Phase transition behavior of a linear macromolecule threading a membrane

Abstract

The problem of a polymer molecule whose two ends reside on opposite sides of a membrane or partition separating two solutions is solved exactly in the limit of no self-excluded volume. The monomers can go from one side of the membrane to the other only by threading serially through one hole in the membrane. The ends can be free, confined to run freely on the membrane surfaces, or be fixed to specific points on the membrane. It is found that the equilibrium thermodynamic phase transition is first order in all cases so that slight changes in pH, ionic strength, or temperature can move the polymer from being completely on one side of the membrane to being completely on the other side. Application to two biological problems are suggested: (1) the breaching of cell walls by the nuclear material of T2 bacteriophages, and (2) the transport of drugs that are affixed to these translocating polymers. The relation of this newly discovered transition to four other phase transitions that occur in isolated macromolecules (helix–random coil; equilibrium polymerization; polymer collapse; surface adsorption) is briefly discussed.

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

“…(18). More precisely, they focused on geometrical structural parameters like the porosity, the percolation threshold and the dimensionality of the systems studied.…”

“…Over the years, several theoretical papers have attempted to capture the dynamics of polymer translocation [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. In almost all cases, however, the dynamics is being projected onto a quantity known as the translocation coordinate and defined as the length (or the fractional length) of the polymer on one side of the pore.…”

Polymer translocation through a nanopore: A two-dimensional Monte Carlo study

“…Inspired by the experiments, 7 a number of recent theories [15][16][17][18][19][20][21][22][23][24][25][26][27][28] have been developed for the dynamics of polymer translocation. Even without an external driving force, polymer translocation remains a challenging problem.…”

“…6 In addition to its biological relevance, the translocation dynamics is also a challenging topic in polymer physics. Accordingly, the polymer translocation has attracted a considerable number of experimental, [7][8][9][10][11][12][13][14] theoretical, [15][16][17][18][19][20][21][22][23][24][25][26][27][28] and numerical studies. [29][30][31][32][33][34][35][36] The translocation of a polymer through a nanopore faces a large entropic barrier due to the loss of a great number of available configurations.…”

DNA in Nanopores: Counterion Condensation and Coion Depletion

“…These studies, as well as other models of polymer translocation through narrow pores [8,9,10,11,12,13,14,15], focused on the polymer aspects of the problem such as the effect of confinement-induced entropy losses on the translocation of a Gaussian chain and on the effective friction between the chain and the narrow pore.…”