# A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

## Abstract

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from referencemore »

- Authors:

- Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich (Switzerland)
- Department of Biomedical Engineering and Center for Biological Systems Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1097, St. Louis, Missouri 63130 (United States)

- Publication Date:

- OSTI Identifier:
- 22419877

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; COUPLING; DECOUPLING; DEGREES OF FREEDOM; EFFECTIVE MASS; EQUATIONS OF MOTION; PEPTIDES; POLYMERS; SOLVENTS; STABILITY

### Citation Formats

```
Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch, and Pappu, Rohit V.
```*A simple molecular mechanics integrator in mixed rigid body and dihedral angle space*. United States: N. p., 2014.
Web. doi:10.1063/1.4887339.

```
Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch, & Pappu, Rohit V.
```*A simple molecular mechanics integrator in mixed rigid body and dihedral angle space*. United States. doi:10.1063/1.4887339.

```
Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch, and Pappu, Rohit V. Mon .
"A simple molecular mechanics integrator in mixed rigid body and dihedral angle space". United States.
doi:10.1063/1.4887339.
```

```
@article{osti_22419877,
```

title = {A simple molecular mechanics integrator in mixed rigid body and dihedral angle space},

author = {Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch and Pappu, Rohit V.},

abstractNote = {We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.},

doi = {10.1063/1.4887339},

journal = {Journal of Chemical Physics},

number = 3,

volume = 141,

place = {United States},

year = {Mon Jul 21 00:00:00 EDT 2014},

month = {Mon Jul 21 00:00:00 EDT 2014}

}