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The technique of constraining high frequency modes of molecular motion is an effective way to increase simulation time scale and improve conformational sampling in molecular dynamics simulations. However, it has been shown that constraints on higher frequency modes such as bond lengths and bond angles stiffen the molecular model, thereby introducing systematic biases in the statistical behavior of the simulations. Fixman proposed a compensating potential to remove such biases in the thermodynamic and kinetic properties calculated from dynamics simulations. Previous implementations of the Fixman potential have been limited to only short serial chain systems. In this paper, we present a spatial operator algebra based algorithm to calculate the Fixman potential and its gradient within constrained dynamics simulations for branched topology molecules of any size. Our numerical studies on molecules of increasing complexity validate our algorithm by demonstrating recovery of the dihedral angle probability distribution function for systems that range in complexity from serial chains to protein molecules. We observe that the Fixman compensating potential recovers the free energy surface of a serial chain polymer, thus annulling the biases caused by constraining the bond lengths and bond angles. The inclusion of Fixman potential entails only a modest increase in the computational cost in these simulations. We believe that this work represents the first instance where the Fixman potential has been used for general branched systems, and establishes the viability for its use in constrained dynamics simulations of proteins and other macromolecules. [ABSTRACT FROM AUTHOR]

The generalized Newton-Euler inverse mass operator (GNEIMO) method is an advanced method for internal coordinates molecular dynamics (ICMD). GNEIMO includes several theoretical and algorithmic advancements that address longstanding challenges with ICMD simulations. In this article, we describe the GneimoSim ICMD software package that implements the GNEIMO method. We believe that GneimoSim is the first software package to include advanced features such as the equipartition principle derived for internal coordinates, and a method for including the Fixman potential to eliminate systematic statistical biases introduced by the use of hard constraints. Moreover, by design, GneimoSim is extensible and can be easily interfaced with third party force field packages for ICMD simulations. Currently, GneimoSim includes interfaces to LAMMPS, OpenMM, and Rosetta force field calculation packages. The availability of a comprehensive Python interface to the underlying C11 classes and their methods provides a powerful and versatile mechanism for users to develop simulation scripts to configure the simulation and control the simulation flow. GneimoSim has been used extensively for studying the dynamics of protein structures, refinement of protein homology models, and for simulating large scale protein conformational changes with enhanced sampling methods. GneimoSim is not limited to proteins and can also be used for the simulation of polymeric materials. [ABSTRACT FROM AUTHOR]

Internal coordinate molecular dynamics (ICMD) methods provide a more natural description of a protein by using bond, angle, and torsional coordinates instead of a Cartesian coordinate representation. Freezing high-frequency bonds and angles in the ICMD model gives rise to constrained ICMD (CICMD) models. There are several theoretical aspects that need to be developed to make the CICMD method robust and widely usable. In this article, we have designed a new framework for (1) initializing velocities for nonindependent CICMD coordinates, (2) efficient computation of center of mass velocity during CICMD simulations, (3) using advanced integrators such as Runge-Kutta, Lobatto, and adaptive CVODE for CICMD simulations, and (4) cancelling out the 'flying ice cube effect' that sometimes arises in Nosé-Hoover dynamics. The Generalized Newton-Euler Inverse Mass Operator (GNEIMO) method is an implementation of a CICMD method that we have developed to study protein dynamics. GNEIMO allows for a hierarchy of coarse-grained simulation models based on the ability to rigidly constrain any group of atoms. In this article, we perform tests on the Lobatto and Runge-Kutta integrators to determine optimal simulation parameters. We also implement an adaptive coarse-graining tool using the GNEIMO Python interface. This tool enables the secondary structure-guided 'freezing and thawing' of degrees of freedom in the molecule on the fly during molecular dynamics simulations and is shown to fold four proteins to their native topologies. With these advancements, we envision the use of the GNEIMO method in protein structure prediction, structure refinement, and in studying domain motion. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The challenge in protein structure prediction using homologymodelingis the lack of reliable methods to refine the low resolution homologymodels. Unconstrained all-atom molecular dynamics (MD) does not servewell for structure refinement due to its limited conformational search.We have developed and tested the constrained MD method, based on thegeneralized Newton–Euler inverse mass operator (GNEIMO) algorithmfor protein structure refinement. In this method, the high-frequencydegrees of freedom are replaced with hard holonomic constraints anda protein is modeled as a collection of rigid body clusters connectedby flexible torsional hinges. This allows larger integration timesteps and enhances the conformational search space. In this work,we have demonstrated the use of torsional GNEIMO method without usingany experimental data as constraints, for protein structure refinementstarting from low-resolution decoy sets derived from homology methods.In the eight proteins with three decoys for each, we observed an improvementof ∼2 Å in the rmsd in coordinates to the known experimentalstructures of these proteins. The GNEIMO trajectories also showedenrichment in the population density of native-like conformations.In addition, we demonstrated structural refinement using a “freezeand thaw” clustering scheme with the GNEIMO framework as aviable tool for enhancing localized conformational search. We havederived a robust protocol based on the GNEIMO replica exchange methodfor protein structure refinement that can be readily extended to otherproteins and possibly applicable for high throughput protein structurerefinement. [ABSTRACT FROM AUTHOR]