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

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.