Chemical modification of proteins: plotting of the remaining activity against the number of residues modified.

In the study of chemical modification of proteins, it has been a common practice to plot the fractional remaining activity against the number of residues modified per protein molecule. Extrapolation of the initial, nearly linear portion of the curve to the axis giving numbers of residues has often been presumed to specify the actual number of critical groups modified, i.e., the stoichiometry of the modification and the inactivation reactions. However, this extrapolation method is not generally applicable (Horiike, K. & McCormick, D.B. (1979) J. Theor. Biol. 79, 403-414). This paper describes further examination of the underlying theoretical framework of the extrapolation method. The properties and features of the extrapolated values are considered and presented with numerical and graphical examples. And the theoretical conditions with which the extrapolated value gives the number of essential residues are derived.