Conventional Molecular Dynamics (MD) studies are limited by accessible time scales - up to several nanoseconds at most. Using the Lagrangian and Quaternion formalism we have developed a new MD model, using internal - curvilinear, rotational and translational degrees of freedom. In this model it is possible to increase the time-step of the integration of the equations of motion by an order of magnitude, from 0.5 - 1 fs, that are typicaly used in MD simulations to 10 - 20 fs.
In this formalism, a simulated system consists of atoms, pseudoatoms with internal degrees of freedom as well as rigid and pseudoelastic bodies with rotational translational and internal degrees of freedom. Internal degrees of freedom are coupled with the Cartesian coordinates in two ways:
the potential of the bonded interactions can be parametrized by the internal parameters, as well as
selected properties of the rigid bodies can be parametrized by the internal parameters.
The open structure of this approach allows for applying models of varying resolution for different parts of the system. In particular, a part of a given system can be described using the all-atom model, while its rest can be modeled using various types of reduced representations. The equations of motion for the molecular system are obtained from the Lagrange function. Rigid body motion equations are solved using quaternion parameters. This model is called Lagrangian and Quaternion Molecular Dynamics (LQMD).
The theoretical derivation of the LQMD equations, their implementation into a functional code and results of test simulations performed for model double helical oligonucleotides will be presented. Possible applications to other systems like proteins, polymers or nanostructures will be discussed.
Rudnicki, W.R.; Lesyng, B.; and Harvey, S.~C. (1994) Biopolymers 34, pages 383-392. Lagrangian molecular dynamics using selected conformational degrees of freedom, with application to the pseudorotation dynamics of furanose rings
Rudnicki, W.R.; and Lesyng, B., (1997) Mol. Sim. 19 pages 247-266. Conformational correlations in DNA. molecular dynamics studies
Rudnicki, W.R.; Bakalarski G.; and Lesyng, B., submitted to Molecular Simulation. Lagrangian and Quaternion Dynamics of Nucleic Acids.