Molecular Dynamics Studies of Polyethylene Oxide and Polyethylene Glycol Using All-Atom and Coarse-Grained Models : Conformation, Hydrodynamics, and Biophysical Applications

Polyethylene oxide (PEO) and polyethylene glycol (PEG) are polymers with the subunit C-O-C. Due to their low toxicity and high solubility in water, they are conjugated (or PEGylated) to an array of pharmaceuticals to overcome limitations of low solubility, short circulating lifetime, and immunogenicity. Also, low molecular weight PEG readily passes through the pores of membrane proteins, and, in fact, can be sized by single channels. To investigate their conformation and hydrodynamics, we improved all-atom (CHARMM) ether force field. Molecular dynamics (MD) simulations of 9, 18, 27, and 36-mers of PEO and 27-mers of polyethylene glycol PEG in water yield a persistence length l = 3.7 �, in quantitative agreement with experimentally obtained values; agreement with experimental values for hydrodynamic radii of comparably sized PEG is also excellent. The exponent u relating the radius of gyration and molecular weight (R_g � M_w^v) of PEO from the simulations equals 0.515 � 0.023, consistent with experimental observations that low molecular weight PEG behaves as an ideal chain. The dimension of the middle length for each of the polymers nearly equals the hydrodynamic radius R_h obtained from diffusion measurements in solution.  This explains the correspondence of R_h and R_p, the pore radius of membrane channels: a polymer such as PEG diffuses with its long axis parallel to the membrane channel, and passes through the channel without substantial distortion.

Many important PEG-containing assemblies are too large for all-atom MD simulation.  To overcome this limitation, a coarse-grained (CG) model for PEO is developed within the framework of the MARTINI CG model using the distributions of bond, angle, and dihedral from our all-atom force field. Simulations of PEO9 to PEO158 (442 < M_w < 6998) in explicit water yield M_w = 1630 for the turnover from v =0.52 to 0.58 in the relation R_g � M_w^v, and R_g = 19.8 � for PEO76, both in excellent agreement with the experimental targets M_w = 2000 and R_g = 19.7 �, respectively. R_h of PEO calculated from water viscosity and diffusion coefficients of PEO also agree well with experiment. Simulations of PEO grafted on the hydrophobic surface show that size of mushroom, thickness of brush, and their transition point compare favorably with those from theories by Alexander and de Gennes.