Seminar #7 - Thermodynamics - Free energy Calculation I

2024 Winter Molecular Simulation Seminar
Room 302, the 2nd experimental building at POSTECH
Presenter: Seonghyeon Kang

When we analyze chemical phenomena by various molecular simulation tools, the most powerful information that we can derive is free energy diagram. This is also true for molecular dynamics and monte-carlo simulation. However, conducting free energy calculation and constructing free energy diagram are not trivial processes. It also has several issues which mislead into incorrect or incomplete energy diagram. Especially, there are two main issues, defining reaction coordinate and sampling all regions related to the phenomenon. The former one is the question how we can choose proper domain variable for describing reaction coordinate axis. Because of extremely high degree of freedom of complex system, dimensionality reduction technique is needed to visualize reaction pathway easily. The latter one is corresponded to the question about overcoming high energy barrier for sampling configurational space enough. This problem leads to novel simulation and sampling techniques, metadynamics and umbrella sampling. These two techniques enable to sample free energy landscape where ergodicity was hindered.

In this seminar, three topics of this scheme will be treated. The first topic is ‘How can we define proper and optimal reaction coordinate?’. In this topic, the theoretical foundation[1] and well-known strategies of constructing reaction coordinates[1-3] will be introduced. The second topic is umbrella sampling. It includes theoretical basis[4], methods, sampling, analyzing[5] technique, and statistical error analysis[6]. The last topic is metadynamics. In the last topic, basic principles of metadynamics, choosing CV(collective variable), computing free energy will be treated as theoretical aspect[7]. Then, the free energy space of alanine dipeptide case study[8] and accuracy of metadynamics[9] will be introduced as practical aspect.

References

[1] Zinovjev, K., & Tuñón, I., Reaction coordinates and transition states in enzymatic catalysis. Wiley Interdiscip. Rev. Comput. Mol. Sci., 2018, 8(1), e1329.
[2] Banushkina, P. V., & Krivov, S. V., Optimal reaction coordinates. Wiley Interdiscip. Rev. Comput. Mol. Sci., 2016, 6(6), 748-763.
[3] Wu, S., Li, H., & Ma, A., A rigorous method for identifying a one-dimensional reaction coordinate in complex molecules. J. Chem. Theory Comput., 2022, 18(5), 2836-2844.
[4] Torrie, G. M., & Valleau, J. P., Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comput. Phys., 1977, 23(2), 187-199.
[5] Kästner, J., Umbrella sampling. Wiley Interdiscip. Rev. Comput. Mol. Sci., 2011, 1(6), 932-942.
[6] Kästner, J., & Thiel, W., Analysis of the statistical error in umbrella sampling simulations by umbrella integration. J. Chem. Phys., 2006, 124(23).
[7] Bussi, G., & Laio, A., Using metadynamics to explore complex free-energy landscapes. Nat. Rev. Phys., 2020, 2(4), 200-212.
[8] Vymetal, J., & Vondrášek, J., Metadynamics As a Tool for Mapping the Conformational and Free-Energy Space of Peptides - The Alanine Dipeptide Case Study. J. Phys. Chem. B, 2010, 114(16), 5632-5642.
[9] Laio, A., Rodriguez-Fortea, A., Gervasio, F. L., Ceccarelli, M., & Parrinello, M., Assessing the accuracy of metadynamics. J. Phys. Chem. B, 2015, 109(14), 6714-6721.