General solution to the inverse problem of the differential equation of the ultracentrifuge

Whenever experimental data can be simulated according to a model of the physical process, values of physical parameters in the model can be determined from experimental data by use of a nonlinear least-squares algorithm. We have used this principle to obtain a general procedure for evaluating molecular parameters of solutes redistributing in the ultracentrifuge that uses time-dependent concentration, concentration-difference, or concentration-gradient data. The method gives the parameter values that minimize the sum of the squared differences between experimental data and simulated data calculated from numerical solutions to the differential equation of the ultracentrifuge.