Born energy

Using liposomes made from phospholipids as models of membrane barriers, Chakrabarti and Deamer [417] characterized the permeabilities of several amino acids and simple ions. Phosphate, sodium and potassium ions displayed effective permeabilities 0.1-1.0 x 10 12 cm/s. Hydrophilic amino acids permeated membranes with coefficients 5.1-5.7 x 10 12 cm/s. More lipophilic amino acids indicated values of 250 -10 x 10-12 cm/s. The investigators proposed that the extremely low permeability rates observed for the polar molecules must be controlled by bilayer fluctuations and transient defects, rather than normal partitioning behavior and Born energy barriers. More recently, similar magnitude values of permeabilities were measured for a series of enkephalin peptides [418]. 

Dielectric Constant Low dielectric in hydrocarbon zone not suitable for ion solvation, Born energy effects Chemical/Electrostatic... 

Another possible treatment [9] is to define the Born energy in term of a local dielectric constant e(x) ... 

When the interface is charged, the Poisson-Boltzmann equation predicts stronger fields and higher ionic concentrations in the vicinity of the surface, therefore a dielectric constant smaller than in the bulk, and the local Born energy indicates that the ions are repelled by the interface. However, a neutral surface depleted of ions should have a dielectric constant larger than the bulk and the ions should be attracted, not repelled by such an interface. Therefore, other interactions should be included to explain the ion depletion near a neutral surface. 

A simple treatment, which circumvents this difficulty, uses an alternative approximate treatment of the image forces. Because the Born energy of ions in bulk water is given by... 

Both the image force and the local approximation for the Born energy approaches account for the ion hydration, through the macroscopic dielectric constant of water, assumed a continuous dielectric. Because none of them could explain satisfactorily the distribution of ions near a water—air interface, it was suggested that another effect plays the main role, namely the van der Waals interactions between ions and the rest of the system. These ion-dispersion forces can be described by an equation of the type10... 

In the region where the water density is lower than that of the bulk, the dielectric constant is expected to be smaller than in the bulk, and a Spaarnay-like local approximation of the Born energy of ions is given by12... 

AGs is also referred to as the free energy of -> solvation of the ions in the respective medium. The Born energy (AGs) required to transfer one mole of ions from one phase with dielectric constant 1 into another phase of dielectric constant 2, is given by [ii] ... 

The calculated values of the solvation free energy for this protein are 239.8 kcal/mol, -142.5 kcal/mol, -620.6 kcal/mol and -523.3 kcal/mol for gc, gi, gB and A (g— m), respectively. In the hydrophobic part of the solvation free energy of this protein, gc and gi compensate each other. In the solvation free energy of the protein, the Born energy is much larger than other terms, because hydrophilic residues are ionized in water. The Bom energy calculated here is the preliminary one, so more investigation is needed. 

Combining Equations 7.10 through 7.12 and summing the individual Born energies, we have... 

The hydration energy is experimentally accessible (to within 3-4 kT at 300 K) the cavity term is a Born energy, determined by the ion s cavity radius in the channel and the stabilization energy is computed using standard perturbation methods [9]. 

Krishtalik s attempt to include the field of the protein polar part in a spherical model of the protein [16] has not reproduced any catalytic effects. All the intraglobular field in chymotrypsin reported in Ref. [16] is extremely small except for the field from Asp 102, which is a part of the reactant system rather than a source for a field on this system. Hence the resultant large Asp"ImH ion-pair stabilization in a low dielectric medium is an artifact of neglecting the Born energy of transferring the ions from water to the hypothetical low dielectric protein [19]... 

A strongly attractive but short-range term F vdw, which nevertheless exhibits an energy well since, at distances of a few nanometres, it becomes strongly repulsive (the Born energy). 

The interatomic distance R is of the order of 3 A or 6B. The repulsion energy at this distance if the charge is 1 (for example, Li+, Na+, or K+) is thus 1/6 H in vacuum and, since 1 H is equal to 27.2 eV, the attractive potential energy is about 5 eV or 500 kJ/ mol. This is an enormously large number. In the next section, we will calculate the enthalpy gain, the Born energy, when ions are placed in polarizable solvents. 

Figure 22.12 Transferring an ion from one medium to another—vacuum to soivent in this case—can be modeiled with Born energies in a thermodynamic cycle. We compute here only the electrostatic free energy AG = ziGi.i. 

The Born energy is the energy cost of transferring an ion from a medium having dielectric constant Di to a medium having dielectric constant Dj. 

Optical Born energy of the electron. This contribution is due to the interaction of the electron with the second layer of solvent molecules. Apparently, this type of interaction is quite complicated to evaluate hence this second layer is considered to be a continuum. This means that the electron derives energy from the continuum due to optical Born charging according to... 

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