772 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



(D) Polylinear chains. If an inhibitor acts to varying degrees on the dif- 

 ferent pathways of a multishunt system, such as: 



(15-44) 



it has been shown in chapter 7 that the over-all inhibition on the rate of 

 formation of the product will be given by: 



% = ' " " (15-45) 



^1 -t- t'2 + ••• + 1'n 



A change of the temperature will alter the rates of the different pathways 

 to varying degrees indicated by the factor g\ thus i\ will become gfiV^, etc. 

 In addition, the individual inhibitions may change with temperature, so 

 that t'l is now ty, etc. The over-all inhibition at this new temperature will 

 then be: 



(15-46) 



fi'l^^l + giV<, -f ... -f gnVn 



The change in the over-all inhibition with temperature will obviously not 

 be directly related to any single pathway or individual inhibition and no 

 thermodynamically significant characteristics may be obtained from the 

 experimental data. 



{E) Cyclic systems. The temperature dependence of rates in cyclic systems 

 is too complex to analyze in detail. Reference to Eqs. 7-37 and 7-38, and 

 the use of the graphical method outlined in Chapter 7, make possible qual- 

 itative predictions as to how the concentrations of tlie cycle intermediates 

 may change as the temperature is varied, if the temperature characteristics 

 for the various constants are assumed. In general it may be noted that the 

 rates in cyclic systems are not usually limited by single reactions and hence 

 that the results from the variation of temperature cannot be interpreted 

 in simple terms. 



It is unnecessary to deal with any other multienzyme systems because 

 the general conclusions relative to the effects of temperature are clearly 

 illustrated in the cases discussed. Discussions of multienzyme systems in 

 the past have dealt almost exclusively with monolinear chains. Here it is 

 possible to have a limiting reaction and the effects of temj^erature can often 

 be related to this reaction. In other types of multienzyme systems this is 

 not true and temperature effects cannot be attributed to single reactions. 



