THE MATHEMATICAL BASIS OF TSOU PLOT
邹承鲁作图法的数学证明

A method was proposed by Tsou in 1962 of plotting the data obtained during chemical modification of proteins for the determination of the number of essential groups involved.A mathematical proof for this method is presented herewith.Let the number of the protein molecules involved in the reaction system be scontaining all together n reactive groups. Among q (q = s/n)reactive groups per protein molecule, r are essential for its activity.When the groups involved are equally reactive,then,when number of the modifier molecules that have reacted with the protein molecules are m, the probability, P(k),that exactly k protein molecules remain activity is given by:The mean number of active protein molecules isAs under most conditions, we have n -m>>r,the fractional activity remaing, a, will beFrom the well known Chebyshev's inequality, it has been shown that the possible error as could be derived from the Tsou plot will be much smaller than the usual experimental error obtainable.