  Protein-nucleic acid complexes are important for many cellular processes
including the most essential function such as transcription and translation.
For many protein-nucleic acid complexes, flexibility of both macromolecules has
been shown to be critical for specificity and/or function. Flexibility-rigidity
index (FRI) has been proposed as an accurate and efficient approach for protein
flexibility analysis. In this work, we introduce FRI for the flexibility
analysis of protein-nucleic acid complexes. We demonstrate that a multiscale
strategy, which incorporates multiple kernels to capture various length scales
in biomolecular collective motions, is able to significantly improve the state
of art in the flexibility analysis of protein-nucleic acid complexes. We take
the advantage of the high accuracy and ${\cal O}(N)$ computational complexity
of our multiscale FRI method to investigate the flexibility of large ribosomal
subunits, which is difficult to analyze by alternative approaches. An
anisotropic FRI approach, which involves localized Hessian matrices, is
utilized to study the translocation dynamics in an RNA polymerase.
