Umbrella Sampling

Tutorial Created with Software Release: 2025-4
Topics: Consumer Packaged Goods, Pharmaceutical Formulations, Polymeric Materials
Methodology: All-Atom Molecular Dynamics
Products Used: Desmond, MS Maestro

Tutorial files

0.42 GB
This tutorial is written for use with a 3-button mouse with a scroll wheel.
Words found in the Glossary of Terms are shown like this: Workspacethe 3D display area in the center of the main window, where molecular structures are displayed

 

Tip: You can hover over a glossary term to display its definition. You can click on an image to expand it in the page.
Abstract:

 

In this tutorial, we will learn to calculate the free energy profile for butanol permeation through a DMPC membrane using umbrella sampling.

 

Tutorial Content

  1. Introduction

  1. Creating Projects and Importing Structures

  1. Free Energy Profile of Butanol Permeating Through DMPC Bilayer

  1. Conclusion and References

  1. Glossary of Terms

1. Introduction

Understanding the energetic landscape of molecular processes is often hindered by sampling challenges in simulations due to the presence of energy barriers. The system might get stuck in a metastable state and rarely have enough energy to overcome the barrier and explore other important configurations. It's challenging to capture such rare events within the time scale of typical Molecular Dynamics (MD) simulations. In such cases, enhanced sampling methods are used to understand the free energy landscape.  An important step in umbrella sampling is to identify one or more collective variables (CVs) that effectively describe the process. Examples of CVs include distance between two atoms or groups of atoms, angles or dihedral angles etc. The Potential of Mean Force (PMF) represents the statistical mechanical average of the force exerted along the CV, providing a quantitative measure of the relative free energy landscape as a function of this coordinate.

Umbrella Sampling is a widely employed enhanced sampling technique designed to overcome these sampling limitations. Rather than relying on spontaneous barrier-crossing events, this method strategically introduces a series of external, biasing potentials, often referred to as "umbrella potentials," along the CV. Each umbrella potential modifies the energy landscape, effectively encouraging the system to sample configurations within a specific, often localized, region of the reaction coordinate. This allows for the exploration of energetically unfavorable regions that would be rarely visited in an unbiased simulation (see References).

The implementation of Umbrella Sampling involves performing multiple independent simulations, each initiated with the system constrained within a specific sampling window by a harmonic potential. Each simulation provides statistical information about the system's behavior under the influence of the applied bias within its respective window. The crucial step in Umbrella Sampling is the subsequent unbiasing of these individual simulations. Through the application of statistical techniques, such as the Weighted Histogram Analysis Method (WHAM) the effects of the artificial umbrella potentials are removed. This allows for the combination of the biased sampling data from all windows to reconstruct the unbiased PMF along the chosen reaction coordinate. The resulting PMF provides a free energy profile of the process, revealing the magnitudes of free energy barriers, the relative stability of different states and the thermodynamic driving force for the process.

In this tutorial, we will utilize the Umbrella Sampling Calculations and Viewer panels to construct the free energy profile for the permeation of a butanol molecule through a 1,2-Dimyristoyl-sn-glycero-3-phosphocholine (DMPC) membrane - a model system for understanding solute transport across biological membranes. The overall workflow is as shown:

2. Creating Projects and Importing Structures

At the start of the session, change the file path to your chosen Working Directorythe location where files are saved in MS Maestro to make file navigation easier. Each session in MS Maestro begins with a default Scratch Projecta temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project, which is not saved. A MS Maestro project stores all your data and has a .prj extension. A project may contain numerous entries corresponding to imported structures, as well as the output of modeling-related tasks. Once a project is saved, the project is automatically saved each time a change is made.

Structures can be built in MS Maestro or can be imported using File > Import Structures (or drag-and-dropped), and are added to the Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion and Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data. The Entry Lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion is located to the left of the Workspacethe 3D display area in the center of the main window, where molecular structures are displayed. The Project Tabledisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data can be accessed by Ctrl+T (Cmd+T) or Window > Project Table if you would like to see an expanded view of your project data.

  1. Double-click the Materials Science icon

Figure 2-1. Change Working Directory option.

  1. Go to File > Change Working Directory
  2. Find your directory, and click Choose
  3. Pre-generated files are included for running jobs or examining output. Download the zip file here: schrodinger.com/sites/default/files/s3/release/current/Tutorials/zip/umbrella_sampling.zip
  4. After downloading the zip file, unzip the contents in your Working Directorythe location where files are saved for ease of access throughout the tutorial

Figure 2-2. Save Project panel.

  1. Go to File > Save Project As
  2. Change the File name to umbrella_sampling_tutorial, click Save
    • The project is now named umbrella_sampling_tutorial.prj

Figure 2-3. Viewing the structure in the workspace.

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the tutorial files (presumably your working directory) and choose input_system.cms from the provided files

Note: Feel free to visualize and stylize the imported structure. The input system contains a butanol molecule (shown in CPK representation) in water with a DMPC bilayer. Refer to the Introduction to Materials Science Maestro, Adsorption of Panthenol on Skin with All-Atom Molecular Dynamics, and Calculating Surfactant Tilt and Electrostatic Potential of a Bilayer System tutorials to practice preparing the input structures.

3. Free Energy Profile of Butanol Permeating Through DMPC Bilayer

In this section, we will use the Umbrella Sampling Calculations and Umbrella Sampling Viewer panel to construct the free energy profile of butanol permeating through a DMPC membrane.

Figure 3-1. Opening the Umbrella Sampling Calculations panel.

  1. Select(1) the atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection". Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries and includethe entry is represented in the Workspace, the circle in the In column is blue the DMPC_water_butanol entry in the entry lista simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion
  2. Go to Tasks > Materials > Classical Mechanics > Umbrella Sampling > Umbrella Sampling Calculations

Before we proceed, let’s understand the panel in detail. In the Setup tab, the panel has options for setting up the parameters for the umbrella sampling calculations. The initial step is to define the Stationary and the Mobile groups:

In our implementation of Umbrella Sampling, we define the collective variable, Z, as the one-dimensional distance between the centers of mass (COM) of a stationary group and mobile group. Throughout the workflow, the COM of the stationary group will be held near the origin (Z=0) using a harmonic biasing potential. The mobile group will be moved in discrete steps along the user-defined range of the CV (see Window Setup below) with the aid of a separate harmonic biasing potential. In the context of the butanol-DMPC bilayer system, the DMPC bilayer functions as the stationary group while the butanol molecule constitutes the mobile group.

Alongside the ASL selections for the stationary and mobile groups are corresponding force constants which control the strength of the harmonic biasing potential applied to each group. Although default values are provided, it is likely necessary to fine tune these values for a given system.

Next, the location of each umbrella potential is defined by dividing the space between a user-defined lower and upper bound of the CV into a number of discrete units, or windows, controlled by the window size. For each window, a separate MD simulation will be run in which the position of the mobile group is biased towards the window center. It is important that the window size is compatible with the mobile group force constant such that the mobile group sufficiently explores the entire umbrella window.

The parameters for the MD simulations within each window  are defined in the Simulation Protocol tab. Because the input structure is passed from the output of an adjacent window, a preparation stage is used to reposition the mobile group within the current sampling window. To further ensure stability of the simulation,  selecting the Add Relaxation option adds an additional relaxation step at the beginning of the preparation  stage.

Finally, the output of the Preparation stage is passed to the Sampling stage. The appropriate choice of simulation time depends strongly on the system of interest. In general, mobile groups that are larger and more flexible require more simulation time to reliably converge the PMF.

Figure 3-2. Choosing the atoms for the stationary group.

  1. Click the Edit button () for the Stationary group and enter the ASLAtom Specification Language is a collection of Maestro-specific commands that can be used to define sets of atoms in complex macromolecular systems. ((res.ptype DMPC)) AND (atom.molnum 115,79,39,3)
  2. Click OK

Figure 3-3. Viewing the atoms of the DMPC lipid that are chosen for applying restraints.

For the Stationary group atoms to be restrained, we choose the four carbon atoms in the DMPC lipid as shown in the figure. There are 135 DMPC lipids in the system which corresponds to 540 restrained atoms on the stationary group.

 

Note: There are many valid ways to define the stationary group. However, the computational efficiency of the sampling stage has a dependence on the total number of atoms in the selection. Our ASL choice attempts to minimize the total number of selected atoms while holding the bilayer in place effectively. 

Figure 3-4. Choosing the butanol molecule as the mobile group.

  1. Click the Edit button () for the Mobile group and enter the ASLAtom Specification Language is a collection of Maestro-specific commands that can be used to define sets of atoms in complex macromolecular systems. (mol.num   8614)
    • This corresponds to the butanol molecule in the system.
  2. Click OK

Figure 3-5. Setting the Umbrella Sampling window range.

The panel updates with the provided information Separation between the stationary and mobile groups: 29.71Å.

  1. Change the Collective Variable between 0 Å and 32.00 Å
    • Note: the initial separation between stationary and mobile groups should be contained within the range of the collective variable.
  2. Click Preview  

Figure 3-6. Preview the mobile group motion.

We can now visualize the relative position of the mobile group in the workspace.

  1. Adjust the slider to change the Relative mobile group position
  2. Click OK to close the window

Figure 3-7. Setting up and running the job.

  1. Go to the Simulation Protocol tab
  2. Check Remove center of mass motion
  3. Check Add Relaxation
  4. Change the job name to umbrella_sampling_DMPC_butanol
  5. Adjust the job settings () as needed
    • This job requires a CPU and a GPU host. Running in serial, the job can be completed in about 36 hours. Automatic parallelization can reduce this time significantly, depending on available resources.

If you would like to run the job, proceed to click Run. If you would prefer to proceed with imported files, please proceed to the next steps.

 

We will assume that you have not run the calculation, and instruct for importing:

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the tutorial files and choose the Section_03 > umbrella_sampling_DMPC_butanol > umbrella_sampling_DMPC_butanol-out.cms file.
  3. Close the Umbrella Sampling Calculation panel.

Figure 3-8. Opening the Umbrella Sampling Viewer.

  1. Use the WAM button () to open the Umbrella Sampling Viewer panel
    • Alternatively, go to Tasks > Materials > Classical Mechanics > Umbrella Sampling > Umbrella Sampling Viewer
    • The Umbrella Sampling Viewer opens. The default number of iterations is 4000.

Figure 3-9. WHAM convergence and free energy profile.

The WHAM converged after 1600 iterations.

  1. Click the Distribution tab

Figure 3-10. The Biased Distribution.

  1. Move your cursor over the histograms to see the window center position for each one

 

The plots display histograms representing the center-of-mass position of the mobile group within each umbrella window. These histograms are considered "biased" because a harmonic potential is applied to maintain the mobile group at specific, desired positions, causing their centers to align with the approximate center of each umbrella window.

 

To obtain the underlying "unbiased" distribution—which reflects the solute's natural position without the harmonic potential—the points within these histograms are reweighted. These unbiased distributions are then combined to construct the Potential of Mean Force (PMF), which is presented in the first tab.

 

Reviewing these biased distributions is crucial for assessing the reliability of the PMF. A key indicator of trustworthiness is sufficient overlap between the tails of the biased distributions. This tab serves as a visual method to check for this overlap. While more quantitative overlap metrics are under development, most users currently rely on this qualitative visual assessment.

Peaks in this profile represent energy barriers, while valleys indicate regions of lower energy and thus higher probability of finding the molecule. Additionally, the density profile could be viewed to see the concentration of lipids as a function of the same reaction coordinate. It is thermodynamically more favorable for butanol to be located within the membrane's lipid structure than in the surrounding aqueous environment. The free energy profile also exhibits a peak, representing the maximum energy that butanol must overcome to move from the aqueous region to the center of the membrane. This peak defines the free energy barrier for permeation. A barrier of approximately 5 kcal/mol indicates that at typical temperatures, only a small fraction of butanol molecules will possess enough thermal energy to spontaneously cross the membrane.

4. Conclusion and References

In this tutorial, we learned how to perform umbrella sampling calculations to construct the free energy profile for butanol permeation through a DMPC membrane.

For further learning:

For introductory content, focused on navigating the Schrödinger Materials Science interface, an Introduction to Materials Science Maestro tutorial is available. Please visit the materials science training website for access to 70+ tutorials. For scientific inquiries or technical troubleshooting, submit a ticket to our Technical Support Scientists at help@schrodinger.com.

For self-paced, asynchronous, online courses in Materials Science modeling, including access to Schrödinger software, please visit the Schrödinger Online Learning portal on our website.

For some related practice, proceed to explore other relevant tutorials:

For further reading:
  • Potential Mean Force from Umbrella Sampling Simulations: What Can We Learn and What Is Missed?, DOI:10.1021/acs.jctc.8b01142
  • Tutorial on Umbrella Sampling Simulation with a Combined QM/MM Potential: The Potential of Mean Force for an SN2 Reaction in Water, DOI:10.1021/acs.jpcb.4c05926
  • Free Energy Analysis of Peptide-Induced Pore Formation in Lipid Membranes by Bridging Atomistic and Coarse-Grained Simulations, DOI:10.1021/acs.jpcb.4c03276

5. Glossary of Terms

Entry List - a simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion

Included - the entry is represented in the Workspace, the circle in the In column is blue

Project Table - displays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data

Recent actions - This is a list of your recent actions, which you can use to reopen a panel, displayed below the Browse row. (Right-click to delete.)

Scratch Project - a temporary project in which work is not saved, closing a scratch project removes all current work and begins a new scratch project

Selected - (1) the atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection". Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries

Working Directory - the location where files are saved

Workspace - the 3D display area in the center of the main window, where molecular structures are displayed

ASL - Atom Specification Language is a collection of Maestro-specific commands that can be used to define sets of atoms in complex macromolecular systems.