  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 (ABF) 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 increases the computational cost of biased MD
calculations. In addition, a 2D bottleneck can provide enough information of
the different states, while the optimal bottleneck dimension is five. For the
2D bottleneck, the two-dimensional CV is directly used in biased MD
simulations. For the 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 to observe transitions
between native states when running free energy biased dynamics.
