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Dynamics and structure of polyelectrolyte complexes

Interaction of charged macromolecules among themselves and with charged interfaces in salty aqueous medium is a common phenomenon prevalent in biology and synthetic systems. We have addressed several inter-related issues in this general context. First we present a theory of adsorption of polyelectrolytes on the interior and exterior surfaces of a charged spherical vesicle. We derive the critical adsorption condition and the density profile of the polymer in terms of various characteristics of the polymer, vesicle, and the solution, such as the length and charge density of polymer, the radius and charge of the vesicle, the salt concentration of the solution, and the dielectric constant of the solvent. We have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. For the polyelectrolyte inside the vesicle, the competition between the loss of conformational entropy and the attractive electrostatic energy between the vesicle and the polyelectrolyte, results in two different encapsulated states. By considering the adsorption from outside, we calculate the entropic and the energetic contributions to the free energy for the polymer being adsorbed in the interior and exterior states and the free energy penalty for the polyelectrolyte being expelled from the vesicle. The kinetics of the polyelectrolyte complexation have been studied using the Smoluchowski equation. We derive the mean distance between two oppositely charged polyelectrolytes and the reaction rate for the complexation in terms of the salt concentration and polyelectrolyte characteristics. We also calculate the half-time for the complexation process at different salt concentrations and initial distances.\\ For a vesicle, we have derived the free energy landscape of translocation through the pore by accounting for the energy penalty of bending and stretching the vesicle from due to deformation by pore. Using the Fokker-Planck formalism, we have calculated the average translocation time corresponding to the various free energy landscapes representing different parameter sets. We also discuss the dependencies of the average translocation time on the strength of the external force, vesicle size, bending and stretching moduli of the vesicle, and the radius and length of the pore. Finally, we formulate a theory of the effects of long-range interactions on surface tension and spontaneous curvature of proteinaceous shells based on the general Deryaguin-Landau-Verwey-Overbeek (DLVO) theory. we have derived the renormalized spontaneous curvature as a function of capsid's inner and outer charge density and solution properties.
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