Determination of Sedimentation Coefficients in Rapidly Equilibrating Polymerizing Systems

Abstract

WHEN systems undergoing a rapid chemical re-equilibration between monomers and a single higher polymer are examined in the ultracentrifuge, a bimodal reaction boundary is predicted, if the degree of polymerization is greater than two^1,2. The sedimentation coefficient of the monomer at infinite dilution, (S_M)_O may be found by extrapolation of the weight-average values, s̄, determined from the rate of movement of the position corresponding to the square root of the second moment of the entire schlieren diagram at a series of total protein concentrations³, or by examining the system in an environment where aggregation is inhibited. For example, the latter procedure was used to estimate (S_M)_O for α-chymotrypsin as ∼ 2.5 S^4,5. The determination of the sedimentation coefficient of the polymer, s_p, however, at a particular concentration (and hence (s_p)_O at infinite dilution) is difficult, for there is no defined position on the experimental schlieren pattern which corresponds to the position of the polymer at a given time. Certainly, an extrapolation of s_fast, found from the rate of movement of the faster peak of the bimodal boundary, leads to serious error^6,7. A value may be estimated on the basis of elementary theory⁸ and the equations of Perrin⁹, by assuming a model and assigning values to (S_M)_O and n^2,7. The latter procedure is not satisfactory, in view of the importance of s_p as an essential parameter in determining: (1) the value of the equilibrium constant from s data, which could be compared with that obtained from the Gilbert theory¹; (2) the theoretical concentration dependence of s values for observed peaks in sedimentation velocity experiments^1,7.