Autoencoders for dimensionality reduction in molecular dynamics: Collective variable dimension, biasing, and transition states.

The heat shock protein 90 (Hsp90) is a molecular chaperone that controls the folding and activation of client proteins using the free energy of ATP hydrolysis. The Hsp90 active site is in its N-terminal domain (NTD). Our goal is to characterize the dynamics of NTD using an autoencoder-learned collective variable (CV) in conjunction with adaptive biasing force Langevin dynamics. Using dihedral analysis, we cluster all available experimental Hsp90 NTD structures into distinct native states. We then perform unbiased molecular dynamics (MD) simulations to construct a dataset that represents each state and use this dataset to train an autoencoder. Two autoencoder architectures are considered, with one and two hidden layers, respectively, and bottlenecks of dimension k ranging from 1 to 10. We demonstrate that the addition of an extra hidden layer does not significantly improve the performance, while it leads to complicated CVs that increase the computational cost of biased MD calculations. In addition, a two-dimensional (2D) bottleneck can provide enough information of the different states, while the optimal bottleneck dimension is five. For the 2D bottleneck, the 2D CV is directly used in biased MD simulations. For the five-dimensional (5D) bottleneck, we perform an analysis of the latent CV space and identify the pair of CV coordinates that best separates the states of Hsp90. Interestingly, selecting a 2D CV out of the 5D CV space leads to better results than directly learning a 2D CV and allows observation of transitions between native states when running free energy biased dynamics.

Chasing Collective Variables Using Autoencoders and Biased Trajectories.

Free energy biasing methods have proven to be powerful tools to accelerate the simulation of important conformational changes of molecules by modifying the sampling measure. However, most of these methods rely on the prior knowledge of low-dimensional slow degrees of freedom, i.e., collective variables (CVs). Alternatively, such CVs can be identified using machine learning (ML) and dimensionality reduction algorithms. In this context, approaches where the CVs are learned in an iterative way using adaptive biasing have been proposed: at each iteration, the learned CV is used to perform free energy adaptive biasing to generate new data and learn a new CV. In this paper, we introduce a new iterative method involving CV learning with autoencoders: Free Energy Biasing and Iterative Learning with AutoEncoders (FEBILAE). Our method includes a reweighting scheme to ensure that the learning model optimizes the same loss at each iteration and achieves CV convergence. Using the alanine dipeptide system and the solvated chignolin mini-protein system as examples, we present results of our algorithm using the extended adaptive biasing force as the free energy adaptive biasing method.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.