Umbrella sampling simulation is a 'biased molecular dynamics' method, in which the interactions of the system are modified in order to make the 'unfavourable states' more likely to be explored by the particle. It is a commonly used enhanced sampling method in molecular dynamics and Monte Carlo simulation. It mainly solves the problem that the number of samples at high potential energy is difficult to increase, and the related physical quantities are difficult to accurately obtain. In molecular dynamics, umbrella sampling simulation method usually divides the original potential energy surface into multiple intervals, and superimposes some biases (such as harmonic potentials) to retain the sampling points as much as possible inside each interval. Finally, the weighted histogram analysis method is used to eliminate the partial sampling, and the probability distribution is connected to obtain the correct statistical results.
Figure 1. Schematic representation for the umbrella sampling simulation of different host-guest systems as a function of the center of mass (COM) - center of mass (COM) distance between the host and the guest molecules. (Paul, R.; Paul, D. S. 2020)
Since the umbrella sampling method creates a distance constraint between two structures, and the two structures are required to conduct a simulation, for example, an initial and a final structure. The only information necessary to perform umbrella sampling calculations are detailed three-dimensional structures for the complex in both an initial and a final, or target, state.
1) Prepare topology file
Obtain the coordinate file of the molecular structure to be studied, and then generate the topology.
Some systems require special consideration (such as protein-ligand complexes, membrane proteins, etc.).
2) Define the unit cell
3) Add solvent and ions
4) Energy minimization and balance
We use the steepest descent method to perform energy minimization, and then the NPT balance is conducted.
Generate a series of configurations along the reaction coordinates. Some of these configurations will be used as the initial configuration of the umbrella sampling window.
The PMF value is the difference between the highest value and the lowest value of the curve, and the PMF needs to converge to a stable value at a large centroid distance.
1) Check convergence
The general practice for deciding the equilibration time and checking convergence of umbrella sampling simulations is to perform WHAM for consecutive blocks of time and check how the free energy profile evolves.
2) Check sampling
Checking for sufficient sampling along the reaction coordinate tends to be a relatively arbitrary check that the histograms from each window look sufficiently overlapped.
3) Calculate free energy
Return the value of the free energy change along the reaction coordinate (e.g. binding free energy when reaction coordinate is distance between two molecules) from the profile.
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