26 



SUBCELLULAR PARTICLES 



one sees concentrations, whereas partitioning takes place according to chemical 

 potentials. 



The chemical potential for hydrogen ions in bulk is given by 



^b = /All,, + RT !U Ab = /i-o,, + RT !U fi,Cb 



and near the surface, at some point in the double layer, by 



jUg = /xog + RTi»v As = /A(,^ + RT Av f gCs 



where /to,j — /^is is the chemical potential of a standard state and A^, fb, Cb and 

 Ag, fs, Cs are activities, activity coefficients and concentrations in bulk and surface 

 volumes respectively. At equilibrium, according to Gibbs," Ab = As and 



Cb_ fg 

 Cg fb 



In dilute solutions fi.^i, so that C=^-r- 





Equation 5 can be evaluated via electrophoretic measurements by substituting, 



for large particles, the Smoluchowski relationship u = — . We thereby arrive at 



the experimentally useful equation 



pHs = pHb + o.2i7u. (6a) 



The mobility of a particle u is reckoned negative for motion toward an anode, in 

 microns per second per volt per centimeter; D is the dielectric constant and 7/ is 

 the viscosity of the disperse medium at the same temperature. 



In table i are some values for ApH = pHb — pHg evaluated by means of the 

 equation of Hartley and Roe. Included are some data on roots obtained by still 

 another approach, which will not be discussed here (27). 



We may now inquire as to some of the biochemical and biological consequences 

 of the existence of ApH. 



Action of Proteolytic Enzymes on Proteins. Equation i may be written as 



pH.-pH.= -logI^=logM = -ApH (7) 



and Danielli (8) pointed out that the pH at the surface of a protein would there- 

 fore be different from that in bulk, and to an extent determined in part by the 

 ionic strength of the salts present. For small particles Hartley and Roe give, at 



o 



25 > 



pHg-pHb = C/6o = o.325u= -ApH. (61?) 



„ • . limit Ab 



- /xo, IS set equal tn /x., bv choice of a reference state such that ^ --— = fi, ^ i and as 

 " ' c — >o Cb 



Cb approaches zero so docs Cs. Since Ab = As and Cb 7^ Cs, it is clear that any difference 



between pHs and pHb reflects differences in concentrations of H*s and H*b. 



