IRREVERSIBLE MONOLINEAR CHAINS 323 



Vgi shall designate the steady-state rate of the system as a whole, usually 

 experimentally determined by the formation of the product C. 



Concentration of the Internnediate B 



If Michaelis-Menten kinetics hold for each enzyme, the individual rates 

 are given by: 



F.(A) y=(B) 



"■ ^ (ir-TKr "- = wtk: "■'' 



where K^ and K.2 are the Michaelis constants and F^ and Fg are the maximal 

 rates for reactions 1 and 2, respectively. Setting v^ = v^ and solving for 

 (B), the steady-state concentration is found to be: 



(B) ^ M^^A^ (7-3) 



^ ' (A)(F. - F,) + F.A^ 



Since F^ = l\{Ei)i and F, = h^iEi)^, where A-^ and h.y are the rate constants 

 for the breakdown of the ES complexes, (B) depends on the Michaelis con- 

 stants, rate constants, and enzyme concentrations of both reactions. It may 

 be noted, however, that (B) depends on the ratio F1/F.2 and not on the 

 absolute values. The variation of (B) with the concentration of substrate 

 A as it depends on VJV2 is shown in Fig. 7-1. The value of (B) can theo- 

 retically be greater or smaller than (A) in the steady state. However, lim- 

 its to which (B) can rise are generally imposed by the nature of the sys- 

 tem. In reactions run in homogeneous closed systems (as with enzyme 

 solutions in reaction vessels), (B) must always be a small fraction of (A), 

 since otherwise it would imply that an appreciable amount of A had been 

 reacted and its concentration reduced from the initial value. In open sys- 

 tems where (A) can be maintained constant from an outside source, or in 

 nonuniform systems where B can be trapped, (B) can rise to values higher 

 than (A). The level to which (B) can rise often determines whether the 

 system will be in a steady state or not, and this will be considered in more 

 detail later. It may also be noted that (B) is not necessarily linearly re- 

 lated to (A), except when F^ = Fg. 



The Over-All Steady-State Rate, /gt 



When the system is in a steady state, the rate of disappearance of the 

 substrate, — d(A)ldt, is equal to the rate of formation of the product, 

 d{C)l(h, and this rate will be determined by the first reaction. Thus Vg^ 

 will always be Fi(A)/[(A) + K^] in the steady state. However, if the system 

 in not in a steady state and B is being formed faster than it can be utilized, 

 diQl'dt will not be equal to — d{A)jdt but will depend on (B) and will not 



