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Umbrella sampling is a means of "bridging the gap" in this situation.
Umbrella sampling is a related free energy method.
It is related to umbrella sampling in computational physics.
First equilibrium folding simulations were done using implicit solvent model and umbrella sampling.
The factor C(t) at this specific time can be computed with a combination of path sampling and umbrella sampling.
Through umbrella sampling, all of the system's configurations-both high-energy and low-energy-are adequately sampled.
Umbrella sampling is used to move the system along the desired reaction coordinate by varying, for example, the forces, distances, and angles manipulated in the simulation.
Metadynamics has the advantage, upon methods like adaptive umbrella sampling, of not requiring an initial estimate of the energy landscape to explore.
Alternatives to umbrella sampling for computing potentials of mean force or reaction rates are free energy perturbation and transition interface sampling.
Series of umbrella sampling simulations can be analyzed using the weighted histogram analysis method (WHAM) or its generalization.
MTD closely resembles a number of recent methods such as adaptively biased molecular dynamics, adaptive reaction coordinate forces and local elevation umbrella sampling.
Subtleties exist in deciding the most computationally efficient way to apply the umbrella sampling method, as described in Frenkel & Smit's book Understanding Molecular Simulation.
Often PMF simulations are used in conjunction with umbrella sampling because typically the PMF simulation will fail to adequately sample the system space as it proceeds.
A popular method of computing PMF is through the weighted histogram analysis method (WHAM), which analyzes a series of umbrella sampling simulations.
Umbrella sampling is a technique in computational physics and chemistry, used to improve sampling of a system (or different systems) where ergodicity is hindered by the form of the system's energy landscape.
The umbrella sampling technique advanced by Torrie and Valleau for estimating free energies was followed in this work for calculating the excess Helmholtz free energy for the Lennard–Jones (6:12) fluid at 48 points.
For this purpose, the high-resolution structure of the gramicidin A dimer is embedded in a dimyristoylphosphatidylcholine bilayer, and the potential of mean force of a K+ ion is calculated alson the channel axis using the umbrella sampling method.
To do this precisely one would have to already know the integral, but one can approximate the integral by an integral of a similar function or use adaptive routines such as stratified sampling, recursive stratified sampling, adaptive umbrella sampling or the VEGAS algorithm.