Kinetics of Haemoglobin in Red Blood Corpuscle 



by those interested, since limitations of present space prevent any 

 detailed description of them. All that can be done here is to give an 

 outline of the assumptions, upon which the new mathematical investi- 

 gation has been based, and of the more important results which it has 

 yielded, together with a brief discussion of its future prospects. 



In working out the rate of entrance of dissolved CO (or O a ) into the 

 corpuscle, it is assumed that 



1 The concentration of dissolved gas remains constant at the surface 

 of the corpuscle membrane. 



2 The corpuscle membrane is devoid of haemoglobin, and no 

 chemical reaction, but only diffusion, takes place therein. 



3 The diffusion of dissolved gas both through the membrane and 

 the interior of the corpuscle obeys Fick's Law, according to which 

 the quantity diffusing in unit time = concentration gradient 

 x diffusion coefficient X area surface through which diffusion 

 occurs. 



4 Diffusion of haemoglobin within the corpuscle can be neglected 

 owing to the size of the molecule and also (especially) to its close 

 packing 19 . The haemoglobin is assumed to be uniformly dis- 

 tributed throughout the interior of the corpuscle. 



5 The kinetics of the reaction in the corpuscle are given by 

 d&Hbydt = k! [X][Hb] - k [XHb], the values of the velocity 

 constants k', k being the same as in solution. 



6 The corpuscle is assumed to be equivalent to an infinitely extended 

 parallel layer of haemoglobin, bounded by a haemoglobin-free 

 membrane (for justification of this model see Roughton 6 ). The 

 thickness and concentration of the haemoglobin layer are supposed 

 to be the same as the average thickness and concentration in the 

 red blood corpuscle. 



The results of the mathematical treatment based on these assump- 

 tions will now be given briefly. 



Figures 3 and 4 show the calculated rate of uptake of CO and of 2 

 by the haemoglobin layer without membrane, as compared with the 

 observed rates in the case of homogeneous solutions. The dotted 

 curves in the two figures show the maximum and minimum solutions 

 previously obtained by Roughton 6 . All he could then say was that 

 the true solutions must He somewhere between the dotted curves, and 

 it is interesting to find, with the modern methods of calculation, that 

 they do in fact lie almost exactly half way between his extremes. 



Figure 5 A, B shows the observed results for the rate of uptake of 

 CO by a haemoglobin solution and corpuscle suspension prepared 

 from the blood of a pregnant ewe, kindly supplied by the late Sir 

 Joseph Barcroft. Figures 5C, 5D show the calculated results, assuming 



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