Dielectric inside proteins

Early theoretical attempts to examine the field inside and around the protein using X-ray structures (Johannin and Kellersohn, 1972 Hayes and Kollman, 1976) suggested that the field inside proteins can be significant but these studies did not consider the induced dipoles of the protein and, more importantly, the solvent around it, that in most cases reduce electrostatic effects by a factor of 40 The fundamental problem that prevented a proper estimate of electrostatic effects in proteins was the fact that these interactions cannot be evaluated without the knowledge of the "dielectric constant" at the protein active site. Estimating this value from studies in water is not justified and assuming a low dielectric constant for the polar environment provided by proteins is also unjustified (Warshel and Russell, 1984 King et al, 1991). The first... 

An alternative to the continuum model is to model the protein electrostatic field directly. This is normally achieved by carrying out a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment in which the active site model is treated with DFT while the rest of the protein is modelled via classical molecular mechanics (MM) [44]. The MM charges then implicitly define the dielectric inside the protein. In either event, it appears that excessive charges are to be avoided. That is, the quantum mechanical part of the model system will normally not have an overall charge greater in magnitude than one. 

Here, T = eelectrostatic potential, with representing the electrostatic potential, kg the Boltzmann s constant, T the temperature, and e the elementary charge co is the permeability of free space, while Ed is the dielectric constant within the volume element dv. We take Ed as 2.0 inside the membrane and the protein and as 80.0 in the aqueous solution. The integration in Eq. (3) is performed over the volume V of the entire space. 

However, in many cases the last term of Eq. (18) is incorrectly ignored. Another interesting problem is what dielectric constant to choose for the description of a protein. Proteins are complex molecules containing polar groups inside, so it is not likely that there is a single dielectric constant that can be used for describing the Coulomb interactions inside a protein. Calculations of solvation energies, however, show that reasonable results are obtained when the ss constant is somewhere between 2 and 4. 

If the dielectric constant of the aqueous phase enclosed inside the heme binding site of apomyoglobin can be measured and the dielectric constant of the protein is deduced from that data (26), there is no reason why the same procedure cannot be applied to membrane proteins. If the geminate recombination of proton-excited pyranine anion can be monitored in the anion channel of the Pho-E protein (27), the interior of other channels can also be investigated. 

Here, the notation A app indicates that the local field, at the site of the chromo-phore (i.e. inside the protein), is unknown, and is augmented, with respect to the applied field, by dielectric enhancement. The apparent dipole moment changes are therefore overestimated, by a factor of 1.3 - 1.7 at 77 Kwith respect to the intrinsic ones.l ... 

Furthermore, the assumption of a uniform dielectric constant for all water structures interacting with protein-based machines and materials conceals the occurrence of competition for hydration between hydrophobic groups and charged groups. In the past there has been the practice of using a dielectric constant of 80 (that for bulk water) up to the surface of the protein and then decreasing the dielectric constant to 5 or less when within the protein. However, what Solomonic wisdom suffices for choice of dielectric constant to be used for ion-pair formation within the tortuous surfaces with clefts of varying shapes from acute to obtuse. As seen in Chapter 8, these clefts may reside inside the protein-based machine, as found in ATP synthase, or outside the protein-based machine, as occurs for the myosin II motor. 

Substitution of water by deuterium oxide is known to affect both the functional properties and the conformational stability of biomolecules (1). The interpretation of such kind of effects is difficult, in view of the variety of phenomena involved. These are essentially of two types i) effects due to the replacement of hydrogen by deuterium inside the protein (in polypeptides, the deuterium bond appears to be stronger and longer than hydrogen bond (2,3) ), ii) solvent effects (e.g., the dielectric constant of D2O is lower than that of H2O, hydrophobic interactions appear to be stronger in... 

---