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Unbiased Rotational Moves for Rigid-Body Dynamics

Daniel A. Beard ^* and Tamar Schlick 

^* Department of Bioengineering, University of Washington, Seattle, Washington; and Department of Chemistry, Courant Institute of Mathematical Sciences, and Howard Hughes Medical Institute, New York University, New York, New York

Correspondence: Address reprint requests to Tamar Schlick, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012. Tel.: 212-998-3116; Fax: 212-995-4152; E-mail: schlick{at}nyu.edu.

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach—based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity—removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying the noncommuting rotational matrices in an arbitrary order. Our algorithm should thus replace standard approaches to rotate local coordinate frames in Langevin and Brownian dynamics simulations.

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