62 JOHN G. KIRKWOOD 



there exist many possible configurations of the protons, differing Uttle in free 

 energy among which fluctuations induced by thermal motion, may occur. 

 Fluctuations in the number and configuration of the mobile protons impart to 

 the molecules fluctuating charges and fluctuating electric multipole moments. 

 Let us consider two protein molecules in fixed orientation separated by a dis- 

 tance R. As the result of fluctuations in charge distribution, associated with 

 the Brownian motion of the mobile protons, each molecule produces an alter- 

 nating electric field at the point of location of its neighbor. These alternating 

 electric fields produce in turn a mutual electrical polarization of the average 

 proton distributions on the two molecules. When averaged over a time long 

 relative to the periods of Brownian motion, this polarization gives rise to the 

 supplementary attractive force between the two molecules with a potential 

 diminishing asymptotically as 1/R^. In the presence of an electrolytic environ- 

 ment, the long range of this force is substantially diminished by Debye-Hiickel 

 screening. Fluctuations in charge and charge configuration associated with 

 bound ions other than protons also make a contribution to this special type of 

 intermolecular force. 



Although it is not in general possible to distinguish between the fluctuating 

 and static electrical interaction between protein molecules by thermodynamic 

 measurements, that part of the fluctuating force arising from total charge 

 fluctuation is a salt-free isoionic solution may be isolated from effects due to 

 all other intermolecular forces, since it gives rise to a term in the excess chemical 

 potential proportional to the square root of the protein concentration, while 

 all other intermolecular forces, both van der Waals forces and electrostatic 

 forces associated with permanent and fluctuating multipoles, contribute only 

 terms proportional to the first and higher powers of the concentration. Tima- 

 sheff, Dintzis, Kirkwood and Coleman (1955) have carried out measurements 

 of the excess chemical potential and activity coefficient of isoionic bovine serum 

 albumin by the well known technique of light-scattering. Their results verify 

 the prediction of the theory of Kirkwood and Shumaker that the excess chem- 

 ical potential should decrease asymptotically with the square root of protein 

 concentration at high dilutions, as a consequence of the long range interaction 

 produced by fluctuations in total charge. They determine the value of 3.5 pro- 

 tonic units for the root-mean-square charge fluctuation of a molecule of BSA 

 in isoionic solutions. This value is in excellent agreement with value 3.4 which 

 has been calculated from the titration date of Tanford. Similar measurements, 

 to be reported later, have been carried out on human serum mercaptalbumin 

 and bovine serum mercaptalbumin. The results may be quantitatively inter- 

 preted by means of the charge fluctuation theory. 



Kirkwood (1955) has recently used the concept of interaction through charge 

 fluctuations to provide an interesting explanation for the participation of the 

 protein moiety of an enzyme molecule in the mechanism of hydrolytic enzy- 



