ON THE PHENOMENOLOGICAL TREATMENTS OF OPTICAL ROTATORY DISPERSION OF POLYPEPTIDES AND PROTEINS* BY JEN Tsi YANG
CARDIOVASCULAR RESEARCH INSTITUTE, AND DEPARTMENT OF BIOCHEMISTRY, UNIVERSITY OF CALIFORNIA (SAN FRANCISCO) Communicated by Paul J. Flory, December 8, 1964 Since the discovery of the anomalous dispersion of a-helical polypeptides1' 2 and the introduction of the Moffitt equationl 4 ORD has been applied extensively to conformational studies of proteins and polypeptides. Although the early theories3' I were unsatisfactory,6 we do not yet have a relationship as simple as Moffitt's to describe ORD in the visible region. Instrumental limitation confined almost all early experimental data to wavelengths above 300 mg. Now that measurements can be extended to about 185 m/i, we detect conformation-dependent Cotton effects7' 8 (and CD9) between 180 and 240 mj.. It seems desirable to re-evaluate ORD analysis in the visible region. All treatments proposed are phenomenological, and success should be tempered with caution in interpreting the experimental results quantitatively or semiquantitatively. The Moffitt Equation.-Moffitt's equationl 4
[m'] = aoX02/(X2-X62) + boXO4/(X2 - (1) greatly stimulated the study of ORD of proteins and polypeptides because of its theoretical overtones. In particular, the virtual constancy of the bo value in various solvent media as predicted by Moffitt and confirmed by experiments (about -630 deg. cm2 decimole-1 for a right-handed a-helix with Xo = 212 mu)4 is very useful in estimating the helicity of proteins. Although initially the equation gained wide acceptance, it has now come to be regarded as empirical,6 and not especially characteristic of helices.10 The Drude equation [mn'] = E a)2X2/(X2 - X,2) (2)
can always be expanded in inverse powers of (X2 - X62) where the parameter Xo is to be determined: [mn'] E ani2/(X2 - X02) + E ajX2(Xf2 - X02)/(X2 - X02)2 + 0[(X2 - X02)-3] (3) which is converted into equation (1) provided that ao 2 = ajXj2 boX04 = E ajX2(XA2 - Xo2) Za6Xi2(X2 - X02)2 - 0. (4a-c) It will be valid whenever XoI, so determined, is positive and considerably less than X2. If ao0XO4 happens to be equal to E ajXj4 [eq. (4a, b) ], i.e., boX04 = 0, then equation (2) becomes a one-term Drude equation: [m'] = ao0X2/(X2 - Xo2) or [m'] = k/(X2 - X2) (5) (In this case Xc = Xon) Moffitt proposed that the amide absorption bands, which are responsible for the 438 Downloaded by guest on September 27, 2021 VOL. 53, 1965 CHEMISTRY: J. T. YANG 439
helical rotations of polypeptides, are split into perpendicular and parallel (to the helical axis) components. Accordingly, a rotation in the visible region can be written as4 Z E + 2) (6) [in'] i a1XX1,/(X'-X2) i a11iX1112/(X'- Further he noted that the Ri of each parallel component may be exceedingly large, but is almost exactly compensated by the opposing Ri of its perpendicular partner, i.e., a1l -alli(ai's being proportional to the Ri's). Under these conditions, we can let X = Xo(l- A/2), X11i = Xo(l + A/2). (7) According to equation (4b), boX04 for such a band pair will not vanish, since the two terms on the right-hand side would have the same sign. The form of equation (1) is easily obtained by substituting equation (7) into equation (3) with only one band pair and by defining Ai = (eVs- XI )/XOi, b0i = (all - a1I)Ai, and a0i = (aIi + ai) + b,, (8) provided that A << 1 (say, JX1lj - Xli < 10 mu) and o,<
[Xi'] = A193X1932/(X2 - X1932) + A225X2252/(X2 - X2252), (10) an equation similar to equation (9). The A-parameters were determined for both the helical and coiled conformations; these reference values were then used to estimate the helicity in proteins through simple interpolation. A linear relation was also obtained by plotting A225 against A193 for various helical contents, but the intercept varied with the solvents used. It was further stipulated that the two measures from experimental A193 and A225 agreed with each other if only a-helices and random conformations are present in proteins. (Actually, in an [M'](X2/ 1932-1) versus 1/(X2/X2252 - 1) plot, A225 is derived from the slope A225(X2252/X1932 - 1), but, in contrast, A193 is computed from the intercept (A193 + A225X2252/X1932). Thus, the two A-parameters cannot be independently obtained by this graphical pro- cedure. In particular, since the intercept is usually the difference between two large numbers (e.g., A193 = +2900 and A225 = -2050 for PGA at pH 414) and therefore a small number, A193, so determined, largely reflects the numerical value of A225 over most of the helix-coil transition region, except for low helical content. It is not too surprising that an A193-A225 plot gives very nearly a straight line.17 Theoretically, equation (2) must satisfy the condition (noting aiaRi) :18 Eaj=o° (11) Therefore, a one-term Drude equation [equation (5) ] is empirical; the same is true for a two-term Drude equation unless the two equal but opposite Ri's and thereby the two aiX,2/(X2 - X,2) terms are so strong that they overwhelm the contributions of the remaining terms in equation (2). (Of course, under special circumstances the sum. of the Drude terms [equation (2)], excluding the two terms under con- sideration, could happen to be close to zero, even though their corresponding Re's are large. Then the sum of R1 and R2 may not be zero.) Experimentally, CD measurements of the helical form reveal one positive and two (not one) negative dichroic bands at 190, 206, and 222 muA with Ri's of +81 X 10-4,-29 X 10-40, and -22 X 10-40 erg cnm3 rad.9 These must be attributed to the 7r-7r* transitions and the n-7r* transition (the latter was not considered by i\Ioffitt). Obviously, the sum of R.'s in the present case does not satisfy equation (11); thus, the ORD of the helical conformation in the visible region can be represented by: [I'] = a1X19o2/(X2 - X1902) + a2X2o62/(X2 - X2062) + a3X2222/(X2 -222') n + E aj2Xj/(X2 - X22). (12) i = 4 The last term on the right-hand side may be approximated as another Drude term. If the X193 term in equation (10) is identified with the 190-m/A dichroic band, then the 206- and-222 muA Drude terms in equation (12) must, be combined into the X225 term of equation (10). However, it can easily be shown'9 that such a combined term must have a X2 in between, not greater than, 206 and 222 mu, since the numer- ators of the two terms have the same sign (both negative in this case). Thus, at least one positive Drude term must be present in order to reach a compromise X225 term in equation (10). We are, however, not even convinced that the X190 term in equation (12) would remain unaffected by such arbitrary manipulations; indeed, part of this positive term could be combined with the two negative terms. To Downloaded by guest on September 27, 2021 VOL. 53, 1965 CHEMISTRY: J. T. YANG 441
force a multi-term (at least four) Drude equation into two terms is purely an ex- pediency for graphical treatment; consequently, any attempt to calculate the apparent R,'s from equation (10) and identify them with the experimental values obtained directly from the CD measurements is very dubious. (It can be shown that many pairs of Xi and X2 other than 193 and 225 my are equally usable in equation (10) (see also refs. 12, 17, and 20). With each set of new parameters, new reference values must be defined. That such a choice of parameters is not unique is also shown by data on poly-L-serine and poly-L-proline II, for example, which are known to have different conformations from the a-helix and yet can still be fitted with equation (10).) The AMoffitt equation incorporates all the partial rotations other than those due to the helical conformations into the ao term [equation (1)]. A modified equation has since been proposed21
[in'] = alR'X2/(X2 - X12) + faoHX02/(X2 - Xo2) + fboHo4/(X2 - X02)2 (13)
[in] - (a,RX2 + faoHXo2)/(X2 - Xo2) + (fboHX04 + al1Xi2(X12 - X02))/(X2 - X02)2 (14) where f is the percent of helicity and alRX,2/(X2 - Xi2) is an approximation of the summation in equation (2) excluding those terms due to helical conformations. Thus, the experimental bo [equation (1) ] does not represent all the helical rotations unless 'X = Xo; this is a problem in the use of the Moffitt equation and must be solved soon. With a computer, we should now be able to fit the Cotton effect curve of the helical conformation on the basis of the observed CD results, which in turn could predict the rotations in the visible region. In practice, with several parameters to be determined, there is reason to doubt that such numerical solution would be unique in spite of its attractiveness. In aqueous solutions the error involved in neglecting the nonhelical portion of the bo value might not be too serious because the denatured proteins appear to have a N, [equation (5) ] close to 212 mwA. Thus, the aRX,2(N,2 - Xo2) term in equation (14) can be small as compared with fboHXo4 in most cases (although the aiR and Ni in native proteins may differ from those in denatured ones). The beH value in organic solvents is less certain; if Ni # No, the boH in equation (14) could differ from -630. Recently, Cassim and Taylor22 reported a linear relationship between bo and the refractive index of the solvent for PBG; however, they indicated that there was no conformational change in all the 55 solvents studied. Whether this variation in the parameters arises from the nonhelical or helical term or from both remains to be answered. The use of the two-term Drude equation presents different problems. Most important, the partial rotations other than those due to the known Cotton effects are not defined. Either they must have been considered insignificant or have been incorporated into the two Drude terms [equation (10)]. This ambiguity is very unfortunate since the current interest in the hydrophobic interactions prompts us to look into the residue rotations (aRXN2/(X2 - N12)) [equation (13) ]. If such contribu- tions are not recognized, the conclusions are questionable. For example, poly-L- methionine in chloroform had A193 = 3020 and A225 = -1900, and the corresponding values for PBG in three helix-promoting solvents were 2600 to 2710 and -1680 to -1810."1 If the former was assumed to represent 100 per cent helix, we are led to believe that PBG in the three solvents had only 89-93 per cent helicity," although Downloaded by guest on September 27, 2021 442 CHEMISTRY: J. T. YANG PROC. N. A. S.
the light-scattering and hydrodynamic properties of PBG in the same solvents actually support a rigid rod rather than a rod with nonhelical portions.23 Per- 1 u haps a more plausible explanation for + ;! such variation in the A-values is that the side groups and their environment Oo-a\',\12~ affect the rotations, not a variation in _-ig\,<.- / helical content. (Note that the cur- -\\4,.S434 rent ORD treatments still do not '\:.// warrant an estimate of helicity good 1 \ / to the first significant figure.) 2/ Apart from ORD in organic solvents, reference values in aqueous solutions are a problem. PGA, at present widely 2 200 220 240 260 used as a model polymer, becomes in- soluble in moderate concentrations be- A\ (m>ng) low pH 4. Even when one obtains a FIG. 1.-Ultraviolet rotatory dispersion of clear dilute solution at pH 4, minor poly-L-glutamic acid at pH 7.3. Concentrations * * * of KF: 1, none; 2, 2 M; 3, 4 M; and 4,6 aggregationmaystilloccurwhicho might M (Cary 60 spectropolarimeter). affect the ORD of the solution. Differ- ent preparations could also vary the re- sults ;24, 25 all one can say is that these reference values may still be subject to revision. Equally worrisome is the choice of the reference value for the nonhelical form. First of all, the side groups of the model polypeptide are all exposed to the solvent medium, whereas most of the nonionized amino acid residues in a protein molecule are buried inside the molecule. The rotations in the two cases may differ significantly. Furthermore, the rotations of the polyelectrolyte (the coiled form) depend strongly on the ionic strength of the solvent (less levorotatory in the visible region as the salt concentration increases).26 E. -izukaof our laboratory has also observed significant change in the Cotton effects with salt concentration (Fig. 1). Obviously this would affect the reference values of the parameters in equation (10). Indeed, we found that A193 and A225 for PGA at pH 7.3 decreased gradually from -880 and -100 in water to-70 and-390 in 6 M KF. True, the proteins are seldom studied ill such high salt concentrations, but neither is the extended form of the poly- electrolyte in water without salt typical of a compact protein molecule. With different sets of reference values, we can still obtain two estimates of the helical content in good agreement with each other but different from those using another set of reference values. For example, a 50 per cent helical content would have A193 = + 1075 and A225 = -1055 ;14 but, if the reference values for the coiled form in 6 M KF were used, the calculated helicity from A193 and A225 would have been 39 and 40 per cent. (Note that the nonhelical portion of the bo value in equation (14) varied from +50 in water to -50 in 6 M KF.) One should therefore not be misled by the apparent internal agreement of such estimates which may still be inaccurate. That equation (10) appears to offer two measures of helical content is indeed interesting, but as we have just shown, they do not necessarily assure the accuracy of the estimates. On the other hand, comparison of the estimates provides a Downloaded by guest on September 27, 2021 VOL. 53, 1965 CHEMISTRY: J. T. YANG 443
criterion for the presence of structures other than a-helix. Actually, the aoH method [equation (14) ] also provides a measure of helicity with ao' = 68027 (the uncertainty lies in the determination of aR and Xi, which must be subtracted from the experimental a021). If we are interested only in finding out the presence of structures other than a-helix, equation (14) should be more than adequate.28 /- Lactoglobulin is a notable example: the estimated helicity from boH was essentially zero, whereas that from ao0 was about 70 per cent.2' (For comparison, A193 and A225 of this protein gave 32 and 18% helices using Shechter and Blout's analyses. 14) It is for this reason that we suspect that f3-lactoglobulin contains the 3-form or has strong hydrophobic interactions that make the use of ao0 inaccurate. The A193 and A225 values in equation (10) were reported to vary with the solvent used, in particular, with the dielectric constant of the solvent.'5 This raises an intriguing question about the use of equation (10): amino acid residues inside a protein molecule are buried in an environment of very low dielectric constant, quite different from that of water. What reference values for equation (10) should then be used for proteins in aqueous solutions? For example, Blout29 reported recently that the A-parameters of apomyoglobin actually fall on the A,93 versus A225 plot in organic solvents rather than in aqueous solutions. The understandable enthusiasm for equation (10) has led some workers to make another criticism, based on certain misconceptions, against the current treatment of the 1Mioffitt equation. The X0 = 212 m1L used in equation (1) is experimentally observed. It must not be changed arbitrarily. Originally, its uncertainty was set at 4-5 mpu. Reinvestigating the ORD of PBG in several organic solvents, P. K. Sarkar of our laboratory found that XA = 212 m,.t is still valid down to 300 nmw and, in a few cases, to 270 mA. Following the methods of Sogami et al.,30 we found the uncertainty in Xo to be about 4 2 mjA. Since the average of 193 and 225 m/A [equation (10) ] is 209 my, it is tempting to assume that Xo must take the same value according to equation (7). But with A << 1, equation (4c) predicts that a1i -alli. Similarly, if A << 1, A193 and A225 in equation (10) must be almost equal but opposite in sign when a substitution similar to equation (7) is used. On the other hand, we can assume X193 = Xo(1 - A/2) and X225 = Xo(l + A'/2) instead of using a single A, and this will still convert equation (10) into equation (1). The important point is that Xo must then be determined experimentally. Actually, since there are three, not two, dichroic bands for the helical conformation, the averaging of 193 and 225 mis simply loses its physical meaning. True, the difference between 212 and 209 seems small, but each time a different Xo is proposed, the numerical values of the parameters in equation (1) will all be changed. We are not implying that Xo must always be 212 mis, and it is quite possible that future experiments with many other polypeptides might suggest a somewhat different X0 value, but what we do argue is that in the absence of a satisfactory theory, any such change must be based on sound experimental measurement, not on conjecture. For the foregoing reason it is small wonder that the calculated rotations below 310 mg between those based on equation (10) and those using 209 mu in equation (1) were found to differ widely. It is indeed contrary to historical fact to believe that the current use of X0 = 212 md,' not 209 mu, in equation (1) is an attempt to fit the ORD data beyond the region of validity of the Moffitt equation. It is equally fallacious to assume that the use of bo (with Xo = 212 mM) in equation (1) as a linear function of helical content necessi- Downloaded by guest on September 27, 2021 444 CHEMISTRY: J. T. YANG PROC. N. A. S.
tates a calibration based on X0 = 209 mi, a value which, as we have shown, has no sound justification whatsoever. We believe that a different Xo may be used in different wavelength ranges; this must again be based on experimental determina- tion. Although equation (1) or (10) should cover as wide a range of wavelength as possible, curve fitting below 300 mju may not have any great practical value, since proteins absorb near 280 m,1, making measurements less precise in this region than in the visible region. The physical significance of any working hypothesis or phenomenological equa- tion must, of course, be derived from theories. Very probably the equations that are now used will undergo many further modifications as we investigate further the far-ultraviolet region. The final equation may be entirely different from, and almost certainly more complicated than, the Moffitt equation. We are not con- vinced that the Cotton effects below 185 m1A are unimportant, as some workers suggest. Meanwhile, we will continue to use the Moffitt equation, which does give us at least a semiquantitative estimate of the helicity of proteins. Naturally, it is always advantageous to have more than one method as additional check; thus, we can use, if we wish, any of the two-term Drude equations with different sets of reference values (which are still uncertain) for the helical and coiled conformations. At present it is highly desirable to use equation (1) with X0 preset at 212 mgs in all cases in order to allow a comparison of bo among various proteins, especially for determining helical content. Summary.-In the absence of a satisfactory theory, the Moffitt equation does provide a simple, and at least semiquantitative, estimate of the helicity in proteins. The recently proposed two-term Drude equation presents new unanswered prob- lems, notwithstanding repeated claims to the contrary. The author wishes to thank Professor M. F. Morales and Dr. L. Peller of this Institute, and Drs. G. Holzwarth and P. Urnes for their critical comments on this manuscript. Abbreviations used in this work: ORD, optical rotatory dispersion; CD, circular dichroism; Ri, rotational strength; PBG, poly-y-benzyl-Lglutamate; PGA, poly-Lglutamic acid. * This work was aided by grants from the U.S. Public Health Service (GM-K3-3441, GM-10880, HE-06285). 1 Doty, P., and J. T. Yang, J. Am. Chem. Soc., 78, 478 (1956). 2 Yang, J. T., and P. Doty, J. Am. Chem. Soc., 79, 761 (1957). 3 Moffitt, W., J. Chem. Phys., 25, 467 (1956). 4 Moffitt, W., and J. T. Yang, these PROCEEDINGS, 42, 596 (1956). 6Fitts, D. D., and J. G. Kirkwood, these PROCEEDINGS, 42, 33 (1956). 6 Moffitt, W., D. D. Fitts, and J. G. Kirkwood, these PROCEEDINGS, 43, 723 (1957). 7Simmons, N. S., C. Cohen, A. G. Szent-Gy6rgyi, D. B. Wetlaufer, and E. R. Blout, J. Am. Chem. Soc., 83, 4766 (1961). 8 Blout, E. R., I. Schmier, and N. S. Simmons, J. Am. Chem. Soc., 84, 3193 (1962). 9 Holzwarth, G. M., W. B. Gratzer, and P. Doty, J. Am. Chem. Soc., 84, 3194 (1962); Holz- warth, G. W., Ph.D. thesis, Harvard University, 1964. 10 Kauzmann, W., Ann. Rev. Phys. Chem., 8, 413 (1957). 11 Moscowitz, A., in Optical Rotatory Dispersion, ed. C. Djerassi (New York: John Wiley & Sons, 1960), chap. 12. 12 Imahori, K., presented at the Symposium on High Polymers, Japanese Chemical Society, Nagoya, Japan, October 1963; Kobunshi [High Polymer], 12, Suppl. 1, 34 (1963). 13 Yamaoka, K. K., Biopolymers, 2, 219 (1964). 14 Shechter, E., and E. R. Blout, these PROCEEDINGS, 51, 695 (1964). '5Ibid., 794 (1964). Downloaded by guest on September 27, 2021 VOL. 53, 1965 PHYSICS: H. FERNANDEZ-MORAN 445
16Shechter, E., J. P. Carver, and E. R. Blout, these PROCEEDINGS, 51, 1029 (1964). 17 Urnes, P., private communication. An alternate graphical solution of equation (10) is to plot [m'] (X2/X1"2 - 1) against (X2/X1932 - 1)/(X2/X222- 1), which directly yields Am5 as the slope and A193 as the intercept. 18 Rosenfeld, L., Z. Physik, 52, 161 (1928). 19 Iizuka, E., and J. T. Yang, Biochemistry, 3, 1519 (1964). 20 Katzin, L. I., and E. Gulyas, J. Am. Chem. Soc., 86, 1655 (1964). 21 Yang, J. T., in Polyamino Acids, Polypeptides, and Proteins, ed. M. A. Stahmann (Madison, Wisconsin: University of Wisconsin Press, 1962), p. 225. 22 Cassim, J., and E. W. Taylor, Abstracts, 5th Annual Meeting, Biophysical Society, Chicago, 1964, p. TC5. 23 Doty, P., A. M. Holtzer, J. H. Bradbury, and E. R. Blout, J. Am. Chem. Soc., 76, 4493 (195-1). 24 Yang, J. T., and T. Samejima, J. Biol. Chem., 238, 3262 (1963). 25 Yang, J. T., and W. J. McCabe, to be published. 26Yang, J. T., Federation Proc., 21, 406 (1962). 27 Doty, P., and R. D. Lundberg, these PROCEEDINGS, 43, 213 (1957). 28 Yang, J. T., Tetrahedron, 13, 143 (1961). 29Blout, E. R., presented orally at the 6th International Congress of Biochemistry, New York, 1964. 30 Sogami, M., W. J. Leonard, Jr., and J. F. Foster, Arch. Biochem. Biophys., 100, 260 (1963).
ELECTRON MICROSCOPY WITH HIGH-FIELD SUPERCONDUCTING SOLENOID LENSES* BY HUMBERTO FEIIANDNDEZ-MORAN DEPARTMENT OF BIOPHYSICS, UNIVERSITY OF CHICAGO Communicated by W. Bloom, December 21, 1964 The resolving power of the electron microscope has extended the range of direct visualization to structural details of the order of a few angstroms. This corresponds to the size of small molecules and to the atomic spacing in crystalline lattices.'3' 9 However, although the wavelength of electrons in standard microscopes is 100,000 times shorter than the wavelength of light, the best electromagnetic and electro- static lenses available have usable apertures limited, by aberrations, to semiangles of the order of l/loo radian as compared with the numerical apertures of 1.5 of the best light microscope lenses. Considering the numerous complex instrumental and preparative factors involved,1-3' 9 the major steps which have to be taken for attainment of the ultimate theoretical resolution are correction of lens aberrations (mainly spherical and chromatic aberrations), stabilization of the lens excitation current, and accelerating voltage. Thus, the degree of stability required for very high resolving powers (in the range of 4 A) is of the order of 1 to 2 parts per million, since the focal length of a magnetic lens is dependent on the electron energy as well as on the lens excitation current. In addition, if the present limitations of the strength and configuration of the axially symmetrical field formed by iron pole pieces could be overcome, "stronger lenses" of shorter focal length could be designed with correspondingly reduced aberrations. With the introduction and availability of new high-field superconducting sole- noi.ds of alloys of nipobjqum-irconium and niobium-tin,4-7 it is now possible to obtain Downloaded by guest on September 27, 2021