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Typus
Verschleierung
Bearbeiter
Klgn
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Untersuchte Arbeit:
Seite: 64, Zeilen: 1 ff. (entire page)
Quelle: Anézo 2003
Seite(n): 145, 147, Zeilen: 145:4ff; 147:1-9
[Applied to the permeation process of a solute molecule across a lipid bilayer, the umbrella sampling method enables one to compute the free energy profile along the] bilayer normal (taken as z-direction). In a series of independent simulations, the solute molecule is restrained at various depths in the bilayer by means of a biasing potential, helping to achieve a more efficient sampling. The biasing umbrella potential (Vumb) is usually a harmonic potential of this form:

V_{umb}(z)=\frac{k(z-z_o)^2}{2} (2.19)

where k is force constant, z is the z-coordinate of the center of mass of the solute, and z0 is the center of the umbrella potential. k defines the width of the umbrella potential: high values of k correspond to narrow potential, i.e. to very restraining potentials. Note that only the z-coordinate of the solute center of mass is restrained, which means that the solute is free to rotate in all three directions around its center of mass and also free to diffuse in the plane perpendicular to the bilayer normal. For a given window, the free energy ΔG can be derived from the probability distribution ρumb of the solute in the membrane in the presence of the umbrella potential according to the relation:

\Delta G(z)=-R_c T \ln \rho_{umb}(z)+C-V_{umb}(z) (2.20)

where C is an integration constant.

Average force method on constrained particle. An alternative method to compute the free energy profile across the membrane is the average force method on constrained particle. In this approach, the solute molecule is constrained at a given depth in the membrane and the force needed to keep the constraint is calculated. The norm of this force corresponds to the derivative (or slope) of the free energy at a given depth in the membrane. Repeating this constraining procedure at different depths in the membrane enables one to construct the free energy profile across the membrane. This method can be viewed as a limiting case of the umbrella sampling method, i.e. with an infinite force constant.

[page 145]

Applied to the permeation process of a solute molecule across a lipid bilayer, the umbrella sampling method enables one to compute the free energy profile along the bilayer normal (taken as the z-direction). In a series of independent simulations, the solute molecule is restrained at various depths in the bilayer by means of a biasing potential, helping to achieve a more efficient sampling. The biasing umbrella potential (Vumb) is usually a harmonic potential of this form:

V_{umb}(z)=\frac{1}{2} \cdot k \cdot (z-z_o)^2 (5.5)

where k is a force constant, z the z-coordinate of the center-of-mass (COM) of the solute, and z0 the center of the umbrella potential. k defines the width of the umbrella potential: high values of k correspond to narrow potentials, i.e. to very restraining potentials. Note that only the z-coordinate of the solute COM is restrained, which means that the solute is free to rotate in all three directions around its COM and also free to diffuse in the plane perpendicular to the bilayer normal. For a given window, the free energy ∆G can be derived from the probability distribution ρumb of the solute in the membrane in the presence of the umbrella potential according to the relation:

\Delta G(z)=-R_c T \ln \rho_{umb}(z)+C-V_{umb}(z) (5.6)

where C is an integration constant. [...]

[page 147]

Average force method on constrained particle An alternative method to compute the free energy profile across the membrane is the average force method on constrained particle. In this approach, the solute molecule is constrained at a given depth in the membrane and the force needed to keep the constraint is calculated. The norm of this force corresponds to the derivative (or slope) of the free energy at a given depth in the membrane (see Figure 5.4 for clarity). Repeating this constraining procedure at different depths in the membrane enables one to construct the free energy profile across the membrane. This method can be viewed as a limiting case of the umbrella sampling method, i.e. with an infinitely narrow restraining potential.

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(Klgn), WiseWoman

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