Dielectric Relaxation of Biological Water ² Nilashis Nandi and Biman Bagchi* ,‡ Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India 560012 ReceiVed: June 9, 1997; In Final Form: September 30, 1997 X Dielectric relaxation and NMR spectrum of water in biological systems such as proteins, DNA, and reverse micelles can often be described by two widely different time constants, one of which is in the picosecond while the other is in the nanosecond regime. Although it is widely believed that the bimodal relaxation arises from water at the hydration shell, a quantitative understanding of this important phenomenon is lacking. In this article we present a theory of dielectric relaxation of biological water. The time dependent relaxation of biological water is described in terms of a dynamic equilibrium between the free and bound water molecules. It is assumed that only the free water molecules undergo orientational motion; the bound water contribution enters only through the rotation of the biomolecule, which is also considered. The dielectric relaxation is then determined by the equilibrium constant between the two species and the rate of conversion from bound to free state and vice versa. However, the dielectric relaxation in such complex biomolecular systems depends on several parameters such as the rotational time constant of the protein molecule, the dimension of the hydration shell, the strength of the hydrogen bond, the static dielectric constant of the water bound to the biomolecule, etc. The present theory includes all these aspects in a consistent way. The results are shown to be in very good agreement with all the known results. The present study can be helpful in understanding the solvation of biomolecules such as proteins. I. Introduction Many biological systems such as proteins and enzymes are inactive without water. For a complete knowledge of the function of such systems, an understanding of the structure and dynamics of the aqueous environment surrounding the concerned biomolecule is thus essential. The properties of water molecules in the vicinity of a biomolecule differ appreciably from those of bulk water. 1-4 The water molecules enclosed within the solvation shell present in the immediate vicinity of the biomol- ecule are termed “biological water”. The dynamics and structure of biological water near proteins, DNA, and in reverse micelles have been the subject of intense research over several decades. 1-28 Dielectric spectroscopy and nuclear magnetic resonance spec- troscopy (NMR) are the two most extensively used techniques to understand the interaction of water with proteins. Both of these two methods essentially probe molecular orientational relaxation. It is now known that the hydration shell surrounding a protein molecule comprises different types of water. 1-3 Few water molecules remain rigidly bound to the protein for a very long time. In the immediate vicinity of the surface of the protein, there are water molecules that experience much faster rotational and translational diffusion rate than the water molecules directly bound to the biomolecule. Thus, biological water is believed to consist of two kinds of water molecules, usually referred to as “bound” and “free”, depending on their momentary states of existence. There is, of course, dynamic exchange between the two species. On the basis of the experimental studies of the dynamic behavior of water near biomolecules, it has been established that the frequency dependent dielectric constant of the combined biomolecule-water system can be written as a sum of four dispersion terms as follows: 5a,8k with ǫ ∞ denoting the infinite frequency dielectric constant of bulk water, ∆ i the relative weight of a given relaxation type, and τ i is the respective time constant. ∆ 1 and τ 1 are the relative weight and time constant associated with the orientational motion of the biomolecule. For a typical protein solution such as the myoglobin-water system, τ 1 is about 74 ns. 5,8 (∆ 2 , τ 2 ) and (∆ 3 , τ 3 ) correspond to the relaxation of biological water associated with the protein. Although these two relaxation phenomena are quite different, they have approximately equal weights. The relaxation times are about τ 2 ) 10 ns and τ 3 ) 40 ps, respectively. This behavior is nearly universal and is typically referred to as the bimodality of the reorientational response of biological water. In Table 1, we show a few examples of the bimodal nature of reorientational dynamics of biological water as observed by dielectric relaxation and NMR studies. Finally, ∆ 4 corresponds to the relative weight of the rotational relaxation of bulk water, and τ 4 is the corresponding relaxation time equal to 8.3 ps. This bimodal behavior is typical and has been observed with DNA, with water enclosed within the cavities of cyclodextrin, and also in the aqueous medium of reverse micelles. Many workers have reviewed the results of dielectric measurements on protein-water systems. 1-3 The earliest measurement of the dielectric properties of protein-water system was made by Oncley 6 who concluded that the carboxy- hemoglobin molecule is associated with a rotational relaxation time constant of 84 ns. Later, Buchanan et al. 7a and Haggis et al. 7b carried out measurements at higher frequencies and found that about one-third of the total hydration sphere is bound tightly to the water molecule and does not contribute to the dielectric dispersion. The most detailed characterization of a protein- water solution has been provided by Grant et al. 8 who showed * To whom correspondence should be addressed. E-mail: bbagchi@ sscu.iisc.ernet.in. FAX: 91-80-3341683; 91-80-3311310. ² Dedicated to our teacher Professor Mihir Chowdhury on his 60th birthday. ‡ Also at Jawharlal Nehru Center for Advanced Scientific Research, Bangalore, India. X Abstract published in AdVance ACS Abstracts, November 15, 1997. ǫ(ω) ) ǫ ∞ + ∆ 1 1 + iωτ 1 + ∆ 2 1 + iωτ 2 + ∆ 3 1 + iωτ 3 + ∆ 4 1 + iωτ 4 10954 J. Phys. Chem. B 1997, 101, 10954-10961 S1089-5647(97)01879-8 CCC: $14.00 © 1997 American Chemical Society