Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction

Abstract

The definition of reaction coordinates for the characterization of a protein-folding reaction has long been a controversial issue, even for the ''simple'' case in which one single free-energy barrier separates the folded and unfolded ensemble. We propose a general approach to this problem to obtain a few collective coordinates by using nonlinear dimensionality reduction. We validate the usefulness of this method by characterizing the folding landscape associated with a coarse-grained protein model of src homology 3 as sampled by molecular dynamics simulations. The folding freeenergy landscape projected on the few relevant coordinates emerging from the dimensionality reduction can correctly identify the transition-state ensemble of the reaction. The first embedding dimension efficiently captures the evolution of the folding process along the main folding route. These results clearly show that the proposed method can efficiently find a low-dimensional representation of a complex process such as protein folding.reaction coordinate ͉ transition state ͉ manifold ͉ embedding ͉ ISOMAP

Multiscale modeling of emergent materials: biological and soft matter

“…Such techniques could be applied to, e.g., internal coordinates of a macromolecule to distinguish characteristic conformational changes from local fluctuations. [102][103][104] Traditional methods such as principal component analysis are linear, and are not always suitable for analysis of complex data where the relationships are typically non-linear. 105 Traditional non-linear projection techniques, such as Sammon mapping, can be computationally costly for large amounts of data.…”

A comparative analysis of clustering algorithms: O2 migration in truncated hemoglobin I from transition networks

“…61,62 In the following, we briefly summarize the different approaches employed in the present work, including k-means clustering, [61][62][63][64] MCL, 65 and the locally scaled diffusion map (LSDMap) methods. 66 All of them are applied to the same data set consisting of the Cartesian coordinates of O 2 from reoriented trajectories with the Fe-atom at the origin and the least-squares plane containing the four nitrogen atoms of the heme group of the protein in the x y-plane. The total number of configurations available is 6.4·10 5 of which 5.8·10 5 were analyzed, except for LSDMap, as explained below.…”

Algorithmic dimensionality reduction for molecular structure analysis

“…Nguyen 39 40 algorithm to the analysis of folding simulation data for a coarse-grained bead model representative of a protein backbone, demonstrating that nonlin-ear dimensionality reduction provided a more accurate embedding of the reaction coordinates than linear techniques. 41 However, despite their promise, it is difficult to accurately assess the efficacy of nonlinear dimensionality reduction algorithms for molecular structure analysis. The difficulty arises from two factors: ͑1͒ the intrinsic dimensionality for most problems is unknown, and ͑2͒ there is debate for some problems as to whether simulation approaches can provide sufficient sampling of the phase space to facilitate an accurate analysis of dimensionality reduction.…”