346 SPECULATIONS ON CELLULAR ACTIONS 



magnitudes. If m/r = 2 and n/s = 1, or vice versa, the frequency dis- 

 tribution looks unfamiliar; and when mir = n/s = 1, the distribution 

 function is an exponential. I have never heard of an observed exponential 

 frequency distribution for any biological property, and I believe I am 

 safe in stating that, if any are reported in the hterature, they are ex- 

 ceedingly rare. Accordingly it seems to me that frequency distribution 

 of radiosensitivity cannot explain exponential survival curves, and that 

 it is an unlikely explanation for survival curves formally described by 

 Eq. 1 with m/r = 2 and n/s = 1, or vice versa. On the other hand, 

 when the experimental data can be fitted by Eq. 1 only by using values 

 of m/r and n/s whose product is greater than 2, our general biological 

 experience does not enable us to rule out the frequency distribution as 

 the cause, or at least the partial cause, of the shape of the survival curve. 

 However, if we adhere to our scheme of mechanism (Fig. 2), it is 

 evident that, despite biological variation, Eq. 1 is fundamental to the 

 dose-effect relationship. Since the dose-effect curve is determined by 

 m/r, n/s, and h, biological variation can operate only through variations 

 in one or more of these quantities. Any or all of these variations can be 

 taken into theoretical account by substituting suitable summations and 

 integrations for m/r, n/s, and h in Eq. 1. The resulting expressions are, 

 of course, so comphcated that at present there is no hope of using them 

 in determining m/r, n/s, or h for any real radiobiological action. How- 

 ever, I should hke to emphasize that, since a cell consists of a finite num- 

 ber of molecules, and since irradiation can therefore initiate only a finite 

 number of individual series of relevant processes and states, survival 

 curves can always be described by theoretical equations if sufficient in- 

 formation is available, this despite any biological variation. 



Before leaving our analogies with target theory, let us briefly consider 

 the nature of a hit. As noted above, a hit may be identified with our 

 "decisive process" or a group of such processes. I beheve that most 

 writers on formal target theory visualize a hit to be an individual energy 

 transfer, or group of transfers, producing one or more ionized or excited 

 molecules, in an especially "sensitive" volume of the cell, which may be 

 roughly identified with our "precursor" of a decisive entity. Referring 

 to Figs. 1 and 2, we can see that a hit (or decisive process) does not have 

 to be an initial energy transfer or an ionization; it may be a chemical re- 

 action. Moreover, it may occur considerably later than the initial en- 

 ergy transfer; thus there may be time for the chemical species involved 

 in the relevant processes to diffuse some distance from the point of en- 

 ergy transfer before the hit (decisive process) occurs. Accordingly the 

 initial energy transfer does not necessarily have to occur in the "sensitive 

 volume" (precursor). 



