Umbrella Sampling

In this tutorial, we will explore the Umbrella Sampling technique by revisiting the classical pDynamo examples (Examples 23 and 24 from the pDynamo book), which can be found in the examples directory of your pDynamo3 installation.

This tutorial is very similar to Tutorial 1, in which we performed a potential energy scan of the hydrogen bond present in blocked alanine (bALA). However, there is a fundamental difference between these two approaches.

In a potential energy scan, the reaction coordinate is systematically modified, and a geometry optimization is performed at each point. In Umbrella Sampling, on the other hand, each point along the reaction coordinate (commonly referred to as a window) corresponds to a molecular dynamics simulation, in which a harmonic biasing potential is applied to keep the system close to a predefined value of the reaction coordinate. This approach provides the statistical sampling required to compute free energy profiles.

1 - Opening System 

As in Tutorial 1, we will start from the optimized geometry of bALA.

2 - Defining the Reaction Coordinate

Open the bALA system and, using the Picking selection mode, select atoms H17 and O5.

Next, open the Umbrella Sampling window using one of the following options:

the corresponding toolbar button (purple icon); or

Simulations → Umbrella Sampling.

In the Umbrella Sampling window, click Import from Picking Selection. The selected atoms will automatically be used to define the reaction coordinate. In this example, the reaction coordinate is simply the distance between two atoms. In later tutorials, we will explore more sophisticated reaction coordinates, such as distance differences and coordinates involving multiple atoms.

3 - Configuring the Simulation

Set the simulation parameters according to Example 23 from the pDynamo tutorial:

• Step Size: 1.0 Å

• Force Constant: 20 kcal·mol⁻¹·Å⁻²

• Number of Steps (Windows): 5

• Initial Distance: 1.5 Å

The remaining parameters can be left at their default values, which are sufficient for this example.

Configure the molecular dynamics simulation with:

• 20,000 equilibration steps

• 50,000 production (data collection) steps

After reviewing the parameters, choose an output directory and run the simulation.

4 - Analyzing the Results with WHAM

Once all Umbrella Sampling windows have finished, the free energy profile can be reconstructed using the WHAM (Weighted Histogram Analysis Method).

Open the WHAM tool from:

Analysis → WHAM

Then:

1. Add the production trajectories located in the directory

2. umbrella_sampling/data_collection/

3. Select the five folders corresponding to the five simulation windows.

4. Verify that all five windows appear in the WHAM tree view.

5. Select a working directory for the output files.

6. Click Run to start the WHAM calculation.

Before running WHAM, verify the following:

• The temperature specified for the WHAM analysis must be the same as the temperature used during the molecular dynamics simulations.

• The number of bins should be sufficiently large to accurately represent the histograms. As a general guideline, the number of bins should be at least twice the number of simulation windows. In this example, we have only five windows, so 100 bins is more than adequate.

• A reliable free energy profile requires good overlap between the histograms of neighboring windows. If the windows are spaced too far apart or the force constant is too large, the overlap may become insufficient, reducing the accuracy of the reconstructed free energy profile.

After the calculation is completed, EasyHybrid will generate the free energy profile (PMF) along the selected reaction coordinate.

5 - Additional Notes

To better understand the results, keep the following points in mind:

• The reaction coordinate used here corresponds to the distance between the hydrogen atom (H17) and the oxygen atom (O5), describing the formation and breaking of a hydrogen bond.

• Umbrella Sampling computes a Potential of Mean Force (PMF), which represents a free energy profile rather than a simple potential energy curve.

• Compared to the potential energy scan performed in Tutorial 1, Umbrella Sampling explicitly accounts for thermal fluctuations through molecular dynamics, making it a much more appropriate method for estimating free energy barriers.

• In subsequent tutorials, we will extend this methodology to more complex reaction coordinates and to enzymatic QM/MM simulations, where Umbrella Sampling becomes an essential tool for investigating reaction mechanisms.