I have recently written, for WIREs Computational Molecular Science, a review article on the use of Principal Component Analysis (PCA) in the study of dynamical systems, with a particular focus on molecular dynamics (MD) simulations of biomolecules [1]. The aim of this work is to provide a clear and practical overview of how PCA has become a central tool for extracting meaningful collective motions from high-dimensional simulation data, and how modern methodological extensions continue to expand its capabilities.

Advances in computational power and simulation algorithms have transformed molecular dynamics into a routine tool in structural biology. Today, simulations of large proteins, including membrane-embedded systems, can reach microsecond timescales on relatively modest hardware. While this progress is remarkable, it comes with a familiar challenge: how to extract physical insight from vast amounts of data. Principal Component Analysis offers an elegant solution. Originally developed as a statistical method for dimensionality reduction, PCA identifies correlations among variables and reorganizes high-dimensional datasets into a smaller set of collective modes that capture the dominant variance. These modes often correspond to physically meaningful motions.

PCA as a Tool for Dynamical Systems

Although PCA is widely used across many disciplines—ranging from image processing and computer science to astrophysics, geography, and biology—its role in dynamical systems is particularly illuminating. In such systems, PCA helps separate fast, uncorrelated fluctuations from slower, collective motions. In the context of biomolecules, these slow modes are often linked to function. Molecular motion, famously described by Richard Feynman as the “jiggling and wiggling of atoms,” includes both rapid thermal vibrations and coordinated structural rearrangements. PCA allows us to focus on the latter.

PCA in Molecular Dynamics Simulations

Molecular dynamics simulations model atoms as classical particles interacting through approximate force fields. Since the pioneering simulations of simple liquids in the 1950s and the first protein simulation by McCammon, Gelin, and Karplus in 1977, MD has evolved into a mature and widely used methodology. The first applications of PCA to MD trajectories appeared in the early 1990s and were later popularized under the name essential dynamics. This approach highlights the ability of PCA to isolate large-scale, functionally relevant motions from quasi-harmonic fluctuations. Its integration into widely used software packages, such as GROMACS, further accelerated its adoption across structural biology.

The review I recently wrote complements existing theoretical treatments by adopting a practical, application-oriented perspective. It:

• Introduces PCA using simple dynamical systems as illustrative examples
• Discusses different coordinate choices for biomolecular PCA
• Reviews commonly used computational tools and workflows
• Presents representative case studies on peptides and proteins
• Briefly surveys modern extensions, including time-lagged methods, Markov state models, nonlinear dimensionality reduction, and machine learning approaches

Together, these elements show how PCA continues to evolve as a unifying framework for analyzing complex dynamical behavior. More than 30 years after its first application to molecular dynamics simulations, PCA remains one of the most intuitive and effective methods for exploring high-dimensional trajectories. Its continued relevance lies in its ability to connect statistical variance with physical motion, providing insight into conformational transitions, free-energy landscapes, and functional mechanisms.

With this review, my goal was to offer readers—particularly students and researchers entering the field—a clear guide to both the foundations and modern developments of PCA-based analysis in molecular dynamics.

REFERENCE

[1] D. Roccatano. Principal Component Analysis of Molecular Dynamic Trajectories: Concepts, Tools, and Applications.  WIREs Computational Molecular Science, 15(6), e70060, (2025). Invited Overview paper. DOI:https://doi.org/10.1002/wcms.70060