CYCLIC SYSTEMS 



349 



mation of Y may be calcvilated from (B), the rate characteristics of the 

 system may be derived from an expression for (B) in terms of (X), (M)^ 

 and the constants of the cycle enzymes. The steady-state values for (A) 

 and (C) may be easily shown to be: 



(A) 



V,KAB) 



(C) 



V,[(B) +K,] -{B)V 

 F,A^(B) [(X) + K,] 



F3(X)[(B) +K,] -(B)F,[(X) +K,] 



(7-37) 



(7-38) 



and by substitution of these in the conservation equation, an expression 

 for (B) may be obtained. This expression is a cubic equation with coefficients 

 of many terms, the solution of which is arduous. However, it is possible 

 to obtain values for (A), (B). and (C) by graphical methods when the con- 

 stants of the system are known. 



The graphical method used consists of the following. Accurate v-(S) 

 curves are plotted for each reaction of the cycle; precision is often increased 

 by the use of semilog paper. A complete solution is obtained by finding a 

 horizontal line that intersects the curves so that (A) + (B) + (C) is equal to 

 the assumed total concentration of intermediates, (M);. The height of this 

 line gives the steady-state rate (Fig 7-15). The effects of inhibition of any 



(B)+(A)+(C) 



(MK 



(S)- 



FiG. 7-15. Illustration of the graphical method 



for the determination of steady-state rates and 



concentrations in cyclic systems. See text for 



explanation. 



enzyme in the cycle may be determined by the same procedure using 

 the appropriately modified w-(S) curve for that enzyme. This method is 

 believed to be generally better than the simplification of the complete equa- 

 tions by assuming the relative unimportance of certain factors, inasmuch 



