MDAnalysis (http://mdanalysis.org) is a library for structural and temporal analysis of molecular dynamics (MD) simulation trajectories and individual protein structures. MD simulations of biological molecules have become an important tool to elucidate the relationship between molecular structure and physiological function. Simulations are performed with highly optimized software packages on HPC resources but most codes generate output trajectories in their own formats so that the development of new trajectory analysis algorithms is confined to specific user communities and widespread adoption and further development is delayed. MDAnalysis addresses this problem by abstracting access to the raw simulation data and presenting a uniform object-oriented Python interface to the user. It thus enables users to rapidly write code that is portable and immediately usable in virtually all biomolecular simulation communities. The user interface and modular design work equally well in complex scripted work flows, as foundations for other packages, and for interactive and rapid prototyping work in IPython / Jupyter notebooks, especially together with molecular visualization provided by nglview and time series analysis with pandas. MDAnalysis is written in Python and Cython and uses NumPy arrays for easy interoperability with the wider scientific Python ecosystem. It is widely used and forms the foundation for more specialized biomolecular simulation tools. MDAnalysis is available under the GNU General Public License v2.
We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes–Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter’s sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein–protein binding in the Kd ≈ 10-mM regime.
We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.
Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K d , and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B 2 . As a measure of nonspecific binding and stickiness, B 2 is receiving renewed attention in the context of so-called liquid−liquid phase separation in protein and nucleic acid solutions. We show that K d is fully determined by B 2 and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B 2 . From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B 2 from insertion and removal energies by applying Bennett's acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B 2 from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K d and B 2 allow us to separate out the contributions of nonbinding interactions to B 2 . Comparison of calculated and measured values of K d and B 2 can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K d and B 2 calculations make them well suited for high-throughput studies of large interactomes.
We show that the rotational dynamics of proteins and nucleic acids determined from molecular dynamics simulations under periodic boundary conditions suffer from significant finite-size effects. We remove the box-size dependence of the rotational diffusion coefficients by adding a hydrodynamic correction k T/6 ηV with k Boltzmann's constant, T the absolute temperature, η the solvent shear viscosity, and V the box volume. We show that this correction accounts for the finite-size dependence of the rotational diffusion coefficients of horse-heart myoglobin and a B-DNA dodecamer in aqueous solution. The resulting hydrodynamic radii are in excellent agreement with experiment.
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