Mean residual rotation

Fig. 4. Equilibrium curves for the unfolding and refolding of penicillinase in guanidinium chloride measured by viscosity (1), difference spectroscopy (2), and mean residue rotation [m jiM (3). Redrawn with permission from Robson and Pain (1976b).

Cotton effects which result from the random coil and a-helical forms of polylysine (37). The ordinate is the reduced mean residue rotation, which is defined as... 

Figure 5. Effect of pH upon aggregation and ORD of mitochondrial structural protein in xoater. The curves are trough position (O), absorbance (%), and reduced mean residue rotation (V). Dashed lines show region where precipitation prevented dependable measurements, but spectra of the precipitate in glycerol suggest that here the trough position may be at about...

Nuclease behaves like a typical globular protein in aqueous solution when examined by classic hydrodynamic methods (40) or by measurements of rotational relaxation times for the dimethylaminonaphth-alene sulfonyl derivative (48)- Its intrinsic viscosity, approximately 0.025 dl/g is also consistent with such a conformation. Measurements of its optical rotatory properties, either by estimation of the Moffitt parameter b , or the mean residue rotation at 233 nin, indicate that approximately 15-18% of the polypeptide backbone is in the -helical conformation (47, 48). A similar value is calculated from circular dichroism measurements (48). These estimations agree very closely with the amount of helix actually observed in the electron density map of nuclease, which is discussed in Chapter 7 by Cotton and Hazen, this volume, and Arnone et al. (49). One can state with some assurance, therefore, that the structure of the average molecule of nuclease in neutral, aqueous solution is at least grossly similar to that in the crystalline state. As will be discussed below, this similarity extends to the unique sensitivity to tryptic digestion of a region of the sequence in the presence of ligands (47, 48), which can easily be seen in the solid state as a rather anomalous protrusion from the body of the molecule (19, 49). 

Figure 4. Effect of chain length on Cu(II)-induced changes in rotation for single-stranded poly(A) and oligo(A) in water at 25°. Presented as % change in mean residue rotation at trough (see...

In the denatured (or essentially random coil) form, both collagen (as gelatin) and the a-helix-forming proteins typically exhibit specific rotations close to the mean residue rotation of the component amino acids ([al —90° to —120°) and values of X of 205 to 215 mju. 

Let us begin by examining the optical rotatory dispersions of two typical synthetic pol3q>eptides and a well-studied protein, as illustrated in Fig. 1. The spectral range along the abscissa is that usually available for polarime-try, while the ordinate is the reduced mean residue rotation, a quantity that will be defined by Eqs. (1) and (4). For each of the three substances, two different conformations are represented. Those denoted by PEG refer to poly- -benzyl-L-glutamate, which exists as a flexible, random coil in... 

These polypeptides nonetheless present a problem for characterizing the dispersion of the helix itself. If X for these disordered chains does not equal Xo, with the consequence that bo does not vanish when the helical form is destroyed, should not the foregoing derivation, based on the equality of Xc and Xo, be rejected It will be retained for reasons that are discussed below, but let us first consider an alternative device for assimilating simple dispersion to the Moffitt form, one which circumvents this assumption. What can be adequately represented with two constants, Xc and a°, can equally well be described with three, Xo, a , and bo. Consequently, the reduced mean residue rotation for the disordered form may be written... 

Reduced mean residue rotations for helical L-polypeptides extrapolated to meso-composition. Solvent abbreviations CHCI3, chloroform DCA, dichloroacetic acid DMF, dimethyl formamide. 

Before looking directly at these results, let us first set out a formal combination of helical and random dispersion on the assumption that helical and disordered structures contribute to the total rotatory dispersion in a strictly proportional manner. By this means, the way in which the dispersion parameters may be expected to vary with helical content will become clear. The optical rotation of a mixture of random regions and helical segments within a single molecule can be expressed as the sum of the mean residue rotations for a random coil and a helix, [m ]x and [m ]f, respectively, each weighted according to that fraction, fp or / , of the total number of residues which is embodied in the respective conformation. The net rotation of the mixture is thus... 

The assumption underlying this equation, that the mean residue rotations obtained from measurements on long random coils and helical structures will adequately represent shorter lengths of chain expected in mixtures, must, however, be examined in the light of end effects. Because the rotatory power of a residue is dependent upon its environment, its proximity to the end of a structure will endow it with a rotation that is not representative of residues at the interior, each of which may be considered to exist in an equivalent environment. Residues at the ends of random coils and helical segments therefore will not contribute to the net rotation in a manner proportional to the length of the structure. 

Figure 42. Differential scatter of left and right circularly polarized light by poly-L-glutamic acid particles. Curve a, mean residue rotation of PGA reference state plotted on right-hand ordinate. Curve b, contribution of differential scatter term only, (Asi. —Asr) 3300/Cl. Curve c, total change in mean residue ellipticity due to differential scatter, includes differential scatter component of the (Aol— 4or) term. Curve d, comparison of empirical lO " values with total differential scatter. Curve e, approxima-...

Figure 4 Reduced mean residue rotation and c as a function of guanidine-HCl concentration at 25°C.

The Moffitt parameter b was evaluated from optical rotatory dispersion (ORD) da a measured by a Yanagimoto OR-100 Type spectropolarimeter using a tungsten lamp as the light source in a temperature range of 10 to 40 C. The reduced mean residue rotation, [m ], at a wave length X is obtained from the observed rotation a by... 

Since the concentration dependence of [ ]( is sometimes negligible it is customary to omit the superscript c. Also, the conditions of temperature and wavelength are sometimes specified in the text so that there is then no need to specify them explicitly in the symbol. Thus, the specific rotation is often written simply as [o]. A convenient related quantity is the mean residue rotation, [7i], or the value [/2vac], defined by... 

In the study of macromolecules, such as proteins and nucleic acids, optical rotation is expressed in mean residual rotation [M] ... 

Analysis of protamine by optical rotatory dispersion shows that its value is about zero and a mean residue rotation at 233 nm, [R ]233> about —2900 (Table IX-1). These two parameters, which are often used as a measure of the helix content of proteins, also indicate that protamine has a random-coil structure in aqueous solution (Bradbury et al. 1967). 

Some CD data in the literature are presented in l - r, which emphasizes the relationship of CD to normal absorption spectroscopy. However, most data are presented in [0] because many commercial instruments are so designed. Before ORD was replaced by CD for conformational studies of biopolymers, the chiroptical phenomenon of a biopolymer was often reported in both mean residue rotation and mean residue ellipticity. 

---