46 YOS, BADE AND JEHLE 



tions of monomer units, other effects might still come into play which will 

 again substantially raise the VY term for which 1.1 kT was estimated as a 

 minimum in the case of a glycine residue. 



In comparing large with small molecules, the values of R equation (18), are 

 used which are large and small, respectively. 



In the classical region the Kirkwood-Shumaker (1952a and b) proton fluctua- 

 tions play a decisive role. Even though these are not oscillations but simply fluct- 

 uations with relaxation times of the order of 10~~* sec, their influence is like that 

 of classical polarizable oscillators. The Kirkwood-Shumaker dipolemoment 

 fluctuations may give cause to an addition to the polarizability, equal to the 

 mean square deviation of the dipole moment divided by 3 kT. Using Kirk- 

 wood's data, one may get for the square of the CI term listed in (17b) a value 

 of 65 kT, in the case of a human serum albumin molecule. In the case of smaller 

 molecules the effect is again smaller, perhaps kT for a molecule of the size of 

 an aminoacid residue. 



These Kirkwood-Shumaker forces depend on the right kind of ionic concen- 

 trations in the medium. Even if one is not near the isoelectric point, their in- 

 fluence, though not quite as strong, is still important. 



It is to be kept in mind that sialic electric charge distributions on the inter- 

 acting molecules (often causing repulsion between identical molecules) are 

 readily compensated by small ions from the medium; fluctuations of proton 

 distributions are, on the other hand, difficult to compensate when the interact- 

 ing molecules are close together. Forces due to charge fluctuations are simply 

 there. 



The classical terms of the formulae (17) refer to oscillators of low frequency. 

 The Kirkwood-Shumaker interaction includes not only fluctuations of electric 

 dipolemoments (and higher moments) due to mobile protons but also fluctua- 

 tions of electric charge due to the same protons. The Kirkwood-Shumaker in- 

 teraction energy, if one disregards the shielding effect of the Debye-Hueckel 

 atmospheres, has thus an R dependence which for large R (where the fluctuat- 

 ing charges give the predominant influence) approaches R~~. This is different 

 from the R~^ dependence of the classical oscillator interaction. A little closer 

 inspection (cf. Kirkwood-Shumaker, 1952b, p. 869, formula (13)) shows that 

 nevertheless the interaction of pairs of adjacenl molecules can be estimated by 

 simply taking as their oscillator polarizabilities the mean square deviation of 

 their dipolemoments of mobile protons divided by ikT, and using the oscillator 

 formulae. 



London Formulae Derived from the Matrix Formulae 



The formulae (la) and (Ic) are limit cases of the general matrix results 

 (7), (9), i.e. 



A^in = -y2kT 2^ tr (-k^\-i-W.„), (19) 



