Comparing geometric and kinetic cluster algorithms for molecular simulation data

Abstract

The identification of metastable states of a molecule plays an important role in the interpretation of molecular simulation data because the free-energy surface, the relative populations in this landscape, and ultimately also the dynamics of the molecule under study can be described in terms of these states. We compare the results of three different geometric cluster algorithms (neighbor algorithm, K-medoids algorithm, and common-nearest-neighbor algorithm) among each other and to the results of a kinetic cluster algorithm. First, we demonstrate the characteristics of each of the geometric cluster algorithms using five two-dimensional data sets. Second, we analyze the molecular dynamics data of a beta-heptapeptide in methanol--a molecule that exhibits a distinct folded state, a structurally diverse unfolded state, and a fast folding/unfolding equilibrium--using both geometric and kinetic cluster algorithms. We find that geometric clustering strongly depends on the algorithm used and that the density based common-nearest-neighbor algorithm is the most robust of the three geometric cluster algorithms with respect to variations in the input parameters and the distance metric. When comparing the geometric cluster results to the metastable states of the beta-heptapeptide as identified by kinetic clustering, we find that in most cases the folded state is identified correctly but the overlap of geometric clusters with further metastable states is often at best approximate.

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

“…DS2: Data are derived from recently published simulations on the intrinsically disordered peptide Aβ [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . 39 The trajectory contained 7.5x10 5 snapshots saved at an interval of 20 ps, and the same 144, partially redundant internal distances that DS1 was originally derived from were extracted at each frame (D = 144).…”

“…39 The trajectory contained 7.5x10 5 snapshots saved at an interval of 20 ps, and the same 144, partially redundant internal distances that DS1 was originally derived from were extracted at each frame (D = 144). For the data in Table 1, backbone (φ/ψ/ω) dihedral angles of residues 14-24 of the peptide (D = 66), their sine/cosine terms (D = 66), the respective terms weighted by inertial masses (see equation 6), or the Cartesian coordinates of backbone nitrogen and oxygen atoms of residues [14][15][16][17][18][19][20][21][22][23][24] (D = 66) were also extracted.…”

“…17 Due to the sheer number of terms, convergence of transition probabilities often requires frequent recording of trajectory information, which potentially gives rise to very large datasets. 18,19 When using geometric criteria for clustering, 20 mesostates should not differ drastically in phase space volume (resolution) since conformational diffusion in the absence of significant barriers sets a fundamental timescale. If for example one were to combine all "unstructured" states into a single, "entropic" mesostate, kinetics of pathways passing through such a significantly larger mesostate will be incorrectly described at the network level.…”

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

“…A major challenge in constructing such a Markov state model [3][4][5][6][7] is the identification of the metastable regions of the free energy surface that partition the system into discrete states. The identification of metastable states is frequently done by performing actual simulations to harvest trajectories that are then used to cluster conformations of similar geometries, either manually [8,9], using clustering methods [4,[10][11][12], or using distance metrics [4,6,10]. Rates between states are then estimated based on transitions observed in trajectories based on discrete state count matrices [12].…”

Communication: Microsecond peptide dynamics from nanosecond trajectories: A Langevin approach

“…[8][9][10][11][12][13][14][15][16] This is achieved by partitioning the continuous MD a) Present address: Biozentrum, University of Basel and Swiss Institute of Bioinformatics, Basel, Switzerland. b) A. Rzepiela and N. Schaudinnus contributed equally to this work.…”