The Newton-Euler Inverse Mass Operator (NEIMO) algorithm and software that implements the algorithm have been developed to reduce the amount of time needed to perform computational simulations of the dynamics of macromolecules. The NEIMO algorithm and the associated software are intended, in particular, for simulations of molecular motions at a space-time mesoscale, defined here as a length scale ranging from nanometers to micrometers and a time scale ranging from microseconds to milliseconds. Older molecular-dynamics algorithms and computer programs are not suitable for mesoscale simulations because they were formulated for the time scales, of the order of a microsecond or less, characteristic of such high-frequency degrees of freedom as stretching of molecular bonds.

If, in a macromolecular-dynamics computation, one constrains the high-frequency degrees of freedom and uses internal coordinates, one not only reduces the number of degrees of freedom but also enables the use of a larger time step in numerical integration. Doing so also eliminates friction in the simulated system, enabling fast and efficient searches among conformations. On the other hand, the use of internal coordinates leads to coupled equations of motion. The solution of the equations involves inversion of a dense mass matrix. Older algorithms that solve coupled equations of motion exhibit computational complexity proportional to O(N3), where O(X) signifies a number of the order of X and N is the number of degrees of freedom in a simulated system. For example, for a rhinovirus containing nearly 500,000 atoms, it would be necessary to invert a 167,000-by-167,000 matrix at every time step — clearly impractical.

The NEIMO algorithm was derived within the theoretical framework of the spatial-operator formulation of multibody dynamics. This formulation, which has been discussed in a number of previous issues of NASA Tech Briefs, was conceived for modeling the dynamics of complex, articulated collections of bodies (principally, multiple-link robot arms); since its conception, this formulation has also been found to be useful for simulating the dynamics of a variety of complex systems, including molecules. The software that implements the NEIMO algorithm is a modified version of the DARTS computer program, which was also based on the spatial-operator formulation and was reported in "Program for Simulating Dynamics of Multibody Systems" (NPO-20168), NASA Tech Briefs, Vol. 22, No. 2 (February 1998), page 70.

The great advantage of NEIMO is that in comparison with the older algorithms, it involves much less computation. The computational complexity of the NEIMO algorithm is proportional to O(N) — much less than O(N3) for multiple degrees of freedom. The NEIMO algorithm solves the constrained equations of motion efficiently by keeping all high-frequency modes fixed and reduces the number of degrees of freedom from 3M (where M is the number of atoms) to M. The remaining degrees of freedom are the dihedral ones.

This work was done by Abhinandan Jain, Guillermo Rodriguez, and Nagaranjan Vaidehi of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at  under the Physical Sciences category.

This software is available for commercial licensing. Please contact Don Hart of the California Institute of Technology at (818) 393-3425. Refer to NPO-20796.

This Brief includes a Technical Support Package (TSP).
Algorithm for Computing Dynamics of Molecules

(reference NPO-20796) is currently available for download from the TSP library.

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This article first appeared in the October, 2001 issue of NASA Tech Briefs Magazine.

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