26 2. THE KINETICS OF ENZYME REACTIONS 



strates react with the enzyme are discussed in a later section. The problem 

 of interactions between adjacent substrate sites is also dealt with later. 



Assumption That Concentrations of Reactants May Be Used Instead of 



Activities 



This simplification is not unique to the Michaelis-Menten theory but has 

 been used in most enzyme kinetic w^ork for the reasons that either the de- 

 viations produced were considered negligil^ly small or that no accurate esti- 

 mation of the activity coefficients of the substances involved could be made. 

 The activity coefficient (y) is the factor by which the concentration must be 

 multiplied to give the activity or thermodynamic concentration, and it is 

 this activity that ideally should be used in kinetic and equilibrium expres- 

 sions. The activity is equivalent to the concentration only in ideal or very 

 dilute solutions; solutions in which enzyme reactions are run are generally 

 not ideal, nor is the intracellular medium. The activity coefficient of an 

 ion decreases with increasing charge on the ion and increasing ionic strength 

 of the solution. The ionic strengths of enzyme reaction media vary greatly and 

 the exact intracellular ionic strength is not known. Examples of calculated 

 ionic strengths of possible reaction media are given in the tabulation below. 



Solution Ionic strength 



10 m3I Sodium acetate (pH 7 - 7.4) 0.010 



10 mil/ Sodium succinate (pH 7 — 7.4) 0.025 



20 mM Phosphate buffer (pH 7.4) 0.039 



10 mM Sodium succinate in phosj^hate buffer 0.064 



154 mM Sodium chloride (0.9%) 0.154 



10 m3I Sodium succinate in 0.9% sodiiun chloride 0.179 



10 m3/ Sodium succinate in phosiihate buff'er and 0.9°'o sodium chloride 0.218 



The ionic strength of Krebs-Ringer media is approximately 0.161 and it is 

 probably safe to assume that the bulk cytov)lasmic ionic strength is not 

 very far from this figure. Using the Debye-Hiickel equation, including the 

 salting-out effect, the activity coefficient of a single-charged ion at this ionic 

 strength can be calculated to be aijjn'oximately 0.76 and of a double-charged 

 ion approximately 0.31, values which check reasonably well with those de- 

 termined experimentally. Even at an ionic strength of 0.01, the activity 

 coefficient of a uni-univalent salt is around 0.90. 

 For an equilibrium of the type: 



^ (E)(S) 

 ' |(ES) 



