The Mechanism of Action of Methyl Xanthines in Mutagenesis 143 



where k^ and k^ are characteristic constants. The steady-state solution of this 

 pair of equations is 



P = p (,\Vki^k^l \ 



(2) 



where P^) and A^,, depend on the initial conditions and the constants Aj and ko. 

 Thus both P and A^ increase exponentially at the same rate and each therefore 

 appears to be 'autocatalytic'. 



Clearly, processes of this kind are responsible for the maintenance of constant 

 growth rates and constant composition of cells during the exponential growth 

 of bacteria. However, the control of the system by this type of interaction 

 cannot explain the regulation of synthesis of intermediates for the biosynthesis 

 of either P or A'^. Additional regulatory processes must be considered. From 

 equation (2) it is evident that for any constituent of the cell (intermediate or 

 enzymatic catalyst) the steady concentration increases autocatalytically. If 

 expressed as amount per unit number of bacteria or per unit bacterial mass, 

 any cell constituent may be considered constant. Thus, if such a transformation 

 is made, we can consider a system with time-invariant concentrations of inter- 

 mediates and catalysts and also time-invariant fluxes. Thus, the steady-state 

 treatment of reaction rates is immediately applicable to our problem. The most 

 general formulation is that of Christiansen and has been well described by 

 Hearon (18, 19). 



In essence the rate expression for each step of a concatenated reaction 

 scheme, in which a substance is produced in one step and utilized in the next, 

 is written down. Each of the terms in these expressions is the product of the 

 intermediate with a rate constant and also with either unity or with the concentra- 

 tion(s) of the other chemical reactant(s). If the product of the two latter factors is 

 set equal to a quantity W, bearing suitable subscripts to identify the term, and 

 if the usual steady-state assumptions are made, then the solutions for both the 

 flux of the system or the over-all reaction rate v and the concentration of each 

 intermediate [A'J may be computed. If the very last reaction is irreversible, 

 equations (3) and (4) are obtained. 



W.W^W^"- W, 



[X,] = V 





(3) 



Wi-,1 '"W^ 



(4) 



The assumption of the irreversibility of the last step is made necessary by 

 the well-known metabolic stability of DNA. Recent experiments (20) demon- 

 strate the extreme irreversibility in the normal adult rat. The evidence 

 for growing cultures of E. coU is less stringent (21, 22) but does permit this 

 assumption in comparison with the tremendous synthetic rate in these 

 organisms. 



