The statistical estimation of molecular weights from normal and difference ultracentrifuge boundaries

1. To determine molecular weights from boundary data taken from a sedimentation velocity experiment in an ultracentrifuge, the parameter s/D must be estimated. This can be obtained by using non-linear statistical methods to fit a mathematical model [the Fujita & MacCosham (1959) equation] to the results. 2. The statistical method chosen was the simplex method of Nelder & Mead (1965), which was found to be ideal for this problem. Internal errors were calculated at the end of the search for the minimum in the residuals, but in general these errors were found to not represent the overall true error of the experiment. 3. Calculations of molecular weights of myoglobin showed that instabilities at low concentrations of protein (less than 0.8mg/ml) disturbed the calculation of s/D. If 1% (w/v) sucrose was included in the solvent, these instabilities were decreased, and extrapolating to infinite time the linear function of s versus 1/(time) gave an acceptable value for s with an error of +/-4.8%. The estimates of the molecular weights were less well-defined and the mean value was low by 8%, with an estimated error of the mean of +/-3%. The conclusion was that vibration was responsible for the instabilities without sucrose. 4. The Fujita-MacCosham equation can be extended to make it possible to estimate ratios of sedimentation and molecular weights for difference boundaries. Tests using two solutions of orosomucoid in which a 2% decrease in velocity of one boundary was achieved by adding a calculated quantity of sucrose showed that the analysis gave realistic values for the two ratios, and the error for the ratio of sedimentation coefficients was +/-10%. The error was larger for the estimated ratio of the molecular weights, but the analysis gave the expected value for the ratio.