THERMAL INACTIVATION OF VIRUSES 107 



Returning to the schematic drawing of part of a protein 

 molecule shown in Fig. 4.1, the effect of thermal agitation is to 

 cause excitation of many of the weaker bonds and, possibly 

 to a lesser extent, of the covalent bonds. As the temperature 

 increases, this excitation increases. The excitation is not uniform, 

 except on a long time average, but abnormal excitations can 

 occur. If one such causes a bond to break, there is a chance that a 

 general irreversible modification of the molecule can follow. 

 This modification may destroy the biological function and, if it 

 does, the assay procedure will detect it as an inactivated 

 molecule. 



The number, dn, of such molecules inactivated will clearly 

 depend on the time, dt, and on the number, n, of intact molecules 

 present but, because it is not concerned with reaction with 

 external agents in the chemical sense, it will not depend 

 on concentration in any way. The reaction equation is then 

 — dn/dt — kiU, where A'l is the reaction constant. This can be 

 integrated to give the relation In {n/no) = —kit, where n/rio is 

 the fraction of activity remaining at time t. This is usually 

 easily measured, and so the measurement of ki is inherently not a 

 difficult matter. 



Now the theory of absolute reaction rates (see Stearn, 1948) 

 states that if a monomolecular-type reaction that obeys the 

 above relation takes place, then 



A-i = ~i^ e R'r (4.5) 



where AF* is the free energy of activation for the process, R is the 

 usual gas constant and h is Planck's constant. 



This can be written in terms of the heat of activation, A//^ 

 which is the change in internal energy for volume change, and the 

 entropy, A»S^ of activation by using the constant- volume relation 



^F^ = Afft - T^S^ 



If the variation in volume warrants it, the relation 



^F^ = MP - TAS^ + PAV^ 

 must be used. 



