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)

### Application of Umbrella Sampling Simulation

- Evaluate the binding affinity of a complex
- Study protein binding-unbinding processes
- Protein engineering

### Our Umbrella Sampling Simulation Process

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.

- Generate a series of configurations along a single degree of freedom (reaction coordinate)

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.

- Extract frames from the trajectory that correspond to the desired COM spacing

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.

- Run umbrella sampling simulations on each configuration to restrain it within a window corresponding to the chosen COM distance
- Use the Weighted Histogram Analysis Method (WHAM) to extract the potential of mean force (PMF) and calculate ΔG
_{bind}.

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.

### Our Services

- We apply the umbrella sampling method to estimate the affinity which is computed as the difference between the largest and smallest values of the free energy change, obtained by using a PMF analysis.
- Our experts can also use umbrella sampling to conduct the potential of mean force calculation to study protein binding-unbinding processes.
- We carry out umbrella sampling studies on mutational variants of some protein to see effect of the mutations on the folding pathway of the protein which may be helpful for predicting fast folding mutants or protein engineering.

### Our Advantages

- Our scientists have rewritten the towing codes and thoroughly inspected them, helping to perform a rapid umbrella sampling simulation.
- We can set up and run a umbrella sampling simulation to calculate the binding energy between the two species.
- We have basic knowledge of topological organization and are experienced in the simulation methods.

Our umbrella sampling simulation services remarkably reduce the cost, promote further experiments, and accelerate the process of drug design for customers worldwide. Our personalized and all-around services will satisfy your innovative study demands. If you are interested in our services, please don't hesitate to contact us. We are glad to cooperate with you and witness your success!

Reference

- Paul, R.; Paul, D. S. Computational Study of Encapsulation of Polyaromatic Hydrocarbons by Endo-Functionalized Receptors in Non-Polar Medium.
*Journal of chemical information and modeling*, 2020, 60(1): 212-225.