Unbinding transition from fluid membranes with associated polymers

Abstract

We consider two neighboring fluid membranes that are associated with long flexible polymers (proteins or other macromolecules). We are interested in two physical systems consisting of i) two adjacent membranes with end-grafted (or adsorbed) polymers (system I), or ii) two membranes confining a polymer solution (system II). In addition to the pure interactions between membranes, the presence of polymers gives rise to new induced mediated interactions, which are repulsive, for system I, and attractive, for system II. In fact, repulsive induced interactions are caused by the excluded-volume forces between grafted polymers, while attractive ones, by entropy loss, due to free motion of polymers between membranes. The main goal is a quantitative study of the unbinding transition thermodynamics that is drastically affected by the associated polymers. For system I, the repulsive polymer-mediated force delays this transition that can happen at low temperature. To investigate the unbinding phenomenon, we first present an exact mathematical analysis of the total potential that is the sum of the primitive and induced potentials. This mathematical study enables us to classify the total interaction potentials, in terms of all parameters of the problem. Second, use is made of the standard variational method to calculate the first moments of the membrane separation. Special attention is paid to the determination of the unbinding temperature. In particular, we discuss its dependence on the extra parameters related to the associated polymers, which are the surface coverage and the polymer layer thickness on each membrane (for system I) or the polymer density and the gyration radius of coils (for system II). Third, we compute the disjoining pressure upon membrane separation. Finally, we emphasize that the presence of polymers may be a mechanism to delay or to accentuate the appearance of the unbinding transition between fluid membranes.

Effective interactions between fluid membranes

“…If so, what is the order of the unbinding transition and the threshold value of the (attractive) inter-action strength for the membranes to unbind? Besides the presence of additional interactions in real systems, the membranes themselves can be multi-component, e.g., consist of a mixture of lipids and lateral inclusions that may undergo phase separation [15], and the solution may also contain polymers (such as proteins) which then interact with the membranes and anchor or adsorb onto the membrane surfaces [16].…”

“…Theoretical treatments of such problems have traditionally fallen into four classes: mean-field or Flory-Huggins-type approaches (see, e.g., [15,[17][18][19]), variational Gaussian approximation (VGA) schemes (see, e.g., [5][6][7]16]), FRG-based methods (see, e.g., [12,[20][21][22][23][24][25][26][27]), and Monte Carlo simulations of different flavours (see, e.g., [28][29][30][31][32][33]). For the simpler case of a pair of single-component membranes interacting via a direct potential that consists of a long-range attractive van der Waals tail and a short-range repulsive hydration potential, mean-field theory (MFT) based on the simple addition of the direct potential with the fluctuation-induced steric potential predicts a first order unbinding transition at a critical strength of the Hamaker coefficient [17], whereas a Flory-Huggins-type theory, modeled after the van der Waals theory of liquid-gas condensation, predicts a continuous unbinding transition at a critical strength of the Hamaker coefficient W = W c and scaling behavior d ∼ |W − W c | −1 [18].…”