Equatorial waves

General description

The PMF is a type of experiment which can be done in Monte Carlo or Molecular Dynamics simulations which examines how a system's energy changes as a function of some specific reaction coordinate parameter. For example, it may examine how the system's energy changes as a function of the distance between two residues, or as a protein is pulled through a lipid bilayer. Often PMF experiments are used in conjunction with umbrella sampling because typically the PMF experiment will fail to adequately sample the system space as it proceeds.

Mathematical description

The Potential of Mean Force of a system with N molecules is strictly the potential that gives the average force over all the configurations of all the n+1...N molecules acting on a particle j at any fixed configuration keeping fixed a set of molecules 1...n

$-{\mathrm{\nabla }}_j{w}^{(n)}=\frac{\int e^{-\beta V}(-{\mathrm{\nabla }}_{j}V)d{q}_{n+1}...d{q}_N}{\int e^{-\beta V}d{q}_{n+1}....d{q}_N}j=1,2,....,n$

Above, ${\mathrm{\nabla }}_j{w}^{(n)}$ is the averaged force, i.e. "mean force". And $w^{(n)}$ is the so-called potential of the mean force. For $n=2$, $w^{(2)}(r)$ is the average work needed to bring the two particles from infinite separation to a distance $r$. It is also related to the radial distribution function of the system, $g(r)$, by:

$g(r)=e^{-\beta w^{(2)}(r)}$

See also

• Statistical potential

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

Further reading

• McQuarrie, D. A. Statistical Mechanics.
• Chandler, D. (1987). Introduction to Modern Statistical Mechanics. Oxford University Press.

External links

• Potential of Mean force

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