The paper deals with a model-free approach to the analysis of quasielastic neutron scattering int... more The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝tα, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.
We describe a numerical method for calculating hydrodynamic interactions between spherical partic... more We describe a numerical method for calculating hydrodynamic interactions between spherical particles efficiently and accurately, both for particles immersed in an infinite liquid and for systems with periodic boundary conditions. Our method is based on a multipole ...
382 chain deformations are more important and seem to be strongly correlated with the side-chain ... more 382 chain deformations are more important and seem to be strongly correlated with the side-chain rotations. Comparing the simulated coherent scattering function of C-phycocyanin to a neutron spin-echo spectrum we show that our model can also describe collective ...
HAL (Le Centre pour la Communication Scientifique Directe), Oct 26, 2019
This ActivePaper file contains all the code and data that was used in generating the figures for ... more This ActivePaper file contains all the code and data that was used in generating the figures for the article "Memory Effects in a Random Walk Description of Protein Structure Ensembles" by Gerald R Kneller and Konrad Hinsen, J. Chem. Phys. <strong>150</strong>, 064911 (2019); https://doi.org/10.1063/1.5054887
A coarse-grained geometrical model for protein secondary-structure description and analysis is pr... more A coarse-grained geometrical model for protein secondary-structure description and analysis is presented which uses only the positions of the C(α) atoms. A space curve connecting these positions by piecewise polynomial interpolation is constructed and the folding of the protein backbone is described by a succession of screw motions linking the Frenet frames at consecutive C(α) positions. Using the ASTRAL subset of the SCOPe database of protein structures, thresholds are derived for the screw parameters of secondary-structure elements and demonstrate that the latter can be reliably assigned on the basis of a C(α) model. For this purpose, a comparative study with the widely used DSSP (Define Secondary Structure of Proteins) algorithm was performed and it was shown that the parameter distribution corresponding to the ensemble of all pure C(α) structures in the RCSB Protein Data Bank matches that of the ASTRAL database. It is expected that this approach will be useful in the development of structure-refinement techniques for low-resolution data.
We present a new version of the program package nMoldyn, which has been originally developed for ... more We present a new version of the program package nMoldyn, which has been originally developed for a neutron-scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys. Commun. 1995, 91, 191) and was later rewritten to include in-depth time series analyses and a graphical user interface (Rog et al., J. Comput. Chem. 2003, 24, 657). The main improvement in this new version and the focus of this article are the parallelization of all the analysis algorithms for use on multicore desktop computers as well as distributed-memory computing clusters. The parallelization is based on a task farming approach which maintains a simple program structure permitting easy modification and extension of the code to integrate new analysis methods. V
In order to perform a specific function, a protein needs to fold into the proper structure. Predi... more In order to perform a specific function, a protein needs to fold into the proper structure. Prediction the protein structure from its amino acid sequence has still been unsolved problem. The main focus of this thesis is to develop new approach on the protein structure modeling by means of differential geometry and integrable theory. The start point is to simplify a protein backbone as a piecewise linear polygonal chain, with vertices recognized as the central alpha carbons of the amino acids. Frenet frame and equations from differential geometry are used to describe the geometric shape of the protein linear chain. Within the framework of integrable theory, we also develop a general geometrical approach, to systematically derive Hamiltonian energy functions for piecewise linear polygonal chains. These theoretical studies is expected to provide a solid basis for the general description of curves in three space dimensions. An efficient algorithm of loop closure has been proposed.
Starting from the N-body friction matrix of an unconstrained system of N rigid particles immersed... more Starting from the N-body friction matrix of an unconstrained system of N rigid particles immersed in a viscous liquid, we derive rigorous expressions for the corresponding friction and mobility matrices of a geometrically constrained dynamical system. Our method is based on the fact that geometrical constraints in a dynamical system can be cast in the form of linear constraints for the Cartesian translational and angular velocities of its constituents. Corresponding equations of motion for Molecular Dynamics simulations have been derived recently [1]. Using the concept of generalized inverse matrices, we find the form of the constrained friction and mobility matrix in Cartesian and in reduced coordina tes. We show that the equations of motion for Stokesian Dynamics can be derived from a minimum principle which is similar to Gaus’ principle of least constraint in classical mechanics. We relate our approach for deriving constrained friction and mobility matrices to Kirkwood’s method where holonomic constraints acting between point-like particles are described by generalized coordinates and tensor algebra in curvilinear space. As an application, we perform a Stokesian Dynamics simulation of sedimentation of a small model polymer consisting of five spherical monomers connected by massless sticks and joints.
Acta Crystallographica Section D-biological Crystallography, Nov 9, 2012
Acta Crystallographica Section D: Biological Crystallography welcomes the submission of papers co... more Acta Crystallographica Section D: Biological Crystallography welcomes the submission of papers covering any aspect of structural biology, with a particular emphasis on the structures of biological macromolecules and the methods used to determine them. Reports on new protein structures are particularly encouraged, as are structure-function papers that could include crystallographic binding studies, or structural analysis of mutants or other modified forms of a known protein structure. The key criterion is that such papers should present new insights into biology, chemistry or structure. Papers on crystallographic methods should be oriented towards biological crystallography, and may include new approaches to any aspect of structure determination or analysis. Papers on the crystallization of biological molecules will be accepted providing that these focus on new methods or other features that are of general importance or applicability.
We present a model for the local diffusion-relaxation dynamics of the Cα-atoms in proteins descri... more We present a model for the local diffusion-relaxation dynamics of the Cα-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ⩾ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the Cα-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.
Proteins: Structure, Function, and Bioinformatics, 1993
The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics s... more The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two typesof rigid‐body motions are considered: one in which the helices are rigid units and one in which the side‐chains are rigid units. Using a quaternionbased algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid‐body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean‐square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen: rigid‐helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the hel...
382 chain deformations are more important and seem to be strongly correlated with the side-chain ... more 382 chain deformations are more important and seem to be strongly correlated with the side-chain rotations. Comparing the simulated coherent scattering function of C-phycocyanin to a neutron spin-echo spectrum we show that our model can also describe collective ...
We present a new version of the program package nMoldyn, which has been originally developed for ... more We present a new version of the program package nMoldyn, which has been originally developed for a neutron-scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys. Commun. 1995, 91, 191) and was later rewritten to include in-depth time series analyses and a graphical user interface (Rog et al., J. Comput. Chem. 2003, 24, 657). The main improvement in this new version and the focus of this article are the parallelization of all the analysis algorithms for use on multicore desktop computers as well as distributed-memory computing clusters. The parallelization is based on a task farming approach which maintains a simple program structure permitting easy modification and extension of the code to integrate new analysis methods. V
We analyze the angular distributions for the (α, 3 He) and (α, t) reactions on 28 Si for projecti... more We analyze the angular distributions for the (α, 3 He) and (α, t) reactions on 28 Si for projectile energies ranging from 50 to 120 MeV based on the partial-wave representation of the transfer amplitude expressed in terms of the S-matrices for the entrance and exit channels, with an emphasis on identifying Airy minima of various orders. The calculations have been performed using a six-parameter S-matrix model and S-matrix parameters obtained from the analysis of elastic scattering data. The first-and (or) second-order Airy minima are clearly identified in the analyzed transfer reaction angular distributions at intermediate angles. The detected Airy minima are found to be due to the interference between several inner and surface partial waves. The impact parameters of these waves are in the range of 1-6 fm, the upper boundary of which is less than the strong absorption radius.
Dynamics of Biological Macromolecules by Neutron Scattering provides insight into the study of th... more Dynamics of Biological Macromolecules by Neutron Scattering provides insight into the study of the dynamics of biological macromolecules by neutron scattering techniques. The applicability of neutron scattering to expanding fields of biological studies is very extended and the neutron scattering community is interested in using these unique technologies to their best advantage. The book is focused on recent scientific results on biomolecular motions obtained by using neutron spectroscopy, and also discusses likely directions of future work on biological macromolecular systems while outlining some challenging, hitherto inaccessible problem areas. The Ebook should be very useful for biophysicists, biochemists, experts and non-experts in neutron scattering.
Quaternions are generalized complex numbers and represent rotations in space as ordinary complex ... more Quaternions are generalized complex numbers and represent rotations in space as ordinary complex numbers represent rotations in a plane. In the context of molecular dynamics (MD) simulations they have been ‘rediscovered’ for the integration of the rotational equation of motion of rigid molecules since they allow one to write down these equations in a singularity-free form. In this paper applications to the analysis of molecular systems are described.
The paper deals with a model-free approach to the analysis of quasielastic neutron scattering int... more The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝tα, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.
We describe a numerical method for calculating hydrodynamic interactions between spherical partic... more We describe a numerical method for calculating hydrodynamic interactions between spherical particles efficiently and accurately, both for particles immersed in an infinite liquid and for systems with periodic boundary conditions. Our method is based on a multipole ...
382 chain deformations are more important and seem to be strongly correlated with the side-chain ... more 382 chain deformations are more important and seem to be strongly correlated with the side-chain rotations. Comparing the simulated coherent scattering function of C-phycocyanin to a neutron spin-echo spectrum we show that our model can also describe collective ...
HAL (Le Centre pour la Communication Scientifique Directe), Oct 26, 2019
This ActivePaper file contains all the code and data that was used in generating the figures for ... more This ActivePaper file contains all the code and data that was used in generating the figures for the article "Memory Effects in a Random Walk Description of Protein Structure Ensembles" by Gerald R Kneller and Konrad Hinsen, J. Chem. Phys. <strong>150</strong>, 064911 (2019); https://doi.org/10.1063/1.5054887
A coarse-grained geometrical model for protein secondary-structure description and analysis is pr... more A coarse-grained geometrical model for protein secondary-structure description and analysis is presented which uses only the positions of the C(α) atoms. A space curve connecting these positions by piecewise polynomial interpolation is constructed and the folding of the protein backbone is described by a succession of screw motions linking the Frenet frames at consecutive C(α) positions. Using the ASTRAL subset of the SCOPe database of protein structures, thresholds are derived for the screw parameters of secondary-structure elements and demonstrate that the latter can be reliably assigned on the basis of a C(α) model. For this purpose, a comparative study with the widely used DSSP (Define Secondary Structure of Proteins) algorithm was performed and it was shown that the parameter distribution corresponding to the ensemble of all pure C(α) structures in the RCSB Protein Data Bank matches that of the ASTRAL database. It is expected that this approach will be useful in the development of structure-refinement techniques for low-resolution data.
We present a new version of the program package nMoldyn, which has been originally developed for ... more We present a new version of the program package nMoldyn, which has been originally developed for a neutron-scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys. Commun. 1995, 91, 191) and was later rewritten to include in-depth time series analyses and a graphical user interface (Rog et al., J. Comput. Chem. 2003, 24, 657). The main improvement in this new version and the focus of this article are the parallelization of all the analysis algorithms for use on multicore desktop computers as well as distributed-memory computing clusters. The parallelization is based on a task farming approach which maintains a simple program structure permitting easy modification and extension of the code to integrate new analysis methods. V
In order to perform a specific function, a protein needs to fold into the proper structure. Predi... more In order to perform a specific function, a protein needs to fold into the proper structure. Prediction the protein structure from its amino acid sequence has still been unsolved problem. The main focus of this thesis is to develop new approach on the protein structure modeling by means of differential geometry and integrable theory. The start point is to simplify a protein backbone as a piecewise linear polygonal chain, with vertices recognized as the central alpha carbons of the amino acids. Frenet frame and equations from differential geometry are used to describe the geometric shape of the protein linear chain. Within the framework of integrable theory, we also develop a general geometrical approach, to systematically derive Hamiltonian energy functions for piecewise linear polygonal chains. These theoretical studies is expected to provide a solid basis for the general description of curves in three space dimensions. An efficient algorithm of loop closure has been proposed.
Starting from the N-body friction matrix of an unconstrained system of N rigid particles immersed... more Starting from the N-body friction matrix of an unconstrained system of N rigid particles immersed in a viscous liquid, we derive rigorous expressions for the corresponding friction and mobility matrices of a geometrically constrained dynamical system. Our method is based on the fact that geometrical constraints in a dynamical system can be cast in the form of linear constraints for the Cartesian translational and angular velocities of its constituents. Corresponding equations of motion for Molecular Dynamics simulations have been derived recently [1]. Using the concept of generalized inverse matrices, we find the form of the constrained friction and mobility matrix in Cartesian and in reduced coordina tes. We show that the equations of motion for Stokesian Dynamics can be derived from a minimum principle which is similar to Gaus’ principle of least constraint in classical mechanics. We relate our approach for deriving constrained friction and mobility matrices to Kirkwood’s method where holonomic constraints acting between point-like particles are described by generalized coordinates and tensor algebra in curvilinear space. As an application, we perform a Stokesian Dynamics simulation of sedimentation of a small model polymer consisting of five spherical monomers connected by massless sticks and joints.
Acta Crystallographica Section D-biological Crystallography, Nov 9, 2012
Acta Crystallographica Section D: Biological Crystallography welcomes the submission of papers co... more Acta Crystallographica Section D: Biological Crystallography welcomes the submission of papers covering any aspect of structural biology, with a particular emphasis on the structures of biological macromolecules and the methods used to determine them. Reports on new protein structures are particularly encouraged, as are structure-function papers that could include crystallographic binding studies, or structural analysis of mutants or other modified forms of a known protein structure. The key criterion is that such papers should present new insights into biology, chemistry or structure. Papers on crystallographic methods should be oriented towards biological crystallography, and may include new approaches to any aspect of structure determination or analysis. Papers on the crystallization of biological molecules will be accepted providing that these focus on new methods or other features that are of general importance or applicability.
We present a model for the local diffusion-relaxation dynamics of the Cα-atoms in proteins descri... more We present a model for the local diffusion-relaxation dynamics of the Cα-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ⩾ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the Cα-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.
Proteins: Structure, Function, and Bioinformatics, 1993
The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics s... more The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two typesof rigid‐body motions are considered: one in which the helices are rigid units and one in which the side‐chains are rigid units. Using a quaternionbased algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid‐body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean‐square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen: rigid‐helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the hel...
382 chain deformations are more important and seem to be strongly correlated with the side-chain ... more 382 chain deformations are more important and seem to be strongly correlated with the side-chain rotations. Comparing the simulated coherent scattering function of C-phycocyanin to a neutron spin-echo spectrum we show that our model can also describe collective ...
We present a new version of the program package nMoldyn, which has been originally developed for ... more We present a new version of the program package nMoldyn, which has been originally developed for a neutron-scattering oriented analysis of molecular dynamics simulations of macromolecular systems (Kneller et al., Comput. Phys. Commun. 1995, 91, 191) and was later rewritten to include in-depth time series analyses and a graphical user interface (Rog et al., J. Comput. Chem. 2003, 24, 657). The main improvement in this new version and the focus of this article are the parallelization of all the analysis algorithms for use on multicore desktop computers as well as distributed-memory computing clusters. The parallelization is based on a task farming approach which maintains a simple program structure permitting easy modification and extension of the code to integrate new analysis methods. V
We analyze the angular distributions for the (α, 3 He) and (α, t) reactions on 28 Si for projecti... more We analyze the angular distributions for the (α, 3 He) and (α, t) reactions on 28 Si for projectile energies ranging from 50 to 120 MeV based on the partial-wave representation of the transfer amplitude expressed in terms of the S-matrices for the entrance and exit channels, with an emphasis on identifying Airy minima of various orders. The calculations have been performed using a six-parameter S-matrix model and S-matrix parameters obtained from the analysis of elastic scattering data. The first-and (or) second-order Airy minima are clearly identified in the analyzed transfer reaction angular distributions at intermediate angles. The detected Airy minima are found to be due to the interference between several inner and surface partial waves. The impact parameters of these waves are in the range of 1-6 fm, the upper boundary of which is less than the strong absorption radius.
Dynamics of Biological Macromolecules by Neutron Scattering provides insight into the study of th... more Dynamics of Biological Macromolecules by Neutron Scattering provides insight into the study of the dynamics of biological macromolecules by neutron scattering techniques. The applicability of neutron scattering to expanding fields of biological studies is very extended and the neutron scattering community is interested in using these unique technologies to their best advantage. The book is focused on recent scientific results on biomolecular motions obtained by using neutron spectroscopy, and also discusses likely directions of future work on biological macromolecular systems while outlining some challenging, hitherto inaccessible problem areas. The Ebook should be very useful for biophysicists, biochemists, experts and non-experts in neutron scattering.
Quaternions are generalized complex numbers and represent rotations in space as ordinary complex ... more Quaternions are generalized complex numbers and represent rotations in space as ordinary complex numbers represent rotations in a plane. In the context of molecular dynamics (MD) simulations they have been ‘rediscovered’ for the integration of the rotational equation of motion of rigid molecules since they allow one to write down these equations in a singularity-free form. In this paper applications to the analysis of molecular systems are described.
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Papers by Gerald Kneller