POLYLINEAR CHAINS (SHUNT SYSTEMS) 345 



transformation, where reaction 1 is catalyzed by phosphorylase kinase and 

 reaction 2 by a phosphoprotein phosphatase, 4 ATP molecules being 

 required for the formation of one molecule of phosphorylase a. Such a sys- 

 tem operating as an ATPase would have complex kinetics and quite different 

 inhibition behavior compared to the single enzyme ATPase. 



POLYLINEAR CHAINS (SHUNT SYSTEMS) 



A multienzyme system wherein a substrate can be transformed to some 

 product by two or more different pathways may be termed a polylinear 

 chain. Many examples are known: electron-transport systems in which the 

 electrons may flow through different channels to oxygen (Mahler, 1956; 

 Singer et al., 1957); the two pathways of pyruvate ^ acetyl-CoA in yeast, 

 one by pyruvic oxidase and the other through pyruvic decarboxylase, 

 aldehyde dehydrogenase, and aceto-CoA-kinase (Holzer and Goedde, 1957); 

 the two routes by which coenzyme A is formed from pantothenic acid, one 

 involving pantetheine, and the other phosphopantothenic acid (Brown, 

 1959); and the well-known hexose monophosphate shunt. The kinetics will 

 depend on whether the chains branch from the substrate or from an inter- 

 mediate whose concentration can vary. The former system may be re- 

 presented as: 



A-m*'"*P (7-30) 



>-:y 



(n) ^ ^ 



where the over-all rate of formation of P, v = u^ + Vg + -•• + v^. Inhi- 

 bition of the first enzyme of any sequence will reduce d{V)jdt but inhibition 

 of the succeeding enzymes may not because the intermediate can increase 

 in concentration. If an inhibitor is assumed to exert an inhibition of i-^ 

 on pathway (1), i^, on pathway (2), etc., the inhibition of the over-all rate 

 will be: 



i{Vi + ^2^2 + ... + inVn 



Vi + Vi -\- ... + w„ 



(7-31) 



so that the inhibition on the over-all rate will always be less than on the 

 individual enzymes. Such polylinear chains are perhaps responsible for many 

 instances of inhibitor-resistant metabolism in the cell. When the sequences 

 are irreversible, each sequence operates independently of the others and 

 the effect that some modification of a single sequence will have on the 



