The Influence of Dipole Moment Fluctuations on the Dielectric Increment of Proteins in Solution Author(s): John G. Kirkwood and John B. Shumaker Source: Proceedings of the National Academy of Sciences of the United States of America, Vol. 38, No. 10 (Oct. 15, 1952), pp. 855-862 Published by: National Academy of Sciences Stable URL: http://www.jstor.org/stable/88714 Accessed: 01/10/2008 17:57 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=nas. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact
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VOL. 38, 1952
CHEMISTRY:
KIRKWOOD AND SHUMAKER
855
Massachusetts Institute of Technology, June, 1952. It is a pleasure to acknowledge the guidance and encouragement of Prof. F. O. Schmitt in this work. t The author is indebted to the Commonwealth Scientific and Industrial Research Organization, Melbourne, Australia, for a Senior Studentship during the tenure of which much of the work described here was carried out. The investigation was supported in part by a grant from the Trustees under the wills of Charles A. King and Marjorie King. 1 Hall, C. E., Jakus, M. A., and Schmitt, F. 0., J. App. Phys., 16, 459 (1945). 2 Bear, R. S., J. Am. Chem. Soc., 66, 2043 (1944). Cannan, Cecily, M. M., Ph.D. Thesis, MIT, June, 1950. 3 However, the small angle diffraction pattern of intact clam muscle shows, in addition to the paramyosin reflections, a set of reflections corresponding to the so-called "myosin" net. The latter reflections are relatively strong in the red and weak in the white portions of the muscle, an observation in accord with the fact that the white portions contain a larger proportion of paramyosin. Furthermore, it seems likely that the treatment used in preparation of purified suspensions of paramyosin fibrils (maceration in dilute salt solution and repeated centrifugation) results in the elimination of the material giving rise to the "myosin" net reflections (presumably actomyosin). 4 Highberger, J. H., Gross, J., and Schmitt, F. O., PROC.NATL. ACAD. SCI., 37, 286, 1951.
THE
OF DIPOLE
INFLUENCE ON
THE
DIELECTRIC
PROTEINS
IN
MOMENT INCREMENT
FLUCTUATIONS OF
SOL UTION*
BY JOHN G. KIRKWOOD AND JOHN B. SHUMAKERt STERLING
CHEMISTRY
LABORATORY,
YALE
UNIVERSITY,
NEW
HAVEN,
CONNECTICUT
Communicated July 23, 1952 Proteins in solution are known to produce' remarkably large increments in the dielectric of water. constant These increments have been conattributed to molecular electric ventionally large permanent dipole mowhich are partially oriented an external An electric field. ments, by alternative mechanism of dielectric of conmacromolecules polarization is taining a large number of loosely bound ions, for example, protons, provided by the migration of the small ions within the molecule under the action of the external field. For proteins, containing a number of neutral and negatively and -COO-, to which charged basic sites, such as -NH' protons are bound, this mechanism might be especially significant. Except in highly acid solutions, the number of basic sites generally exceeds the so that there exist average number of protons bound to the molecule, of the protons, differing little in free energy. many possible configurations in the configuration Fluctuations of the protons should be associated with a non-vanishing mean square electric dipole moment, even if the mean moment were zero. In the present article we shall investigate permanent
856
CHEMISTRY: KIRKWOOD AND SHUMAKER
PROC.N. A. S.
of protein molecules the contribution to the dielectric polarization arising in charge and configuration of mobile protons in the from fluctuations of many proteins molecule. We shall show that the dielectric increments for by this mechanism of polarization can be entirely accounted without of permanent electric moments. the existence Fluctuations postulating in the charge and configuration of mobile protons also make an important to the force between protein molecules. contribution A theory of intermolecular forces of this new type will be presented in a later article. the theories of Onsager2 For liquid solutions of high dielectric constant, conrelation between the dielectric and Kirkwood3 lead to the following stant D and the molar polarizations Pj of the several components,
D
1+9
4rN P,
P 23 [aj + (+yj)av./3kTl
(1)
and {(2)av. is the mean square of where aj is the optical polarizability in the orientation Correlations the dipole moment of a molecule of type j. the of will be in treated of neighboring Kirkwood, molecules, theory in for molecules an here, protein adequate approximation neglected of moment a mean For the solution. protein square dipole aqueous of its mobile protons, we shall molecule, averaged over-all configurations write, (=
(2)av.
2
=
+
(l)av.2
(((
-
A/2
( U)bv.)aV
(2)
where ({t)av- is the mean permanent dipole moment and A,u2 is the dipole in charge and configuraassociated with fluctuations moment fluctuation tion of the mobile protons. v basic groups of intrinsic We consider a protein molecule containing charges, ei, situated at points Ri relative to the molecule center of mass. variable Xi for each basic group to be unity We define a proton occupation The electric when that group is occupied by a proton and zero otherwise. A/I2 may moment Ut of the molecule, its mean value (t )av. and fluctuation then be expressed
in the form,
U = E (es + exi)Ri i=
( i)av. =
1
Z
i=
A/2 = e2
1
(ej + e (xi)Y.)Ri E
i,k =
[(XiXk)av. -
(Xi)av. (