Polymer conformations in internal (polyspherical) coordinates

Pesonen, Janne; Henriksson, Krister O. E.

doi:10.1002/jcc.21474

Cited by 8 publications

(5 citation statements)

References 16 publications

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“…This resulted in a total of 177 degrees of freedom. All calculations were carried out using the previously developed methodology [34,35] as implemented in the computer code tod.…”

Section: Test Casementioning

confidence: 99%

Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

et al. 2012

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Normal mode analysis (NMA) was introduced in 1930s as a framework to understand the structure of the observed vibration-rotation spectrum of several small molecules. During the past three decades NMA has also become a popular alternative to figuring out the large-scale motion of proteins and other macromolecules. However, the "standard" NMA is based on approximations, which sometimes are unphysical. Especially problematic is the assumption that atoms move only "infinitesimally", which, of course, is an oxymoron when large amplitude motions are concerned. The "infinitesimal" approximation has the further unfortunate side effect of masking the physical importance of the coupling between vibrational and rotational degrees of freedom. Here, we present a novel formulation of the NMA, which is applied for finite motions in non-Eckart body-frame. Contrary to standard normal mode theory, our approach starts by assuming a harmonic potential in generalized coordinates, and tries to avoid the linearization of the coordinates. It also takes explicitly into account the Coriolis terms, which couple vibrations and rotations, and the terms involving Christoffel symbols, which are ignored by default in the standard NMA. We also computationally explore the effect of various terms to the solutions of the NMA equation of motions.

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“…This resulted in a total of 177 degrees of freedom. All calculations were carried out using the previously developed methodology [34,35] as implemented in the computer code tod.…”

Section: Test Casementioning

confidence: 99%

Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

et al. 2012

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“…It is well known that the B-matrix has a compact expression when using two orthonormal bases [64]. The configuration of a molecule can be generated from its internal coordinates using either Euler angles [76,16] or geometric (Clifford) algebra [17]. The calculation of the first derivatives has therefore also been made using geometric algebra to avoid the Gimbal lock problem [77].…”

Section: Introductionmentioning

confidence: 99%

“…It is easy to see that they only depend on the internal coordinates [16,17]. Hereby, all the atoms can be transformed to a basis system with a set of rigid transformations.…”

mentioning

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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“…[18,19] or geometric (Clifford) algebra. [20] The calculation of the first derivatives has, therefore, also been made using geometric algebra to avoid the Gimbal lock problem. [21] A method to calculate the second derivatives of an internal coordinate using a single orthonormal basis can be found in Ref.…”

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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Polymer conformations in internal (polyspherical) coordinates

Cited by 8 publications

References 16 publications

Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

Protein structure refinement by optimization

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

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