Konrad Hinsen

Analysis of domain motions by approximate normal mode calculations

The identification of dynamical domains in proteins and the description of the low‐frequency domain motions are one of the important applications of numerical simulation techniques. The application of these techniques to large proteins requires a substantial computational effort and therefore cannot be performed routinely, if at all. This article shows how physically motivated approximations permit the calculation of low‐frequency normal modes in a few minutes on standard desktop computers. The technique is based on the observation that the low‐frequency modes, which describe domain motions, are independent of force field details and can be obtained with simplified mechanical models. These models also provide a useful measure for rigidity in proteins, allowing the identification of quasi‐rigid domains. The methods are validated by application to three well‐studied proteins, crambin, lysozyme, and ATCase. In addition to being useful techniques for studying domain motions, the success of the approximations provides new insight into the relevance of normal mode calculations and the nature of the potential energy surface of proteins. Proteins 33:417–429, 1998.

The molecular modeling toolkit: A new approach to molecular simulations

The Molecular Modeling Toolkit is a library that implements common molecular simulation techniques, with an emphasis on biomolecular simulations. It uses modern software engineering techniques (object‐oriented design, a high‐level language) to overcome limitations associated with the large monolithic simulation programs that are commonly used for biomolecules. Its principal advantages are (1) easy extension and combination with other libraries due to modular library design; (2) a single high‐level general‐purpose programming language (Python) is used for library implementation as well as for application scripts; (3) use of documented and machine‐independent formats for all data files; and (4) interfaces to other simulation and visualization programs.

Analysis of domain motions in large proteins

We present a new approach for determining dynamical domains in large proteins, either based on a comparison of different experimental structures, or on a simplified normal mode calculation for a single conformation. In a first step, a deformation measure is evaluated for all residues in the protein; a high deformation indicates highly flexible interdomain regions. The sufficiently rigid parts of the protein are then classified into rigid domains and low‐deformation interdomain regions on the basis of their global motion. We demonstrate the techniques on three proteins: citrate synthase, which has been the subject of earlier domain analyses, HIV‐1 reverse transcriptase, which has a rather complex domain structure, and aspartate transcarbamylase as an example of a very large protein. These examples show that the comparison of conformations and the normal mode analysis lead to essentially the same domain identification, except for cases where the experimental conformations differ by the presence of a large ligand, such as a DNA strand. Normal mode analysis has the advantage of requiring only one experimental structure and of providing a more detailed picture of domain movements, e.g. the splitting of domains into subdomains at higher frequencies. Proteins 1999;34:369–382.

Friction and mobility of many spheres in Stokes flow

An efficient scheme is presented for the numerical calculation of hydrodynamic interactions of many spheres in Stokes flow. The spheres may have various sizes, and are freely moving or arranged in rigid arrays. Both the friction and mobility matrix are found from the solution of a set of coupled equations. The Stokesian dynamics of many spheres and the friction and mobility tensors of polymers and proteins may be calculated accurately at a modest expense of computer memory and time. The transport coefficients of suspensions can be evaluated by use of periodic boundary conditions.

Harmonicity in slow protein dynamics

The slow dynamics of proteins around its native folded state is usually described by diffusion in a strongly anharmonic potential. In this paper, we try to understand the form and origin of the anharmonicities, with the principal aim of gaining a better understanding of the principal motion types, but also in order to develop more efficient numerical methods for simulating neutron scattering spectra of large proteins. First, we decompose a molecular dynamics (MD) trajectory of 1.5 ns for a C-phycocyanin dimer surrounded by a layer of water into three contributions that we expect to be independent: the global motion of the residues, the rigid-body motion of the sidechains relative to the backbone, and the internal deformations of the sidechains. We show that they are indeed almost independent by verifying the factorization of the incoherent intermediate scattering function. Then, we show that the global residue motions, which include all large-scale backbone motions, can be reproduced by a simple harmonic model which contains two contributions: a short-time vibrational term, described by a standard normal mode calculation in a local minimum, and a long-time diffusive term, described by Brownian motion in an effective harmonic potential. The potential and the friction constants were fitted to the MD data. The major anharmonic contribution to the incoherent intermediate scattering function comes from the rigid-body diffusion of the sidechains. This model can be used to calculate scattering functions for large proteins and for long-time scales very efficiently, and thus provides a useful complement to MD simulations, which are best suited for detailed studies on smaller systems or for shorter time scales.

nMoldyn: A program package for a neutron scattering oriented analysis of molecular dynamics simulations

We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191–214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high‐level language, Python, and of modern object‐oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean‐square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies.

Structural flexibility in proteins

MOTIVATION In the study of the structural flexibility of proteins, crystallographic Debye-Waller factors are the most important experimental information used in the calibration and validation of computational models, such as the very successful elastic network models (ENMs). However, these models are applied to single protein molecules, whereas the experiments are performed on crystals. Moreover, the energy scale in standard ENMs is undefined and must be obtained by fitting to the same data that the ENM is trying to predict, reducing the predictive power of the model. RESULTS We develop an elastic network model for the whole protein crystal in order to study the influence of crystal packing and lattice vibrations on the thermal fluctuations of the atom positions. We use experimental values for the compressibility of the crystal to establish the energy scale of our model. We predict the elastic constants of the crystal and compare with experimental data. Our main findings are (1) crystal packing modifies the atomic fluctuations considerably and (2) thermal fluctuations are not the dominant contribution to crystallographic Debye-Waller factors. AVAILABILITY The programs developed for this work are available as supplementary material at Bioinformatics Online.

Fractional Brownian dynamics in proteins.

Correlation functions describing relaxation processes in proteins and other complex molecular systems are known to exhibit a nonexponential decay. The simulation study presented here shows that fractional Brownian dynamics is a good model for the internal dynamics of a lysozyme molecule in solution. We show that both the dynamic structure factor and the associated memory function fit well the corresponding analytical functions calculated from the model. The numerical analysis is based on autoregressive modeling of time series.

Tertiary and quaternary conformational changes in aspartate transcarbamylase: a normal mode study

Aspartate transcarbamylase (ATCase) initiates the pyrimidine biosynthetic pathway in Escherichia coli. Binding of aspartate to this allosteric enzyme induces a cooperative transition between the tensed (T) and relaxed (R) states of the enzyme which involves large quaternary and tertiary rearrangements. The mechanisms of the transmission of the regulatory signal to the active site (60 Å away) and that of the cooperative transition are not known in detail, although a large number of single, double, and triple site‐specific mutants and chimeric forms of ATCase have been obtained and kinetically characterized. A previous analysis of the very low‐frequency normal modes of both the T and R state structures of ATCase identified some of the large‐amplitude motions mediating the intertrimer elongation and rotation that occur during the cooperative transition (Thomas et al., J. Mol. Biol. 257:1070–1087, 1996; Thomas et al., J. Mol. Biol. 261:490–506, 1996). As a complement to that study, the deformation of the quaternary and tertiary structure of ATCase by normal modes below 5 cm−1 is investigated in this article. The ability of the modes to reproduce the domain motions occurring during the transition is analyzed, with special attention to the interdomain closure in the catalytic chain, which has been shown to be critical for homotropic cooperativity. The calculations show a coupling between the quaternary motions and more localized motions involving specific residues. The particular dynamic behavior of these residues is examined in the light of biochemical results to obtain insights into their role in the transmission of the allosteric signal. Proteins 1999;34:96–112.

A simplified force field for describing vibrational protein dynamics over the whole frequency range

The empirical force fields used for protein simulations contain short-ranged terms (chemical bond structure, steric effects, van der Waals interactions) and long-ranged electrostatic contributions. It is well known that both components are important for determining the structure of a protein. We show that the dynamics around a stable equilibrium state can be described by a much simpler midrange force field made up of the chemical bond structure terms plus unspecific harmonic terms with a distance-dependent force constant. A normal mode analysis of such a model can reproduce the experimental density of states as well as a conventional molecular dynamics simulation using a standard force field with long-range electrostatic terms. This finding is consistent with a recent observation that effective Coulomb interactions are short ranged for systems with a sufficiently homogeneous charge distribution.