A Probabilistic Framework for Constructing Temporal Relations in Replica Exchange Molecular Trajectories

Abstract

Knowledge of the structure and dynamics of biomolecules is essential for elucidating the underlying mechanisms of biological processes. Given the stochastic nature of many biological processes, like protein unfolding, it is almost impossible that two independent simulations will generate the exact same sequence of events, which makes direct analysis of simulations difficult. Statistical models like Markov chains, transition networks, etc. help in shedding some light on the mechanistic nature of such processes by predicting long-time dynamics of these systems from short simulations. However, such methods fall short in analyzing trajectories with partial or no temporal information, for example, replica exchange molecular dynamics or Monte Carlo simulations. In this work, we propose a probabilistic algorithm, borrowing concepts from graph theory and machine learning, to extract reactive pathways from molecular trajectories in the absence of temporal data. A suitable vector representation was chosen to represent each frame in the macromolecular trajectory (as a series of interaction and conformational energies), and dimensionality reduction was performed using principal component analysis (PCA). The trajectory was then clustered using a density-based clustering algorithm, where each cluster represents a metastable state on the potential energy surface (PES) of the biomolecule under study. A graph was created with these clusters as nodes with the edges learned using an iterative expectation maximization algorithm. The most reactive path is conceived as the widest path along this graph. We have tested our method on RNA hairpin unfolding trajectory in aqueous urea solution. Our method makes the understanding of the mechanism of unfolding in the RNA hairpin molecule more tractable. As this method does not rely on temporal data, it can be used to analyze trajectories from Monte Carlo sampling techniques and replica exchange molecular dynamics (REMD).

Sampling Performance of Multiple Independent Molecular Dynamics Simulations of an RNA Aptamer

“… 48 This approach optimizes the one-to-one mapping of high dimensional objects to a 2D space by reproducing joint Gaussian probabilities in high-dimensional space with a heavy-tail Student t -distributed 2D space. 49 In this step, only points that are extremely close in the high-dimensional conformation space lie in close proximity to each other in the 2D-reduced space. Density-based clustering was conducted on the 2D data from t -SNE using the DBSCAN algorithm.…”

Artificial intelligence: machine learning for chemical sciences

“…ML has made a variety of contributions to the analysis and simulation of MD trajectories. 98 , 99 For instance, it has enabled the estimation of free energy surfaces. Along with enhanced sampling methods, it has also attempted to learn the free energy surface on the fly.…”

Machine Learning for Accurate Force Calculations in Molecular Dynamics Simulations

“…The effects of such fitted potentials on the calculation of physical properties obtained from their trajectories, at different physical conditions, such as temperature and pressure, need to be studied to further reinforce on their future applications. Machine learning is also being successfully used to analyze longtime scale simulation data on large systems. , …”