Coupling of the Polymer Threading a Membrane Transition to the Membrane Adsorption Transition

A polymer molecule threading through a pore in a plane membrane is allowed to adsorb on either or both sides of the membrane. Further, it is confined to the vicinity of the membrane by two plane barriers lying on either side of the membrane. A lattice model of this problem is exactly solvable by matrix techniques. The equilibrium translocation behavior is described as a function of the polymer MW, the membrane adsorption energies, the solution properties, the barrier separations, applied force, and the temperature. The transition is first-order, meaning that small changes in any of these 9 quantities can in the limit of infinite MW, completely translocate the polymer. The work of Park and Sung who used Smoluchowski-like equations to calculate translocation transit times can be generalized by use of the sea-snake model which is relevant to isolated polymer chains in solution. The physics behind the sea-snake model is that if one monomer is pulled into the membrane, the distance the center of mass of the untranslocated portion of the chain moves is MW^?1/2 of the distance between monomer units. This reduces the effective friction coefficient by MW^1/2. It is found for the sea-snake model that the MW dependence of transit times varies as MW^3/2 or MW depending on whether we use a free draining or a non-free draining picture for the polymer.