Constraint dynamics algorithm for simulation of semiflexible macromolecules

Semiflexible models are often used to study macromolecules containing stable structural elements. Based on rigid body dynamics, we developed a rigid fragment constraint dynamics algorithm for the simulation of semiflexible macromolecules. Stable structural elements are treated as rigid fragments. Rigid fragment constraints, defined as combinations of distance constraints and position constraints, are introduced to limit internal molecular motion to the required mode. The constraint forces are solved separately for each rigid fragment constraint and iteratively until all constraint conditions are satisfied within a given tolerance at each time step, as is done for the bond length constraint in the SHAKE algorithm. The orientation of a rigid fragment is represented by the quaternion parameters, and both translation and rotation are solved by the leap-frog formulation. We tested the algorithm with molecular dynamics simulations of a series of peptides and a small protein. The computation cost for the constraints is roughly proportional to the size of the molecule. In the microcanonical ensemble simulation of polyvalines, the total energy was conserved satisfactorily with time steps as large as 20 fs. A helix folding simulation of a synthetic peptide was carried out to show the efficiency of the algorithm in a conformational search.