Dynamical Self-Consistent Field Theory for Polyelectrolytes in Solution
In an effort to model biophysical systems, we incorporate charge interactions and solvent species into polymeric dynamical self-consistent field theory (dSCFT). The dynamics are described by microscopic Langevin equations for each species. These equations are recast into a dynamical partition function which integrates over collective field variables. Then a saddle-point approximation results in a set of dynamical mean-field equations, including a Poisson-Boltzmann equation satisfied by the electric potential. This approach reduces the many-chain system to a single chain interacting with dynamical mean fields. We develop a set of numerical strategies to solve the mean-field equations, and apply them to simulations designed to model charge-driven protein reconstitution. We successfully simulate neutral, weakly charged, and strongly charged triblock copolymer membranes. We also show insertion of a toy protein into a membrane in both the weakly charged and neutral cases. In the strongly charged case the protein causes significant membrane deformation.