Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

Abstract

Using the helix-coil transitions of alanine pentapeptide as an illustrative example, we demonstrate the use of diffusion maps in the analysis of molecular dynamics simulation trajectories. Diffusion maps and other nonlinear data-mining techniques provide powerful tools to visualize the distribution of structures in conformation space. The resulting low-dimensional representations help in partitioning conformation space, and in constructing Markov state models that capture the conformational dynamics. In an initial step, we use diffusion maps to reduce the dimensionality of the conformational dynamics of Ala5. The resulting pretreated data are then used in a clustering step. The identified clusters show excellent overlap with clusters obtained previously by using the backbone dihedral angles as input, with small-but nontrivial-differences reflecting torsional degrees of freedom ignored in the earlier approach. We then construct a Markov state model describing the conformational dynamics in terms of a discrete-time random walk between the clusters. We show that by combining fuzzy C-means clustering with a transition-based assignment of states, we can construct robust Markov state models. This state-assignment procedure suppresses short-time memory effects that result from the non-Markovianity of the dynamics projected onto the space of clusters. In a comparison with previous work, we demonstrate how manifold learning techniques may complement and enhance informed intuition commonly used to construct reduced descriptions of the dynamics in molecular conformation space.

Characterizing molecular flexibility by combining least root mean square deviation measures

“…As illustrated by this example, the ability to identify structurally conserved motifs and to combine their lRMSD makes a dramatic difference in the overall comparison of two conformations. This problem is well‐known, for example, for the analysis of molecular dynamics trajectories, where erroneous assignments of structures to the same clusters/meta‐stable states may jeopardize free energy calculations …”

“…This problem is well-known, for example, for the analysis of molecular dynamics trajectories, where erroneous assignments of structures to the same clusters/meta-stable states may jeopardize free energy calculations. 32…”

Multiscale analysis of structurally conserved motifs

“…The second class is the analysis of thermodynamics and dynamics from simulations (molecular dynamics, Monte Carlo sampling and their generalizations). In this setting, it is indeed well known that reliable thermodynamic and kinetic estimates requires accurate clustering algorithms to group conformations easily interconvertible into one another [3].…”

Characterizing molecular flexibility by combining lRMSD measures

“…This problem is well known e.g. for the analysis of molecular dynamics trajectories, where erroneous assignments of structures to the same clusters / meta-stable states may jeopardize free energy calculations [27].…”