A dimensionality reduction approach to modeling protein flexibility

Teodoro, Miguel L.; Phillips, George N.; Kavraki, Lydia E.

doi:10.1145/565196.565235

Cited by 31 publications

(33 citation statements)

References 42 publications

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“…To determine the classical cadherin energy landscape, we used PCA to evaluate the most important coordinate variations (24,25) from a set of 11 classical cadherin dimeric crystal structures that include both X-dimers and S-dimers. The entire structural variation present in the set could be summarized in only a few important motions or principal components (PCs), which provided the directions of fluctuation of each residue along the x, y, and z coordinates.…”

Section: Cadherin Energy Landscape and Transition Pathway For The Intmentioning

confidence: 99%

“…We first build the energy landscape for Ecad trans dimers and investigate the transition pathway for the interconversion between X-dimers and S-dimers by evaluating the principal motions (24,25) of cadherin experimental structures using principal component analysis (PCA). Construction of the multidimensional energy landscape of cadherins sheds light on the different conformations of Ecad dimers and the steric constraints that govern their interconversion.…”

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confidence: 99%

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Molecular determinants of cadherin ideal bond formation: Conformation-dependent unbinding on a multidimensional landscape

Manibog

Sankar

Kim

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Classical cadherin cell-cell adhesion proteins are essential for the formation and maintenance of tissue structures; their primary function is to physically couple neighboring cells and withstand mechanical force. Cadherins from opposing cells bind in two distinct trans conformations: strand-swap dimers and X-dimers. As cadherins convert between these conformations, they form ideal bonds (i.e., adhesive interactions that are insensitive to force). However, the biophysical mechanism for ideal bond formation is unknown. Here, we integrate single-molecule force measurements with coarsegrained and atomistic simulations to resolve the mechanistic basis for cadherin ideal bond formation. Using simulations, we predict the energy landscape for cadherin adhesion, the transition pathways for interconversion between X-dimers and strand-swap dimers, and the cadherin structures that form ideal bonds. Based on these predictions, we engineer cadherin mutants that promote or inhibit ideal bond formation and measure their force-dependent kinetics using single-molecule force-clamp measurements with an atomic force microscope. Our data establish that cadherins adopt an intermediate conformation as they shuttle between X-dimers and strandswap dimers; pulling on this conformation induces a torsional motion perpendicular to the pulling direction that unbinds the proteins and forms force-independent ideal bonds. Torsional motion is blocked when cadherins associate laterally in a cis orientation, suggesting that ideal bonds may play a role in mechanically regulating cadherin clustering on cell surfaces.T he formation and maintenance of multicellular structures rely upon specific and robust intercellular adhesion (1). Cell-cell adhesion proteins, such as classical cadherins, are crucial in these processes (2-4). Cadherins are Ca 2+ -dependent transmembrane proteins that mediate the integrity of all soft tissues. One of their principal functions is to bind cells and dampen mechanical perturbations; however, the biophysical mechanism by which cadherins tune adhesion is not understood. Here, we combine predictive simulations with quantitative single-molecule force-clamp measurements to show that E-cadherin (Ecad), a prototypical classical cadherin, dampens the effect of tugging forces by switching conformations and unbinding along a strongly preferred pathway on a multidimensional landscape.Cadherin adhesive function resides in their ectodomain that is comprised of five extracellular (EC) domains arranged in tandem (5-9). Structural studies (10-15) and single-molecule fluorescence measurements (16) show that opposing ectodomains bind in two distinct trans conformations: strand-swap dimers (S-dimers) and X-dimers. S-dimers, which have a higher binding affinity, are formed by the exchange of a conserved tryptophan at position 2 (W2) between binding partners (10, 13, 17-19). In contrast, low-affinity X-dimers are formed by extensive surface interactions around the linker region that connects the two outermost domains (EC1-EC2) (11,12,(14)(15)...

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Section: Cadherin Energy Landscape and Transition Pathway For The Intmentioning

confidence: 99%

mentioning

confidence: 99%

Molecular determinants of cadherin ideal bond formation: Conformation-dependent unbinding on a multidimensional landscape

Manibog

Sankar

Kim

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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“…Some authors have reported preliminary results showing that an angle-based analysis of conformational data is very sensitive to noise and prone to error. 50 Further, allowing fluctuations in bond lengths and angles might have the effect of making the DHAs more flexible, 18 as evidenced by differences obtained from normal mode analysis when using DHAs rather than Cartesian coordinates.…”

Section: B High-dimensional Encodingsmentioning

confidence: 99%

Algorithmic dimensionality reduction for molecular structure analysis

Brown

Martin

Pollock

et al. 2008

The Journal of Chemical Physics

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Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing low-dimensional representations of molecular motion. This has been used to help visualize complex energy landscapes, to extend the time scales of simulation, and to improve the efficiency of optimization. Until recently, linear approaches for dimensionality reduction have been employed. Here, we investigate the efficacy of several automated algorithms for nonlinear dimensionality reduction for representation of trans, trans-1,2,4-trifluorocyclo-octane conformation-a molecule whose structure can be described on a 2-manifold in a Cartesian coordinate phase space. We describe an efficient approach for a deterministic enumeration of ring conformations. We demonstrate a drastic improvement in dimensionality reduction with the use of nonlinear methods. We discuss the use of dimensionality reduction algorithms for estimating intrinsic dimensionality and the relationship to the Whitney embedding theorem. Additionally, we investigate the influence of the choice of high-dimensional encoding on the reduction. We show for the case studied that, in terms of reconstruction error root mean square deviation, Cartesian coordinate representations and encodings based on interatom distances provide better performance than encodings based on a dihedral angle representation.

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“…It is used in many fields where subspace identification is needed, and in particular in [19], in a motion planning context. The use of PCA there is different than ours though, since it is only applied to motion description, while we use it to control and generate motion.…”

Section: Contributionmentioning

confidence: 99%

Control of Probabilistic Diffusion in Motion Planning

Dalibard

Laumond

2009

Springer Tracts in Advanced Robotics

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The paper presents a method to control probabilistic diffusion in motion planning algorithms. The principle of the method is to use on line the results of a diffusion algorithm to describe the free space in which the planning takes place. Given that description, it makes the diffusion go faster in favoured directions. That way, if the free space appears as a small volume around a submanifold of a highly dimensioned configuration space, the method overcomes the usual limitations of diffusion algorithms and finds a solution quickly. The presented method is theoretically analyzed and experimentally compared to known motion planning algorithms.1 Problem statement, related work and contribution General FrameworkMotion planning problems have been intensively studied in the last decades, with applications in many diverse areas, such as robot locomotion, part disassembly problems, digital actors in computer animation, or even protein folding and drug design. For comprehensive overviews of motion planning problems and methods, one can refer to [10], [1] and [13].In the past fifteen years, two kinds of configuration space (CS) search paradigms have been investigated with success.• The sampling approach, first introduced in [8] as probabilistic roadmaps (PRM), consists in computing a graph, or a roadmap, whose vertices are collision free configurations, sampled at random in the free space and whose edges reflect the existence of a collision free elementary path between two configurations. It aims at capturing the topology of the free space in a learning phase in order to handle multiple queries in a solving phase. • The diffusion approach, introduced in both [5] and [9], which includes RRT planners, consists in solving single queries by growing a tree rooted at the start configuration towards the goal configuration to be reached. † This work is partly supported by the French ANR-RNTL project PerfRV2. Sébastien Dalibard and Jean-Paul LaumondThese methods have been proven to be efficient and suitable for a large class of motion planning problems. Work has been done to analyze and validate theoretically these algorithms. Probabilistic completeness has been studied and proved for RRT [9], as well as for PRM [7]. Narrow PassagesIn some environments, however, passing through so-called narrow passages is a difficult task for probabilistic motion planners. A lot of work has been done to evaluate this difficulty, as well as to overcome it.The formalism of expensive spaces was first presented in [5]. It quantifies the complexity of a configuration space from a randomized planning point of view. This formalism helps understanding what makes a motion planning problem difficult. Narrow passages and the configuration space dimension are identified as the main sources of complexity.It is believed that probabilistic planning algorithms have an exponential complexity with respect to the dimension of the configuration space, as the number of nodes needed to describe the free space has a combinatorial explosion. The presence of nar...

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A dimensionality reduction approach to modeling protein flexibility

Cited by 31 publications

References 42 publications

Molecular determinants of cadherin ideal bond formation: Conformation-dependent unbinding on a multidimensional landscape

Molecular determinants of cadherin ideal bond formation: Conformation-dependent unbinding on a multidimensional landscape

Algorithmic dimensionality reduction for molecular structure analysis

Control of Probabilistic Diffusion in Motion Planning

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