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Permeation of Organometallic Compounds through Phospholipid Membranes

von Dr. Raycho Yonchev

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$R=\frac{1}{P}=\int_{0}^{d}\frac{\exp(\Delta G(z)/R_cT)}{D(z)}dz$ (2.18)

Permeability is therefore a rate process that contains contributions from both an equilibrium (partitioning) and non-equilibrium (transverse diffusion) step. Partitioning into the membrane can be well described by the free energy profile across the membrane, i.e. the free energy barrier to be overcome by the solute to permeate through the membrane. The challenge is thus to determine the free energy barrier as well as the local diffusion coefficient of the solute in the membrane. The permeability coefficient can be then obtained by numerical integration of Equation (2.18).

II.3.3 Defect model

The formation of transient aqueous pores produced by thermal fluctuation within the membrane has been shown to contribute to the permeability of the bilayer to ions, water, and small neutral molecules [67,68]. As is known, the bilayer membrane represents a two dimensional liquid crystal with a rather high lateral mobility of the lipid components; the large fluctuations in the bilayer structure may give rise to transient defects. Two types of through-going pores, namely, with hydrophilic or hydrophobic lateral surface, can be distinguished [69]. During the formation of a transient hydrophobic defect, the lipid molecules are moved apart by thermal fluctuations, so that the membrane hydrophobic core is penetrated by the aqueous bulk phase, resulting in the formation of a pore. There are two possibilities for the development of such a pore. One of them is the collapse of the pore, with the simultaneous return of the lipid molecules to their original positions. The other possibility involves the reorientation of the lipid molecules resulting in the covering of the inner surface of the pore by the polar lipid headgroups, i.e. an inverted pore is formed. In both hydrophobic and hydrophilic defects, pore formation results from dynamic properties of the lipid bilayer, and the equilibrium pore distribution is relatively constant over time. By passing through such hydrated defects, the permeating molecule can avoid the high-energy barrier associated with partitioning into the hydrophobic [membrane interior.]

67. Weaver, J. C.; Powell, K. T.; Mintzer, R. A. Bioelectrochem. Bioenerg. 1984, 12, 405.

68. Nagle, J. F.; Scott, H. L. Biochim. Biophys. Acta 1978, 513, 236.

69. Abidor, I. G.; Arakelyan, V. B.; Chernomordik, L. V.; Chizmadzhev, Y. A.; Pastuschenko, V. F.; Tarasevich, M. R. Bioelectrochem. Bioenerg. 1979, 6, 37.

[page 141]

$R=\frac{1}{P}=\int_{0}^{d}\frac{\exp(\Delta G(z)/R_cT)}{D(z)} \cdot \mathrm{d}z$ (5.4)

Permeability is therefore a rate process that contains contributions from both an equilibrium (partitioning) and a non-equilibrium (transverse diffusion) step. Partitioning into the membrane can be well described by the free energy profile across the membrane, i.e. the free energy barrier to be overcome by the solute to permeate through the membrane. The challenge is thus to determine the free energy barrier as well as the local diffusion coefficient of the solute in the membrane. The permeability coefficient can be then obtained by numerical integration of Equation 5.4.

[page 142]

5.2.1.3 Defect model

The formation of transient aqueous pores produced by thermal fluctuation within the membrane has been shown to contribute to the permeability of the bilayer to ions, water, and small neutral molecules [169,170]. As is known, the bilayer membrane represents a two-dimensional liquid crystal with a rather high lateral mobility of the lipid components; the large fluctuations in the bilayer structure may give rise to transient defects. Two types of through-going pores, namely, with hydrophilic or hydrophobic lateral surface (see Figure 5.1), can be distinguished [171]. During the formation of a transient hydrophobic defect, the lipid molecules are moved apart by thermal fluctuations, so that the membrane hydrophobic core is penetrated by the aqueous bulk phase, resulting in the formation of a pore. There are two possibilities for the development of such a pore. One of them is the collapse of the pore, with the simultaneous return of the lipid molecules to their original positions. The other possibility involves the reorientation of the lipid molecules resulting in the covering of the inner surface of the pore by the polar lipid headgroups, i.e. an inverted pore is formed. In both hydrophobic and hydrophilic defects, pore formation results from dynamic properties of the lipid bilayer, and the equilibrium pore distribution is relatively constant over time [172]. By passing through such hydrated defects, the permeating molecule can avoid the high-energy barrier associated with partitioning into the hydrophobic membrane interior.

[169] J. F. Nagle and H. L. Scott. Biochim. Biophys. Acta, 513:236–243, 1978.

[170] J. C. Weaver, K. T. Powell, and R. A. Mintzer. Bioelectrochem. Bioenerg., 12:405–412, 1984.

[171] I. G. Abidor, V. B. Arakelyan, L. V. Chernomordik, Yu. A. Chizmadzhev, V. F. Pastushenko, and M. R Tarasevich. Bioelectrochem. Bioenerg., 6:37–52, 1979.

[172] A. G. Volkov, S. Paula, and D. W. Deamer. Bioelectrochem. Bioenerg., 42:153–160, 1997.

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