612 B. Chance 



and oxygen (Lehninger, 1954; but cf. Slater, 1958) tells us very little about 

 the pair of carriers between which phosphorylation occurs, since three 

 possibiHties exist: 



c-^a-^a^--0, (15) 



In a similar fashion, no fragmentation method has identified the pair of 

 carriers involved in the additional phosphorylation obtained in the presence 

 of succinate, where various possibilities also exist, viz., 



succinate -^ fp -^ Z> -^ q -^ c (16) 



or with DPNH-linked phosphorylation: 



DPNH -- fp -- ^ -- f 1 -- c (17) 



The use of inhibitors to segregate portions of the respiratory chain is also 

 ineffective with those compounds available at present, since specific inhibitors 

 for each portion of the chain between the carriers are unknown. Further- 

 more, as indicated above, thermodynamic properties of the isolated system 

 may be very diflficult to apply to the intact system, since energy conserved 

 at one point could supplement that conserved at another point. Thus 

 fragmentation and inhibition have limited usefulness for 'pin-pointing' 

 interaction sites. 



MATHEMATICAL PROPERTIES OF SEQUENTIAL 

 ENZYME SYSTEMS 



The complexity of the respiratory chain and its associated reactions is 

 sufficient that kinetic studies based on the application of a simple Michaehs 

 representation of a one-enzyme system need considerable elaboration for their 

 effective application to the respiratory chain. For this reason, we have spent 

 some time in this laboratory on the study of sequential enzyme systems. The 

 mathematical studies of complex differential equations which represent the 

 system can be solved for limited experimental conditions, such as the steady 

 state. In addition, some useful approximations may be obtained for a 

 transient portion of the kinetics (Higgins, 1959), and various theorems 

 relating the properties of the mathematical system to the experimental data 

 have been derived. Supplementing this approach is that of the analogue 

 computer, where a somewhat simplified representation of the electron 

 transfer system gives kinetic and steady-state solutions useful in testing 

 theorems based on approximate mathematical solutions or theorems derived 

 empirically from a study of the analogue computer data. Most recently 

 complete representations of all known components and their intermediates 

 may be obtained by the digital computer, and on this basis much more 

 critical tests of general theorems concerning the respiratory chain may be 

 made. 



