Organization of Charged Molecules in Heterogeneous Media

We propose to implement numerically an efficient method to determine the polarizability that is induced at dielectric interfaces in systems with deformable boundaries. The problem of finding the media's dielectric response and the motion of the charges is inherently coupled. The conventional ("brute-force") methods treat the two calculations separately and only after one is completed the other is taken up. Instead, we have designed a method, which can be implemented in simulation, that mimics nature's way of simultaneous updating of both the charge configuration and media's dielectric response. As a first step, this kind of simulation requires us to view the electrostatic problem as an energy minimizing problem. We have formulated a new energy variational principle which enables to update charges and the medium's response in the same simulation time step. We propose to develop this method further to determine the effect of dielectric heterogeneities in gels and thin membranes. We aim to determine the structure of polyelectrolyte gels as a function of salt concentration. Our models should apply to understanding the coupling of electrostatics and elasticity. In our previous work we have developed a model to determine the elasticity of closed membranes with non-uniform elastic properties. These elastic heterogeneities may develop in multicomponent membranes to minimize the strain energy. The work lead to the discovery of various regular and irregular polyhedral shells that occur in biology, such as organelles and halophilic organisms. It is known that surface nanopatterns arise due to the competition of short and long range interactions on surfaces such as by a dipolar field competing with van der Waals interactions. Instead, in closed membranes the elastic energy alone (that is, without net van-der-Waals interactions) can lead to surface heterogeneities. Cross-linked membranes can also store elastic energy. Therefore, the interplay between elasticity and electrostatics in tethered charged molecules can lead to unique surface patterns.