Related Experiment Video
Updated: Aug 11, 2026
08:10
Molecular Spring Constant Analysis by Biomembrane Force Probe Spectroscopy
Published on: November 20, 2021
Calculating potentials of mean force from steered molecular dynamics simulations
Sanghyun Park1, Klaus Schulten
1Beckman Institute and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
The Journal of Chemical Physics
|July 23, 2004
Summary
This study shows how to use Jarzynski's equality with steered molecular dynamics (SMD) to calculate potentials of mean force (PMF). The work distribution in SMD simulations with stiff springs is Gaussian, simplifying PMF calculations.
Area of Science:
- Computational chemistry
- Molecular dynamics
- Statistical mechanics
Background:
- Steered molecular dynamics (SMD) enables efficient molecular process investigation by focusing on specific degrees of freedom.
- Calculating potentials of mean force (PMF) is crucial for understanding molecular interactions and processes.
- Jarzynski's equality provides a theoretical link between nonequilibrium processes and equilibrium properties.
Purpose of the Study:
- To explain the application of Jarzynski's equality within the SMD framework for PMF calculation.
- To generalize Jarzynski's equality for isobaric-isothermal processes.
- To analyze the implications of Jarzynski's equality for thermodynamics and computational simulations.
Main Methods:
- Utilizing steered molecular dynamics (SMD) simulations.
- Applying Jarzynski's equality (nonequilibrium work relation).
- Performing theoretical derivations and generalizations for isobaric-isothermal conditions.
Main Results:
- Demonstrated that work distribution in SMD with stiff springs is Gaussian, irrespective of simulation speed.
- Showed that the cumulant expansion of Jarzynski's equality can be truncated at second order under these conditions.
- Illustrated a practical method for PMF calculation using an exemplary simulation, confirming the Gaussian work distribution.
Conclusions:
- Jarzynski's equality offers a robust method for calculating PMF from SMD simulations.
- The Gaussian nature of work distribution simplifies theoretical analysis and computational implementation.
- This approach enhances the efficiency and accuracy of molecular simulations for studying equilibrium properties.
Related Concept Videos
02:49Calculating Standard Free Energy Changes
The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
01:58Mechanical Protein Functions
Proteins perform many mechanical functions in a cell. These proteins can be classified into two general categories- proteins that generate mechanical forces and proteins that are subjected to mechanical forces. Proteins providing mechanical support to the structure of the cell, such as keratin, are subjected to mechanical force, whereas proteins involved in cell movement and transport of molecules across cell membranes, such as an ion pump, are examples of generating mechanical force.
01:13Force and Potential Energy in One Dimension
Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
01:04Force and Potential Energy in Three Dimensions
Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
01:27Calculations of Electric Potential II
An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
Consider a...
01:24Potential Due to a Magnetized Object
Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
The vector...