Internal‐to‐Cartesian back transformation of molecular geometry steps using high‐order geometric derivatives

Rybkin, Vladimir V.; Ekström, Ulf; Helgaker, Trygve

doi:10.1002/jcc.23327

Cited by 8 publications

(7 citation statements)

References 23 publications

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“…One more approach to the reverse-transformation problem was used by Dachsel et al [9] and V. V. Rybkin et al [10] for visualization of curvilinear molecular vibrations. It finds a discrete path in Cartesian coordinates corresponding to a set of finite displacements in curvilinear normal coordinates using the Taylor expansion of the former with respect to the latter.…”

Section: Related Workmentioning

confidence: 99%

GPU implementation of reverse coordinate conversion for proteins

Bayati

Bardhan

Leeser

2015

2015 IEEE High Performance Extreme Computing Conference (HPEC)

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We describe the first parallel algorithm to obtain Cartesian coordinates of a molecular structure from internal coordinates. This algorithm is important for problems such as protein engineering and fitting protein structures to experimental data. Proteins contain thousands to millions of atoms. Their positions can be represented using one of two methods: Cartesian or internal coordinates (bond lengths, angles, etc.). In molecular dynamics and modeling of proteins in different conformational states, it is often necessary to transform one coordinate system to another. In addition, since protein structures change over time, any computation must be done over successive time frames, increasing the computational load. To lessen this computational load we have applied different parallel techniques to the coordinate conversion problem. Converting Cartesian coordinates to internal ones is easily parallelized, and we have previously reported a GPU implementation. On the other hand, the reverse computation has inherent linear dependency because bond lengths and angles are relative to neighboring atoms. Existing implementations walk over a protein structure in a sequential fashion. This paper presents the first parallel implementation of internal to Cartesian coordinates, in which substructures of the protein backbone are converted into their own local Cartesian coordinate spaces, and then combined using a reduction technique to find global Cartesian coordinates. We observe one order of magnitude speedup using parallel processing on a GPU.

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Section: Related Workmentioning

confidence: 99%

GPU implementation of reverse coordinate conversion for proteins

Bayati

Bardhan

Leeser

2015

2015 IEEE High Performance Extreme Computing Conference (HPEC)

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“…The expressions have been known for decades, and they are long and cumbersome; in particular for the second derivatives of proper and improper torsion angles. The calculation can be performed using a program for symbolic or automatic differentiation [63] but the method is unsatisfactory when there exist a set of simple rules to perform the same calculation. By representing a molecule in internal coordinates and using fundamental concepts from linear algebra, simple rules to calculate the first-and second-order derivatives of an internal coordinate can be formulated.…”

Section: Introductionmentioning

confidence: 99%

“…The Wilson B-matrix is required to calculate the gradient with respect to the Cartesian coordinates which is used in geometry optimization. Furthermore, its pseudo-inverse is important, for example to optimize molecular structures using internal coordinates instead of Cartesian coordinates [75,63].…”

Section: Introductionmentioning

confidence: 99%

Protein structure refinement by optimization

Carlsen

Røgen

2015

Proteins

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SummaryProteins are the main active elements of life whose chemical activities regulate cellular activities. A protein is characterized by having a sequence of amino acids and a three dimensional structure. The three-dimensional structure has only been determined experimentally for 50000 of the seven million sequences that are known. Determining the protein structure from its sequence of amino acids is therefore a major problem in computational structural biology and is referred to as the protein folding problem. The folding problem is solved using de novo methods or comparative methods depending on whether the three-dimensional structure of a homologous sequence is known. Whether or not a protein model can be used for industrial purposes depends on the quality of the predicted structure. A model can be used to design a drug when the quality is high.The overall goal of this project is to assess and improve the quality of a predicted structure. The starting point of this work is a technique called metric training where a knowledge-based protein potential, for a fixed set of native protein structures and a set of deformed decoys for each native structure, is designed to have native-decoy energy gabs that correlates maximally to a native-decoy distance. The main contribution of this thesis is methods developed for analyzing the performance of metrically trained knowledge-based potentials and for optimizing their performance while making them less dependent on the decoy set used to define them. We focus on using the gradient and the Hessian in the analysis and present a novel smooth solvation potential but otherwise the studied potential is kept close to standard coarse grained potentials.We analyze the importance of the choice of metric both when used in metric training and when used in the evaluation of the performance of the resulting potential and find a significant improvement by using a metric based on intrinsic geometry. It is well-known that energy minimization of a potential that is efficient in ordering a fixed set of decoys need not bring the decoys closer to the native state. The next part of the work is focused on improving the convergence of decoy structures and we present a method that significantly improves the results of shorter energy minimizations of a metrically trained potential and discuss its limitations. In an ideal potential all nearnative decoys will converge toward the native structure being at-least a local minimum of the potential. To address how far the current functional form of the potential is from an ideal potential we present two methods for finding the optimal metrically trained potential that simultaneous has a number of native structures as a local minimum. Our results generally indicate that a more fine-grained potential is needed to meet desired model accuracies but even with our coarse-grained model we obtain good results and there is an unexplored possibility to combine it with comparative modeling.To allow fast energy minimization in Matlab a new set of more sparse formulas...

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“…The Wilson B‐matrix is required to calculate the gradient with respect to the Cartesian coordinates which is used in geometry optimization. Furthermore, its pseudoinverse is important, for example, to optimize molecular structures using internal coordinates instead of Cartesian coordinates …”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, its pseudoinverse is important, for example, to optimize molecular structures using internal coordinates instead of Cartesian coordinates. [5,17] The first derivatives of an internal coordinate with respect to the Cartesian coordinates can be simplified if they are expressed in two orthonormal bases. Two orthonormal bases are connected by a transformation matrix which only depends on the bond angles and the torsion angles.…”

Section: Introductionmentioning

confidence: 99%

Using operators to expand the block matrices forming the Hessian of a molecular potential

Carlsen

2014

J Comput Chem

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We derive compact expressions of the second-order derivatives of bond length, bond angle, and proper and improper torsion angle potentials, in terms of operators represented in two orthonormal bases. Hereby, simple rules to generate the Hessian of an internal coordinate or a molecular potential can be formulated. The algorithms we provide can be implemented efficiently in high-level programming languages using vectorization. Finally, the method leads to compact expressions for a second-order expansion of an internal coordinate or a molecular potential.

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Internal‐to‐Cartesian back transformation of molecular geometry steps using high‐order geometric derivatives

Cited by 8 publications

References 23 publications

GPU implementation of reverse coordinate conversion for proteins

GPU implementation of reverse coordinate conversion for proteins

Protein structure refinement by optimization

Using operators to expand the block matrices forming the Hessian of a molecular potential

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