Protein aggregation is a key event in a number of diseases such as Alzheimer's disease, Park... more Protein aggregation is a key event in a number of diseases such as Alzheimer's disease, Parkinson's disease and prion diseases. Dual-color scanning for intensely fluorescent targets (SIFT), which has been used in the diagnosis of prion diseaes, is presented here as a general ...
Viele biochemische Prozesse werden durch hochspezifische Bindungen zwischen exakt aufeinander abg... more Viele biochemische Prozesse werden durch hochspezifische Bindungen zwischen exakt aufeinander abgestimmten molekularen Partnern vermittelt. Gestützt auf kraftmikroskopische Experimente konnten wir mit Computersimulationen Einblicke in den atomaren Mechanismus solcher selektiven Wechselwirkungen gewinnen
... We propose a local anti-Hebbian rule for lateral, hierarchically organized weights within the... more ... We propose a local anti-Hebbian rule for lateral, hierarchically organized weights within the output layer. ... The weights between the two layers converge to the eigenvectors of the covariance matrix of input patterns, ie the network performs a principal-component analysis of the ...
Berichte der Bunsengesellschaft für physikalische Chemie, 1981
The influence of amino substituents on the excited π-π* singlet states of phenazine is investigat... more The influence of amino substituents on the excited π-π* singlet states of phenazine is investigated by absorption, fluorescence, and polarization spectroscopy at 77 K and by PPP-SCF-CI calculations including all single and double excitations from the SCF ground state. The Coulomb interaction of the free electron pair of the amino groups with the π-electrons of phenazine is shown to be responsible, essentially, for the drastic changes in the observed electronic spectra.
We discuss to what extent recent vibrational spectra of 14-2H, 15-2H and 14,15-2H isotopically la... more We discuss to what extent recent vibrational spectra of 14-2H, 15-2H and 14,15-2H isotopically labelled L550 provide evidence for the occurrence of 13-cis, 14-s-trans or 13-cis, 14-s-cis chromophore structures in bacteriorhodopsin's photocycle. The discussion is based on a quantum chemical (MNDO) vibrational analysis of four molecular fragments as models for the retinal chromophore in bacteriorhodopsin.
Nonlinear associative memories as realized, e. g., by Hopfield nets are characterized by attracto... more Nonlinear associative memories as realized, e. g., by Hopfield nets are characterized by attractor type dynamics. When fed with a starting pattern they converge to exactly one of the stored patterns which is supposed to be the most similar one. These systems cannot render hypotheses of classification, i.e. render several possible answers to a given classification problem. Inspired by C. von der Malsburg’s correlation theory of brain function we extend conventional neural network architectures by introducing additional dynamical variables, the so-called phases, one for each formal neuron in the net. The phases measure detailed correlations of neural activities neglected in conventional neural network architectures. Using simple selforganizing networks based on feature map algorithms we present an associative memory that actually is capable of forming hypotheses of classification.
We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations... more We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations, which has provided an efficient and accurate solution of the Poisson equation, to ionic solvents as described by the linearized Poisson-Boltzmann (LPB) equation. We start with the formulation of a general theory for the electrostatics of an arbitrarily shaped molecular system, which consists of partially charged atoms and is embedded in a LPB continuum. This theory represents the reaction field induced by the continuum in terms of charge and dipole densities localized within the molecular system. Because these densities cannot be calculated analytically for systems of arbitrary shape, we introduce an atom-based discretization and a set of carefully designed approximations. This allows us to represent the densities by charges and dipoles located at the atoms. Coupled systems of linear equations determine these multipoles and can be rapidly solved by iteration during a MD simulation. The multipoles yield the reaction field forces and energies. Finally, we scrutinize the quality of our approach by comparisons with an analytical solution restricted to perfectly spherical systems and with results of a finite difference method.
ABSTRACT We present a combination of the structure adapted multipole method with a reaction field... more ABSTRACT We present a combination of the structure adapted multipole method with a reaction field (RF) correction for the efficient evaluation of electrostatic interactions in molecular dynamics simulations under periodic boundary conditions. The algorithm switches from an explicit electrostatics evaluation to a continuum description at the maximal distance that is consistent with the minimum image convention, and, thus, avoids the use of a periodic electrostatic potential. A physically motivated switching function enables charge clusters interacting with a given charge to smoothly move into the solvent continuum by passing through the spherical dielectric boundary surrounding this charge. This transition is complete as soon as the cluster has reached the so-called truncation radius R-c. The algorithm is used to examine the dependence of thermodynamic properties and correlation functions on R-c in the three point transferable intermolecular potential water model. Our test simulations on pure liquid water used either the RF correction or a straight cutoff and values of R-c ranging from 14 Angstrom to 40 Angstrom. In the RF setting, the thermodynamic properties and the correlation functions show convergence for R-c increasing towards 40 Angstrom. In the straight cutoff case no such convergence is found. Here, in particular, the dipole-dipole correlation functions become completely artificial. The RF description of the long-range electrostatics is verified by comparison with the results of a particle-mesh Ewald simulation at identical conditions. (C) 2003 American Institute of Physics.
ABSTRACT We present a continuum approach for efficient and accurate calculation of reaction field... more ABSTRACT We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method. (C) 2003 American Institute of Physics.
The aim of molecular biology is to understand the relationship between structure and function of ... more The aim of molecular biology is to understand the relationship between structure and function of biological molecules, i.e., proteins, lipids or nucleic acids. In the recent decade it became clear that the motion of individual atoms plays a crucial role in determining many aspects of molecular properties. Since this motion is hard to observe in experiments directly, one has to use a sufficiently realistic model to obtain detailed insight into the dynamics at an atomic level.
Femtochemistry and Femtobiology: Ultrafast Events in Molecular Science, 2004
The sequence of amino acids determines the three-dimensional structure and the function of the pr... more The sequence of amino acids determines the three-dimensional structure and the function of the protein. After synthesis of a protein in the ribosomes, the amino acid chain is in a non-specific, the “random coil” conformation. Only after the subsequent folding of the amino acid chain into a well-defined three-dimensional structure - the “native form” - the protein is enabled to fulfill its biological functions. Folding of a typical protein is finished on the time scale of seconds. At present, an understanding of the protein folding process is not possible. Even numerical methods as e.g. molecular dynamics simulations do not lead to realistic predictions. Experiments on the folding process have been performed initially on the millisecond timescale. It was only recently that new techniques - temperature jump or triplet-triplet quenching experiments - allowed a first access to the nanosecond time domain. However, the elementary reactions in protein folding occur on the femto-to picosecond time-scale. This chapter presents recent experiments on different types of azobenzene molecules with transient visible and IR-spectroscopy that show that ultrafast structural changes of peptide molecules occur on the time-scale of 10 ps.
ABSTRACT: Within molecular dynamics simulations of protein]solvent systems the exact evaluation o... more ABSTRACT: Within molecular dynamics simulations of protein]solvent systems the exact evaluation of long-range Coulomb interactions is computationally demanding and becomes prohibitive for large systems. Conventional truncation methods circumvent that computational problem, but are hampered by serious artifacts concerning structure and dynamics of the simulated systems. To avoid these artifacts we have developed an efficient and yet sufficiently accurate approximation scheme which combines the structure-. wadapted multipole method SAMM C. Niedermeier and P. Tavan, J. Chem. .xPhys., 101, 734 1994 with a multiple-time-step method. The computational effort for MD simulations required within our fast multiple-time-step structure-.adapted multipole method FAMUSAMM scales linearly with the number of particles. For a system with 36,000 atoms we achieve a computational speed-up by a factor of 60 as compared with the exact evaluation of the Coulomb forces. Extended test simulations show that ...
Protein aggregation is a key event in a number of diseases such as Alzheimer's disease, Park... more Protein aggregation is a key event in a number of diseases such as Alzheimer's disease, Parkinson's disease and prion diseases. Dual-color scanning for intensely fluorescent targets (SIFT), which has been used in the diagnosis of prion diseaes, is presented here as a general ...
Viele biochemische Prozesse werden durch hochspezifische Bindungen zwischen exakt aufeinander abg... more Viele biochemische Prozesse werden durch hochspezifische Bindungen zwischen exakt aufeinander abgestimmten molekularen Partnern vermittelt. Gestützt auf kraftmikroskopische Experimente konnten wir mit Computersimulationen Einblicke in den atomaren Mechanismus solcher selektiven Wechselwirkungen gewinnen
... We propose a local anti-Hebbian rule for lateral, hierarchically organized weights within the... more ... We propose a local anti-Hebbian rule for lateral, hierarchically organized weights within the output layer. ... The weights between the two layers converge to the eigenvectors of the covariance matrix of input patterns, ie the network performs a principal-component analysis of the ...
Berichte der Bunsengesellschaft für physikalische Chemie, 1981
The influence of amino substituents on the excited π-π* singlet states of phenazine is investigat... more The influence of amino substituents on the excited π-π* singlet states of phenazine is investigated by absorption, fluorescence, and polarization spectroscopy at 77 K and by PPP-SCF-CI calculations including all single and double excitations from the SCF ground state. The Coulomb interaction of the free electron pair of the amino groups with the π-electrons of phenazine is shown to be responsible, essentially, for the drastic changes in the observed electronic spectra.
We discuss to what extent recent vibrational spectra of 14-2H, 15-2H and 14,15-2H isotopically la... more We discuss to what extent recent vibrational spectra of 14-2H, 15-2H and 14,15-2H isotopically labelled L550 provide evidence for the occurrence of 13-cis, 14-s-trans or 13-cis, 14-s-cis chromophore structures in bacteriorhodopsin's photocycle. The discussion is based on a quantum chemical (MNDO) vibrational analysis of four molecular fragments as models for the retinal chromophore in bacteriorhodopsin.
Nonlinear associative memories as realized, e. g., by Hopfield nets are characterized by attracto... more Nonlinear associative memories as realized, e. g., by Hopfield nets are characterized by attractor type dynamics. When fed with a starting pattern they converge to exactly one of the stored patterns which is supposed to be the most similar one. These systems cannot render hypotheses of classification, i.e. render several possible answers to a given classification problem. Inspired by C. von der Malsburg’s correlation theory of brain function we extend conventional neural network architectures by introducing additional dynamical variables, the so-called phases, one for each formal neuron in the net. The phases measure detailed correlations of neural activities neglected in conventional neural network architectures. Using simple selforganizing networks based on feature map algorithms we present an associative memory that actually is capable of forming hypotheses of classification.
We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations... more We extend our continuum description of solvent dielectrics in molecular-dynamics (MD) simulations, which has provided an efficient and accurate solution of the Poisson equation, to ionic solvents as described by the linearized Poisson-Boltzmann (LPB) equation. We start with the formulation of a general theory for the electrostatics of an arbitrarily shaped molecular system, which consists of partially charged atoms and is embedded in a LPB continuum. This theory represents the reaction field induced by the continuum in terms of charge and dipole densities localized within the molecular system. Because these densities cannot be calculated analytically for systems of arbitrary shape, we introduce an atom-based discretization and a set of carefully designed approximations. This allows us to represent the densities by charges and dipoles located at the atoms. Coupled systems of linear equations determine these multipoles and can be rapidly solved by iteration during a MD simulation. The multipoles yield the reaction field forces and energies. Finally, we scrutinize the quality of our approach by comparisons with an analytical solution restricted to perfectly spherical systems and with results of a finite difference method.
ABSTRACT We present a combination of the structure adapted multipole method with a reaction field... more ABSTRACT We present a combination of the structure adapted multipole method with a reaction field (RF) correction for the efficient evaluation of electrostatic interactions in molecular dynamics simulations under periodic boundary conditions. The algorithm switches from an explicit electrostatics evaluation to a continuum description at the maximal distance that is consistent with the minimum image convention, and, thus, avoids the use of a periodic electrostatic potential. A physically motivated switching function enables charge clusters interacting with a given charge to smoothly move into the solvent continuum by passing through the spherical dielectric boundary surrounding this charge. This transition is complete as soon as the cluster has reached the so-called truncation radius R-c. The algorithm is used to examine the dependence of thermodynamic properties and correlation functions on R-c in the three point transferable intermolecular potential water model. Our test simulations on pure liquid water used either the RF correction or a straight cutoff and values of R-c ranging from 14 Angstrom to 40 Angstrom. In the RF setting, the thermodynamic properties and the correlation functions show convergence for R-c increasing towards 40 Angstrom. In the straight cutoff case no such convergence is found. Here, in particular, the dipole-dipole correlation functions become completely artificial. The RF description of the long-range electrostatics is verified by comparison with the results of a particle-mesh Ewald simulation at identical conditions. (C) 2003 American Institute of Physics.
ABSTRACT We present a continuum approach for efficient and accurate calculation of reaction field... more ABSTRACT We present a continuum approach for efficient and accurate calculation of reaction field forces and energies in classical molecular-dynamics (MD) simulations of proteins in water. The derivation proceeds in two steps. First, we reformulate the electrostatics of an arbitrarily shaped molecular system, which contains partially charged atoms and is embedded in a dielectric continuum representing the water. A so-called fuzzy partition is used to exactly decompose the system into partial atomic volumes. The reaction field is expressed by means of dipole densities localized at the atoms. Since these densities cannot be calculated analytically for general systems, we introduce and carefully analyze a set of approximations in a second step. These approximations allow us to represent the dipole densities by simple dipoles localized at the atoms. We derive a system of linear equations for these dipoles, which can be solved numerically by iteration. After determining the two free parameters of our approximate method we check its quality by comparisons (i) with an analytical solution, which is available for a perfectly spherical system, (ii) with forces obtained from a MD simulation of a soluble protein in water, and (iii) with reaction field energies of small molecules calculated by a finite difference method. (C) 2003 American Institute of Physics.
The aim of molecular biology is to understand the relationship between structure and function of ... more The aim of molecular biology is to understand the relationship between structure and function of biological molecules, i.e., proteins, lipids or nucleic acids. In the recent decade it became clear that the motion of individual atoms plays a crucial role in determining many aspects of molecular properties. Since this motion is hard to observe in experiments directly, one has to use a sufficiently realistic model to obtain detailed insight into the dynamics at an atomic level.
Femtochemistry and Femtobiology: Ultrafast Events in Molecular Science, 2004
The sequence of amino acids determines the three-dimensional structure and the function of the pr... more The sequence of amino acids determines the three-dimensional structure and the function of the protein. After synthesis of a protein in the ribosomes, the amino acid chain is in a non-specific, the “random coil” conformation. Only after the subsequent folding of the amino acid chain into a well-defined three-dimensional structure - the “native form” - the protein is enabled to fulfill its biological functions. Folding of a typical protein is finished on the time scale of seconds. At present, an understanding of the protein folding process is not possible. Even numerical methods as e.g. molecular dynamics simulations do not lead to realistic predictions. Experiments on the folding process have been performed initially on the millisecond timescale. It was only recently that new techniques - temperature jump or triplet-triplet quenching experiments - allowed a first access to the nanosecond time domain. However, the elementary reactions in protein folding occur on the femto-to picosecond time-scale. This chapter presents recent experiments on different types of azobenzene molecules with transient visible and IR-spectroscopy that show that ultrafast structural changes of peptide molecules occur on the time-scale of 10 ps.
ABSTRACT: Within molecular dynamics simulations of protein]solvent systems the exact evaluation o... more ABSTRACT: Within molecular dynamics simulations of protein]solvent systems the exact evaluation of long-range Coulomb interactions is computationally demanding and becomes prohibitive for large systems. Conventional truncation methods circumvent that computational problem, but are hampered by serious artifacts concerning structure and dynamics of the simulated systems. To avoid these artifacts we have developed an efficient and yet sufficiently accurate approximation scheme which combines the structure-. wadapted multipole method SAMM C. Niedermeier and P. Tavan, J. Chem. .xPhys., 101, 734 1994 with a multiple-time-step method. The computational effort for MD simulations required within our fast multiple-time-step structure-.adapted multipole method FAMUSAMM scales linearly with the number of particles. For a system with 36,000 atoms we achieve a computational speed-up by a factor of 60 as compared with the exact evaluation of the Coulomb forces. Extended test simulations show that ...
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Papers by Paul Tavan