Adaptive anisotropic kernels for nonparametric estimation of absolute configurational entropies in high-dimensional configuration spaces

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 1):011913. doi: 10.1103/PhysRevE.80.011913. Epub 2009 Jul 20.


The quasiharmonic approximation is the most widely used estimate for the configurational entropy of macromolecules from configurational ensembles generated from atomistic simulations. This method, however, rests on two assumptions that severely limit its applicability, (i) that a principal component analysis yields sufficiently uncorrelated modes and (ii) that configurational densities can be well approximated by Gaussian functions. In this paper we introduce a nonparametric density estimation method which rests on adaptive anisotropic kernels. It is shown that this method provides accurate configurational entropies for up to 45 dimensions thus improving on the quasiharmonic approximation. When embedded in the minimally coupled subspace framework, large macromolecules of biological interest become accessible, as demonstrated for the 67-residue coldshock protein.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Alkanes / chemistry
  • Anisotropy
  • Dipeptides / chemistry
  • Entropy*
  • Heat-Shock Proteins / chemistry
  • Molecular Conformation*
  • Quantum Theory


  • Alkanes
  • Dipeptides
  • Heat-Shock Proteins
  • alanylalanine