Polymers Pushing Polymers: Polymer Mixtures in Thermodynamic Equilibrium with a Pore

Abstract

Studies on the ejection of viral genomes from capsids use osmotic stress to push a DNA molecule into the viral capsid by the action of PEG in solution. Identities of the polymer forced into the nano-cavity (DNA) and the polymer pushing it (PEG) differ. We analyze a variation on the problem with a simple model of a binary polymer mixture and find that polymer size dependent partitioning into a pore also has a complex dependence on the composition of the polymer mixture and the pore-penetration penalty. We analyze a polydisperse polymer solution of big and small polymer chains (bPEG and sPEG, respectively) of which only the sPEG is allowed to pay an energy penalty and enter the pore. We introduce an ansatz for the free energy of the polymer mixture that is consistent with our previous phenomenological fit to the equation of state of bulk uncharged polymers. We then analyze the osmotic pressure of this solution in equilibrium with a pore for various amounts of sPEG. Calculating the corresponding partition coefficient allows us to assess the pushing forces exerted by the external polymer solution via its osmotic pressure and ascertain that some polymers can push others to enter the pore in a kind of osmotic tug-of-war. We find that pore penetration is governed by two different penetration free energy scales. One scale represents the osmotic pushing strength of the external polymer mixture. The other scale comprises the interplay between the pore energy penalty and the translational mixing entropy (van't Hoft) and configurational (des Cloizeaux) fluctuations of the external solution. This principle should have applications in many areas of nano-science dealing with partitioning of polymer chains into small enclosures.