Internal Dynamics of a Coarse-Grained Protein Using Analytical Harmonic Representation.

An analytical coarse-grained model (ACG) is introduced to represent individual macromolecules for simulation of dynamic processes in cells. In the ACG model, a macromolecular structure is treated as a fully coarse-grained entity with a uniform mass density without the explicit atomic details. The excluded volume and surface of the ACG macromolecular species are explicitly treated by a spherical harmonic representation in the present study (although ellipsoidal, solid, and radial augmented functions can be used), which can provide any desired accuracy and detail depending on the problem of interest. The present paper focuses on the description of the internal fluctuations of a single ACG macromolecule, modeled by the superposition of low frequency quasiharmonic modes from explicit molecular dynamics simulation. A procedure for estimating the amplitudes, time scales of the quasiharmonic motions and the corresponding phases is presented and used to synthesize the complex motion. The analytical description and numerical algorithm can provide an adequate representation of the internal protein fluctuations revealed from the corresponding atomistic simulations, although the internal motions of ACG macromolecules do not explore motions not exhibited in the dynamic simulations.