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Klgn
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Untersuchte Arbeit:
Seite: 65, Zeilen: 1 ff. (entire page)
Quelle: Anézo 2003
Seite(n): 147, 148, 150, Zeilen: 147:10-14; 148:1-6; 150:1-11
The free energy profile, also called potential of mean force, is obtained upon integration of the constraining force across the membrane:

\Delta G(z)=\int_{0}^{z}\left \langle F_z (z) \right \rangle dz (2.21)

where <Fz(z)> is the z-component of the force imposed on the solute, averaged over the constraint ensemble. This force can be monitored during a constrained simulation as follows: the constrained [sic] is imposed by resetting the z-coordinate of the center of mass of the solute molecule each step to its initial, constrained value z0 , and the force needed to keep the constraint on the solute is directly proportional to the distance over which the z coordinate is reset. As in umbrella sampling method, the solute molecule is free to rotate around its center of mass and free to diffuse in the plane of the membrane.

The advantage of the average force method over the umbrella sampling approach is that the local diffusion coefficient of the solute in the bilayer can be computed simultaneously by applying the force autocorrelation method. This method, generally used to study diffusion over free energy barriers, is based on the fluctuation-dissipation theorem [73]. This theorem relates a time dependent friction function ζ(t) to the autocorrelation function of a Gaussian random force f(t) with zero average:

\zeta(t)=\frac{\left \langle f(t)f(0) \right \rangle}{R_c T} (2.22)

The random force f(t) can be identified with ΔFz(z,t), the deviation of the instaneous [sic] force from the average force acting on the constrained solute at a position z along the bilayer normal:

\Delta F_z(z,t)=F_z(z,t)-\left ( \left \langle F_z(z,t) \right \rangle \right ) (2.23)


73. Kubo, R. Rev. Mod. Phys. 1966, 29, 255.

[page 147]

The free energy profile, also called potential of mean force, is obtained upon integration of the constraining force across the membrane:

\Delta G(z)=\int_{0}^{z}\left \langle F_z (z) \right \rangle \cdot \mathrm{d}z (5.7)

where \left \langle F_z (z) \right \rangle is the mean force on the constraint (or, more precisely, the z-component of the force imposed on the solute, averaged over the constraint ensemble). This force can be

[page 148]

monitored during a constrained simulation as follows: the constraint is imposed by resetting the z-coordinate of the COM of the solute molecule each step to its initial, constrained value z0, and the force needed to keep the constraint on the solute is directly proportional to the distance over which the z-coordinate is reset. This procedure is schematically described in Figure 5.5. As in the umbrella sampling method, the solute molecule is free to rotate around its COM and free to diffuse in the plane of the membrane.

[page 150]

The advantage of the average force method over the umbrella sampling approach is that the local diffusion coefficient of the solute in the bilayer can be computed simultaneously by applying the force autocorrelation method. This method, generally used to study diffusion over free energy barriers [181], is based on the fluctuation-dissipation theorem [182]. This theorem relates a time-dependent friction function ξ(t) to the autocorrelation function of a Gaussian random force f(t) with zero average:

\zeta(t)=\frac{\left \langle f(t) \cdot f(0) \right \rangle}{R_c T} (5.8)

The random force f(t) can be identified with ∆Fz(z,t), the deviation of the instantaneous force from the average force acting on the constrained solute at a position z along the bilayer normal:

\Delta F_z(z,t)=F_z(z,t)-\left ( \left \langle F_z(z,t) \right \rangle \right ) (5.9)


[181] B. Roux and M. Karplus. J. Phys. Chem., 95:4856–4868, 1991.

[182] R. Kubo. Rev. Mod. Phys., 29:255–284, 1966.

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