Relative Principal Components Analysis: Application to Analyzing Biomolecular Conformational Changes

A new
method termed “Relative Principal Components Analysis”
(RPCA) is introduced that extracts optimal relevant principal components
to describe the change between two data samples representing two macroscopic
states. The method is widely applicable in data-driven science. Calculating
the components is based on a physical framework that introduces the
objective function (the Kullback–Leibler divergence) appropriate
for quantifying the change of the macroscopic state affected by the
changes in the microscopic features. To demonstrate the applicability
of RPCA, we analyze the thermodynamically relevant conformational
changes of the protein HIV-1 protease upon binding to different drug
molecules. In this case, the RPCA method provides a sound thermodynamic
foundation for analyzing the binding process and thus characterizing
both the collective and the locally relevant conformational changes.
Moreover, the relevant collective conformational changes can be reconstructed
from the informative latent variables to exhibit both the enhanced
and the restricted conformational fluctuations upon ligand association.