, Schellman, 1968.) (ii) If/~e and/l mhad been perpendicular to one another, no rotational strength would have developed by this mechanism even in the presence of an asymmetdc field; this situation is likely to be encountered in heterocycles with in-plane rr--rr* and perpendicular n--,rr* transitions (Rich and Kasha, 1960). A more sophisticated treatment would include interactions with higher energy electrically allowed transitions fll assuming explicit forms were available for computing the corresponding terms V~#j; the conservation law would then hold over the set of (a, flj) interactions. The conformational dependence of this mechanism resides in the nature of the asymmetric perturbation. This determines the sign of V~B, hence the phase relations of CI and C2 and the ultimate absolute sign of R1 and R2. The symmetry rule for the peptide follows a quadrant rule based on the C-~O atoms (Schellman, 1966a). For carbonyl alone, an octant rule is predicted (Moffitt et al., 1961). The symmetry rules for optical rotation have been described in detail (Schellman, 1968). In the case ofpolypeptides, the contribution of this CAE mechanism to the n-'rr* rotational

14

P.M.

BAYLEY

strength of the a helix was evaluated by Schellman and Oriel (1962); here the asymmetric electrostatic field is that due to the formal charges of the a helical array. Negative rotational strength was predicted for the R H helix, as is observed. However this mechanism, treated in isolation, is unlikely to be sufficient for multiple chromophore systems because of the additional interactions present, and its usefulness is for the single chromophore perturbed by an asymmetric environment (as in Moffitt's definition). A critical appraisal of the approximations involved has recently been made by Stigter and Schellman (1969).

4.2. The Coupling o f Transitions If two chromophores are sufficiently close for the excitation of one to be affected by the state of excitation of the other, they may be said to be "coupled". This corresponds to the "coupled oscillator" model of Born; it was put into quantum-mechanical form by Kirkwood (1937). The interaction of the excited states leads to two new states which correspond to the in-phase and out of phase coupling of the basis states. For a dimer with an electrically allowed transition from ground state [0> to excited state [fl> represented as [t31> and [/32 > in the two groups, the secular matrix ,'nay be written

E~I

V~:2 =0

v.:2 E~2 from which two new states may be obtained, given by

When E¢~ = E,2 : E , (identical chromophores) C1 = C2 = 1/~/2 and [~A > and [~s > are the in-phase and out of phase states respectively: 1

1 These functions could be written down by considerations of symmetry and normalization alone. They correspond to the excitation states of a two-component excitation (McRae and Kasha, 1964). For the dimer, the secular matrix formulation shows that the eigenvalues are given by

E,N = Ee + r e : : E o v T = E# - - Vaa,2,

where V , : ~ represents < 31 [V[32 > and is the interaction energy of the excited states. When the transition dipole approximation is used for the electric transition dipole, i.e, < 0IEI3, > = pl, this term may be represented by VB 1/]2

-

-

/z~-p=

3(/~, .r) (it2 .r)

r 3

r5

'

THE ANALYSISOF CIRCULAR DICHROISM OF BIOMOLECULES

15

The coupled oscillotor

I

%%%

/~t + # z In phase ~T3rN _-~-I

Out of phase

(qh + q~z)

~our=~" (~/I-~z)

FIG. 5. The coupled oscillator model. Two electrically allowed (monomer) transitions/tx and /*2 in the in-phase and out of phase combinations which have left-handed and right-handed helical symmetry respectively.

where r is the separation o f / ~ and ~.t2. For strongly allowed transitions, in chromophores with suitable orientations, VB~a2will be large enough to produce a significant splitting: cr = EIN - - E o v r = 2Vtqo2.

The way in which the in-phase and out of phase states give rise to optical activity in the coupled oscillator mechanism is illustrated in Figs. 5 and 6. Qualitatively [q~N> has the elements of a left-handed helix and I~ouT> a right-handed helix. In more detail, in Fig. 6, in the in-phase combination, the x components o f / t l and #2 combine to give a resultant electric transition dipole in x while the y components constitute a rotational motion giving a resultant magnetic transition dipole also in x. The resultant #e and/tin are parallel and hence RIN is positive. Conversely, R o u t is negative. By symmetry it can be seen that R~N = --RouT, and, again, rotational strength is conserved, i.e. ~R~ = 0. The spectroscopic results are therefore an excition splitting to E -4- VBla2, a redistribution of intensity corresponding to the vector addition of/tl a n d / t 2 in the two modes, and the development of -+-R separated by ~. The latter appears as equal and opposite bands in CD and has been termed the "couplet" (Schellman, 1968). The effect of conformation is expressed entirely through the off-diagonal element VB~a2, which in a simple stacked dimer is determined by stacking angle. The rotational strength of the in-phase (+), and out of phase (--) transitions due to

16

P . M . BAYLEY

/~e

/Zm

X

~y In phase

Out of phase

FIG. 6. The coupled oscillator model. The components of the vectors/tx and a2 in x and y combine to produce/re by translation and am by rotation about an axis, such that R~N is positive and Rout negative.

coupling two dipoles/ta and/t2 separated by distance ra2 is given by Tg

R ± = T~

{r12"/ll"#2}-

For a stacking angle of a, defined as positive for a right-handed stack and for a planar stack separated by distance r, 77

R ± ~ ~ ~-~ r./~1"/z2 sin a, and the spectroscopic splitting is given by e = 2V = 2 tza "t*z cos a/r a.

(4.1)

For an identical dimer cr will frequently be less than A, the m o n o m e r bandwidth, when it is found that R + and e cannot be determined independently from experimental spectra ( § 6). The product Re, corresponding to the "couple" of rotational strength 4-R separated by e, is seen to depend upon the product tLa2./z22 sin a cos a. Thus although R has a maxim u m value at a = 90 °, corresponding to the maximal values of/te'/t,,, the spectroscopic splitting has now decreased to zero because of the orthogonality of/t~ and P2. Likewise at a = 0 °, V is maximal, but R = 0 since the molecule now has a plane of symmetry. The amplitude of the couplet has maximum value at a -~ rr/4, 5rr/4, and minimum value at a = 3rr/4, %'/4 with zero values at a = mr/2 for n = 0-4. These results are summarized in Fig. 7. The effect of decreasing the stacking distance is to increase V: at distances as close as the van der Waals contact, the evaluation of V by the dipole-dipole expression is, in any case, approximate. A more sophisticated treatment would evaluate V, using a monopolar representation of electric transition dipoles, with point monopoles located over the whole o f the polyatomic chromophores like purine or pyrimidine which are often involved in stacking interactions. The effect of tilting of the stacked chromophores is seen in both rotational strength and splitting: on this simple two-state model, rotational strength would .still be conserved. This model has been used successfully for the stacked dimer model of dinucleotides by

TIlE ANALYSIS OF CIRCULAR DICIIROISM OF BIOMOLECULES

17

Bush and Tinoeo (1967), with further extensions by Johnson and Tinoco (1969b), Schneider and Harris (1969), and Johnson et al. (1972); for the "reciprocal relations" of certain nucleotide derivatives (Miles and Urry, 1967); and for accounting for certain properties of the Kirkwood coupling component of dipeptides (Schellman and Nielsen, 1967b; Bayley et al., 1969). Interpretation of experimental results on this model is indicated in situations when the "couplet" phenomenon is observed: the two-transition model necessarily produces a conservative system. Non-conservative systems may be treated by extension of the treatment to include higher energy transitions (Bush and Brahms, 1967). Oimer- 2 transitions as f {angle)

CO

Rot 1

I t,

ltrength - - 0 ~" ' ' O :

PHase tn

out

t. . . . . 0

"

in

out

t_x t

t ~5

in

x

out

x cJo

0-------0-,.

in

t

out

in

t xt 1~5

t3 18o

Angle

FIG. 7. The coupled oscillator model. Optical properties for two transitions of a stacked dimer as a function of the (right-handed) stacking angle a. F o r each case the relative energies of the in-phase and out of phase combinations, together with rotational strengths and CD profile. F o r negative a, phase relations are as for positive ~; signs of the rotational strengths and CD profiles are reversed. For the system in Figs. 5 and 6, a is approximately --75 °.

Extensions of the principle of coupling to polymeric systems follow logically: for N groups with M transitions per group the secular matrix will be of dimension (NM) × (NM). For helical polymers the coefficients contained in the eigenvectors may be derived by symmetry (cf. Motfitt, 1956); absorption properties are readily interpreted in terms of these exciton functions. The hypochromism of the a helix, and the hyperchromism of fl structure are both rationalized satisfactorily (Tinoco et aL, 1962), and their =-=* rotational strengths are largely determined by this mechanism. Similarly, the properties of polynucleotides have been satisfactorily accounted for in terms of this relatively simple theory and its extensions (Johnson and Tinoco, 1969a, b). 5. THE OPTICAL PROPERTIES OF PEPTIDES 5.1. Dipeptides This term is used for a molecule containing two peptide chromophores. When two peptide chromophores interact, both of the two mechanisms previously desc~bed are operative, together with a third. Combining the two secular matrices to repre-

18

P, M. BAYLEY

sent the interactions between two transitions a and/3 in each chromophore (subscripted 1 and 2), results in E~ i

F~a~

V~xB~ /~

0

E~I

CAE1

0

Ku12

CAE1

EB~

Ku21

Klz

0

Ku21

Ea2

CAE2

Ku12

K12

CAE2

EB2

V~B:

V~B~ v ~ or

0

V~2fll

E~2

V~B2

V~qa2 VBaa2 V~,2a2 Ea2

This 4 × 4 matrix contains off-diagonal elements V,,a, (CAEI) corresponding to the CAE mechanism in group i; the element V&h (Ktj) corresponding to the coupled oscillator (Kirkwood) mechanism; and the terms V,,B~, V,ja, corresponding to the interaction of the n-r:* transition in one group with the ~r-~r* transition of the other. This (/t-m) mechanism was foreseen by Kuhn (1930), and the off-diagonal element is labelled K/t~j K#jt. The diagonalization of this matrix produces four new states I~ >, 142 >, [4a > and [44 >, where 141 > and 14a > are derived from the n-rr* states (and have energies close to E,~ and E~2) and 142 > and ]4,~> derive mainly by I~rkwood coupling through the dominant offdiagonal term K u. Applying the eigenvectors to the properties of the basis states allows evaluation of the transition electric and magnetic dipoles, and hence the rotational strength for the transitions for a given conformation of the molecule, in terms of the two dihedral angles, (4, 4). The parameters used in evaluating the off-diagonal elements of the matrix have been tabulated (Bayley et aL, 1969). The transition electric dipole is given in the equivalent monopole representation with half-charges located at points given by the uniformly charge sphere approximation (Pariser and Parr, 1952). The n--~* transition quadrupole is represented as the quadrupolar charges q-q at C and O. The off-diagonal terms are then generally given by sums of the type

V,i=~

qj--@, t

j

rij

where q~, qj represent the static charges, or the monopole, dipole, or quadrupole representation of transition moments. The result of such interactions is: (i) exciton splitting of fl~ and f12, (ii) negligible energy perturbation of a~ and a2, (iii) rotational strength develops in all transitions by a combination of the mechanisms described. These properties are totally dependent upon conformation which determines the off-diagonal dements, the eigenvectors c~, and the relative orientations of the component/te and/t,,. The calculations have provided a satisfactory rationalization of the rotatory properties of dipeptides with conformational possibilities restricted by the presence of rings (e.g. proline) and strongintramolecular interactions (e.g. hydrogen bonding). Thus the strong negative Rn_~. of N-acetyl-L-proline amide (Fig. 8a) observed in dioxan is predicted for a conformation 4 = --60° (proline ring), 4 = + 50° and the intramolecular hydrogen bond, predicted also by conformational energy calculations, forms a structure previously inferred for peptides (Tsuboi et aL, 1959). Other proline derivatives have been examined in detail by Madison and Schellman (1970a, b, c) and the system of N-acetyl-L-proline methyl amide

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

19

(o},(b)ON~~~.. ~) /C~, CH3

H/N'-~R 0~

0 (d)

FIG. 8. Model compounds for dipeptide optical activity. (a) N-acetyl-L-prolineamide R = H. (b) N-acetyl-L-prolineN'methylamide R = CH3. (c) L-proline diketopiperazine (L-PDKP). (d) The folded diketopiperazinering: 7 is the dihedral angle of fold. For L-PDKP the L-conformation at C~ dictates a folded structure with 7 ~ 300 from model building: for L-alaninediketopiperazine(L-ADKP)the methyl substituent at C~ is best accommodatedin a non-planar structure. (Fig. 8b) has been shown to exhibit conformational mobility with properties corresponding closely to the polyproline transition. A further experimental system which has proved extremely useful for evaluating the predictions of the theory is the molecule L-proline-diketopiperazine (PDKP, Fig. 8c). Diketopiperazines (piperazine-diones) had been observed by Schellman and Neilsen (1967b) and Balasubramanian and Wetlaufer (1966) to have interesting optical properties. The diketopiperazine ring system restricts available angles of (4, ~b) to small ranges along the twofold axis; but a degree of freedom exists in the angle of folding y which is present when the diketopiperazine includes at least one asymmetric centre (Fig. 8d). In the case of P D K P the presence of the two proline rings causes the structure to be completely defined. The calculations for P D K P and for a secondary DKP are shown as a function of conformational angle in Tables 2A and 2B. The inclusion of the # - m (Kuhn) then determines the sign of R, . . . . Analyses of ORD data for P D K P and for L-alanine-diketopiperazine, A D K P (Schellman and Nielsen, 1967b), and more recent CD data for both compounds indicate signs for the R,_~., RI and R2 of (-- ÷ --) and (q- -- ÷ ) respectively: in PDKP, the rr--rr* absorption is shifted to the blue. Magnitudes of rotational strengths, splittings, and dipole strengths (Table 2A) are consistent with 7 ~ 30° for L-PDKP and by comparison with the data for the secondary diketopiperazine, for a smaller angle of folding in the opposite sense for L-ADKP (Schellman et al., 1972). These results correlate satisfactorily with X-ray data for the related proline compound cyclo L-prolyl-L-leucyl (Karle, 1972) for ADKP, a conformation opposite to that in the crystal is indicated (cf. Benedetti et al., 1969; Sletten, 1970). Diketopiperazines have previously been treated as planar structures (Urry, 1968). These calculations of rotational properties are readily extended to cover the full (~b, ~h) plane (Bayley et al., 1969). The results are best presented in the form of maps of the proper-

20

P. M. BAYLEY TABLE2A. ROTATIONALSTRENGTHCALCULATIONSFOR L-PDKP ASf(~,~b)a Cis-cis, tertiary-tertiary dipeptide: Energies as for water: E~ = 210.0 nm; Et~ = 196.0 nm R,_~.

--60

--45

--35

+55

+40

+30

Rl

A1

R2

A2

02

(%)

C 0.030 K CK 0.026 CKK --0.141

--0.017 0.750 0.746 0.721

196.0 199.3 199.3 199.3

--0.014 --0.750 --0.772 --0.580

196.0 192.8 192.8 192.8

95.2

C 0.030 K CK 0.025 CKK --0.134

--0.014 0.543 0.541 0.526

196.0 199.4 199.4 199.4

--0.016 --0.543 --0.566 --0.392

196.0 192.7 192.7 192.7

98.4

C 0.028 K CK 0.022 CKK --0.124

--0.012 0.386 0.385 0.377

196.0 199.5 199.5 199.5

--0.016 --0.386 --0.407 --0.253

196.0 192.7 192.7 192.7

99.8

Mechanisms: C CAE terms K Kirkwood terms CK CAE + Kirkwood terms. CKK Full Theory -- CAE + Kirkwood + Kuhn. The angles (~, ~b)lie close to the diagonal of the (~, ~b)plane and simulate a molecule with C2v symmetry. Values of R evaluated on a molar basis, i.e. DM per dimer. D2: ~ dipole strength associated with the transition at ;~2. a Bayley (1967), Schellman et aL (1972). ties as a function o f the two conformational variables. A separate m a p is made for the various combinations o f primary, secondary, and tertiary substitutions and for cis-trans isomerization. Typical results are presented in Figs. 9 - I 1 for the c o m m o n e s t combination, namely a secondary-secondary dipeptide in the trans-trans form. The rotational strength o f the longer wavelength ~r-Tr* transition is seen (Fig. 9a) to undergo a striking variation in sign and magnitude as a function o f conformation. Comparison with the exciton splitting (Fig. 9b) shows that the discontinuous changes in sign in R1 occur at nodes in the splitting (i.e. VB1B2 ---- 0). The continuous changes in sign in Fig. 9a occur where the optical symmetry is changing sense. Figures 9c and 10a and b show the p r o d u c t o f the two, corresponding to the magnitude o f the amplitude o f the 0r-~-*) C D at specific points on conformational plane, and indicating b o t h classes o f nodes; the values m a y be contrasted (Fig. 10c) with the n-rr* properties for the same regions. It is to be emphasized that these variations occur for a dipeptide, with a fixed configuration at the central C~. Numerical values for the variation o f the n-rr* properties are shown in Fig. 1 la. A considerable rotational strength (ca. ~ 0 . 2 D M ) is predicted for several allowed regions of conformational space. Figure 1 l b shows the development o f R . . . . by the various combinations o f mechanism, for a typical region o f conformational space. Different mechanisms predominate in different regions, and the mechanisms are not strictly additive. This nonadditivity is to be expected, since deletion o f off-diagonal elements in the secular matrix clearly leads to different sets o f eigenvectors. The ability o f the matrix m e t h o d to handle several mechanisms simultaneously and in a consistent m a n n e r is a great advantage in any situation where a n u m b e r o f transitions and transition types are involved.

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THEANALYSOF ISCIRCULAD RICHROISM OFBIOMOLECULES

25

(a)

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O" JeO"

(b)

| 8 0 1 ~ 0* ~'

180

~ |801 ~0"

*~

~

180=

Y2"

(e)

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FIG. I0. Optical properties of dipeptides as f(¢,, ~): trans-trans, secondary-secondary dipeptide; full theory. (a) The couplet: full plane at 20° increments. (b) The couplet: fully and partially allowed regions of conformational space only (all others have been equated to zero). (c) R,-.n, for the same regions as (b). Scaling is arbitrary (Couplet = R,a). These results show clearly that, for a given configuration, the optical properties for two interacting peptide chromophores show marked conformational dependence in both the n-~* and =-~* regions. This finding is clearly important for the conformational analysis of peptides: the parameters which may be used are R, . . . . R1, R2 and the rr-=* splitting. In addition it encourages extension of these concepts to the case of larger peptide assemblies and provides the rationale for assigning more complicated structures on the basis of their optical properties (Madison and Schellman, 1972: and see § 10). Caution should, however, be exercised where non-conservatism or hyper- and hypochromic properties are noted. The simple four-transition model necessarily produces conservation of rotational and dipole strength. Strong interactions with even higher energy transitions must be included to account for these non-conserved properties.

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28

P.M. BAYLEY 5.2. Extensions to Polymers

Extending the above formalism for dipeptides to the case of a polypeptide containing N groups, and considering two transitions (a and/~) per group, the chromophore-chromophore interactions are represented by a symmetrical 2N × 2N matrix of the form: E, 1 CAE1 EBx

0

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0

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0

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Ku2x

K12

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Ku4a

K14

E~2

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0

Ku34

etc. In this matrix, the terms Ktj and Ku~j represent the pairwise interactions corresponding to the Kirkwood and Kuhn (#-m) terms previously described. In the evaluation of the CAE terms, the electrostatic field is that of the full array of N groups. Diagonalization (maintaining the order of the eigenstates) and use of the eigenvectors of states ]q~j> (j = 1 to 2N) is exactly analogous to the cases described previously. The spectroscopic results show complicated distribution of dipole strength between the even-numbered states deriving from flj, when energies are considerably perturbed from the initial values E~,, and again negligible energetic differences are introduced into the odd-numbered states, deriving from aj. Rotational strength develops in all transitions. As illustrated in the case of the dimer, the magnitude of these properties is strongly dependent upon conformation. The degree of mixing and coupling is once more determined by the off-diagonal elements, and the optical properties are determined by the combination of the eigenvectors with the properties of the basis states (aj, flj). In the case of regular geometries, e.g. helices, the geometrical relationship between corresponding constituent groups is constant. The same correspondence holds for the off-diagonal terms, e.g. Kij, K,+I), o+1~, K(i+2), o+2) will be identical: similarly for Kuij and (neglecting end-effects) CAEv The secular matrix thus has a certain symmetry and this is reflected in the eigenvectors which approximate to the symmetry determined coefficients, as used by Moffitt (1956) for the a helix. The eigenvalues likewise segregate into a small number of symmetry determined states, corresponding to the allowed and forbidden states as described by McRae and Kasha (1964). In the case of irregular structures, no such correspondence exists and, as will be shown later, each case must be treated on its merits. 5.3. Summary of the Position This brief treatment indicates that the property of rotational strength is sufficiently well understood to be calculated for systems of chromophores. Approximations are inevitable: a complete theory would require treatment of all interactions of all possible transitions of all component chromophores. Any practicable treatment requires the isolation of recognizable mechanisms and a limited number of transitions. In § 10 the results of such a theoretical approach to the CD properties of specific molecules are presented, and the uses indicated for the theory at its present level of development.

THE ANALYSIS OF CIRCULARDICHROISMOF BIOMOLECULES

6. T H E

DERIVATION OF ROTATIONAL STRENGTH ORD AND CD SPECTRA

29

FROM

By analogy with the dipole strength (defined in § 3 as the integrated intensity beneath an absorption band), the rotational strength is the integrated intensity beneath a band in circular dichroism. If the Kth band is Gaussian with wavelength, (h=

A

exp

AK~ 2

-

,

the area is given by A = ~/(rr) AE°xAr/AX.For Ar and Ar in rim, the rotational strength RK is derivable from Aer, molecular circular dichroism, or [O°]rmolecular ellipticity, by [0 "]K AK

A¢~ A K

RK

2.25Ar

or

7514AK"

(6.1)

The relationship between a single (Gaussian) CD band and the corresponding ORD band is shown in Fig. 12. It may be shown that the extrema of the ORD curve occur at Ar 0.93AK and that the rotational strength is derivable from the magnitude of the peak and trough of the molecular rotation by [0~] = 4- 0.82 ([~pk] -- [q~tr]). It is notable that the line shapes of both ORD and CD are determined by the parameters ~K and At: for example, rearranging eqns. (6.1) the maximum of the dichroism is dependent upon both of these parameters. A~, =

2.28 Rr hr AK

:ilJ 20001 o 12.0o do xa 800 r~ ca

40O

0.00~ -4 00-800-12.00

/

186.00

206.00

226.00

Wavetength,

240 00

260.00

nm

FiG. 12. The relationship of CD and ORD. Computed curves for R = 1.0 DM; Ao = 220 nm; Ao = 10 nm; Units of [0] and [¢]: degree cm~/decimole.

30

P . M . BAYLEY 20 O0 1800. 16.00 1400

/

2.00 0 O0 ~ J J 180.00

200.00

"-'-~ 220.00

Wavelength,

24600

26600

nm

FIG. 13. C D b a n d o f c o n s t a n t rotational strength as f(A). R = 1.0 D M ; Ao -----2 0 0 n m ; A = 10 rim, 12 rim, a n d 15 n m . T h e a m p l i t u d e is inversely p r o p o r t i o n a l to A.

10.001 800 /

6 O0

/

4 O0 2.00 ×

o

0.00 --2" O0

400

-600 -800 - 10.00

18600

206 oo

22600

Wavelenglh,

246.00

266.00

nm

FIG. 14. O R D spectra for c o n s t a n t rotational strength as f(A). P a r a m e t e r s as Fig. 13. Amplit u d e s are inversely proportional to A; ([¢pk] - - [¢t,]) is proportional to A (see text).

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

31

Thus, changes in h r affect the observed band maximum (Fig. 13). Similarly, Fig. 14 shows the effect of varying AKupon the observed line shape in ORD: as AKincreases the amplitude at the extrema decreases: as ()~ -- ~K) >~ AK the effect of AK is not visible and the curve approximates to the simple Drude function A2

[~]~ oc

RK ~2 _

~,.

Finally, it may be seen that R K acts as a scaling factor for both ORD and CD curves: for a single band at constant AK and ~Kthe magnitude of either the ORD peak to trough amplitude or the CD maximum is directly proportional to RK. It is therefore a relatively simple matter to derive the rotational strength of a single, isolated optically active band. Such separate bands occur only rarely in biological molecules. The n-~* transitions of ketones provides a band which is isolated, spectroscopically, from nearby 7T-~* transitions and provides a useful calibration standard in both ORD and CD: D-10 camphorsulphuric acid in water has AE29s ~---+ 2.20, [0298] = 7260 degree cm 2 decimole -1 (Cassim and Yang, 1969). The band may be resolved into two components w i t h R 2 9 2 . 5 = 0.018 DM, R 2 a 6 = 0.042 DM: integration over the whole band, or evaluation from ORD data gives Rtota~ = 0.060 to 0.061 DM (Urry, 1969). There are two principle reservations to the use of the eqns. (6.1). Firstly, even apparently simple bands have several components of the same sign associated with the vibrational components of the electronic transitions ("vibronic" transitions); and, secondly, individual transitions frequently overlap other transitions of the same or opposite sign. In both cases, some resolution into component parts must be attempted. Because of the dispersive nature of optical rotation, considerable overlap of adjacent effects is generally to be expected. The derivation of RK from ORD spectra is then an exercise in finding effectively the CD spectrum which transforms into the observed ORD spectrum. Computational methods are available (Carver et al., 1966) and these have been applied typically to the analysis of ORD of peptides (Nielsen and Schellman, 1971) and haem proteins (King et al., 1969, 1971 ; Yong et al., 1968). The success of this analytical procedure is enhanced by assigning fixed values to as many as possible of the parameters A~, Al and producing good curve fitting with Rl as variables. Although ORD is currently less popular than CD, not the least because of the loss of resolution through extensive overlapping, the transformation methods are still important because of the relatively high precision attainable in ORD measurements. Measurement of CD is clearly a more direct route to evaluating Rr; the band shapes are of limited breadth, and hence overlap less extensively (Fig. 12). Thus the basic problem in both cases is the simulation of the CD spectrum, and this will be considered exclusively. In spite of the power of computational methods and the use of curve simulators, it will be seen that, when effects have opposite signs, it is not in general possible to resolve rotational strengths unambiguously.

6.1. Resolution of Overlapping Effects of the Same Sign The CD spectra of 3(+) methyl cyclopentanone in the gas phase and in cyclohexane show a high degree of vibrational structuring in the n-~r* transition (Urry, 1968); the rotational strength of individual vibronic components may therefore be resolved. The total ellipticity is close to that in water, but in this case fine structure is virually absent. Even the

32

P.M. BAYLEY

standard compound D10-CSA contains multiple components in its spectrum (see, for example, Cassim and Yang, 1969). No ambiguity results if the rotational strength is cited as being that of the entire band, or that of specific vibronic transitions (where these have been assigned). Recent work has been directed towards the assignment of the optical activity of vibronic bands, in ketones (Weigang, 1966), and in aromatic chromophores (Horwitz et aL, 1969; Strickland et al., 1969, 1972). The resolution of the fine structure of model aromatic compounds provides the basis for analysis of the complex CD of certain proteins (§ 11.2); the vibrational fine structure is considerably enhanced by the use of very low temperatures (77°K) (Horwitz et aL, 1970). For the aromatic chromophores the rotational strength of vibronic components may be of opposite sign to the non-vibrational CD (Horwitz et aL, 1969). The oppositely signed effects occurring in the longest wavelength vibronic components of ketones may be explicable in terms of the presence of multiple isomers ; production of a single effect at low temperature is generally taken as evidence of a conformational equilibrium (Wellman et aL, 1965a; Snatzke, 1967). Theoretical considerations show that sign changes are possible within the vibrational CD of a single chromophore of appropriate symmetry (Weigang, 1966; Caldwell, 1969). These fine details of the spectra are visible in only a qualitative way in ORD spectra; quantitation requires the CD spectra to be observed at high spectral resolution. Transformation of such complex spectra has been achieved by the methods of Moscowitz (1961) from the component Gaussians for hexahelicene and by Emeis et aL (1967) for hydrindanone derivatives from the total CD curve containing vibrational structure without prior resolution into components. The ability to reproduce a given ORD curve by transformation of the CD indicates a faithful representation of the CD spectrum, but does not indicate that a unique representation has been achieved. Thus several equally good resolutions of the same CD spectrum will transform into the identical ORD spectrum. This point will be further clarified in the following discussion. 6.2. Overlapping Effects of Opposite Signs--Equal Effects (Couplets and Conservative Systems) The possibility of rotational strength with either positive or negative sign presents a real limitation to the resolution of spectra into their component parts. The inspection of experimental curves readily confirms this limitation. However, one experimental line shape is immediately identifiable, corresponding to equal and opposite rotational strength separated by a small interval. Several such effects are shown in Fig. 15 and these are characterized by oppositely signed lobes of approximately equal area. The line shape is readily distinguished from that of a single effect in ORD by the rapid decrease to zero of the spectrum at wavelengths away from Ao. The ORD transforms of these curves are shown in Fig. 16. These shapes are indicative of the "couplet", referred to in § 4.2. Since R~ + R2 = O, the system is conservative. If each optically active transition has Gaussian band-shape, the line-shape of the couplet may be evaluated (Schellman, 1966b) by taking the sum of the two effects located at At and Az: A~=AE~exp-- \

A1 ]

+AE~zexp-- \ - - - ~ z ]

and expanding about the mean wavelength AK.

(6.2)

THE ANALYSIS OF CIRCULAR DICtlROISM OF BIOMOLECULES

24.00 20'00 16 00. 1200 800. 400000

--400. -800 12.00 ,--1600

180.00

200"00 22000 Wavelength, nm

240-00

260"00

FIG. 15~ The appearance o f couplets in CD. ~o ~ 220.0 n m ; R , = 1.0 D M ; R2 = -- 1.0 D M ; Ao = 10.0 n m ; a = 0.2, 0.4, 0.6, 0.8, 1.0 (increasing amplitudes). Only in the latter curves is the line-shape dependent upon e.

32001

28 O01 24001

20 00} 16004 12 001

8 00 4 O0 0.00 -400 800

18000

20000 22000 24000 Wavelength, nm

26000

FIG. 16. The appearance o f couplets in O R D . The transforms o f the curves o f Fig. 15, amplitude increasing with increasing a.

33

34

P. M. BAYLEY For an identical dimer '~1 ~

A2 ~

/'~K,

A~2=--A~=A~

c,

11 = h K ÷ 3, 12 = 1~ -- 8,

Aj c;

-

-

-

-

A2

2S AK

AK

and then (A-- AK] A E = 2 A E ° e \ AK ] e x p - -

( 1 - - ~K]z \ T / "

This function may be shown by differentiation and substitution to have extrerna at 1 = Ag =t2 As/%/2 and the total amplitude is given by {Amp}~_+o = A%k -- Act, = 1.72 Ae°e = 3.9 2 -AK ~ Re.

(6.3)

Thus (i) the extrema do not correspond to the location of the optically active transitions, and within the limitation e < 1.0 are independent of them (also see Wellman et aI., 1965b); (ii) the amplitude reflects only the product of R and e: the amplitude reflects the couple in the same sense as a mechanical couple and the components R and e are not individually distinguishable. This effect is therefore best characterized by its total amplitude, crossover, and monomer bandwidth; it may consequently be simulated from these three parameters. Although the desired information (about rotational strength) is not immediately available, the ease of recognition of the line-shapes of Figs. 15 and 16 affords a valuable tool in analysis of CD spectra. For example, in the case of asymmetric stacking, the sign of stacking is readily inferred from the sign of the couplet; a positive long-wavelength lobe corresponds to the arrangement of transition dipoles in a right-handed stack. This does not necessarily imply that the molecular geometry is of the same handedness, since the structural symmetry may be judged by the relationship of non-chromophoric elements, and requires knowledge of the orientation of transition dipole within the molecular framework (cf. Fig. 3c). The symmetry of the couplet, the proportionality of {Amp } ocRe, the proportionality of the area ( ÷ v e ) to e, and the independence of position of the extrema depend on e < 1.0. From the data in Table 3 it may be seen that for e < 0.8 these relations are true to better than 90 %. Even allowing for a slight lack of symmetry due to RK 11 AE] oc T K

or

R~c(A,c + 8) AK

and AE~ oc

--

R K ~2

AK

or

--

RK(~K

AK

--

~)

,

the restrictions on amplitude and line-shape hold over the same interval. In order to analyse further the amplitude term, e may be inferred from spectral data, or

35

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES TABLE 3. PROPERTIES OF THE COUPLET AS A FUNCTION OF THE SPLITTING tr

o

0.2

0.4

0.6

0.8

1.0

Total {Amp} {Amp}/Ra (%)

0.340 99.07

0.668 97.32

0.968 94.02

1.231 89.68

1.458 84.97

Relative area (+) (Area)e (Area)~ -+ 0

1.99

99.50

3.94 98.50

5.82 97.00

7.58 94.75

9.21 92.1

//o

S" (Uo)

S' (Uo)

S' (uo)

S' (Uo)

S' (Uo)

1.0 O.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0.861 O.936 0.985 1.000 0.975 0.907 0.793 0.638 0.447 0.230 0.000

0.870 0.942 0.988

0.884 0.951 0.992

0.904 0.965 0.999

0.923 0.975

1.000

1.000

1.000

0.973 0.902 0.788 0.633 0.443 0.228 0.000

0.968 0.895 0.779 0.624 0.436 0.224 0.000

0.963 0.885 0.768 0.613 0.427 0.220 0.000

0.992 0.949 0.867 0.747 0.594 0.413 0.212 0.000

Line shape I

1.000

The line-shape S(uo)is expressed in terms of Uo = (~ -- ~o)/Ao;A6° = 1.0. calculated using eqns. (4.1) and (6.3). Since such computations are inevitably made simultaneously with computations of rotational strength, it appears more rational to make a full calculation of the amplitude of the couplet than of the individual components R and o. Here the limitations are: (i) the approximations required in the theory may be of different severity for the optical rotation and splitting calculations, and (ii) the apparently simple band shapes contain multiple vibronic components, as well as potentially closely degenerate electronic transitions (e.g. as in adenine; Clark and Tinoco, 1965). In spite o f the complexities which may develop with real chromophores (see § 11.2) a qualitative interpretation of conservative spectra is generally possible in terms of the relatively simplified analysis given here. The prime requirements for the appearance experimentally of conservative properties is the development of rotational strength between transitions which are approximately degenerate. Identical dimers, and mixed dimers provide the best example; the most likely mechanism is the coupling of ~r--~*, and hypochromism and spectral shifts may result. The participation of n--zr* or weak ~r--cr* transitions cannot be excluded; near degeneracy of energy is still required.

6.3.

OverlappingEffects of Opposite Signs--UnequalEffects (Non-conservativeSystems)

When inspection of an experimental spectrum indicates that positive and negative overlapping regions are clearly unequal, i.e. ~ R~ ~ 0, the system is termed "non-conservative". Such situations arise when significant rotational strength develops in the observable transitions through interactions of the observed transitions with higher energy transitions. The conservation rule must apply eventually if sufficient number of transitions are considered: there is no reason why conservation should necessarily be observed over limited regions.

36

P.M. BAYLEY

The analysis of non-conservative systems requires some source of additional rotational strength to be assigned to a high energy region. In principle this might be derived from the ORD spectrum by subtraction of the KK transform of the observable CD. The resolution of the observable CD into components requires values of AK and A~c to be assigned where possible by comparison with absorption spectra, though this procedure is clearly limited to the strongly allowed electrical transitions. The origins of non-conservative behaviour lie in the nature of the electronic transitions which interact. It is unlikely to reside in a single, simple structural feature, such as the tilting of bases in stacked polynucleotides. While the tilting of chromophores may change the properties from conservative to non-conservative, it is possible for the interactions within untilted systems to give non-conservative behaviour. In the absence of general rules for non-conservative properties, the presence of conservative systems remains the most useful diagnostic feature of oppositely signed effects. An analysis of a simple non-conservative system deriving from the overlap of two oppositely signed bands of unequal amplitude, but identical bandwidth A, split by an interval ~( < A), suggests that such a situation may be readily identified (Bayley, 1972b). Taking the expansion of the couplet as before [eqn. (6.2)], but with amplitudes A and B it is found that the line-shape S(uo) is given by

S(uo) = B(r + 1)e exp(-- Uo 2) [Uo -- o~], where

Uo =

A -- Ao Ao ,

r--

A B'

(6.4)

(r -- 1) co = - - - , i.e. a constant for given r and a. (r + 1)or This is clearly composed of a Gaussian, amplitude [B(r + 1)e] located at Ao, bandwidth Ao multiplied by the ramp function (Uo -- ~o) (Fig. 17). The line shape goes to zero at the origin of the ramp function, and oJ is the difference (in units of A) of the observed crossover and Ao. However, it is more conveniently obtained from the ratio G(o0 of positive and negative lobes, since, by differentiating eqn. (6.4) [ ° J + ~ / ( ° ~ 2 + 2 ) ] e x p - - [W -- ~/(~°2 2 2+ 2)] G(~) =

[ ~ ° - - V ' ( ~ ° 2 + 2 ) ] e x p - - [ ~ + ~ / ( °2j 2 +" 2 )2] Figure 18 shows a set of simulated curves for unequal couplets generated from a fixed Gaussian by multiplication with a set of ramp functions of increasing co. It is noticeable that large inequalities of area (i.e. large G(o0) develop for the range ~o = 0-1.0. The function G(¢o) is shown in Fig. 19. The true non-conservatism is, however, very much less than is implied by these curves. Since oJ is a function of r and ~, only an illustrative example can be given for values of ~ which may be anticipated. These results are given in Table 4 for ~r 0.05, 0.1, and 0.2, where it is clear that relatively small non-conservatism (e.g. r = 1.5, ~r = 0.1) can lead to G > 103.

37

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES 1 "40 / 12 0 ]

F

\ \,

1 O01 0.80 0604 0 40 020 0 O0

\\\

-0.20 -0-40 - 0 60 -5.004:00-3:00-2:00-1:00

0:00

1:00 2:00 3:00 4:00

5"00

Uo units delta

FIG. 17. Generation o f unequal couplets. The Oaussian y = yo exp -- (Uo2) and the r a m p function (~o -- uo), for (1) oJ = 0, (2) o~ = 1.0.

1-40 1 "20 1 O0 0'80 0'60

>." 0.40 020 0.00

-0201 -0-40-

•- 0 60 -500-400-300-2.00-1.00

0"00 100

200

3.00 4.00 500

Uo units delta

FIG. 18. Unequal couplets. The family o f curves generated from the functions o f Fig. 17 for oJ = 0, 0.2, 0.4, 0.6, 0.8, and 1.0, and the parent Gaussian.

38

P . M . BAYLEY

o0

/

0

c~

/oo

/

/:

80

80

60

6C

5C

O

40

/

3O

/

30 i o6

2O

I0

0

~

I 02 04

08

06

/ I0

I 12

I 14

w

FIG. 19. The function G(,o). G is the ratio of oppositely signed lobes in the observed unequal couplet (G > 1): the direction of oJ is always away from Ao towards the smaller band. TABLE 4. PARAMETERSOF THE UNEQUALCOUPLET The relationship between G, the observed ratio of intensities in an unequal couplet generated from th~ ramp function (Uo -- o~): and r, the ratio of inequality. ~- and c~ are evaluated for a given co. Sigma values 0.050 /'/max

--0.659 --0.614 --0.573 --0.535 --0.500 --0.468 --0.439 --0.412 --0.388 --0.366 --0.346 --0.327 --0.3]0 --0.295 --0.281 --0.268 --0.256 --0.245 --0.234 --0.225

G(obs) 1.327 1.764 2.351 3.146 4.234 5.735 7.830 10.785 15.003 21.094 30.003 43.202 63.017 93.173 139.711 212.562 328.283 514.855 820.265 1327.970

0.100

0.200

r(A/B)

Amp

r(A/B)

Amp

r(A/B)

Amp

1.010 1.020 1.030 1.041 1.051 1.062 1.073 1.083 1.094 1.105 1.116 1.128 1.139 1.151 1.162 1.174 1.186 1.198 1.210 1.222

0.049 0.056 0.064 0.072 0.080 0.088 0.097 0.107 0.116 0.126 0.136 0.146 0.156 0.167 0.178 0.189 0.200 0.212 0.223 0.235

1.020 1.041 1.062 1.083 1.105 1.128 1.151 1.174 1.198 1.222 1.247 1.273 1.299 1.326 1.353 1.381 1.410 1.439 1.469 1.500

0.099 0.114 0.130 0.146 0.164 0.183 0.202 0.222 0.244 0.265 0.288 0.312 0.336 0.361 0.387 0.414 0.441 0.470 0.499 0.529

1.041 1.083 1.128 1.174 1.222 1.273 1.326 1.381 1.439 1.500 1.564 1.632 1.703 1.778 1.857 1.941 2.030 2.125 2.226 2.333

0.201 0.233 0.268 0.305 0.346 0.390 0.437 0.487 0.540 0.597 0.658 0.722 0.791 0.863 0.940 1.023 1.110 1.204 1.303 1.410

I

Uma~is the position of the m a x i m u m (units of Ao) relative to ,~o, and A m p is its amplitude.

THE ANALYSIS OFCIRCULARDtCI-moISMOFBIOMOLECULI~S

39

It may be noted that the ramp function with co = 0 differentiates the Gaussian curve: as oJ --> 0 the equal couplet approaches the differential of the curve. This corresponds closely to the convolution operations described by Savitzky and Golay 0964). A full analysis of such systems may now be proposed: (a) The spectrum, evaluated on a molar basis, is transformed into the product of the Gaussian and the ramp function, as follows. (b) o~ is evaluated from G(~o), the ratio of peaks; Uo is found to give the best Gaussian. (c) The intensity of this Gaussian is B(r ~- 1)~r, and this quantity multiplied by ~o gives the true non-conservatism B(r -- 1) = --(,4 q- B). (d) For a chosen or, r--and hence A and B may be obtained. (e) Some limiting conditions may be noted. As ¢r--> 0, ~o--> oo, and Amp --> (r -- 1). As r --> 1, co --> 0, giving the conservative case with G ---- 1.0. This analysis suggests that non-conservative spectra such as shown in Fig. 18 should be examined for their resolution into opposed effects of identical A rather than into grossly unequal effects of different A. Such behaviour may be important in single chromophores where transitions are known to be slightly non-degenerate in energy. This has recently been shown by Hsu and Woody (1971) to be the case for haem. Even slight changes in the asymmetric environment might be expected to change r, and hence produce a dramatic change in G(oJ) and the observed spectrum. Similarly, for interacting chromophores, as in dimers, the method offers a quantitative assessment of the degree of non-conservatism. The extensions to many overlapping curves of alternating signs and the inclusions of optimizing techniques for A, oJ, and G(oJ) are presently under study. Limitations are the precision of experimental data, the restriction to gaussians and the condition of ~ < A, in the above expansions. 7. FACTORS OTHER THAN CONFORMATION AFFECTING EXPERIMENTAL SPECTRA The CD and ORD properties of molecules depend upon a variety of factors which may affect the individual parameters Rr, 2it, and Ax. Each of these parameters contributes to the appearance of experimental spectra. As emphasized in § 4, it is the rotational strength which most clearly reflects conformational properties. The principal use of ORD and CD is to derive information about conformation. It is therefore mandatory to eliminate the nonconformational factors which affect the experimental spectra. These factors may occur in the study of the biomolecules themselves and in comparison of their spectra with those of model compounds. In particular, macromolecular systems are subjected to a variety of perturbations in the interests of promoting conformational change. Such perturbations may by themselves produce spectroscopic changes and these factors must be allowed for before attributing an observed change or difference to a conformational change or difference. 7.1.

Chemical Constitution

The effect of chemical substitution in the chromophores of interest has been studied extensively. The introduction of, for example, methyl groups into an amide or peptide chromophore affects the n--~'* and ~r--~* properties (Nielsen and Schellman, 1967). Oscillator

40

P.M. BAYLEY

strength and hence electric transition dipole, orientation, and transition energy are all sensitive to the chemical constitution. In analysis ofpeptide CD, the most important effect is the uniqueness of tertiary substituted peptides as with proline. The lower energy of the ~r-rr* transition for the N terminal peptide at proline allows greater interaction with the n-r:* transition under the CAE and Kuhn mechanisms. Consequently, peptides with high proline content may be considered atypical." specifically, it implies a reservation in the use of heat-denatured collagen as a model for the random polypeptide chain (see § 8). In the case ofpurine and pyrimidine chromophores the effect of changing ring substituents is even more drastic, although the transitions may in general be correlated with those of simpler aromatic chromophores (Clark and Tinoco, 1965). Apart from the generalization that transitions will be in plane and the lowest energy n-rr* out of plane, the differently substituted molecules must be treated as individual chromophores with characteristic properties. Oscillator strengths, dipole orientation, and transition energies require individual determination. 7.2. p H Closely related to the above is the state of protonation of a chromophore. In the most extreme cases there may be a wholesale change in absorption spectrum, as, for example, with a pH indicator: a relatively minor change in absorption spectrum, e.g. a shift or attenuation of a band may disguise the fact that the dipole orientation has changed within the framework of the chromophore. Larger effects are expected when the dissociable group is intimately involved in the electronic transition (cf. the change between phenol and phenate absorptions in tyrosine); significant effects may be expected in purines and pyrimidines. The importance of the electrostatic state of the non-chromophoric portion of the molecule has been emphasized in connection with the CAE mechanism. Proton dissociation will clearly affect this. It is evident that care must be exercised in using reference compounds in the correct state ofprotonation: valid comparisons with biomolecules requires knowledge of the state of ionization of chromophoric groups within the interior of a complex molecule and this ideal may not be realizable.

7.3. Keto-Enol Tautomerism: Cis-Trans lsomerization In an analogous way to the arguments advanced so far, keto and enol tautomers of a chromophore must be considered as separate entities with characteristic properties. Any factor, e.g. pH, temperature, solvent, affecting an equilibrium between the two would change the spectroscopic properties of a biomolecule containing such a system. In the course of hydrogen bonding and base pairing, tautomerism of purines and pyrimidines might be significant, requiring evaluation of spectroscopic properties of the specific tautomers. Cis-trans isomerization is a structural rearrangement which clearly changes orientational properties of the chromophore. In peptides, the orientation of/re (r-v*) is most affected by cis-trans isomerization at the N terminal peptide. Significantly different properties are found for cis- and trans-dipeptides (cf. Figs. 10 and 11). The isomerization is energetically most feasible with tertiary peptides and is well recognized in model compounds (Madison and Schellman, 1970a) and the poly-proline I ~ poly-proline II interconversion, which may be readily monitored by the considerable change in optical properties.

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

41

7.4. Redox State: Liganding The changes of oxidation state found with the coenzyme molecules generally leads to complete changes in adsorption properties, justifying their treatment as different chromophores (see, for example, King et aL, 1969). In attachment with proteins, the properties of the polypeptide backbone may include (non-conformational) contributions which are dependent upon the oxidation state of the ligand (see also § 7.7 below). Similar arguments apply to cofactors whose optical properties may change dramatically on chelation of a ligand. Such effects are discussed in § 7.7 below. 7.5. Solvent The effect of solvent polarity and polarizability upon the energies of rr--~* and n--rr* transitions has been studied in detail and reviewed (Weber and Teale, 1964). n--rr* transitions in general undergo a blue shift in hydroxylic solvents due to the lowering of the energy of the optical n-electrons by hydrogen bonding from the solvent to the chromophore. A similar effect can be produced by protonation (Kasha, 1961). The effect of solvent upon ~--rr* transitions is more complicated (Bayliss and McRae, 1954). Electrically allowed transitions are generally shifted to the blue in aqueous solvents, due to the lower polarizability of the medium compared to apolar solvents. The mechanism corresponds to the blue shift of aromatic chromophores when transferred from a buried to an exposed aqueous environment (Yanari and Bovey, 1960). This result is general for transitions in which the electric dipole increases upon excitation. Solvent effects with peptides depend upon the substitution of the peptide (Nielsen and Schellman, 1967). In primary and secondary peptides, the N - H function acts as hydrogen bond donor to the solvent, resulting in an overall red shift for the chromophore in water as opposed to an environment which cannot accept hydrogen bond donation (Schellman and Nielsen, 1967a). These effects upon the energy of transitions may be accompanied by effects on bandwidth Ax, and upon vibrational fine structure, both of which would result in changes in the observed spectrum. Polar solvents might easily affect the electrostatic properties of a molecule and hence the rotational strength via the CAE mechanism. The presence of large concentrations of counter ions might similarly affect the development of rotational strength. In addition, the asymmetric binding of polar solvent at the chromophore itself could introduce a variable at/d effectively unpredictable perturbation in all mechanisms for developing rotational strength. The use of solvents of low dielectric constant to enhance the intramolecular interactions and, ideally, select a single rotational isomer of a model compound with limited conformational mobility, has been described for dipeptides in § 6: solvent effects on L-PDKP (Schellman and Nielsen, 1967b) and other rigid systems involving lactams (Goodman et al., 1969) and lactones (Toniolo et al., 1970) have been described. The possibility of asymmetric intermolecular association must always be considered. Conformational selection may be responsible for the striking inversion of sign observed by Horwitz et al. (1970) in the 280 nm region CD for N-acetyl L-tyrosine ethyl ester between methanol (--ve)and dioxan (+re). Correlations between CD and structure of tyrosine derivatives have been presented by Hooker and Schellman (1970). Similarly striking inversions occur with chromophoric derivatives of L-amino acids (Barrett, 1966). The relative importance of intermolecular and intramolecular effects has not been evaluated.

42

P.M. BAYLEY

ORD spectra are customarily corrected for the dispersive effect of the refractive index of the solvent (see, for example, Fasman, 1963), and the corresponding rotational strengths are in vacuo values. CD spectra are generally not corrected, although absorption spectra are usually corrected by a Lorentz factor in the derivation of dipole strength. It is of interest that, using data of very high precision, Cassim and Yang (1970) found an exact agreement between the ORD spectrum and the Kr6nig-Kramers transform of the CD spectrum for a given helical polypeptide in the absence of any solvent corrections. While this consistency is impressive, and suggests that identical corrections should be applied to ORD and CD results in a given solvent, the problem of comparing results between different solvents is not yet fully resolved. 7.6. Temperature Given the relatively limited range of temperature available experimentally for molecules in solution, the effect of temperature upon a single rigid chromophore might be expected to be negligible. Such a result was found for L-proline-diketopiperazine in absorption, CD and NMR (Bayley, 1972b). However, the ability of temperature to introduce several of the factors above suggests that this result is exceptional and likely to be confined to small molecules only. Changes in the population of rotomeric isomers of flexible molecules must be considered likely: the inclusion of such changes within the category of "conformational changes" is a matter of definition. 7.7. The Attachment of Small Molecules The ability of small molecules to bring about conformational changes in polymeric systems constitutes the principle of allosterism and embodies a mechanism for exercising control within macromolecular systems. The hypothesis has now enjoyed a decade of excited interest, and optical methods have been used extensively in assessing the ability of small molecules to act, for example, as allosteric effectors. In the absence of large spectral changes in either component, the only truly conclusive result is a negative one, i.e. that binding produces no conformational change observable by this technique. Spectral changes must be correlated with degree of binding, by use of a titration protocol. When such changes are small, some ambiguity may remain. For example, the observation of small changes in polypeptide CD (200-220 rim) on binding a ligand could indeed result from a change in backbone conformation, but another possibility must be considered. It is known that attached chromophores may develop induced optical activity reflecting the asymmetry of their binding site and exhibit "extrinsic" effects (see Eichorn and Cairns, 1958; Blout and Stryer, 1959; Ulmer and Vallee, 1965): the mechanism for this may well involve coupling with chromophores of the macromolecule. The process of borrowing of intensity (or the reciprocal relations) requires the conservation of rotational strength within the system as a whole, and this may be reflected in an equal and opposite change of rotational strength in the macromolecule. The argument must, in principle, be extended over all transitions of the system, including those of the attached molecule, whether observable or not. It is therefore impossible to say, unequivocally, that a change of rotational strength in the macromolecule is associated with a change in conformation. The relative magnitudes of the effects may be taken as a rough guide: if the change in the properties of the macromolecule is at least as large as the induced property of the attached chromophore, it is a

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

43

strong indication of conformational change and additional information from other spectral regions may well resolve the problem. It may be noted that in the case of induced optical activity the properties of the system will not be the algebraic sum of macromolecule q- ligand even in the absence of conformational change. The attachment may select a specific conformational isomer of a flexible ligand, e.g. in the case of nucleotides and coenzymes. This interpretation has been used for the enhancement of the CD of 3'-GMP on binding in the syn-conformation to RNAse-TI and 2'CMP on binding in the anti-conformation to pancreatic ribonuclease A (Oshima and Imahori, 1971a,b). This is evidently a means of observing the properties of a specific isomeric form of the ligand and implies conformational selection of the ligand rather than a conformational change in the macromolecule. When activity is induced in an attached molecule, it is possible to use this property as a probe for conformation and an indicator of conformational effects due to other ligands or environmental variables. Such an approach is invited by the recent observation of large induced effects in bilirubin upon binding to serum albumin (Blauer and King, 1970; Beaven et al., 1972). These effects are approximately tenfold more intense than the intrinsically disymmetric molecules urobilin and stercobilin (see § 4). The chromophoric tetrapyrrole molecule is evidently bound in a complex fashion involving an intrinsically disymmetric conformation. Interpretation at the conformational level is complicated by the variable stoichiometries observed and the heterogeneity of the spectroscopic properties of the bound molecules. However, the principle of using such a chromophore as a conformational probe is an attractive one, awaiting applications (see §11.2): the independence of the binding sites of the probe and effector molecules must be established in order to eliminate direct or vicinal effects. 7.8. Summary The above discussion indicates the degree of reservation required in attributing spectral changes to conformational origins. Nevertheless, such attributions may regularly be made. The elimination of the above non-conformational factors enhances the value of such conclusions, and assists in carrying the definition of conformational effects to a higher level. 8. THE STANDARD STRUCTURES: POLYPEPTIDES The conformational dependence of optical activity in a polymeric system is most clearly shown for the case of polypeptides by the characteristic spectra of a synthetic polypeptide in different conformations. The CD of poly-L-lysine as an c~helix, fl structure, and random coil has been discussed in detail (Greenfield and Fasman, 1969). Extensive work has been done on synthetic polypeptides as model structures for analysis of proteins, and has been reviewed recently (e.g. Fasman, 1969). The concepts involved in the analysis of experimental spectra in terms of the standard structures are discussed in § 8: the individual spectra are discussed briefly here. Conformational angles of the standard structures are given (in the new convention) in the IUPAC-IUB proposal (1969). 8.1. The a Helix

This conformation, formed as a right-handed structure by polypeptides from amino acids of L-configuration, is the best characterized standard structure. Poly-L-glutamic acid

44

P. M. BAYLEY A

B

C

D

.u /z~ = 0

~.~ = 0

++4-+

t-+-

A E strongly - ve

A E strongty t-re

/z~, xy +4--AE+ve

/z~, ×y 4---+ AE+ve

FIG. 20. Optical activity of the a helix. The planar tetramer model and the effect of introducing (right-handed) helical translation. Forbidden (A) and allowed (C, D) transitions give rise to the red-shifted parallel and the (slightly) blue-shifted perpendicular optically active helix transitions. For the a helix, helix sense, and the handedness of the optical path are reversed for the fully in-phase (parallel) transition, cf. Fig. 3. at p H 4.6-4.8 is widely used as a reference: at lower pH, aggregation occurs, and on ionization of all the carboxylic functions at high pH, disruption of the helix. The procedure for obtaining reproducible reference spectra has been presented in a very careful study of helical polypeptides by Cassim and Yang (1970): poly-L-glutamate, poly-L-lysine in aqueous solution, and poly-y-methyl-L-glutamate in trifluoroethanol have been critically compared. The latter polymer, plus poly-L-methionine, poly-E-N-carbobenzoxy-L-lysine and polyL-homoserine are also a helical in hexafluoroisopropanol, and show small but significant variations in their properties (Parrish and Blout, 1971). The spectral features general to all models for the ~ helix are negative bands at 222 and 209 nm and a positive band at 190 nm. These have been assigned to three major effects: the n-zr* transition (R . . . . ~ --0.22 D M at 223 nm) and to two transitions of the zr--~r* system, Rt ~ --0.22 D M at 206 nm; R2 ~ +0.56 at 190 nm (Cassim and Yang, 1970). The n - r * assignment is consistent with the energy, polarization, and absorption properties and is supported by theoretical calculations. N o striking effects of solvent are seen for solvents which do not bring about disruption of the helix. The n--zr* energy is not further red-shifted by apolar solvents, as would be found with a simple peptide: the extensive hydrogen bonding of the helix involves the n electrons of C - - O (Fig. 2), and not the optical n electrons. These latter are evidently shielded from perturbation by solvent. The ~r--~* properties of the a helix can be understood qualitatively with the model of the asymmetric tetramer formed from a planar tetramer by introducing a helical pitch as shown in Fig. 20: the four states derived by symmetry have the relative phases as shown (McRae and Kasha, 1964; Kasha, 1963): only the two in-plane xy-polarized states (C, D) are electrically allowed in the planar condition. On introducing the helical pitch, state A now gains some translation of charge along z, and becomes an allowed transition parallel to the helix axis :

THE ANALYSISOF CIRCULAR DICHROISM OF BIOMOLECULES

45

the rotation of the excitation about z generates/~s along z, and the transition is optically active. Similarly, transitions C and D now gain #m in the x y plane, i.e. perpendicular to the helix axis, and are therefore optically active. Because of the head-to-tail arrangement of transition dipoles in A, the parallel transition occurs at lower energy (cf. Tinoco et al., 1962). In the case of the ~ helix (3.6 residues per turn) the sense of the structural helix and the helical exciton path are different: the parallel transition gives negative rotational strength for the right-handed helical backbone (cf. Fig. 3c). The effect of different side-chains is to produce a further, generally small, perturbation of the transitions (Tinoco et al., 1962). The presence of a polarizable bond in the vicinity of a chromophore may be thought of as yet another (inducible) oscillator with which the transitions may couple. Such terms in general make only minor contributions to R . . . . for hydrocarbon side-chains, but would be expected to be more significant if the side-chain included highly polarizable groups, or, indeed, further chromophoric groups (e.g. carboxyl). However, for such groups to have any net effect they would have to be asymmetrically arranged relative to the peptide in a consistent manner. Such behaviour is observed most evidently with aromatic side-chains which exhibit optical activity in the aromatic transitions, sometimes to the extent of obscuring the peptide CD completely and making the assignment of conformation quite difficult. Such side-chain effects may derive some of their rotational strength from direct asymmetric aromaticaromatic interactions as well as from interactions between aromatic and peptide transitions (Chen and Woody, 1971). In the latter case there will be the additional effect in the peptide transitions due to coupling with the aromatics, which may produce peptide CD different from that of a non-aromatic polypeptide, although the helical sense and conformation are identical. Such effects could also occur with side-chains which are not themselves chromophoric in the observable region of the spectrum. In practice it is found that only obviously chromophoric side-chains lead to notable distortions of the fundamental helical peptide CD. In extrapolating from the observed properties of the standard ~ helix to the helical regions of the globular proteins, several points are relevant: the length of helices, the conformational angles of the residues, the disposition of side-chains relative to the helix, and the nature of the side-chains involved. While some attempt has been made to assess the importance of the first two points, it has not been possible to make any specific assessment of the latter two with the exception of the appearance of proline as a helix terminator. The sum of nonchromophoric side-chain effects is generally taken to be zero. 8.2. The fl Structure This conformation was proposed as the pleated sheet form of insoluble polypeptides such as silk-fibroin, characterized particularly by the X-ray diffraction and polarized infrared absorption of fibres and films. Under certain conditions, soluble polypeptides may evidently assume the/3 conformation, e.g. poly-L-lysine on heating at pH 11.0 or in the presence of SDS at neutral pH, shows qualitatively similar optical properties associated with this structure, though the amplitudes are considerably different (Greenfield and Fasman, 1969). The conformational angles for the/3 structure are relatively close to the fully extended conformation. The/3 structure is therefore an extended chain: hydrogen bonding to other chains can occur with parallel or antiparallel neighbours, generating sheets. These sheets are puckered with side-chains above and below the plane; sheet-sheet interactions occur in fibrous proteins, where the side-chains are short and frequently apolar. Parallel and antiparallel forms have significantly different values of (4, ~b) cf. IUPAC (1969).

46

P.M. BAYLEY

In the hydrogen-bonded parallel and anti-parallel sheets, the chromophores in adjacent chains are suffÉcientlyclose to interact and distinctive properties are predicted for the two cases Woody (1969), Madison and Schellman (1972). Both alignments have been found in globular proteins: the anti-parallel case is more common in synthetic polypeptides. The properties of poly-L-lysine in aqueous solution are generally taken as characteristic of the fl conformation, but some ambiguity exists because of the dependence of the properties on environmental conditions. In addition two forms of/3 structure, characterized by identical infrared spectra show different CD spectra in films (Stevens et al., 1968). The form in aqueous solution appears to be the anti-parallel/3 structure. The particular variability of the optical properties may be attributed in part to the fact that the interactions responsible for the CD and infrared are at such a point on the conformational plane as to be particularly sensitive to small variations in geometry. Thus the hydrogen bonding in the/3 sheet is, in the ideal situation, between two coplanar residues. As such, the cross-chain interactions contributing to the CAE mechanism are zero; however, any deviation from planarity will introduce cross-chain terms. Similarly, for the parameters of the polymer chain, the (~, ~b) values are close to the diagonal, and relatively close to a node in the Kirkwood mechanism. Again, deviations from the strict geometry of the model structures possibly dependent upon the degree of intermolecular association could produce unpredictable deviations from the ideal behaviour. The X-ray evidence to date indicates that the/3 structure occurring in globular proteins is liable to considerable variability in different cases. Lysozyme contains a small amount of antiparallel structure (Blake et al., 1967); carboxypeptidase contains several strands of /3 structure in both parallel and anti-parallel orientation in a sheet structure which is subject to an overall twist within the globular structure (Lipscomb et al., 1969). Infra-red absorption has been used to detect the presence of/3 structure in a range of proteins, most notably /3-1actoglobulin (Timasheff et al., 1967). Given the diversity of the proteins already known to contain fl structure, and the heterogeneity of the properties associated with this structure, it is clearly a difficult component to assess quantitatively. 8.3• The R a n d o m Coil The conversion of polyglutamic acid or poly-lysine to the fully charged forms, at alkaline and acid pH respectively, causes the collapse of long-range order, and the adoption of a conformation with hydrodynamic properties of a random coil (see, for example, Fasman, 1969). This conformation has been taken as the reference for the irregular portions of globular proteins. The optical properties associated with this conformation are a strongly non-conservative system in CD, with a pronounced negative band at 190 nm and a weak positive band at 217 nm. These bands have, in general, been taken to represent the rr-rr* and n--~* peptide transitions respectively. The validity of these models for the spectroscopic properties of denatured polypeptides has been questioned (Tiffany and Krimm, 1968, 1969). The spectra of globular proteins which have been denatured by concentrated urea or guanidine hydrochloride do not show the positive band. Instead, a negative band of approximately the same intensity is seen, and this is present for polypeptides such as poly-L-glutamate and poly-L-lysine in concentrated solutions of lithium and caesium chloride. They attribute the positive band to the existence of short-range order in the highly charged polypeptides, and conformational energy calculations have been presented in support of an "extended-helical" conformation (Hiltner et al.,

THE ANALYSISOFCIRCULARDICHROISMOFBIOMOLECULES

47

1972). It is argued that a better picture of the random coil is given by polypeptides in concentrated salt solutions, whose spectra also resemble closely that of heat-denatured collagen. It is clear that no unequivocal model of the random coil has yet been found. Objections to the alternative suggested by Krimm are that specific ion effects are known to occur with peptides (e.g. von Hippel and Schleich, 1969) including the promotion of cis-trans isomerization of the peptide link in proline peptides; the spectra of charged homopolymers i~ concentrated salt solutions can be accounted for as a sum of helical and random forms (Dearborn and Wetlaufer, 1970); the fact that collagen and its heat-denatured product are atypical, spectroscopically, because of the high proportion of tertiary peptides (§ 7.1); and the resemblance of the uncharged polymer poly (NS-(2-hydroxyethyl)L-glutamine) to the pGA spectrum (Adler et al., 1968). Krimm's argument does, however, offer an explanation for the positive band in polyglutamic acid and polylysine: calculations at the dipeptide level of R,_~. could not rationalize the observed positive rotational strength as the sum of all available dipeptide conformations, or as a weighted sum allowing for the potential energy distribution of dipeptides. The region around (see Fig. 10c) is the only source of positive R,_.. in dipeptides (Bayley et al., 1969) and it is within this region that the shortrange order predicted by Hiltner et al. 0972) would reside. Alternative explanations have been proposed for the positive band: calculations by Aebersold and Pysh (1970) for a set of random conformations did not simulate the properties of unordered polyglutamate. Only by restricting the potential conformations dramatically was the experimental curve reproduced. This derives from the sum of oppositely signed ~-~* transitions; n-~* transitions were omitted from the calculation. On this explanation, the effect at 217 nm would then be in the tail of much stronger effects located at lower wavelength, and would be critically dependent upon factors governing bandwidth and energy, as pointed out by Woody (1968). In fact, the parameters of the positive band are reproducible and well characterized. Calculations by Zubkov et al. (1971) for n-~* and ~r-~r* rotational strengths for sets of random polypeptides suggest that the positive band derives from ~-~r* interactions between degenerate transitions (i.e. an exciton interaction) and in general, the n - r * transition has weak negative rotational strength. A uniform pattern of (non-conserved) negative rotational strength is found in all allowed regions; it derives from interaction with higher energy transitions and polarizabilitie s. The question still remains as to whether a polypeptide with random conformation has ever been produced experimentally without cis-trans isomerization, specific ion binding, or the production of short-range order. 9. MULTI-COMPONENT ANALYSIS The recognition of characteristic properties of certain standard structures for a given type of biological macromolecule has encouraged attempts to represent the spectra of molecules of unknown structure as linear combinations of the standard components. For synthetic polypeptides, the principal standard structures are the a helix, fl pleated sheet, polyproline and collagen structures, and the random coil. For synthetic polynucleotides, single- and double-stranded helices, and disordered structures are the best defined, a possible major variable being the angle of tilt of the basis in helical structures. Most work has been done on proteins, and this will be discussed here. This "multi-component analysis" assumes a linear relationship between the fraction of residues in a given form and the contribution which it makes to the total spectrum. This

48

P.M. BArLEy

assumption is implicit in both those analyses which use the total ORD and CD spectra and in those which use the characteristic parameters which fit the curves. In the latter category are the parameters at, bo, of the Moffitt equation, ~c of the single term Drude equation (discussed in Schellman and Schellman, 1964) A19 3 and A2zs of the two-term Drude equation (Shechter and Blout, 1964) [m199]and [m233], the amplitudes of the extrema in ORD; and [0119o, [0]208, or [0]222, the extrema of the CD spectrum at the appropriate wavelengths. The degree of sophistication applied in multi-component analysis has increased with: (i) greater information content in the spectra, obtained by extending spectroscopic measurements into the far ultraviolet and improving resolution; (ii) recognition of additional contributing structures; (iii) better theoretical understanding of the spectroscopic effects. While further advances in all three regions are possible and, indeed, likely, a plateau has been reached in this activity. To summarize the state of this work it is fair to say that truly definitive analyses are possible only when the experimental spectrum conforms closely with one of the standard structures. In all other cases the information content of the spectra is insufficient to allow a structural analysis in definitive terms. The limitation to the information content of ORD and CD spectra lies in the way in which the conformation is expressed in terms of the parameters Rt, As, and As: the small differences which occur in ALare frequently obscured by the magnitude of As, and the potentiality for opposite signs of R~ can largely obscure individual properties. The number of parameters needed to fit an experimental spectrum is consequently much less than the theoretical p ~3 × N × M (where N is the number of chromophores and M the number of transitions per chromophore). For example, for lysozyme with 129 amino-acid residues and considering the two peptide transitions in each chromophore, p ---- 774: in practice, analysis is attempted in terms of only two or three parameters, representing the fractional occurrence of a few basic structures. In consequence of the low degree of information available it is unlikely that ORD or CD will give analyses to compare with methods with high information content, like X-ray crystallography or NMR. In spite of this limitation, the force of CD and ORD techniques lie in the ready application to molecules in solution, the enormous range of chromophoric material which is available (and, as yet, largely unexploited), the capability of producing information about processes directly related to function which involve changes in conformation of the chromophoric arrays, and the possibility of direct observation of functionally linked kinetic properties. It is therefore important to know how the best use may be made of conformational analysis by ORD and CD, what are its limitations, and what advances are anticipated. 9.1. Analytical Methods Methods based upon the plain dispersion of ORD (single-term Drude, Moffitt equation and two-term Drude equation) are necessarily undefinitive, and are essentially two-component analyses. The equivalence of these methods has been demonstrated (Timasheff et al., 1967). The correspondence of the analytical parameters with those of standard structures is a valuable indication of conformation, and should readily be substantiated by observation of the far ultraviolet spectra. For analysis of globular proteins, these methods have largely been superseded by methods which depend on ORD and CD spectra observed to the far ultraviolet limit of 185 nm which induce a variety of extrema and characteristic points (Greenfield et aL, 1967; Greenfield and Fasman, 1969). The linear combinations of the

T8~ ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES

0

spectra of a helix [a]~, fl structure [fl]~ and random coil [RC]~ with fractional contributions

f~, fa, fRc allows the spectrum of the sample to be represented as [Sample]a = f,[a]~ q- f~[fll~ + fRc[RClz,

(9.1)

where

L + f . + f R o = 1. In principle this may be solved using only two data points from each spectrum at ,~t, ;% and solving for f , , f~. In practice, initial estimates of the variables are made from characteristic points where possible, and computational methods are used to refine the variables to minimize the difference between the observed and computed spectrum. In assessing what constitutes the best fit of a computed curve to the experimental data, the statistics of the fitting procedure require examination of the following points: (i) Are data points to be taken at equal wavelength intervals ? (ii) Are all points of equal weight or are extrema and cross-over points to be given extra weight ? (iii) To what standard deviation of measurement has the experimental curve been determined ? (iv) What limits can be placed on the final fractional values ? (v) To what extent are the values of final parameters independent of the choice of initial parameters ? General rules are hard to establish for these procedures: if extra weighting is introduced through (i) or (ii), it should also be included in evaluation of the standard deviation in (iii), i.e. a consistent procedure should be adopted throughout. It is unlikely that final parameters will be independent of initial choices, and consequently multiple solutions are likely. Information from other sources must be sought to validate a particular solution, as has been done for the combination of CD and infrared spectra by Timasheff et al. (1967). For details of the analyses of Fasman, the reader is referred to the original papers: in summary the results by ORD showed rather poor correlations of the computed fractions of "a helix" and "random coil" with the known structures of myoglobin, lysozyme, and ribonuclease A. Except in the case of myoglobin in which a large fraction of the residues are in the a-helical conformation, poor agreement was obtained between the experimental spectra and the curves computed with the known fractional contributions of the reference structures. In CD somewhat better results were obtained: the fractional contribution of a helix was estimated from the ellipticity at 208 nm using {[012os 4000} (33,000 -- 4000}" -

A=

-

This equation is essentially a two-component analysis, dependent upon the observation that /3 and RC make approximately the same contribution at 208 nm and may consequently be treated together as a non-helical component. This value o f f , was then used as the starting point for the fitting of the rest of the spectra as a sum off,,fp, andfRc. Reasonable fits were obtained for the spectrum above 220 nm. The results indicate the level of success to be expected: only in the case of myoglobin is there convincing agreement; while CD has the advantage over ORD of less overlap between

50

P.M. BAYLEY

components, and less dispersion to individual components, it is notable that the spectral region below 210 nm was generally only poorly approximated in spite of the use of [612os in setting the initial value off~. 9.2. Limitations The reasons for the limited success, discussed by Greenfield and Fasman (1969), may be considered. (i) Variability of the properties of the reference structures as discussed in § 8 : particular problems are posed in/3 structure, which shows strong environmental dependence of its optical properties, and by random coil where models with strikingly different properties have been proposed. The use of poly-L-serine in 8 M lithium chloride as a model for [RC]~ is reported by Rosenkrantz and Scholtan (1971) to improve the analysis for reference proteins. (ii) CD of the zr-rr* transitions is known to be dependent upon the length of the array for regular helical structures (Woody and Tinoco, 1967; Madison and Schellman, 1972); similar properties may be inferred for the non-helical part. (iii) Contributions from aromatic chromophores are known to be present in the region below 230 nm. The low molar fraction of aromatic residues encourages the view that such contributions may be neglected: however, the presence of even weak dichroism in the lower energy transitions of these chromophores (250-300 nm) is an indication that higher energy transitions are to be anticipated. (iv) The regions which are not a or/3 structure are improperly represented as having the properties of random coil: these regions, constituting the tertiary structure of globular proteins, are completely specified in terms of the set of angles (~l ~b~):neither the distribution of these angles over the allowed regions of conformational space nor the progressions of these values for contiguous residues conform to a state of random orientation. Because of the variety of conformations which are represented in these regions, it is not possible to generalize about their properties, and this constitutes a major objection to the assumptions of the multi-component analysis. It is clearly a pressing point to have some information on these regions: one approach is outlined in § 10.1 for the computation of the optical properties of irregular structures. (v) The crystallographic structures, which are assumed to persist in solution, contain minor distortions from the standard a helix and/3 structure; the computed spectra would therefore themselves be subjected to some considerable variability. It may be noted that a general result is the overestimate of/3 structure: this might be partially in compensation for the model used for random coil; adoption of a reference spectrum more like that proposed by Tiffany and Krimm from the spectrum of heat denatured collagen or the spectra of synthetic polypeptides in the presence of denaturants would reduce the discrepancy. 9.3. Further Developments As a corollary to the above type of approach (§ 9.1), Saxena and Wetlaufer (1971) sought to find the three reference spectra [A]a, [B]x, [C]~ combinations of which in amounts f,(~), fB(~), fRct~) most closely represent the observed spectra of three proteins for which X-ray structures have been determined (represented by subscripts X), i.e.

THE ANALYSISOF CIRCULAR DICHROISMOF BIOMOLECULE$

[Samplel]~

=

fa(x, z

[A]x +f~(x, [B]~ +

[Sample2]~ = fa(x, 2 [A]z [Sample3]~

+f~(x)

1 fRO(x) [RC]~

51

t

[BI~ + fac(x~ 2 [RCh

(9.2)

a [A]~ +f~(x, [BI, + fRC~x~ f~t,, a [RCh

Solutions of these three equations simultaneously at a given A, gives a point [A],,, [B]a,, [C]z, in each spectrum. The results using myoglobin, lysozyme, and ribonuclease give three curves with good resemblance to [~], and moderate similarity to [fl]~ and [RC]~. Less success was found with applying these reference spectra as in eqn. (9.1) to the analysis of chymotrypsin and chymotrypsinogen, though good agreement was found in comparing the analysis of carboxypeptidase A with its known structure. Although an exact solution of eqns. (9.2) is taken, weighting of the results in terms of the initial choices is hard to avoid. The basic principle of representing the observed spectra in terms of only three components raises the same objections discussed in (iv) and (v) above. A similar analysis has been applied in general terms by Chen and Yang (1971) for the evaluation of any spectroscopic parameter P~, P0, PRc (where P refers, for example, to bo, [rn2as], or [0222]) from observed values for proteins of known structure: i.e. Pob, = f~cx~P~ + fBt~ PB + f a c ~ PRc, wheref~t~ is a mole fraction derived from X-ray data. The values for P determined by leastsquares fit for five proteins of known structure are in good agreement with experimental observations; less satisfactory results are found for the other components. Even this success must be viewed against the observed variation of helix parameters for different model helical polypeptides in the same solvent (Parrish and Blout, 1971). These methods suggest a further development which has been investigated by Dalgleish (1972): a full rank analysis of a number (> 3) of spectra gives the number of contributing components which can be taken as representative of a globular protein. This was found to be four. The method does not give the characteristic properties of these components, but provides a realistic assessment of how many components are to be included in a multicomponent analysis. With suitable refinement, the analysis could be extended to include contributions from the aromatic regions (see also § 10.3). If sufficiently sound correlation can be established on practical or theoretical grounds between the optical activity of the low and high energy aromatic transitions, one may anticipate the assessment of non-peptide contributions at 230 nm from the properties at 280 nm. Contributions at the peptide transitions themselves may be anticipated, since it has been shown that the rotational strength of both low- and high-energy transitions in tyrosine derivatives may be accounted for by Kirkwood coupling between these transitions and neighbouring peptide chromophores (Hooker and Schellman, 1970). Additional rotational strength will thereby be generated in the peptide transitions.

10. Q U E S T I O N S

SUSCEPTIBLE SOME

TO THEORETICAL RESULTS

TREATMENT:

In the light of the previous discussion we may summarize the fields in which theoretical investigation may be expected to assist in the analysis of optical activity: (i) The isolation of purely conformational factors affecting optical properties.

52

P.M. BAYLEY (ii) The extension of current treatments of standard structures to include more complete descriptions of the spectroscopic properties of individual groups. (iii) The sensitivity of spectra to parameters representing position and bandwidth, hence the treatment of solvation and general environmental effects. (iv) The assignment of vibronic bands and their relative importance in the development of optical activity; the use of vibrational fine-structure in monitoring conformational properties. (v) The sensitivity of optical properties to conformational factors, conformational angles, length of helices, inter-chain effects. (vi) The properties of irregular regions of naturally occurring biopolymers. (vii) The detection of conformational changes in proteins. (viii) The computation of optical properties for specific molecular structures: small peptide and nucleotide assemblies, the validity of structures derived from conformational calculations, the relationship between X-ray structures and the conformations of biomolecules in solution.

In this section, items (v) to (viii) are considered in some detail, particularly with respect to polypeptides and proteins. Results have recently been presented for a range of standard structures and globular proteins by Madison and Schellman (1972) using the extended treatment previously applied to dipeptides which is described here. The results for one specific case are presented here in some detail, using X-ray crystallographic coordinates for lysozyme (Blake et al., 1967) made available by Prof. D. C. Phillips. In investigating items (v) to (viii), small fragments of the structure have been examined for their individual properties and for the way in which they integrate into the whole molecule. A similar approach has been used in computing the optical properties of the cyclic decapeptide, gramicidin S, in order to present some spectroscopic criteria for choosing between various proposed structures. Results are also presented for the proposed structures of gramicidin A. Finally, a quantitative estimate has been made of the limits of observability of conformational changes in proteins by analysis of peptide CD. 10.1. Irregular Structures: Lysozyme In the crystalline state, the conformation of lysozyme (129 amino-acid residues) is composed of several short regions of a helix, a small amount of/3 structure (anti-parallel), and the major part, the fully specified but irregular regions. Calculations have been performed for the optical properties of the following fragments: (i) (ii) (iii) (iv)

the c~and/3 regions, the irregular regions, regions joined by disulphide bridges; sixteen segments of 8 peptides, 8 segments of 16 peptides, and 4 larger segments of 24-36 peptides.

Comparisons are made at the level of the value of Rn_~.. Calculations of complete envelopes for CD and ORD requires assignment of the sensitive parameters A, AB, E, and EB, whose relative values can have a marked effect on the final spectral profiles (Woody, 1968). Table 5 shows the results for (i) and (ii) and, for comparison the values for the equivalent number of residues in standard structures with conformational angles ct (--57, --48)

THE ANALYSISOF CIRCULARDICHROISM OF BIOMOLECULES

53

TABLE 5. CALCULATIONSOF Rn-~t* FOR REGIONS OF LYSOZYME Residues

N

5- 12 25- 33 80- 84 89- 96 110-113 120-124 Cf. a helix

R._ n •

N

R._ n •

8 9

--0.088 --0.088

8

--0.106

N

R,,_~ •

--0.061

16

41- 46 50- 54 (41- 56) Cf. /3 structure

--0.120

--0.068 --0.061 --0.075

--0.102

+0.025 --0.052 16 16

15- 22 34- 41 42- 49 34- 49 50- 57 58- 65 97-109

--0.009 --0.138

--0.130

--0.119

+0.037 --0.027 --0.001 16

+0.005 --0.048 --0.051

13

--0.086

Note: E~ = 210 nm; E 8 = 190 nm. "a-like", "/3-like" and "irregular" regions are compared.

TABLE 6. CALCULATIONS OF -Rn-Tt* FOR DISULPHIDE-LINKED PEPTIDES AND NON-CONTIGUOUSPEPTIDES Region

SS1 (6-127)

SS2 (30-115)

SS3 (64-80)

SS4 (76-94)

RI

R2

R._n,

Average

5-12 122-129 Both

--0.088 --0.025 --0.055

(--0.056)

26-31 110-120 Both

--0.077 --0.062 --0.067

(--0.069)

63-71 72-80 Both

--0.053 --0.064 --0.049

(-0.058)

75-83 90-98 Both

--0.056 --0.099 --0.075

(--0.078)

5-12 15-22 Both

--0.088 +0.037 --0.030

(--0.025)

34--41 42-49 Both

--0.027 --0.001 +0.005

(--0.014)

Residues

Note: Parameters as in Table 5. The average of the two non-contiguous peptides is compared with the property of the pair together.

54

P.M. BAYLEY

fl (--139, 135). Table 6 shows results for the four pairs of peptides linked by disulphide bridges, which are therefore in close proximity, and for two examples of close but noncontiguous regions R1 and R 2. It is readily seen that the a-helical regions are well behaved, producing R,_~. closely similar to that for the standard structures. For fl structure, the two regions give R . . . . of opposite sign: the variation in results from this type of structure in a number of proteins suggests that it is extremely unlikely to be representable by a single type of spectrum. Likewise the results from the irregular regions show no consistent correlation with conformation" effects of both sign appear, and in the negative effects, rotational strengths are found which approach 50 ~ of the equivalent a helix. A wide range of non-contiguous peptides were studied to evaluate the magnitude of intra-chain effects between sets of chromophores in the same regions of space. In the case of peptides linked by disulphide bridges, it is clear that only minor intra-chain effects are produced by these proximities. For fourteen other pairs of (unlinked) peptides, additivity was closely followed, exemplified by R~ (Table 6): only in the case of two peptides including the intra-chain anti-parallel/3 structure (41-46) was there clear evidence of non-additivity and in this case the effects are relatively weak. It would thus appear that in the absence of effectively the closest possible intra-chain approaches, the rotatory properties of R . . . . are the sum of the component segments. Following this argument, it is justifiable to compute the properties of the whole array as in (iv) above, the various lengths of segment serving as a check that no spurious element is entering the computation as a result of extending the treatment up to thirty-six residues. The results are shown in Table 7 for segments taken irrespective of the nature of the regions involved. The value ot R . . . . is seen to be between 50-60 ~ of that for the corresponding helix, and TABLE 7..Rn_n*

FOR LYSOZYME COMPUTED AS THE SUM OF ITS COMPONENT PEPTIDES

Residues 1-16 9-24 17-32 25-40 33-48 41-56 49-64 57-72 65-80 73-88 81-96 89-104 97-112 105-120 113-128 121-128 1- 8 J Mean N = 16 a helix "%h" Cf. the mean for N = 8 a helix N = 8

R._n • --0.096 --0.028 --0.035 --0.063 --0.014 --0.009 --0.040 --0.052 0.070 --0.086 --0.100 --0.102 0.090 --0.078 --0.052 --0.060 --0.061 --0.120 50%

Residues

R._~•

1-36

--0.093

37-60

--0.001

61-96

0.127

97-129

0.108

Mean N = 36

R._n. --0.054~ .. o --0.102J a'~Y°

0.089 --0.138 64~ -

-

THE ANALYSISOr CIRCULARDICHROISMOr BIOMOLECULES

55

the result is reasonably independent o f the length o f peptides considered. This overall result is rather higher t h a n the value o f 30 ~o apparent helix which is f o u n d f r o m optical rotation data, which coincides with the n u m b e r o f residues in truly a-helical conformation. Closer agreement with experiment has been obtained by M a d i s o n and Schellman (1972) for full C D profiles, assuming bandwidths h~ = 14 n m and A~ = 12 nm. 10.2. Small Peptide S y s t e m s The c o m p u t a t i o n a l methods are ideally suited to evaluating the optical properties of tentative structures deriving f r o m model building, conformational energy calculations, and other spectroscopic sources. Examples are given here for the cyclic decapeptide gramicidin S, and the linear peptide gramicidin A. 10.2.1. Gramicidin S The experimental C D (Balasubramanian, 1967; Laiken et al., 1969b) included in Fig. 23 TABLE8. GRAMICIDINS" CONFORMATIONALANGLESOF MODELSTRUCTURES GS-L-II (~, ~) 1

L Val

2 3 4 5 6 7 8 9 10

L Orn L Leu D Phe L Pro L Val L Orn L Leu D Phe L Pro

--102, --137, --143, 58, --68, --102, --137, --143, 58, --68,

GS-V (~, ¢)

137 142" 82" --116" --36 137 142a 82" --116" --36

--121, --73, --98, --41, --57, --118, --73, --102, --33, --57,

103" 86" 134 --60 --60~ 96" 86" 124 --60 --60"

"Denotes regions with principle contributions of negative

Rn-n* GS-L-I (~, ¢) 1 2 3 4 5 6 7 8 9 10

--65, --50, --60, 90, --65, --65, --50, --60, 90, 65,

--60 --50 --50 -- 10 130 --60 --50 --50 -- 10 130

GS-I (~, ~) --126.9, --110.6, 63.7, 129.1, --67.0, --106.0, --108.7, 63.2, 137.1, --67.0,

--123.8 51.8 60.0 --61.2 123.0 127.2 46.3 50.0 --71.4 145.1

Note: Minor modifications have been made to improve cyclization. References: GS-L-I Liquori et aL, 1966. GS-L-II de Santis and Liquori, 1971. GS-I Vanderkooi et aL, 1966. GS-I Scott et aL, 1967. GS-V Momany et aL, 1969.

56

P. M. BAYLEY 9 9

---(

/

1

6,~ "~3 5 ~" ~

~'~1

4

(a)

(b) 8

/

v

/

i

"--_6y

_

L/

!

_

A

(d) (c) FIG. 21. Proposed structures for gramicidin S. The peptide backbone conformation for (a) GS-V; (b) GS-L-II; (c) GS-L-I; (d) GS-I. Numbering corresponds to the C atoms. Only peptide HO involved in hydrogen bonding are shown: the open arrow, residues 5 and 10, indicates the pyrrolidine ring of proline. indicates a strong negative n-=* rotational strength (approximately --0.20 DM), which is relatively insensitive to different solvents. Hydrogenation of the aromatic residues indicates that this derives from peptide transitions and suggests a specific strongly ordered structure. The model structures which have been investigated (Bayley, 1971a) are indicated in Table 8. The peptide backbones of these structures are shown in Fig. 21. The rotational strength calculations for several structures and some constituent peptides are shown in Table 9. Two parameters are important, namely Rn_~, and the net rotational strength of the two proline residues. Because of the distinctive properties of proline, and the lower zr--=* energy, the rotational strength of these transitions has a marked effect on the appearance of the final spectra. A net negative rotational strength is indicated experimentally. The results show that structures GS-V and GS-L-II both produce strong negative Rn_~.. Calculations on the partial structures show that strong contributions derive from short sequences in fl-like conformation (Table 8: (4, ~b) ~ ( - - t 2 0 °, 120°)). Further, the R,_~, for the total structure is more intense than any constituent peptides or their averaged values.

THE ANALYSISOF CIRCULAR DICHROISM OF BIOMOLECULES

57

TABLE 9. ROTATIONALSTRENGTH CALCULATIONS FOR GRAMICIDINS MODELS AND CONSTrrU~NT PEPT~D~

Residues

R,_ n,

R(Pro)

R,_n,

R(Pro)

(i) Water 1-10

GS-L-I --0.056 --0.093 +0.173

--0.008

1-10

GS-L-II --0.153 --0.063 --0.032

--0.187

+0.013 +0.228

1-5 2-6 3-7 4-8 5-9

--0.132 --0.119 --0.093 --0.089 --0.101

--0.105 --0.136 --0.138 +0.123 --0.183

--0.110 --0.150 --0.165 --0.140 --0.121

+0.284 +0.257 +0.296 +0.161 --0.016

1-3 2-4 3-5 4-6 5-7

--0.112 --0.134 --0.089 --0.035 --0.033

--0.218 --0.181 +0.157

--0.094 --0.052 --0.087 --0.136 --0.158

+0.040 +0.556 +0.349

CL

a (10) AP---fl (10)

(ii) Apolar 1-10 Cf.

a (10) AP---fl (I0)

--0.102 --0.133

Energies: (i) Water: E~ = 210nm; (ii) Apolar: E~ = 220 nm;

GS-V

(5) /3 (5)

GS-L-II --0.080 --0.140 +0.036 --0.052 --0.089

GS-I ] +0.055 --0.051

--0.077 --0.121 GS-V --0.122

--0.151 +0.320

EB = 190 nm (Pro 199 nm). Ea = 185 nm (Pro 200 nm).

Note: R,_n., R(Pro) represent rotational strength per residue. The two structures differ throughout in their predictions of the proline properties. (Both GS-L-I' and GS-I produced couplet-like interactions due to proximity of Pro-5 and Pro-10 in these structures, features which, together with the relatively weak R . . . . . exclude them from further consideration here.) The proline residues in GS-V ~both acquire positive R . . . . . This can be seen from the component pentapeptides to be a feature of the immediate neighbourhood of the proline, and not a trans-annular effect. In GS-L-II, which differs from GS-V principally in the conformation at proline, the effects are both negative. The full rotational strength distributions for GS-L-II and GS-V are shown in Fig. 22 for E, = 210 nm, E B = 190 nm. The highest wavelength rr-~-* transitions derive from proline; the remaining transitions distribute in positive and negative bands. The computed CD spectra with A ~ = 12.5 nm and A ~ _-- 10.0 are shown in Fig. 23 for various combinations with appropriate values of E, and EB simulating typical monomer values in water and apolar solvents respectively. While the computed envelopes are somewhat dependent upon the assigned values, the results for GS-L-II with apolar parameters are in good agreement with experimental results: the computations simulate the intense negative n-,r* trough, the following negative trough and the positive maximum of the experimental spectrum. It

58

P.M. BAYLEY

is notable that, while formally resembling the spectrum of the ~ helix in having two negative peaks, the origin of the effects in gramicidin S is quite different; the n-,-r* intensity derives from essentially anti-parallel/3 structure, and the negative trough at 204 nm contains the contribution of negative rotational strength from the prolines. Both GS-L-II and GS-V might be considered to be structures consistent with anti-parallel /3 structure as proposed by Hodgkin and Oughton (1957) and Schwyzer (1958). The optical calculations are thus strongly in support of the Schwyzer structure in solution and the structure GS-L-II is preferred on the basis of R . . . . the proline properties, and computed profiles. This result is consistent with recent N M R evidence (Ovchinnikov et al., 1970; Schwyzer and Ludescher, 1968; Stern et al., 1968) and the results of tritium exchange (Laiken et al., 1969a).

'°I

1-0

E Q a:=

I~0

=o o

1

200

210

220 nm

J

F_ GS-V

G S - L - Fr .

I -I0

-ioL

FIG. 22. Rotational strength calculations for gramicidin S. Structures GS-V and GS-L-II. R~.~. indicated by x, located at 210 nm (E~ = 210.0 nm, E a = 190.0nm; Ea(Pro) = 199.0nm. Notable difference at 200 nm where GS-V is strongly positive, GS-L-II strongly negative. 10.2.2. Gramicidin A Model structures have recently been proposed for the alternating LD peptides frequently found in antibiotics, and typified by the linear peptide gramicidin A (Urry et al., 1971, 1972; Glickson et al., 1972; Urry, 1972). The structures comprise a family of helices, the ~rLt) helices, which have the appearance of an extended chain, wound into cylinders of different diameters. Structures generated from values of (~, ~) have been taken, with slight modifications from Urry (1972), in order to compute the optical properties (Table 10). The results are preliminary since the conformation angles themselves are not yet refined to the best possible helical values. Table 10 shows that the ~rLt) model could give a considerable negative R , _ , . for the 4.4 and 6.3 residues per turn; the resemblance of the structure to a "coiled-#" structure might have suggested this. Also the CD profiles tend to resemble the # structure in their two cases, and this result is relatively independent of the values taken for the bandwidths. The computed spectra show a #-like couplet, but shifted ~ 10 nm to higher energy.

THE ANALYSISOF CIRCULAR DICHROISM OF BIOMOLECULES

59

(iv)

(i)

o

%0

200

240

28O

160

200

240

280

,

240

.

28O

(iO E

4

% >o

IJJ

-4 160

200

240

280

i

160

200

4

(iii)

(vO

0

•

-4 .-4 1 0

200

240

280 Wavelength

160

V 200

240

280

in n m

FIG. 23. C o m p u t e d a n d experimental C D for gramicidin S. C D profiles for GS-L-II and (3S-V for A ( = A~ = Aa) as shown and with energies (A) E= = 2 1 0 n m , E B = 190 nm, EB(Pro) = 1 9 9 n m ; 03) E~ = 220 rim, E B = 186 nm, Ea(Pro) = 200rim. (i) GS-L-II: A = 12.5 n m ; energies I(A); 20]). (ii) GS-L-II: A = 1 10.0; 2 = 12.5; energies (B). (iii) GS-V: A = 10.0; energies: I(A); 2(B), (iv) 1: GS-L-II; 2: GS-V; A = 12.5; energies (A). (v) 1: (3S-L-H; 2: (3S-V; A = 10.0; energies (B). (vi) Experimental data for gramicidin S in" (1) methanol, (2) water, and for (3) hydrogenated gramicidin S in methanol. (Replotted from Laiken et aL, 1969b.)

In the case of the 8.4 and 10.4 residues per turn, weaker spectra are found, and effectively a mirror image relationship between the two. Inspection of the structures shows that the parameters generate helices of opposite sense in these two cases. Experimentally, the spectra of gramicidin A are complicated by strong contributions from aromatic chromophores, and the tendency for intermolecular aggregation. The spectra

60

P . M . BAYLEY

TABLE 10. GRAMICIDIN A. --~rLD HELICES: COMPUTED ROTATIONAL STRENGTHS AND C O PROPERTIES

N = 10 Residues/turn (if, q~)Lresidues (~, ~b)aresidues R~_~°

E~ = 210nm

4.4 (--125, 85) (+ 85,--125)

(--135, 105) (+ 90,--145)

8.4 (--145, 135) (+135, --150)

10.4 (--135, 150) (+150, --140)

--0.086

--0.165

--0.041

+0.063

(200) --8.2

(202) -- 9.8

(210) --2.1 (194) --3.7

(210) (194)

(191) (180)

(193) 0 (180) 12.3

(185) (176)

(185) 0 (176) --4.6

6.3 i

CD profiles A~ = 12.5 A# = 12.5

Ep = 190nm

0 9.1

0

5.0

2.9 2.4

• (~, if) Modified from Urry (1972) to eliminate close contacts. The values quoted apply to a single conformational convention irrespective of the configuration at C~ (IUPAC, 1970). are extremely sensitive to solvent (Isbell et al., 1972) and contain strong contributions from tryptophan transitions. While there is a strong formal resemblance between the results for the 10.4 helix and the spectrum in T F E reported by Urry for the hydrogenated gramicidin A' (72 ~o A, 9 ~o B, 19 ~o C), there is strong evidence from infrared that the parent gramicidin A in T F E has a random structure (Isbell et al., 1972). The negative CD at 210 nm for gramicidin A in anhydrous alcohols, e.g. n-propanol (and Brij-35) is more consistent with t-like structure (also supported by infrared). 10.3. Detection of Conformational Changes in Proteins by Peptide CD Since the optical properties of a polypeptide can evidently be taken as the sum of its component oligopeptides, it is useful to compute the magnitude of changes in optical properties which will accompany a given conformational change due for example to the elimination of a small portion of ordered structure. Let us assume that a significant conformational change sufficient to alter the activity of an enzyme is brought about by the transformation of a single turn of helix, say four peptides, into a non-dichroic conformation. Assuming typical values of 30,000 MW (i.e. 300 peptides) and a helical content of 30 ~ , the change in helical content would therefore be from ninety residues to eighty-six residues or a decrease of 5 ~o. The value of A~22o would decrease from --4.0 to --3.8 units. In a typical experimental system, e.g. 0.2 mg ml- 1, 0.1 cm path length, the change in signal would be from 71.4 to 67.5 × 10 -S units, or approximately 4 × 10 -5 units. This is approximately twice the magnitude of the system noise at 220 nm (in the author's experience with the Jouan Dichrograph Mk. II) and may therefore be observed with confidence. Repeated measurements are, in any case, desirable, and, if the system is sufficiently stable, repetitive additive scanning techniques will clearly improve the precision o f the observation and allow the detection of even smaller changes. However, it must be admitted that the change in conformation invoked for this illustration is considerably greater than would be necessary in principle for the modulation of enzyme activity. In the case of synthetic polypeptides undergoing a complete conformational transition, and proteins undergoing full-scale denaturation or renaturation, the calculation shows that

THEANALYSISOFCIRCULARDICHROISMOFBIOMOLECULES

61

the sensitivity of observation, or the limit of the optical criteria for achieving a specific state, is of the order of one half-turn of a helix or its equivalent. 11. EXPERIMENTAL APPLICATIONS CD is now firmly established as the preferred technique for most purposes: ORD finds applications in detecting contributions from transitions in the unobservable region < 185 nm (Cassim and Yang, 1970), in following couplet phenomena (at •o where ORD is maximum, CD is zero as shown in Figs. 15 and 16), and in observing effects in the transparent regions of highly absorbing samples (e.g. nucleoside associations). The ready availability of commercial equipment for measuring CD has led to applications to effectively all categories of chromophoric biomolecules. Past literature is accessible through the reviews of Beychok (1968), Urry (1968), Yang and Samejima (1969), Tinoco and Cantor (1970), Bush (197 l) and Timasheff (1970), and the annual reports of Dalgleish (1970, 1971) and Bayley (1972a). A brief survey of some typical applications is given here from fields related to work in the author's laboratory on non-peptide chromophoric probes. 11.1. Small Molecules: Nucleotide Coenzymes and Analogues

Coenzymes occupy an interesting position amongst biomolecules. They are well-characterized chemically and spectroscopically; for example, the coenzymes NAD +, FAD, etc., derive their properties from the extensively studied constituent nucleotides. In conformational terms, they represent a set of molecules of intermediate size and of potentially mobile conformation. They possess a number of conformational variables but, unlike the larger macromolecules, probably do not have sufficient intramolecular interaction to dictate a single fixed conformation. They also bind to enzymes, potentially in conformations different from those in solution. The analysis of coenzyme conformation therefore requires methods suitably sensitive to changes in shape, where there is a reliable theoretical foundation for the conformational dependence of the observed variable. Given the extensive theoretical work on nucleotide interactions and CD (Johnson and Tinoco, 1969a, b; Tinoco and Cantor, 1970) and following the arguments of § 4 and 6, an approach to coenzyme conformation may be made using circular dichroism. The non-additivity of spectroscopic properties of the adenine and nicotinamide moieties in N A D H and NAD ÷, and of the adenine and riboflavin moieties of FAD has long been recognized (Weber, 1950, 1957, 1958; Whitby, 1953; Siegel et al., 1959); FAD and NADI-I exhibit fluorescence energy transfer; FAD and NAD are hypochromic. These properties indicate intramolecular interactions and have been supported by recent N M R work (Oppenheimer et al., 1971). Striking non-additivity in CD is shown by NAD ÷, compared to the sum of AMP and N M N and by NADH compared to the sum of AMP and N M N H (Fig. 24) (cf. FAD: WeUner, 1966; Simpson and Vallee, 1966; Miles and Urry, 1968). The CD for NAD ÷ resembles a positive couplet with cross-over at 260 nm. This nonadditivity is unlikely to be due simply to the immobilization of the chromophores: such mechanisms may intensify the bands, and, as discussed in § 1, may account for observed enhancements of coenzyme properties (el. N A D H with liver alcohol dehydrogenase; Ulmer and Vallee (1965): the positive and negative A~a4o for N A D H with glutamate dehydrogenase; JaUon and Iwatsubo (1971).) For NAD ÷, a coupling mechanism is more likely and is supported by data on the diadenosine analogue of NAD ÷, diadenosine-5'5'pyrophosphate (Ap2A) (Figs. 25 and 26). AezA shows a striking positive couplet (Massouli6

62

P . M . BAYLEY

1

u

I

f

4-

I

I

F~

~ N ~ D

t~

ILl

/

WCJ A/~P + N M N

_ _ _ 3 _

220

. . . .

2~o

~

I

300 Wavelength

3¢o

38o

mja

F i e . 24. C D o f N A D +, N A D H a n d c o m p o n e n t s . Nucleotide c o n c e n t r a t i o n s 0.1 haM, in 0.1 M Tris p H 8.0, 25°C. T h e noise levels are indicated by vertical arrows. T h e a m p l i t u d e [#pk] -- [#tr] for N A D + couplet is 8 x 103 deg c m 2 decimole -1 or A%k - - A E t r = 2.4 mole -1 c m . 1

I

1

L

1

1

// r x\ Ap2A

"6

A /

Q. Iii

!/

/

/ Ar~3A

i\ // \J I

220

24-0

I

I

260 280 300 Wov¢lcngth m~

l

320

FIG. 25. C D o f adenosine derivatives. D i a d e n o s i n e 5'5' p y r o p h o s p h a t e (Ap2A) a n d diadenosine 5'5' t r i p h o s p h a t e (ApaA): 0.12 mM in 0.1 M Tris p H 8.0, 25°C. A m p l i t u d e s c o r r e s p o n d to [0pk] -- [Ot,] = 22 x 103 deg c m ~ decimole -1 or A~p~ -- A~t, = 6.7 mole -1 c m . N o t e the cross-over at 267 n m .

THE ANALYSISOF CIRCULAR DICHROISM OF BIOMOLECULES I

r

I

I

I

I

63

I

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4- m i l l i d e g r e e s

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FIG. 26. CD of adenosine derivatives. The effect of pyrophosphatase digestion on the CD of Ap2A: (I) Ap2A 0.12 mM, (la) plus PPase, (2) 1 hr, (3) 3 hr digestion (0.1 MTris pH 8.0, 25°C). and Michelson, 1964; Bayley, 1968; Scott and Zamecnik, 1969; Ikehara et al., 1970). Immobilization would give enhanced AMP-like bands with zero or negligible splitting. Further, the molecule Ap3A (Fig. 25) which might be expected to be even less restricted, shows a couplet, but evidently of the opposite chirality. The couplet property of Ap2A (or Ap3A) is eliminated by pyrophosphatase treatment (Fig. 26) and is progressively reduced (reversibly) on heating. The CD amplitude of ApeA is only 30~o that of adenyl-3'5'adenosine, ApA (see van Holde et al., 1965); the cross-over is 267 nm compared to 259 nm for ApA. Ap2A is, however, approximately three-fold more hypochromic than ApA. Different conformations are evidently involved for the two molecules. In seeking to explain these results and to relate them to NAD, it may be noted that the amplitudes for N A D + and Ap2A are at the ratio 1 : 3, correlating with the ratio of extinction coefficients for nicotinamide and adenine. In § 4.2 it was shown that the couplet amplitude is given by {Amp ) oc/z~./~ sin a cos a for a planar stacked system. Since EmaxOC#e 2, the results are consistent with a similar set of conformationalproperties for N A D and Ap2A. In trying to relate the models Ap2A and ApA, the 267 nm cross-over suggests that more than a single 260 nm adenine transition has to be considered. Scott and Zamecnik (1969) considered coupling of two putative 267 nm transitions alone: this ignores the possibility of cross (260-267) interactions which can be seen in the matrix formulation ( § 4) to have a considerable effect. A more general

64

P.M. BAYLEY

formal treatment has been developed (Bayley, 1971b) allowing inter-base coupling between degenerate and non-degenerate pairs. A right-handed stack with a close to zero would produce the observed amplitude and cross-over, the latter deriving from a complex overlap of 260 and 267 nm bands. The conformational mobility expected of these molecules can be treated by combining the results ofconformational energy calculations with theoretical predictions for the CD oi specific structures. This has been done for the CD of random polypeptides by Zubkov et al. (1971; see also Scheraga, 1971), and considered for the NMR of peptides (Feeney et al., 1972) and nucleotides (Barry et al., 1971). Conformational energy calculations to date for nucleotide assemblies (Thornton and Bayley, 1972) reproduce the effect of staggered base stacking as found in the crystal structures of many nucleosides and derivatives (Bugg et al., 1971). The energy of base-base interactions are of the same order of magnitude as the variation in non-bonded energies of the population of molecules derived from the large number of conformational variables, and hence can stabilize specific structures. The results of the energy calculation can be applied by a partition function to the optical calculations to evaluate the predicted properties of the population, and its variation with temperature. Recent work on ApA suggests that the kinetics of conformational rearrangement in small, stacked nucleotide systems are extremely fast, necessitating study by ultrasonic techniques (Rhodes and Schimmel, 1971). Normal CD measurements (cf. Lowe and Schellman, 1972) observe only the time-averaged spectra: immobilization of the coenzyme enzyme at the active site effectively freezes part or all of the conformation, and CD is of value in investigating conformations in such complexes. 11.2. Extrinsic Chromophores as Conformational Probes

Aromatic residues in proteins are optically active by virtue of the interactions with the asymmetric environment, and hence show characteristic CD (see e.g. Timasheff, 1970); the theoretical understanding of the relationship between conformation and optical activity is well established for tyrosine derivatives (Hooker and Schellman, 1970) and disulphides (Linderberg and Michl, 1970). Vibrational fine structure in absorbance and CD of tyrosine, phenyl alanine and tryptophan model compounds (see § 6.1) have been studied extensively at low Itemperatures (Horwitz et al., 1969, 1970; Strickland et al., 1969, 1972); the indole chromophore has recently been studied in detail (Bernadin, 1970). These treatments are particularly valuable in assessing the degree of conformational change required to produce observable CD effects. As may be inferred from the theoretical discussions in § 4, simple rotations across nodal planes in the coupling mechanisms, or into regions of new asymmetry, are sufficient to invert signs and change magnitudes. The aromatic residues are therefore potentially very sensitive conformational probes. Experimentally, the situation is complicated by the simultaneous presence of a number of chromophores with overlapping spectra, necessitating resolution by reference to model compounds (cf. lysozyme, Teichberg et al., 1970). The low temperature techniques (e.g. ribonuclease A, Horwitz et al., 1970; ribonuclease S, Horwitz and Strickland, 1971) may distinguish identical residues in different environments and represent a powerful new approach to the analysis of protein CD. Tryptophan is particularly well resolved by magnetic CD; conformational effects have not yet been reported, although fine-structure features are resolvable (Barth et al., 1971). A combined MCD/CD approach may well assist in resolution.

THEANALYSISOFCIRCULAgDICHROISMOFBIOMOLECULES

65

In using these optical probes in the detection of conformational changes, it is frequently necessary to be able to distinguish direct and indirect effects of ligands which are putative conformational effectors. As with ultraviolet difference spectra, the ability of an effector to change in a concerted fashion the optical properties of a number of different chromophores is good evidence for a conformational change. A detailed description of the nature of that change would not be available from CD data alone. However, compared with the purely absorbance methods, CD properties have the advantage of being both positive and negative sign: a specific chromophore may therefore be observable without the overlying effects of its neighbours. These arguments may in general be extended to the use of extrinsic chromophores both non-covalently attached and chemically linked to the macromolecular structure. Chromophoric cofactors attached to proteins are dearly of interest here. A detailed account has recently been given of the origins of the haem CD in myoglobin and haemoglobin, showing the contributions to rotational strength from coupling of the porphyrin transitions with aromatic residues up to 12 )k removed (Hsu and Woody, 1971). This distance is sufficient to allow interactions between elements of quaternary structure, e.g. the individual subunits in haemoglobin, and this result indicates the wide potential scope of applications of such chromophoric probes. A further degree of sensitivity is available with the haem chromophore, because of its nearly degenerate Soret transitions, in the light of the theoretical results of Hsu and Woody. These show that the observed properties derive from two large, unequal, oppositely signed rotational strengths. In view of the discussion of unequal couplets in § 6, the wide variety of Soret CD observed in the class of haem proteins can readily be explained by a consistent mechanism: relatively minor effects on the two rotational strengths and their ratio can produce a wide range of spectroscopic profiles (Table 4). Such sensitivity to confirmation may be used to monitor functionaUy important conformational changes or to establish a high degree of invariance of structure around the probe in the face of a range of potential conformational effectors. The pyridoxal-5'-phosphate chromophore acquires optical activity in combination with a range of decarboxylase and transferase enzymes, showing pH-dependent bands characteristic of the optical transitions of the Schiff bases. The behaviour of aspartate aminotransferase (AAT) is typical. On addition of substrate, different Schiff bases are evidently formed, and the CD is eliminated. This has been attributed by Ivanov and Karpeisky (1969) to the flexibility of the active site. This interpretation is complicated by the possible flexibility of the pyridoxal-substrate Schiff base. We have made use of the ability of non-metabolizable substrate analogues (dicarboxylates) to cause protonation of the Enzyme-Schiff base complex (Jenkins and Taylor, 1965), and have studied complexes of the holoenzyme with rigid substrate analogues (Harris et aL, 1971). The CD results are shown in Fig. 27 for AAT + p-phthalate. (Raw data is digitized, averaged, and smoothing performed by the method of Savitzky and Golay, 1964.) The enhancement of Ae4as and decrease of A~36s correlate exactly with changes in absorbance, even to the degree of reproducing the nonlinear binding, characteristic of certain aromatic dicarboxylates. The protonation of the Schiff base (increased Ae43s) produces a chromophore of consistent asymmetry for a given ligand. Relative differences in the sensitivity of the two wavelengths for different analogues could be accounted for by conformational adjustments at the active site (Harris and Bayley, 1972). The flavin ehromophore has been extensively studied by Tollin (1968) and Edmondson and Tollin (1971a, b, c) in the Shethna flavoprotein where the bands are fully restored on

66

P.M. BAYLEY

reconstitution of the holoenzyme, and by Brady and Beychok (1971) in lipoamide dehydrogenase. Curve resolution procedures (§ 6.1) applied to flavoprotein CD, indicate a diversity of bands which may be used for characterizing conformational effects. It may be noted that a tractable theoretical description of the extrinsic chromophore is essential in optimizing the conformation from probe experiments. Successful decomposition of complex spectra into component bands is a prerequisite for this operation. 200.00-

%

160.00

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a

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40 O0

0 O0

, 340.00

36() O0

38()00

40(~ O0 42()00

44600

46000

48() O0

50030

520 O0

Wavelength, nm

FIG. 27. CD of aspartate aminotransferasein the presence of ligands. AAT, a isomer, --0.5 mg ml- 1: ~, normalizedto OD28o --~ 10.0: 0.1 Mphosphate, pH 6.5: in the presenceofp-phthalate concentrations (in order of increasing zX~435)are: O, 0.2, 0.4, 0.8, 1.9, 7.5, 33.5 mM. The intense effects in transitions of the tetrapyrrole pigment bilirubin when bound to bovine serum albumin (BSA), observed in ORD by Blauer and King (1970), have been referred to in § 4.7.7. The chromophore contains two unconjugated dipyrrylmethene components, evidently arranged disymmetrically. The system bilirubin-HSA (human serum albumin) is of clinical interest, and shows distinctive properties. Blauer et al. (1970) observed two intense, oppositely signed bands in a complex system which became totally inverted at low pH. A 1 : I complex was inferred, analogous to the BSA case. Salt effects and the effect of pH have been reported (Blauer and Harmatz, 1972; Blauer et al., 1972). Strong coupling and exciton splitting between the chromophoric components have been suggested. From the couplet formula it is clear that the intense/re (cf. the extinction coefficients) can, indeed, generate intense couplets, though the directional properties of the chromophores are more complex than the model systems discussed herein. Beaven et aL (1972) studied both the CD and fluorescence of the HSA-bilirubin system over a wide range of pH, ionic strength and protein-ligand ratio. From the results at high ionic strength (Fig. 28a, b), two binding sites are inferred, with Kass 7 × 106 and 3 × 105 at pH 8.5. At the two sites, bilirubin shows markedly different optical properties. At low ionic strengths, a maximum is observed in the ellipticity at approximately equimolar protein and ligand. The inclusion of a third site with optical parameters of inverse sign is required to simulate the spectral behaviour at several wavelengths. Similar heterogeneity of the sites is observed in fluorescence. The weaker sites have lower fluorescence and higher dichroism than the stronger sites; they are relatively much more labile to high ionic strength.

THE ANALYSIS OF CIRCULAR DICHROISM OF BIOMOLECULES I

1

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FIO. 28 (Beaven et aL, 1972). (a) CD of h u m a n serum albumin-bilirubin complexes at pH 8.5. Protein:bilirubin ratio 1:1, ( ) no salt; ( - - - ) 0.5 M NaCI. 6:1, ( - . - ) n o s a l t ; ( . . . . ) 0 . 5 M NaCI. Molar ellipticity [0] referred to total bilirubin concentration. Co) CD of h u m a n serum albumin-bilirubin complexes at p H 4.1 in the absence of added salt. Protein:bilirubin ratio 1:1,( ); 6:1, ( - - - ) .

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FIo. 29 (Beaven et aL, 1972). CD of h u m a n serum albumin-bilirubin complexes: pH dependence of [0hs7. Protcin:bilirubin ratio 1:1, ( - O - ) no salt; (-I-1--) 0.5 M NaCI. 17:1, ( - @ - ) no salt; ( - m - ) 0.5 M NaCI.

68

P.M. BAYLEY

The pH dependence of the CD (Fig. 29) shows great complexity, with plateaux at pH 8.9, and pH 6.5, and a striking transition close to pH 4, correlating with the N-F transition of the protein. The pH at which the maximum negative ellipticity is observed is dependent upon ionic strength. The low pH system shows hysteresis due to the self-association of bilirubin. True equilibria may be obtained by prior equilibration of the complex at pH 8-9 at low ionic strength. Comparison of these results with the spectra found for bilirubin in human plasma under physiological conditions shows that binding to albumin accounts adequately for the observed properties. The effect of oleate and salicylate have also been studied with reference to the release of bilirubin from plasma (Wooley and Hunter, 1970). As well as these biological applications, the evidence of a marked change in ligand properties in a region of pH where the protein is undergoing a conformational change is an indication of the potential of such chromophores for monitoring conformational events. This could be due to the change in chirality at a given site, or the adoption of a different mode of binding. The need for careful characterization of both ligand and macromolecule properties, the knowledge of stoichiometries and observations taken over a wide range of conditions are notable points in this work. 11.3. Membranes and Related Systems

The CD of membrane suspensions has been studied extensively to attempt to define the conformation of membrane proteins. This technique is liable to serious artefacts resulting in distortion and attenuation of the CD signals. This situation has been evaluated in the work of Schneider (1971), Gordon and Holzwarth (1971a, b), Glaser and Singer (1971), Gordon (1972), and extensively by Urry who has reviewed the subject recently (Urry, 1972). The general conclusion is of a diverse range of protein structures present in membranes from different sources and it is a challenging problem to relate these structures to specific function. The isolation of specific membrane proteins has now been achieved using mild solubilization techniques. Allan and Crumpton (1971) solubilized lymphocyte membranes in 2 ~ sodium deoxycholate (DOC) prior to fractionation of components of lipid-free protein. It was shown (Crumpton and Bayley, 1971) that DOC had no detectable effect on the CD of total lymphocyte protein, and was without effect on the Soret CD of myoglobin, the pyridoxal CD of AAT, the aromatic CD of insulin, and the peptide CD of these proteins. By contrast, sodium dodecyl sulphate had a dramatic effect on the spectra of these globular proteins (cf. Jirgensons and Capetillo, 1970; Lee and Jirgensons, 1971; Visser and Blout, 1971). DOC is widely used in solubilization of lipid-protein complexes; its mildness is shown by the absence of conformational changes during solubilization, readily inferred from CD. The conformation of membrane active peptides can be studied in situations analogous to their functional state at the membrane interface by use of the liposomal preparations of synthetic lipids. The concentrations required are generally higher than necessary for biological action by several orders of magnitude. However, it has been possible to study the conformation of the cyclic polypeptide alamethicin included in the lipid portion of phosphatidylcholine micelles. CD spectra are observed similar to those in organic solvents suggesting location within the apolar bilayer (Bayley and Hesketh, 1972) and are characteristic of highly ordered structure (McMullen et al., 1971). Further, at the same concentra-

THEANALYSISOFCIRCULARDICHROISMOFBIOMOLECULES

69

tions, alamethicin has been shown to accelerate the relaxation process of the micelles, monitored in temperature-jump by bromothymol blue binding (Trauble, 1971), and this process can be detected at a molar ratio of alamethicin :lipid of 1:1000 (cf. Hauser et al., 1970). The inference is that a monomeric form of alamethicin, as found in organic solvents (McMullen and Stirrup, 1971), can affect the dynamic properties of model lipid systems at a very low molar ratio. The molecule is, however, slightly polar, and may undergo some change in state of aggregation at the bilayer interface. CD studies have been performed on valinomycin in the presence of lecithin (Grell et al., 1972): the absence of any effect of potassium (observable in free solution: see Shemyakin et al., 1967) is consistent with the location of the molecule in the non-polar part of the vesicular membrane. Enniatin B, by contrast, shows sensitivity to potassium even when incorporated in the vesicles: a more polar environment, possibly the solvent-membrane interface, is suggested. One final application to the micellar field is the possibility these asymmetric molecules in the micellar state can show intense effects in CD and ORD due to the differential scattering of the circular components of polarized light by extended asymmetric structures which arc large relative to the wavelength of light (Robinson, 1961). In the case of the polyene antibiotic amphotericin B (§ 4; Bayley and Calam, 1972), since such molecules may form micelles, there is a further source of intense CD besides the molecular disymmetry of a twisted polyene chromophore. The X-ray structure indicates a planar all-trans-conformation (Ganis et al., 1971). If intense CD persists in a micellar suspension with lipid, and molecular disymmetry is indicated, such molecules will provide valuable spectroscopic probes for events in the membrane bilayer. 11.4. Fast Kinetic Observations: Instrumental Developments

The speed of kinetic observations of CD is limited by the frequency of Pockels cell modulation, typically several hundred Hz, giving an overall fastest time constant of about 1 sec. A system has been developed to couple the principles of CD spectroscopy with stopped-flow techniques (Bayley and Anson, 1972). In the prototype, a dichroic signal of 10 - 4 0 D units has been observed at < 5 msec resolution, and the means are now available for the direct observation of conformational events at this time scale. Unfolding of proteins, association and dissociation of multimers, binding and discharge of ligands, helix-coil transitions may now be studied using the properties of intrinsic, i.e. functional chromophoric groups. It will be of the greatest interest to see if different spectroscopic techniques, such as absorption, emission, and dichroism are able to resolve different stages of conformational motion of complex biomolecules. Instrumental developments now permit the observation of CD into the vacuum ultraviolet down to 135 nm (Johnson, 1971) and results for peptide films have been reported (Johnson and Tinoco, 1972). Instrumentation for studying the circular polarization of luminescence has been described (Steinberg and Gaffni, 1972), and a general modulation spectrophotometer has been developed for measuring linear dichroism and birefringence circular dichroism, and optical rotation (Hofrichter, 1971). Problems in studying films have been documented (Stevens et al., 1968; Maestre, 1970): similarly, the problems of studying particulate suspensions have been recognized (Urry, 1972) and studies of the larger macromolecular assemblies of viruses, membranes, and chromosomes may be undertaken in the light of this experience.

70

P.M. BAYLEY

The use of signal averaging techniques is now commonplace (see e.g. Tollin, 1968; Horwitz et al., 1968; Myer and Macdonald, 1967). For systems which are stable and insensitive to the high light fluxes, considerable enhancement of signal to noise ratio is achieved. Extra-fine structure may be resolved, and the vicissitudes of making sensitive measurements in regions of absorption--a situation most frequently encountered in CD-may be largely overcome. Finally, the introduction of low-temperature techniques (Horwitz et aL, 1968, 1969, 1970; Stdck/and et al., 1969, 1972) provides a new level of resolution in the spectroscopy of biomolecules. Recent studies on the complexes of visual pigment with detergent, following (at 77°K) changes in CD of the chromophoric pigment, produced evidence of two states interconvertible by illumination with characteristic CD properties (Horwitz and Heller, 1971). The CD spectra reflect the pronounced asymmetry of the chromophore and provide additional criteria for the characterization of the species involved. The understanding of these effects may be expected to produce a clearer understanding of the conformational factors involved in the function of complex biomolecular systems. 12. CONCLUSIONS The physical basis of optical activity has been understood for many years. Notable advances have been made in the past 15 years with the adoption of a quantum-mechanical formulation of the problem. The work of Moffitt, Moscowitz, Tinoco, Schellman, and Woody has led to a relatively simple formalism in matrix or determinantal form, which is ideally suited to the evaluation of rotational strength for biomolecules (§ 2 to 5). It is of interest that Moffitt's original work was the treatment of the properties of helical polypeptides, so that biomolecules may be said to have demanded and stimulated this impressive theoretical development. The present state of theory allows treatment of both periodic (i.e. helical) and non-periodic (irregular) structures. The only unsatisfactory feature is the inability to rationalize the optical properties of conformationally "random" polymers and denatured proteins; controversy exists over the physical state of these supposedly random experimental systems (§ 8). This is a major limitation to the operation of the multicomponent analysis for proteins (§ 9) but the ultimate success of that analysis is in any case limited by the assumptions of the method. The fact that irregular regions are not random, and that in globular proteins these regions produce a wide range of optical properties (§ 10.1), indicates severe limitations to the use of the three-component methods. With the exception of the "random" system, theory allows the computation of properties of a wide range of systems (§ 10.1 and 10.2). The use of theory in selecting between putative structures for some peptide antibiotics has been illustrated for gramicidin S. The results are sensitive to the conformation of the two proline residues, and allows a firm distinction between two closely related structures. The potential power of the method is shown for the preliminary structures of the ~reD helices. The results for both compounds show dearly that the optical properties are determined by the whole conformation: computation at the level of 12-16 peptides simulates the properties of even larger structures (§ I0.1). The appearance of experimental spectra are sensitive to the spectroscopic parameters Al and At, representing bandwidth and energy, and the assigned values have a marked effect in compiling CD profiles from rotational strength calculations (§ 10.2). Conversely the analysis of CD spectra is complicated by the appearance of oppositely signed and

TItE ANALYSISOF CIRCULARDICHROISM OF BIOMOLECULE$

71

overlapping bands (§ 6). The important diagnostic value of the "couplet" line-shape has been emphasized because of its association with specific conformational origins, e.g. coupling phenomena in dimers, indicating proximity and asymmetry. Stacking of planar chromophores in dimeric and polymeric systems is readily diagnosed (§ 6.2). The problem of unequal couplets has been analysed, and a method is described for the quantitative analysis of such non-conservative systems (§ 6.3). The advances made by Tinoco and by Schellman with polynucleotides and peptide systems derive from the intensive theoretical characterization of the purine, pyrimidine, and peptide chromophores. Similar intensive work is required for many other biomolecular chromophores, and is evidently forthcoming for the aromatic residues, haem, flavins, and other cofactors. The way in which the extrinsic chromophores derive rotational strength by interaction with the asymmetric parent macromolecule has now been elucidated in the case of myoglobin by the work of Woody ( § 11.2). This type of rationalization will be applicable to all classes of extrinsic chromophores, and one may expect to see evolving a series of guidelines for the use of conformational probes, utilizing well-characterized chromophores of known symmetry. These would be based upon the behaviour of the same chromophores in model systems where three-dimensional structures have been elucidated by, for example, X-ray crystallography. The basic symmetry rules are recognized and documented: more experience with model systems is required to provide the basis for analysis of extrinsic effects in solution for molecules of unknown conformation (§ 11.2). The progressive refinement of conformational energy calculations has a direct bearing on the power of CD methods. Some of the most important biomolecules are of intermediate size (e.g. cofactors) with a wide range of possible conformations. The energy methods allow suitable relative weightings to be given to members of a population, as well as offering a technique for studying the route and the kinetics of conformational adjustment. The optical properties, as detailed in this review (particularly § 3, 4, and 5), reflect such conformational events. The combination of the theoretical weighting factors and rotational strengths gives a sensitive means of simulating the optical consequences, and hence of establishing the validity of a proposed mechanism of conformational mobility. In the use of CD for following conformational changes, now documented by a large literature, many non-conformational effects are possible; these must clearly be eliminated before the conclusion is drawn that a change in CD spectrum (e.g. of an allosteric enzyme in the presence of an effector) indicates a true change in conformation (§ 7). Sensitivity of peptide CD in following conformational events involving the polypeptide backbone allows the detection of the loss or gain of one half-turn of a helix in a typical globular protein of MW 30,000 (§ 10.3). The more sensitive methods using the properties of aromatic and other chromophores are discussed, and it is concluded that a change as small as the rotation of a single aromatic residue could lead to an observable CD effect. The lowtemperature enhancement of vibrational fine structure is already yielding information of a new degree of resolution in structural terms about the location and behaviour of specific side chains in proteins (§ 6.1, 11.2). These techniques are also providing new means of observing optical species with only transient life-times at normal temperatures ( § 11.2), and are important in studying the mechanism of the visual process. All of these probe methods will be enhanced by the theoretical advances outlined above, and by instrumental advances involving fast observation, relaxation techniques, microscopic methods and observation of effects in the very far ultraviolet spectrum (§ 11.1). The validity of CD methods with particulate and highly scattering solutions is an impor-

72

P.M. BAYLEY

tant advance in the study of biomolecules. Viral suspensions, membrane fragments, subcellular particles, nuclear fragments, films, and layers may all be studied with suitable respect to the problems involved. Information about macroscopic organization, diversity of structure, and functional organization on the large scale, including observations on in vivo systems, may be expected to result. The sensitivity of optical methods, the strong foundations in theory, and the availability of high quality instrumentation for CD indicates that this will be an expanding field for some time. The investigation and application of circular dichroism of biomolecules show the benefit of a combined assault of physical and biological thought: each removes the inhibitions of the other, resulting in new methods, new concepts and a new level of understanding. ACKNOWLEDGEMENTS I would like to acknowledge the generous encouragement of Dr. John Schellman of the University o f Oregon in whose laboratory I began the study of the conformational basis of the optical activity of peptide systems: like many others, I am grateful for his wise counsel and the benefit of his inspired approach to this subject. I would also acknowledge the hospitality of Dr. Lubert Stryer at Stanford University, and Professor R. R. Porter of Oxford in whose laboratories various parts of this work were performed, and Dr. Jack Horowitz of Iowa State University where, as visiting Associate Professor in Biophysics, I began the composition of this manuscript. This work is supported by the Medical Research Council of Great Britain. I am grateful to Prof. D. C. Phillips for the use of lysozyme X-ray crystal coordinates; I would like to thank Dr. G. H. Beaven for access to unpublished work on bilirubin, E. A. Piper and F. G. Tattam (Engineering Division, N I M R ) for help in producing the computer graphics, and Miss Carole Wise for the preparation of this manuscript. REFERENCES ADLER, A. J., HOVING, R., POTI'ER, J., WELLS, M., and FASMAN,G. D. (1968) J. Am. Chem. Soc. 90, 4736. A~BERSOLD,D. and PYSH,E. S. (1970) J. Chem. Phys. 53, 2156. ALLAN,D. and CRUMPTON,M. J. (1971) Biochem. J. 123, 967. BALASUBRAMANIAN,D. (1967) J. Am. Chem. Soc. 89, 5445. BALASUBRAMANIAN,D. and WETLAUFER,D. B. (1966) J. Am. Chem. Soc. 88, 3449. BAm*.ETr,G. C. (1966) J. Chem. Soc. (C), p. 1771. BARRY, C. O., GLASEL, J. A., NORTH,A. C. T., WILLIAMS,R. J. P. and XAVIER, A. V. (1971) Nature 232, 236. BARTH,G., RECORDS,R., BUNNENBERG,E., DJERASSl,C., and VOELTER,W. (1971) J. Am. Chem. Soc. 93, 2545-7. BAYLEY, P. M. (1967) Unpublished work. BAYLEY,P. M. (1968) International Union of Pure and Applied Chemistry, 5th International Symposium, London. BAYLEY,P. M. (1971a) Biochem. J. 125, 90P. BAYLEY,P. M. (1971b) Biochem. J. 125, 91P. BAYLEY,P. M. (1972a) Circular dichroism and optical rotatory dispersion, in Amino Acids, Peptides and Proteins, Vol. 4 (ed. G. T. Young,), Specialist Periodical Reports of the Chemical Society, London. BAYLEY,P. M. (1972b) Unpublished work. BAYLEY,P. M. and ANSON,M. A. (1972) In preparation. BAYLEY,P. M. and CALAM,D. H. (1972) In preparation. BAYLEY,P. M. and HESKETH,T. R. (1972) In preparation. BAYLEY,P. M., NIELSEN,E. B., and SCHELLMAN,J. A. (1969) J. Phys. Chem. 73, 228. BAYLISS,N. S. and MCRAE, E. G. (1954) J. Chem. Phys. 38, 1002. BEAVEN,G. H., D'ALBIS,A., and GRATZER,W. B. (1972) In press. BENEDEa~rLE., CORRADINI,P., and PEDOME,C. (1969) Biopolymers 7, 751.

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