Free energies of pore formation

Wohlert et al. [80] determined the free energy of pore formation in an atomistic DPPC bilayer using the pore radius as the reaction coordinate. From this reaction coordinate, they were able to derive the free energy of pore... 

Figure 4 The free energy of pore formation in a DPPC bilayer. The dashed line is a quadratic function, while the dotted line is a fit to a model of pore expansion with a line tension of 40 pN, and is close to linear (Adapted from ref. 78 courtesy of O. Edholm).

Tolpekina, T.V., den Otter, W.K., Briels, W.J. Nucleation free energy of pore formation in an amphiphilic bilayer studied by molecular dynamics simulations. J. Chem. Phys. 2004, 121, 12060-6. 

Using a similar approach, Notman et al. [81], determined the free energy for pore formation in bilayers composed of ceramide, as a model for the stratum corneum of the skin, both in the presence and in the absence of DMSO. Without DMSO, the bilayer was in the gel phase, and interestingly, a hydrophobic pore was observed with a high free-energy barrier ( 60 kj/mol). In the presence of DMSO, the bilayer was more fluid, and the more typical hydrophilic pore was observed, with a much smaller activation energy of 20kJ/mol. This work provided a thermodynamic and structural explanation for the enhanced permeability of skin by DMSO. 

Lipid membranes are quite deformable, allowing water and head groups into their interiors when perturbed. A "water defect" is shown in Figure 1C, where water and lipid head groups enter the hydrophobic interior of only one of the bilayer leaflets. Figure ID shows a "water pore," where both leaflets are perturbed. At the molecular level, pore and defect formation are directly related to specific lipid-lipid interactions. It is important to understand the free energy required for pore formation in membranes and the effect of lipid composition on the process. In Section 3 of this chapter, we review recent MD studies of the thermodynamics of pore formation. 

We mention a few studies on polar and charged molecule-lipid interactions, as their permeation involves defect and pore formation, which involves lipid-lipid interactions. A detailed examination of small molecule-lipid interactions is beyond the scope of this chapter [74], We have shown that a large component of the free energy of small polar or charged molecule partitioning into lipid bilayers is due to the cost of forming a defect [75]. 

System with random fluxes is defined as the nonequilibrium system where the fluxes of substance, heat, etc. change randomly. One can cite numerous examples of such systems turbulent gas-liquid systems with intensive heat/mass transfer, turbulent fluids containing dispersed solids, etc. In the case of pore formation, such situation is realized when the heat fluxes change randomly because of air fluidization or mechanical mixing. All macroscopic measured parameters of stationary turbulent flows, like their pressure, temperature, excess (free) energy, entropy, etc. do not change with time, while their values and directions in different spots of the flows can vary significantly. 

The capillary condensation theory was first put forward by Zsigmondy in 1911 to explain the adsorption of gases and vapors by porous solids such as charcoals and silica gel, and to explain the adsorption-desorption hystersic in Type IV isotherms. The theory postulates that, in addition to the formation of layers, the adsorbate gas or vapor condenses in the small capillary pores of the adsorbent as a result of the lowering of vapor pressure brought about by surface tension effects. The cause of this vapor pressure lowering hes in a decrease in free energy of the adsorbate molecules in fine capillary pores. 

Figure 15. Electrocapillary energy for the formation of a breakthrough pore in a thin surface oxide film on metals as a function of pore radius.7 AE E - Epzc, where Epzc is the potential-of-zero charge of the film-free metal. Al is the activation banier for the formation of a breakthrough pore and r is its critical radius. M, metal OX, oxide film EL, electrolyte solution, h a 2 x I O 9 m, am = 0.41 J m-2, a = 0.01 J m-2, ACj= 1 F m"2. a, AE=0.89 V b, AE=0.9 V c,A = 1.0 V. (From N. Sato, J. Electmckem. Soc. 129,255,1982, Fig. 2. Reproduced by permission of The Electrochemical Society, Inc.)...

The other major limitation of membrane simulations is the time and length scale we are able to simulate. We are currently able to reach a microsecond, but tens to hundreds of nanosecond simulations are more common, especially in free energy calculations. The slow diffusion of lipids means we are not able to observe many biologically interesting phenomena using equilibrium simulations. For example, we would not observe pore formation in an unperturbed bilayer system during an equilibrium simulation, and even pore dissipation is at the limits of current computational accessibility. 

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