Protein molecular dynamics using quaternions and Monte Carlo methods

We present a new approach to molecular dynamics (MD) of proteins based on Monte Carlo Methods applied to atomic 3D models managed by quaternions. Classical MD simulations provide detailed information on the conformational changes of proteins and nucleic acids. Positions and movements are found as very expensive solutions to complicated differential equations. Finding a faster alternative is challenging. Atoms movements in proteins are constrained by the presence of force-fields related to thermal motion and intermolecular interaction. Our approach to MD combines quaternions, to manage the movements of atoms on their own trajectories, and Monte Carlo Methods, to perform incremental rotations and control energy values. We control the angular trajectories of atoms by using unitary quaternions (Hanson et al., 2012). Modeling molecules with quaternions allows a very handy application of Monte Carlo methods, as rotations become very easy to perform (Karney, 2007). The random incremental rotations can be made specific for each individual amino acid, following its specific propensity to motion. For example, the terminal atoms of amino acids rotate much more easily than the backbone carbons. In our case, we use different ranges of random incremental rotations for every dihedral angle in the protein chain. We carried out preliminary experiments on two small proteins, Calmoduliln (pdb 1cfc) and BPT (Shaw et al., 2010), using the data available from the PDB (Protein Data Bank).