Phase Transitions of a Polymer Threading a Membrane: Character of the Transition When the Molecule Can Undergo a Helix-Random Coil or an Equilibrium Polymerization Transition

Abstract

The polymer threading a membrane transition (PTM) which is a first‐order thermodynamic phase transition for an isolated linear polymer in the limit of infinite molecular weight is coupled to the helix to random coil (HRC) transition and the polymerization (P) transition. In each case an exact expression for the partition function of the coupled pair is given as a 1‐dimensional summation over products of the individual partition functions. For HRC‐HRC there are 8 possible translocation modes. For example, as we raise the temperature we can have H1→H2→R1→R2 in obvious notation. The PTM‐P mode is most interesting because polymer can be created in the PTM side even though the P side is in the depolymerization regime! These exact model solutions provide a base for the study of the kinetics of significant technological problems such as the translocation of DNA through pores in membranes. They also throw light on the nature of polymer‐membrane‐pore interactions in living cells and viruses.