Recently, Coulson & Smith (1968), calculated a critical number of antigen determinants to stimulate a sensitized lymphocyte to transform. The purpose of this note is to point out that the mathematical procedure used in their analysis is not correct. Consequently, the critical number determined by these authors is not valid. Furthermore, we will show that, even with correct mathematical procedure, the model would give unrealistic results. Therefore, we shall conclude that the model itself is not realistic, and an alternate model is suggested.
We repeat the symbols and the starting equation of these authors: n = concentration of sensitized, untransformed cells,
,I 0 = n(t = 0),
P.H. FANG
data ofn from all three donors shows an increase at large Co. The argument of Coulson & Smith (1968) that this increase is caused by statistical errors is not convincing because of distinct numerical values involved. We would like to suggest that the data actually are consistent with the coagulation model of Smoluchowski (1917). In the biological equivalence, the model assumes that a number of lymphocytes can share a single antigen determinant. This certainly is shown in the case of donor pH. However, a serious effort to develop such a theory of coagulation will be pending until the data of large tuberculin concentration with smaller number of sensitized donors are available.