A Study of Aging, Thermal Killing, and Radiation Damage by Information Theory 299 



is known about storage and transfer of information in organisms. For the 

 present it will be necessary to make some simpje assumptions, however. 



It was proposed previously (10) that death occurs when the value of //decays 

 below some limit H^. Let / be the number of organisms in the population 

 representing the ensemble. The probability per unit I of leaving the population 

 {\jl){dHdX) is called the force of mortality. The force of mortality will be the 

 probability density unit per H at //,, after exposure X multiplied by the rate of 

 decrease of H per unit X at //,^. 



\_dl 

 I dl 



p{Ha, A) 



dH 

 ~di 



(1) 



ffrf 



The value of p(//, A) varies continuously with A; no organisms leave the 

 microensemble which at A = lies between H and U + dH. 





dX = p{H„ X) 



cm 



dX 



dX 



(2) 



H. 



The relation of p{H^, X) to p{H, 0) is as follows: 



piH„ X) = p(H, 0) 



i.) 



(3) 



^o + ^. + iIp(0 logo ;>:(/) 



»j 



where p'i(j) is the value corresponding to H^. 

 Equation (1) may be written 



p(Ha, X) 



ffo~-ffa + iIp(i)\og,Pi(j) 



1,3 



J{X) dX 



(4) 



In many cases the action of the deleterious agent will be of the first order 

 so that J{X) = /„, a constant. Let us assume that p{H, 0) is of such shape that 

 p{H^i, X) is a constant. 



Equation (4) may be integrated : 



log, ///o = p{H„ X) 



Ho-H, 



I lp(i) ^0^2 Pi(j) 



J,X 



(5) 



Equation (5) represents haploid survivorship as a function of X for many 

 types of destructive influences under many experimental conditions — but not 

 for all influences, or conditions, or haploid organisms. T. Alper (11) found 

 the rate of inactivation by gamma rays of dysentery phage SI 3 to increase with 

 increasing dose at 130 rad/min. At 5.3 rad/min the survival curves departed 

 markedly from the exponential forni although that form was found when 

 catalase was present. Watson (12) also reported the same phenomenon with 

 phage T2. Alper (13) later showed that the gas treatment of phage could result 

 in departure from the exponential form. A number of cases of a non-exponential 

 inactivation curve for viruses are discussed by Luria in a recent review (6). 



Gates (14) discussed the deviations from an exponential curve for ultra- 

 violet irradiations of bacteria. Recent work by Uretz (15) has shown that 



