Protein dielectric properties

We have recently started to explore a type of calculations in which DFT treatment of the quantum mechanical (QM) site is combined with either continuum electrostatics treatment of the protein, or with microscopic molecular mechanics/dynamics treatment of the protein, or with a combined molecular mechanics and continuum electrostatics treatment of the protein in a truly multiscale type of calculations. All these calculations have a spirit of QM/MM (quantum mechanics combined with molecular mechanics) method, which is currently in wide use in protein calculations. The DFT and the solvation energy calculations are performed in a self-consistent way. The work aims at both improving the QM part of p/ calculations and the MM or electrostatic part, in which of the protein dielectric properties are involved. In these studies, an efficient procedure has been developed for incorporating inhomogeneous dielectric models of the proteins into self-consistent DFT calculations, in which the polarization field of the protein is efficiently represented in the region of the QM system by using spherical harmonics and singular value decomposition techniques [41,42]. 

The charge of a number of proteins has been measured by titration. The early experimental work focused on the determination of charge as a function of pH later work focused on comparing the experimental and theoretical results the latter obtained from the extensions of the Tanford-Kirkwood models on the electrostatic behavior of proteins. Ed-sall and Wyman [104] discuss the early work on the electrostatics of polar molecules and ions in solution, considering fundamental coulombic interactions and accounting for the dielectric properties of the media. Tanford [383,384], and Tanford and Kirkwood [387] describe the development of the Tanford-Kirkwood theories of protein electrostatics. For more recent work on protein electrostatics see Lenhoff and coworkers [64,146,334]. 

Single-step perturbation methods have also been applied to electrostatic processes. One study probed the dielectric properties of several proteins at a microscopic level [41,42], Test charges were inserted at many different positions within or around each protein, and a dielectric relaxation free energy was computed, which is related to a microscopic dielectric susceptibility (see Sect. 12.3). 

The properties of membranes commonly studied by fluorescence techniques include motional, structural, and organizational aspects. Motional aspects include the rate of motion of fatty acyl chains, the head-group region of the phospholipids, and other lipid components and membrane proteins. The structural aspects of membranes would cover the orientational aspects of the lipid components. Organizational aspects include the distribution of lipids both laterally, in the plane of the membrane (e.g., phase separations), and across the membrane bilayer (phospholipid asymmetry) and distances from the surface or depth in the bilayer. Finally, there are properties of membranes pertaining to the surface such as the surface charge and dielectric properties. Fluorescence techniques have been widely used in the studies of membranes mainly since the time scale of the fluorescence lifetime coincides with the time scale of interest for lipid motion and since there are a wide number of fluorescence probes available which can be used to yield very specific information on membrane properties. 

The solubility of a protein in an aqueous solution relies on the distribution of the hydrophilic and hydrophobic groups on its surface. Protein precipitates are formed by the aggregation of protein molecules caused by changes in pH, ionic strength, or solvent dielectric properties, as well as by the addition of a miscible organic solvent, other inert solvents, and... 

B. Protein Solutions. The dielectric properties of proteins and nucleic acids have been extensively reviewed (10, 11). Protein solutions exhibit three major dispersion ranges. One occurs at RF s and is believed to arise from molecular rotation in the applied electric field. Typical characteristic frequencies range from about 1 to 10 MHz, depending on the protein size. Dipole moments are of the order of 200-500 Debyes and low-frequency increments of dielectric permittivity vary between 1 and 10 units/g protein/100 ml of solution. The high-frequency dielectric permittivity of this dispersion is lower than that of water because of the low dielectric permittivity of the protein leading to a high-frequency decrement of the order of 1 unit/g protein/... 

At microwave frequencies the dielectric properties of tissues are dominated by the water relaxation centered near 20 GHz. The magnitude of this water dispersion in tissues is typically diminished by some 20 dielectric units due to the proteins which displace a corresponding volume of water. 

The dielectric properties of tissues and cell suspensions will be summarized for the total frequency range from a few Hz to 20 GHz. Three pronounced relaxation regions at ELF, RF and MW frequencies are due to counterion relaxation and membrane invaginations, to Maxwell-Wagner effects, and to the frequency dependent properties of normal water at microwave frequencies. Superimposed on these major dispersions are fine structure effects caused by cellular organelles, protein bound water, polar tissue proteins, and side chain rotation. 

Shablakh et al. (1984) investigated the dielectric properties of bovine serum albumin and lysozyme at different hydration levels, at low frequency. Besides a relaxation attributed to the electrode—sample interface, they detected a further bulk relaxation that can be confused with a d.c. conduction effect. The latter relaxation was explained by a model of nonconductive long-range charge displacement within a partially connected water structure adsorbed on the protein surface. This model has nonconventional features that differ from the assumptions of other more widely accepted models based on Debye relaxations. 

The impedance of the skin has been generally modeled by using a parallel resistance/capacitor equivalent circuit (Fig. 4a). The skin s capacitance is mainly attributed to the dielectric properties of the lipid-protein components of the human epidermis [5,8,9,12]. The resistance is associated primarily with the skin s stratum comeum layer [5,8,9,12]. Several extensions to the basic parallel resistor/capacitor circuit model have appeared in the literature [5,8,9,13]. Most involve two modified parallel resistor/capacitor combinations connected in series [5,8,9]. The interpretation of this series combination is that the first parallel resistor/capacitor circuit represents the stratum comeum and the second resistor/capacitor parallel combination represents the deeper tissues [5,8,9]. The modification generally employed is to add another resistance, either in series and/or in parallel with the original parallel resistor/capacitor combination [8,9]. Realize that because all of these circuits contain a capacitance, they will all exhibit a decrease in impedance as the frequency is increased. This is actually what is observed in all impedance measurements of the skin [5,6,8-15]. In addition, note that the capacitance associated with the skin is 10 times less than that calculated for a biological membrane [12]. This... 

Moreover, other effects are as important as the ligands. The dielectric properties of the protein matrix are very different from those of water. It has often been argued that it behaves as a medium with a low dielectric constant (around 4 compared to 80 in water) [47,123,124]. Figure 11 shows that this gives rise to a very prominent change in the reduction potential of a blue-copper site [45]. It increases by 0.8-1 V as the site is moved from water solution to the centre of a protein with a radius of 1.5 nm (like plastocyanin) or 3.0 nm (like an azurin tet-ramer). It can also be seen that it is not necessary to move the site to the centre of the protein to get a full effect. Already at the surface of the protein, 80% of the maximum effect is seen, and when the site is 0.5 nm from the surface (as is typi-... 

It is known that the method used to truncate the interatomic interactions can have an important effect. It has been demonstrated that the dielectric properties of simulated water are a sensitive function of the extent to which the long-range electrostatic interactions are included [40]. Simulations of phospholipid membrane-water systems showed that the behavior of the water near the membrane is incorrectly described if the electrostatic interactions are truncated at too short a distance, and hot water/cold-protein behavior is observed [10]. Given the importance of the potential/force truncation, we have investigated this issue for the copper system being simulated. This has been done in terms of the same properties as were used in examining convergence. 

Takashima, S. Dielectric properties of proteins, I. Dietectric relaxation. In Physical Principles and Techniques of Protein Oiemistry, Part A, Leach, S. J. (Ed) p. 291, New York Academic Press Inc. 1969... 

Polymers such as poly(ethyleneglycol) also serve to dehydrate proteins in solution as do salts, and they alter somewhat the dielectric properties in a manner similar to organic... 

The dielectric properties of proteins reveal again a striking difference between their behavior and that of synthetic long-chain polymers. Polar molecules of the latter type, according to the calculations... 

Oncley, J.L. Studies of the Dielectric Properties of Protein Solutions. 

J. D. Ferry and J. Shack The Dielectric Properties of Protein Solu-... 

Boresch, S., Hochtl, P, and Steinhauser, O. Studying the dielectric properties of a protein solution by computer simulation, /. Phys. Chem. B, 104, 8743, 2000. 

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