Moffitt equation

My interest at that time revolved around evaluating optical rotary dispersion data [12]. The paired values of optical rotation vs. wavelength were used to fit a function called the Drude equation (later modified to the Moffitt equation for William Moffitt [Harvard University] who developed the theory) [13]. The coefficients of the evaluated equation were shown to be related to a significant ultraviolet absorption band of a protein and to the amount of alpha-helix conformation existing in the solution of it. 

The spectrum between 300 and 600 nm generally has been interpreted with the empirical Moffitt equation (317) and the famous coefficient of its second term b0. Some of these values are recorded in Table XVII (318-320). The value of b0 has been converted to percent helix on a purely empirical basis with zero equivalent to no helix and about -630 to 100% helix (321) (see Section V,B,3). By this approach also RNase is inferred to have a low helix content. Regardless of the precise interpretation of the ORD spectrum, changes in the spectrum can be used to reflect changes in conformation. These changes are related to secondary structures in the sense that only the immediate environment of a given chromophore influences its contribution to the observed spectrum. 

C. The Moffitt Equation for the Optical Rotation of Helical Structures... 

Because of instrumental limitations, most optical rotatory measurements upon polypeptides and proteins have thus far been made in the near ultraviolet and visible regions of the spectrum, a range over which the Drude and Moffitt equations are valid. For this reason, attention will henceforth be directed to featureless curves of the type shown in Fig. 1. The immediate concern will be to describe the optical rotatory properties of synthetic polypeptides with respect to conformation in order that these attributes may be subsequently employed in the analysis of protein structure. Synthetic poly-... 

Fig. 7. Graphical treatment by the Moffitt equation (18) with Xo = 212 mu for rotatory dispersions of a synthetic polypeptide, a copolymer of 5% L-tyrosine with...

The constant A in Eq. (11) is here written a, the superscript D designates a disordered form, and a is the rotation coefficient for this conformation. Dispersions for polypeptides in helical form, H, fit the Moffitt equation,... 

The origin of nonzero bo values in these cases is not entirely clear, but it can be formally traced to the difference between Xo and values for the simple dispersion of random coils and hence to a failure of the assumption that Xo equals Xo. If K equals Xo, then the first term of the Moffitt equation will of course be the same as the simple Drude expression known to describe the data and, there being no necessity for a second term, bo will vanish. However, if Xo differs from Xo, the Moffitt plot may still be linear but with a nonvanishing slope. Thus dispersion data that are simple when referred to one dispersion constant may appear complex when plotted against another by a form that sees matters as complex, thereby generating what may be properly suspected as pseudocomplexity. The Moffitt equation was initially intended to describe the complex dispersion of polypeptides for which the simple Drude equation is inadequate, but, as will be seen, its form is also applied to protein dispersions which can be expressed equally well by either formula. It is therefore important to examine more fully the relation of the two equations for cases in which both fit the data. 

The general relation of X to the parameters of the Moffitt equation has been stated by Downie (1960). If a given set of dispersion data obey the simple Drude equation, Xo may be obtained from the slope of [m ]xX plotted against [m ], d([m ]xX )/d[m ]x (see Section II, B). If each value of [w ]x can also be accommodated by the Moffitt equation, a condition which is often satisfied for measurements in the spectral region 350-600 m, then Eq. (18) can be substituted into this slope and the appropriate differentiation carried out with the following result. 

G. The Moffitt Equation for Mixtures of Helices and Random Coils... 

A considerable amount of work on correlations between the optical activity of the far ultraviolet peptide amide bands (n—n near 222 nm and n—n near 206 and 190 nm) and ordered structures in proteins and polypeptides has accumulated over the past 10—15 years. A significant advance in the evaluation of secondary protein structure has been made by application of the Moffitt equation [Ref. (7)] to the ORD of protein systems in solution ... 

Corrected for index of refraction a value of 212 mi> was assumed for Xo (Moffitt equation). 

The proportions of the two units were assessed using IR spectra or the Moffitt equation [91] by using the bo constant. The complex ORD of the copolymer can be explained simply as a result of the sum of the two unit contributions of opposite sign, since the complex ORD curves could be reproduced by mixing the models XXXIXc, d in various proportions. 

Optical rotations [a] d of the two polymers were found to be different, although identical chemical structures (except end groups) were expected according to the literature [34]. In order to clarify the origin of these differences, ORD measurements of polymers and of the monomer (VI) taken as a suitable model compound were undertaken. Rotatory powers and ORD were found to be strongly dependent on the polycondensation medium (Figure 6). In a first step it was found that the polymer prepared in alkaUne condition and the model compound showed very similar ORD in dioxane and both obeyed the one-term DRUDE equation. In contrast, ORD of the polymer prepared in acidic condition was complex and obeyed the Moffitt equation withflio> and Xq constants respectively +492,-755 and 212 quite similar to constants found for helical polypeptides [35, 36]. 

For compound (VIII), each type of monomeric unit brings in partial ORD s of opposite sign as suggested from model compound (IX) and (X) behaviors (Figure 7A). The existence of these partial ORD s leads to a complex total ORD similar to that observed for helical polypeptides. Accordingly, this explains well the obedience of the ORD of (VIII) to Moffitt equation without taking into account macromolecular conformations [26]. 

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