A strategy for analysis of (molecular) equilibrium simulations: Configuration space density estimation, clustering, and visualization

We propose an approach for summarizing the output of long simulations of co mplex systems, affording a rapid overview and interpretation. First, multid imensional scaling techniques are used in conjunction with dimension reduct ion methods to obtain a low-dimensional representation of the configuration space explored by the system. A nonparametric estimate of the density of s tates in this subspace is then obtained using kernel methods. The free ener gy surface is calculated from that density, and the configurations produced in the simulation are then clustered according to the topography of that s urface, such that all configurations belonging to one local free energy min imum form one class. This topographical cluster analysis is performed using basin spanning trees which we introduce as subgraphs of Delaunay triangula tions. Free energy surfaces obtained in dimensions lower than four can be v isualized directly using iso-contours and -surfaces. Basin spanning trees a lso afford a glimpse of higher-dimensional topographies. The procedure is i llustrated using molecular dynamics simulations on the reversible folding o f peptide analoga. Finally, we emphasize the intimate relation of density e stimation techniques to modern enhanced sampling algorithms. (C) 2001 Ameri can Institute of Physics.