BIOLOGICAL TRANSPORT 



a complex CS, which redissociates after passing through the bar- 

 rier, the rate should still be given by 



V = Z D (CS! - CS 2 ) (2) 



Unfortunately, however, the gradient of the solute-carrier com- 

 plex is not an available quantity. 



In terms of the solute concentration, the unidirectional jinx 

 across a membrane by a process utilizing a site or carrier of limited 

 capacity could be expected to be given by the equation of Michaelis 

 and Menten: 



S 



' — ' max \&) 



S + K m 



Several assumptions need, however, to be made. The rate-limit- 

 ing step must be neither the association of C and S nor the dissocia- 

 tion of CS but, instead, the translational event presumablv separating 

 these events. The diffusion constants must be the same for C and 

 CS. To obtain a unidirectional flux, the initial rate must be measured, 

 or at least the level of the solute on the other side of the membrane 

 must be low compared with the K m applying for transport from 

 that side. According to the usual procedure for testing for appli- 

 cability of these relationships, a plot of l/V against 1/S will be 

 linear when the equation applies, and the two parameters V max and 

 K m can then be determined as usual (see textbook discussions of en- 

 zyme kinetics). 



For net transport in a system not able to transport the solute 

 uphill, the net migration rate will be given by 



/ bi bo 



/ Si s 2 \ 



\Si + K m S 2 + K m / 



Here, K m has been assumed the same for the transports in the two 

 directions. Wilbrandt and Rosenberg (1961) call attention to the 

 expectation that, under the foregoing assumptions, K m but not 

 V mnx may be expected to vary for a group of different but analogous 

 substrates. Sen and Widdas (1962) evaluated carefully V max for 

 D-glucose and D-mannose for red cell transport and found essentially 

 identical values. They also measured carefully the effects of tempera- 

 ture and pH on K m and V mai . 



Equation (4) may be rearranged for convenience to the form 



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