Algorithmic dimensionality reduction for molecular structure analysis

Brown, William M.; Martin, Shawn; Pollock, Sara; Coutsias, Evangelos A.; Watson, Jean Paul

doi:10.1063/1.2968610

Cited by 67 publications

(95 citation statements)

References 78 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As a result, we expect that linear projection methods will not necessarily provide us with the optimal (lowest-dimensional) representations that reliably separate conformational basins in a clear and useful form. 4,5 A long-standing goal has thus been to develop nonlinear projection/embedding methods for the a) Currently at Department of Biochemistry and Molecular Pharmacology, University of Massachusetts, Worcester, Massachusetts 01655, USA. b) Authors to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

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

Nedialkova

Amat

Kevrekidis

et al. 2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Nedialkova

Amat

Kevrekidis

et al. 2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…This sacrifice in completeness, though, results in a significant increment in computational efficiency. Thus, whereas some of the existing methods are local in nature [7,61], the proposed procedure provides a global description (of part) of the loop-closure variety and, thus, it gives detailled information on its structure, something only offered by few of the existing methods [55,13,6,39]. This information is obtained directly from the geometric equations, without the need of generating dense sets of points from them [6], with the consequent gain in efficiency.…”

Section: Related Workmentioning

confidence: 99%

“…Thus, whereas some of the existing methods are local in nature [7,61], the proposed procedure provides a global description (of part) of the loop-closure variety and, thus, it gives detailled information on its structure, something only offered by few of the existing methods [55,13,6,39]. This information is obtained directly from the geometric equations, without the need of generating dense sets of points from them [6], with the consequent gain in efficiency. The difference of the proposed approach with respect to other systematic methods using dihedral angles [2,42] is that the approach introduced here does not explore the space of dihedral angles, but directly the variety of loop-closed conformations.…”

Section: Related Workmentioning

confidence: 99%

“…Actually, the situation where a solution set is implicitly defined by some constraints appears in many fields and, formally, such set forms a variety, possibly involving several manifolds. This fact and its possible effects on the algorithms for computational chemistry have been largely disregarded until recent works [6,39]. The immediate consequence is that since the implicit variety is usually intricate and non-parametric, sampling methods have difficulties in fully covering it.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exploring the energy landscapes of flexible molecular loops using higher‐dimensional continuation

Porta

Jaillet

2012

J Comput Chem

View full text Add to dashboard Cite

The conformational space of a flexible molecular loop includes the set of conformations fulfilling the geometric loop-closure constraints and its energy landscape can be seen as a scalar field defined on this implicit set. Higher-dimensional continuation tools, recently developed in Dynamical Systems and also applied to Robotics, provide efficient algorithms to trace out implicitly defined sets. This paper describes these tools and applies them to obtain full descriptions of the energy landscapes of short molecular loops that, otherwise, can only be partially explored, mainly via sampling. Moreover, to deal with larger loops, this paper exploits the higher-dimensional continuation tools to find local minima and minimum energy transition paths between them, without deviating from the loop-closure constraints. The proposed techniques are applied to previously studied molecules revealing the intricate structure of their energy landscapes. This paper introduces the use of higher-dimensional continuation tools to explore the energy landscapes of the implicitly-defined conformational spaces of flexible molecular loops. These tools produce an atlas composed by coordinated charts that parametrize the conformational space. The atlas captures the structure of this space, which determines the motion of the loop and the transition paths between conformations, something that is hard to obtain using existing approaches.

show abstract

“…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.…”

mentioning

confidence: 99%

Topological obstructions in the way of data-driven collective variables

Hashemian

Arroyo

2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

Nonlinear dimensionality reduction (NLDR) techniques are increasingly used to visualize molecular trajectories and to create data-driven collective variables for enhanced sampling simulations. The success of these methods relies on their ability to identify the essential degrees of freedom characterizing conformational changes. Here, we show that NLDR methods face serious obstacles when the underlying collective variables present periodicities, e.g. arising from proper dihedral angles. As a result, NLDR methods collapse very distant configurations, thus leading to misinterpretations and inefficiencies in enhanced sampling. Here, we identify this largely overlooked problem and discuss possible approaches to overcome it. We also characterize the geometry and topology of conformational changes of alanine dipeptide, a benchmark system for testing new methods to identify collective variables.PACS numbers: 87.10. Tf, 87.15.hp Thanks to enhanced sampling techniques, it is possible to connect molecular conformations separated by high energy barriers, and accurately compute free energies in systems exhibiting metastability. The success of these techniques relies on a good set of collective variables (CVs), capturing the metastability of the system with a few degrees of freedom. CVs are commonly chosen out of experience or physical intuition. As increasingly complex systems become accessible computationally, 1 the task of selecting appropriate CVs becomes highly nontrivial. 2 This situation has motivated in recent years intense research aimed at systematic and data-driven approaches to select CVs, often relying on statistical learning methods. In particular, dimensionality reduction techniques automatically identify a reduced set of coordinates capturing the essential behavior of a complex system, starting from a pre-existing ensemble of molecular configurations, called training set.The most widespread dimensionality reduction method is principal component analysis (PCA). 3 PCA is a linear method, which selects mutually orthogonal directions such that, by projecting the data onto a few of them, the variance of the projected data is maximized. PCA has been widely applied to characterize the essential dynamics, 4-8 understand molecular flexibility 9 and enhance sampling in molecular dynamics. 10,11 PCA and in general linear dimensionality reduction methods are very popular because of their simplicity. However, they fail to identify nonlinear correlations in the data, which are often present in molecular systems, e.g. 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, 15-17 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, 18-22 although some systems evolve on non-manifold sets. 23 Difa) Electronic

show abstract

Algorithmic dimensionality reduction for molecular structure analysis

Cited by 67 publications

References 78 publications

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

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

Exploring the energy landscapes of flexible molecular loops using higher‐dimensional continuation

Topological obstructions in the way of data-driven collective variables

Contact Info

Product

Resources

About