Application of nonlinear dimensionality reduction to characterize the conformational landscape of small peptides

Abstract

The automatic classification of the wealth of molecular configurations gathered in simulation in the form of a few coordinates that help explain the main states and transitions of the system is a recurring problem in computational molecular biophysics. We use the recently proposed ScIMAP algorithm to automatically extract motion parameters from simulation data. The procedure uses only molecular shape similarity and topology information inferred directly from the simulated conformations, and is not biased by a priori known information. The automatically-recovered coordinates prove as excellent reaction coordinates for the molecules studied and can be used to identify stable states and transitions, and as a basis to build free-energy surfaces. The coordinates provide a better description of the free energy landscape when compared with coordinates computed using Principal Components Analysis (PCA), the most popular linear dimensionality reduction technique. The method is first validated on the analysis of the dynamics of an all-atom model of alanine dipeptide, where it successfully recover all previously-known metastable states. When applied to characterize the simulated folding of a coarse-grained model of β-hairpin, in addition to the folded and unfolded states, two symmetric misfolding crossings of the hairpin strands are observed, together with the most likely transitions from one to the other.

Nonlinear machine learning and design of reconfigurable digital colloids

“…We anticipate that these cooperative transition pathways correspond to a small number of slow collective modes of the halo particle dynamics 15,19,37 . Extracting these slow modes from the simulation trajectory reveals the multi-body transition pathways governing the digital colloid dynamics, and also presents kinetically meaningful collective coordinates in which to construct low-dimensional free energy surface mapping out the accessible morphologies, stable states, and dynamical transition pathways 15,16,18,19,[38][39][40][41] .…”

Charting molecular free-energy landscapes with an atlas of collective variables

“…[23][24][25] To better capture the nonlinear low-dimensional geometry of the accessible region in conformational space, the more recently introduced techniques for nonlinear dimensionality reduction (NLDR) [26][27][28] were rapidly applied to understand molecular trajectories, with the underlying hypothesis that these evolve close to a nonlinear manifold often called intrinsic manifold. 9,[29][30][31] The idea behind an important subset of NLDR methods is to find a low-dimensional representation or embedding of the set of conformations such that highdimensional distances are preserved as much as possible. The low-dimensional coordinates of the embedding then become the CVs, provided that a differentiable map is available to rep-resent in low-dimensions general conformations (out-of-sample conformations), which are not necessarily those used in the process of identifying the low-dimensional coordinates.…”

Topological obstructions in the way of data-driven collective variables

“…As a result, low dimensional embeddings appear highly distorted, present loops, and partially collapse information. 21,25,31 Furthermore, because of this topological obstruction, NLDR techniques suggest an excessive number of CVs relative to the intrinsic dimension. 26 To illustrate this fact, we analyze a configurational ensemble of alanine dipeptide obtained from multiple shortrun simulations, and shown in dihedral space in Figure 3(a).…”

“…as a result of bond rotations or steric interactions. [12][13][14] Advances in the field of statistical learning, notably in nonlinear dimensionality reduction (NLDR) techniques, [15][16][17] were quickly embraced by the molecular simulation community to visualize trajectories, realizing that conformations often evolve close to a nonlinear manifold often called intrinsic manifold, [18][19][20][21][22] 24 or LSDMap. 25 Building on these techniques, a number of methods have been developed to systematically define differentiable and nonlinear CVs, to be used in enhanced sampling simulations.…”

“…This issue has not been acknowledged in the literature, but is affecting the performance of NLDR methods in a number of recent studies. 21,25,26,31,32 We conceptually identify this problem, and illustrate its impact using a training set for alanine dipeptide, a benchmark in the field. We also take a close look at the geometry of the intrinsic manifold of this molecule.…”