KINETIC APPROACH TO TRANSPORT 



(Si - S 2 )/v m 



' max ~ (43,) 



(S 1 +K m )(S 2 + A' m ) 



Wilbrandt (1956) pointed out that, under limiting conditions 

 of solute concentration, Equation (4a) predicts contrasting charac- 

 teristics for the system. When S x and S 2 are well below saturation 

 (small compared with K,„), the usual expectation will be realized 

 that solutes showing highest affinity will be most rapidly transported. 

 In this case, the denominator of Equation (4a) approaches the square 

 of K m . The rate therefore becomes proportional to the gradient, 

 as for diffusion. This derivation also shows mathematically what 

 one can grasp intuitively, that diffusion-type kinetics never exclude 

 chemical mediation in transport, because the capacity of the media- 

 tor may be higher than the highest levels that have been tested or 

 that can be tested. 



On the other hand, if the concentrations on the two sides of the 

 membrane are much larger than X ra , Equation (4a) approaches the 

 form 



V = V m ^K m (~-~) (5) 



Equation (5) shows the velocity becoming directly propor- 

 tional to K m , which means that the solute with the higher affinity 

 (and hence the lower K m ) will, at such high levels, be the one to 

 reach equilibrium more slowly. One can grasp this intuitively by 

 understanding that, at high saturation levels, the high-affinity solute 

 will rarely permit a transport site to become vacant to transport 

 a new solute molecule. 



Historically, many solutes now known to enter uphill transports 

 were earlier supposed not to be transported at all, simply because 

 the tests were first made at levels too high in relation to the capacity 

 of the system. Red blood cells were initially thought not to admit 

 most amino acids. It was the author's experience to conclude initially 

 that /?-chloroalanine is scarcely transported at all into the Ehrlich 

 cell (Riggs et al., 1954), whereas its affinity actually is so high as 

 to minimize uphill transport except at rather low levels. 



Rosenberg and Wilbrandt (1957) used sugar transport into 

 red blood cells to verify the above conclusion. Subsequently, 

 Finch and Hird (1960) showed the applicability of the concept 

 to the concentrative uptake of amino acids by sections of small 



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