Introduction to Molecular Dynamics (MD) Simulations

Computer-based molecular dynamics (MD) simulations investigate the time-dependent motions of atoms and molecules in biological systems by applying classical laws of motion (1). Since the 1950s, molecular simulations have been used to address problems in condensed matter systems. These early studies laid the foundation for modern MD methodologies (2). For more than 70 years, MD simulations have been widely employed to explore the structure and dynamics of biomolecules (3). MD simulations provide insights into biological processes such as protein folding, drug binding, conformational changes, and substrate transport across membranes.

Theoretical Foundations of Molecular Dynamics

Molecular dynamics (MD) simulations are fundamentally based on Newton’s laws of motion. In this approach, the positions and velocities of atoms are determined over time according to the forces calculated using empirical force fields (You can access the related article here) (4). The simulation procedure proceeds through the iterative updating of atomic positions and velocities, allowing the time-dependent evolution of the system’s conformational space to be examined. In general, for a system composed of interacting particles, Newton’s equations of motion are solved numerically to obtain the paths followed by atoms and molecules, namely trajectories (5). The interaction forces between particles and the corresponding potential energies are defined through molecular mechanics force fields or interatomic potential functions.

1. Equations of Motion

For each atom i in a system, the force is given by the negative derivative of the potential energy (V) with respect to its position (r):

Here, F represents the force, m the mass, and a the acceleration, which corresponds to the second derivative of position with respect to time (6). The computer solves these equations over very small time intervals (typically on the order of femtoseconds, 10⁻¹⁵ seconds) to calculate the subsequent positions of atoms (7).

In practice, an MD simulation cannot be run indefinitely; however, ensuring adequate sampling of phase space is essential. Due to the high computational and data storage demands, MD simulations face challenges when modeling systems containing a large number of atoms. To improve the accuracy of the modeled system and reduce statistical errors, the simulation time step should be chosen as small as possible (8).

Figure 1. A schematic representation of molecular simulations (the image was generated using artificial intelligence).

2. Force Fields

A force field is a mathematical representation that describes the relationship between the energy of a system and the positions of its particles [9]. A molecule is assumed to consist of atoms held together by elastic forces, which are expressed in terms of potential energy functions (such as bond lengths, bond angles, and non-bonded interactions). Accordingly, a force field becomes a combination of potential energy terms, as given in the equation below.

The potential energy functions used in force fields can be divided into two categories: bonded and non-bonded interactions. In the equation given above, the first three terms represent bonded interactions, while the last two terms correspond to non-bonded interactions.

A wide variety of force fields are employed in MD simulations. Some force fields are primarily parameterized based on experimental data, such as X-ray diffraction, whereas others have been developed using quantum mechanical calculations. Although similar functional forms are used in both approaches, they differ mainly in their parameterization strategies. In light of the current literature, AMBER (Assisted Model Building with Energy Refinement), CHARMM (Chemistry at HARvard using Molecular Mechanics), GROMOS (GROningen Molecular Simulation), and OPLS (Optimized Parameters for Large-scale Simulations) force fields are among the most frequently used in MD simulations [10, 11].

References

1. Badar, M. S., Shamsi, S., Ahmed, J., & Alam, M. A. (2022). Molecular dynamics simulations: concept, methods, and applications. In Transdisciplinarity (pp. 131-151). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-94651-7_7

2.Winkler, L. G. (2024). Validating, Assessing, and Improving Force Fields for Molecular Dynamics Simulations of Nucleic Acids (Doctoral dissertation, The University of Utah).

3.Larsen, A. H. (2022). Molecular dynamics simulations of curved lipid membranes. International Journal of Molecular Sciences, 23(15), 8098. https://doi.org/10.3390/ijms23158098    

4. Padhi, A. K., Janežič, M., & Zhang, K. Y. (2022). Molecular dynamics simulations: principles, methods, and applications in protein conformational dynamics. In Advances in protein molecular and structural biology methods (pp. 439-454). Academic Press. https://doi.org/10.1016/B978-0-323-90264-9.00026-X

5. Zhou, K., & Liu, B. (2022). Molecular dynamics simulation: fundamentals and applications. Academic Press.

6. González, M. A. (2011). Force fields and molecular dynamics simulations. École thématique de la Société Française de la Neutronique, 12, 169-200.

7. Hopkins, C. W., Le Grand, S., Walker, R. C., & Roitberg, A. E. (2015). Long-time-step molecular dynamics through hydrogen mass repartitioning. Journal of chemical theory and computation, 11(4), 1864-1874. https://doi.org/10.1021/ct5010406  

8. Shen, W., Zhou, T., & Shi, X. (2023). Enhanced sampling in molecular dynamics simulations and their latest applications—A review. Nano Research, 16(12), 13474-13497. https://doi.org/10.1007/s12274-023-6311-9

9. González, M. A. (2011). Force fields and molecular dynamics simulations. École thématique de la Société Française de la Neutronique, 12, 169-200. https://doi.org/10.1051/sfn/201112009

10. Li, D., & Minkara, M. S. (2024). Comparative Assessment of Water Models in Protein–Glycan Interaction: Insights from Alchemical Free Energy Calculations and Molecular Dynamics Simulations. Journal of Chemical Information and Modeling, 64(24), 9459-9473. https://doi.org/10.1021/acs.jcim.4c01361

11. Beatrice, A. C. (2024). Advancements and Future Directions in Molecular Dynamics (MD) Simulations. IDOSR Journal of Applied Sciences, 9(1), 21-26. https://doi.org/10.59298/JCAS/2024/91.152126001