Solution Properties of Synthetic Polypeptides. VIII. Further Study of the Light-Scattering Function

Abstract

The Rayleigh scattering of light from solutions of polypeptide molecules which are in the helix–coil transition region is discussed in terms of the particle scattering function P(θ) expanded in powers of k2=(16π2/λ′2)sin2(θ/2), where λ′ is the wavelength of the light in the scattering medium. Approximate expressions are derived, under the conditions that N>>1, \\sqrt{σ}<<1, and N\\sqrt{σ}>3, for the coefficients in the series up to the third one and for the fourth moment ‹R4› of the end–to–end distance of the chain. Here N refers to the degree of polymerization and σ to the helix-initiation parameter. It can be shown that a polypeptide chain tends to obey Gaussian statistics at the limit of infinite N unless the helical content is unity. Examination of numerical results indicates that the behavior of a finite chain significantly differs from the Gaussian limit even at an N as large as 4000. Features of P(θ)−1/2 as a function of sin2(θ/2) are examined in relation to the determination of the mean-square radii of gyration of polypeptide samples from light-scattering measurements.