416 Thermodynamics of Enzyme Reactions /22 : 5 



controlled. Surprisingly little information is available in the literature 

 on this subject. The reactions of the transport protein, hemoglobin, 

 with oxygen and carbon monoxide have been shown to be independent 

 of the diffusion rate at room temperature. However, for the catalatic 

 reaction of the heme-type enzyme, catalase, with hydrogen peroxide, it 

 has been shown that the reaction rate constants, k x and k 3 , both become 

 diffusion controlled at viscosities several times that of water. 4 The 

 reaction of the heme protein, myoglobin, with oxygen is similar in its 

 diffusion dependence to that of catalase with hydrogen peroxide. The 

 intermediates of horse-radish peroxidase react with reduced cytochrome 

 c at rates which are altered both by the viscosity of the medium and also 

 by the dielectric constant. 



The results for catalase can be used in the diffusion-controlled region 

 to compute a radius r for the active site at which the hydrogen peroxide 

 reacts. It can be shown that the encounter rate is 



Z e = DrNfQ-\0- 3 (10) 



where 



D = diffusion constant in cm 2 /sec 

 r = radius in cm 

 N = Avogadro's number 



f = factor which includes electrostatic effects 



Q. = solid angle through which the molecules may approach one 

 another to react. 



When catalase reacts with hydrogen peroxide, the rates of reaction are 

 independent of dielectric constant, ionic strength, and pH. Therefore, 

 the factor / in Equation 10 will be one. In the diffusion-controlled 

 region, k 1 and k 3 for catalase will be approximately equal to Z e . A 

 graph of k x or k 3 plotted as a function of D allows one to evaluate rQ.. 

 If it is assumed that the hydrogen peroxide can diffuse at any angle 

 within a hemisphere, it is found that for both k x and k 3 



r= 1 A 



The small value indicates strongly that the reaction occurs at the iron 

 atom in the heme group on the catalase, and that the protein does not 

 act as a semiconductor for the purposes of this reaction. 



Similar experiments for cytochrome c and horse-radish peroxidase 

 indicate that electrostatic effects are important, the two reactants 

 behaving as dipoles oriented to oppose the reaction. Using dipole 

 moments of one electron-A, it is found that the closest approach is 



4 See Chapter 18 for definition of k x and k 3 for this reaction. 



