16:4/ Molecular Action of Ionizing Radiations 305 



elimination of small molecules ; the role of oxygen ; energy transfer ; and 

 damage protection. Dried protein films are simpler than protein solu- 

 tions or biological cells, in that only direct effects are possible. From the 

 variation of molecular destruction in dried films with dose rate, it is 

 possible to compute a sensitive volume for the molecular species being 

 studied. 



4. Target Theory 



Target theory can be used to compute a sensitive volume or target 

 whenever doses of ionizing radiation are used to induce changes in whole 

 animals, in cells, or in dried protein films. The interpretation of the 

 target volume is least ambiguous in the case of dried protein films but 

 use has been made of this concept in Chapters 10 and 14 in discussing the 

 sensitive volume for genetic mutation. It was stated that this volume 

 was computed to be equivalent to a sphere of around 70 A diameter. 

 In living cells, it is sometimes hard to distinguish single-hit targets from 

 those requiring multiple hits to produce any result because the sensitivity 

 may vary from one cell to the next. In a like fashion, even after one 

 has found a sensitive volume, it is not self-evident whether this is associ- 

 ated with a particular molecule or with ionizations produced elsewhere 

 in the cell, the excess energy being transferred to the critical molecules. 

 In this section, the theory necessary to compute the target volume is 

 discussed. 



Suppose a beam of D ionizing particles per unit area strikes a given 

 cell (or dried film) . Further, assume that the only effects occur in one 

 particular type of constituent, of which there are n in the cell (or film) . 

 For simplicity of discussion, it will be assumed that the particles of this 

 constituent are individual molecules, although the theory is in no way 

 altered if this is not true. If the probability of any one molecule of this 

 species being damaged is equal to that of any other, then the probability 

 that an incident particle will cause one change is proportional to the 

 number of molecules n remaining unchanged. As the cell (or film) is 

 bombarded by incident particles, n will decrease. This may be 

 expressed symbolically by 



An = -nSAD (1) 



where the incremental dose AD is a small number of incident particles 

 per unit area, which causes a decrease in n of an amount An, and S is a 

 proportionality constant. The probability of reaction is included in the 

 constant S which has the dimensions of an area; S is called a cross section. 



