32 VIRUSES 



associated with this experiment. Those who know how hard it really is to dif- 

 ferentiate zero, first and second order reactions with systeroa exhibiting any 

 appreciable error might wonder whether the data here seen would not fit the 

 graph of some other kinetic process as well as that here indicated. These data 

 were subjected to an appropriate statistical procedure. It was found that an 

 equation of a first order reaction was overwhelmingly favored. On can then say 

 with practical certainty that heat denaturation of tobacco mosaic virus is a 

 reaction of the first order. 



The next issue of importance is to observe in just what manner the specific 

 rate, the k in equations (1) and (2), varies with the temperature. It is 

 easier to understand the significance of this sort of observation if v/e have in 

 mind some simple theoretical picture of the mechanism of virus denaturation. It 

 is consistent with present day concepts of reaction kinetics to imagine that, 

 for a virus molecule or particle to become denatured it must first pass into an 

 activated state. This reaction can be symbolized by the following equation: 



V^V*-^nD (3) 



V represents a unit of virus in the normal state, V* represents a unit of virus 

 in the activated state, nD represents n units of denatured virus, K is an 

 equilibrium constant, and k' is a rate constant. The activated state is as- 

 sumed to be in reversible equilibrium with the virus in its ordinary state. 

 However, during the short period of time that any one virus particle is in the 

 activated state, there is a certain probability, k', that it will disintegrate 

 or change over into denatured virus. The rate at which the activated virus par- 

 ticle disintegrates can be thought of as being proportional to the concentration 

 of activated virus at the moment. In reality the rate of change of activated 

 virus into denatured material is the rate of change of ordinary virus into de- 

 natured material. Therefore the rate of change of ordinary virus into denatured 

 material is proportional to the concentration of virus in the activated state. 

 Since the activated virus and the normal virus are in equilibrium, the concen- 

 tration of virus in the activated state is equal to the equilibrium constant 

 times the concentration of virus in the normal state. This statement can be 

 only approximately true. It would be more accurate to say that the thermody- 

 namic activity of the virus in the activated state is equal to the equilibrium 

 constant times the thermodynamic activity of the virus in the normal state. On 

 the basis of this reasoning, it can easily be seen that the rate of denaturation 

 of the virus is proportional to the virus concentration and the equilibrium cons- 

 tant for the reaction: normal virus yields activated virus. In order to de- 

 tenrine how the rate of denaturation of virus varies with the temperature or 

 with any other variable, all one needs to determine is how this equilibrium cons- 

 tant varies with the variable under consideration. These considerations can be 

 summarized by a few equations. 



^=._dIpL.i,.tv^ (4) 



^"*' jyf = K I more accurately, f * ]y*T ^ ^ 



Therefore, - ^^ = k« K [v] f/f* (5) 



By comparing (1) and (5), k = k« K f/f* (6) 



and In k = In k'Cf/f* + In K=con8t + In K (7) 



The brackets indicate concentration, f is the activity coefficient of normal 

 virus, and f* is that of virus in the activated state. The problem of 



