Spinor product computations for protein conformations

Chys, Pieter; Chacón, Pablo

doi:10.1002/jcc.23002

Cited by 9 publications

(9 citation statements)

References 21 publications

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“…The development of GA is now expanding rapidly, with benefits being found in research into quantum field theory 16 , quantum tunneling 17 , quantum computing 18 , spacetime 11,19,20 , general relativity and cosmology [21][22][23] , computer vision 24 , protein folding 25 , optics and metamaterials [26][27][28] , conformal algebra 29 , electrodynamics 30 , electrical circuit analysis 31 and EPR-Bell experiments 32 .…”

Section: Discussionmentioning

confidence: 99%

Geometric Algebra: A natural representation of three-space

Chappell¹,

Iqbal²,

Abbott³

2011

Preprint

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Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's quaternions and Gibbs' vector system using the dot and cross products. We illustrate however, that Clifford's geometric algebra (GA) provides the most elegant description of physical space. Supporting this conclusion, we firstly show how geometric algebra subsumes the key elements of the competing formalisms and secondly how it provides an intuitive representation of the basic concepts of points, lines, areas and volumes. We also provide two examples where GA has been found to provide an improved description of two key physical phenomena, electromagnetism and quantum theory, without using tensors or complex vector spaces. This paper also provides pedagogical tutorial-style coverage of the various basic applications of geometric algebra in physics.

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Section: Discussionmentioning

confidence: 99%

Geometric Algebra: A natural representation of three-space

Chappell¹,

Iqbal²,

Abbott³

2011

Preprint

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“…The server is based on our original RCD loop closure algorithm ( 11 ). This ab initio algorithm solved the loop closure problem by analytically optimizing randomly selected bonds with a fast updating of loop backbone conformations based on spinor-matrices ( 13 ). The loop closure sampling was steered by a simplified Ramachandran filter that constrains the backbone φ and ψ dihedral angles, and by a simple geometric filter that prevented clashes between the loop backbone atoms and the local protein surroundings.…”

Section: Methodsmentioning

confidence: 99%

RCD+: Fast loop modeling server

López‐Blanco¹,

Canosa-Valls²,

Li³

et al. 2016

Nucleic Acids Res

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Modeling loops is a critical and challenging step in protein modeling and prediction. We have developed a quick online service (http://rcd.chaconlab.org) for ab initio loop modeling combining a coarse-grained conformational search with a full-atom refinement. Our original Random Coordinate Descent (RCD) loop closure algorithm has been greatly improved to enrich the sampling distribution towards near-native conformations. These improvements include a new workflow optimization, MPI-parallelization and fast backbone angle sampling based on neighbor-dependent Ramachandran probability distributions. The server starts by efficiently searching the vast conformational space from only the loop sequence information and the environment atomic coordinates. The generated closed loop models are subsequently ranked using a fast distance-orientation dependent energy filter. Top ranked loops are refined with the Rosetta energy function to obtain accurate all-atom predictions that can be interactively inspected in an user-friendly web interface. Using standard benchmarks, the average root mean squared deviation (RMSD) is 0.8 and 1.4 Å for 8 and 12 residues loops, respectively, in the challenging modeling scenario in where the side chains of the loop environment are fully remodeled. These results are not only very competitive compared to those obtained with public state of the art methods, but also they are obtained ∼10-fold faster.

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“…Results on the equivalent quaternion-matrix scheme show it to be one of the fastest available methods. 31,32 2.3. Geometric Filters.…”

Section: Methodsmentioning

confidence: 99%

“…Rotation bonds are chosen randomly instead of sequentially, and a hybrid spinor-matrix approach is implemented for fast conformational updating. Spinor-matrices should in principle yield the fastest computational scheme. , For the optimization protocol, a semianalytical procedure is used and is based on theory in ref . A further key element is the introduction of different types of geometrical filters with specific code placement in the algorithm.…”

Section: Introductionmentioning

confidence: 99%

Random Coordinate Descent with Spinor-matrices and Geometric Filters for Efficient Loop Closure

Chys

Chacón

2013

J. Chem. Theory Comput.

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Protein loop closure constitutes a critical step in loop and protein modeling whereby geometrically feasible loops must be found between two given anchor residues. Here, a new analytic/iterative algorithm denoted random coordinate descent (RCD) to perform protein loop closure is described. The algorithm solves loop closure through minimization as in cyclic coordinate descent but selects bonds for optimization randomly, updates loop conformations by spinor-matrices, performs loop closure in both chain directions, and uses a set of geometric filters to yield efficient conformational sampling. Geometric filters allow one to detect clashes and constrain dihedral angles on the fly. The RCD algorithm is at least comparable to state of the art loop closure algorithms due to an excellent balance between efficiency and intrinsic sampling capability. Furthermore, its efficiency allows one to improve conformational sampling by increasing the sampling number without much penalty. Overall, RCD turns out to be accurate, fast, robust, and applicable over a wide range of loop lengths. Because of the versatility of RCD, it is a solid alternative for integration with current loop modeling strategies.

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Spinor product computations for protein conformations

Cited by 9 publications

References 21 publications

Geometric Algebra: A natural representation of three-space

Geometric Algebra: A natural representation of three-space

RCD+: Fast loop modeling server

Random Coordinate Descent with Spinor-matrices and Geometric Filters for Efficient Loop Closure

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