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

Abstract

We propose an approach for summarizing the output of long simulations of complex systems, affording a rapid overview and interpretation. First, multidimensional scaling techniques are used in conjunction with dimension reduction methods to obtain a low-dimensional representation of the configuration space explored by the system. A nonparametric estimate of the density of states in this subspace is then obtained using kernel methods. The free energysurface is calculated from that density, and the configurations produced in the simulation are then clustered according to the topography of that surface, such that all configurations belonging to one local free energy minimum form one class. This topographical cluster analysis is performed using basin spanning trees which we introduce as subgraphs of Delaunay triangulations. Free energysurfaces obtained in dimensions lower than four can be visualized directly using iso-contours and -surfaces. Basin spanning trees also afford a glimpse of higher-dimensional topographies. The procedure is illustrated using molecular dynamics simulations on the reversible folding of peptide analoga. Finally, we emphasize the intimate relation of density estimation techniques to modern enhanced sampling algorithms

Long‐Time Protein Folding Dynamics from Short‐Time Molecular Dynamics Simulations

“…In more complex systems, the coordinates in which dynamics is slow will be much more difficult to discern; some automatic method for the identification of metastable states is necessary. Pure conformational clustering methods [22,20] may prove to be inadequate because they neglect the true locations of kinetic barriers, but attempts to also consider kinetic relationships give promising results but have not yet been applied to large explicitly solvated systems [41,42,40]. This problem is the subject of work soon to be reported [45].…”

Common Nearest Neighbor Clustering—A Benchmark

“…There are several methods known that can extract information from such a trajectory, such as sequence kernels and support vector machines [45][46][47][48][49]. However, most of these are currently not applied to MD data, as these data are described in terms of non-linear internal coordinates in a high-dimensional conformational space.…”

Multiscale modeling of emergent materials: biological and soft matter

“…The clusters can then be represented using simpler representations, e.g., average conformation within the cluster, and analysis of the clustering can yield information on the typical features of the data. 110,111 Such information could also be used to design coarse-grained models that are able to represent the major differences between the clusters, in the hope of being thus able to capture the rough features of the original system. Let us now focus on self-organizing maps (SOMs), 112 which is an approach somewhere in between dimensionality reduction and clustering.…”