Chapter 14. Tension-induced mutual adhesion and a conjectured superstructure of lipid membranes

W. Helfrich
Fachbereich Physik, Freie Universität Berlin,
Arnimallee 14, 14195 Berlin, Germany

1. Introduction

Parallel fluid membranes in water repel or attract each other and the dependence of the forces on spacing can result in an equilibrium state of mutual adhesion. Attraction and adhesion are either spontaneous or induced by lateral tension. In induced adhesion, the tension acts by suppressing out-of-plane fluctuations, thus enabling Van der Waals attraction to prevail over repulsion by fluctuations and other repulsive interactions.

It is not clear whether the most common electrically neutral lipid membranes such as the bilayers of phosphatidylcholine (PC), phosphatidylethanolamine (PE) and digalactosylacylglycerol (DGDG) display spontaneous mutual adhesion. Some researchers inferred this from finding by X-ray diffraction a stationary maximum period of multilayer systems in excess water [1]. Studying giant vesicles, E. Evans and coworkers measured the mutual adhesion energies of PC, PE and DGDG membranes to be (0.01-0.015) mJ/m² , (0.12-0.15) mJ/m² and 0.22 mJ/m² , respectively [2, 3]. Our own experiments on lipid/water systems did not yield any evidence for mutual spontaneous adhesion of PC and PE bilayers. There appears to be a conflict between our results and those of Evans which needs to be resolved. It may be related to the fact that we did not mechanically disturb the membranes but only watched them under the microscope, while in Evans' studies giant vesicles were manipulated with micropipettes. However, we and Evans and many others utilized the spontaneous swelling of these lipids in water to obtain single membranes and vesicles.

A large amount of theoretical work has been devoted in recent years to the 'unbinding transition' of fluid membranes, i.e. the transition from mutual spontaneous adhesion to the unbound state, as some parameter is varied. These studies started with the renormalization group treatment by Lipowsky and Leibler [4] and were continued mostly by Lipowsky and his group [5], with a few contributions from others [6-9]. Lateral tension, which by definition is not required for spontaneous adhesion, was taken to be zero in these calculations. The renormalization group flow equations of fluid membranes with a bending stiffness in three dimensions are identical to those of stretched polymers in two dimensions [10]. Although the identity holds only to a first approximation [6, 8], it is often invoked since the polymer problem can be expressed exactly by a Schrödinger-type equation, thus allowing analytical solutions. Numerical studies and other theoretical methods all showed the equilibrium mean spacing <z>_eq of parallel undulating membranes to obey

(1)

as the control parameter A approaches from below its critical value A_c where the membranes cease to adhere. The control parameter may be the strength of an attractive interaction potential (A < 0) or temperature (A > 0). The critical exponent of unbinding is generally predicted to be y = 1 for a pair of adhering membranes. Recent numerical results suggest y < 1 for three and more equal membranes in mutual spontaneous adhesion [11], which is contested on analytical grounds in the case of stretched polymers [9].

On the experimental side, there is to date only one known example of an unbinding transition [12]. DGDG in 100 mM NaCl solution was found to swell indefinitely at elevated temperatures. Adjacent membranes went into spontaneous adhesion when subsequently the temperature was lowered. The reversible transition appeared to be continuous, but it was not possible to check the scaling law (1). The transition temperature varied wildly among seemingly equal samples and decreased slowly in the course of days. Spontaneous adhesion was never seen when no salt was present. Adhesion induced by lateral tension occurs with PC, PE and DGDG bilayers [13-17]. Its accidental occurrence in highly swollen lipid samples is a rare phenomenon which we overlooked for years. Induced adhesion, unlike spontaneous adhesion, is characterized by contact angles of the adhering single membrane that are practically independent of lateral tension. In general, the tensions are below 10^-3 mN/m so that they can be read from the contact rounding, i.e. a rounding of the membrane next to the area of adhesive contact. Contact angles are always less than 90^o , as is necessary since the component of the tension parallel to the contact area has to be positive in the case of induced adhesion.

The experiments with DGDG in salt solution, showing both kinds of adhesion, confirmed that we had seen induced adhesion with PE and PC. Moreover, induced adhesion could be brought about willfully by two reversible procedures which were investigated with egg yolk PC (EYPC). One of them is osmotically controlled, the tension being generated by osmotic inflation of vesicles [14, 15]. The other is temperature controlled and operates in multilayer systems, the lateral tension resulting from membrane area contraction due to cooling. In both cases there was little or no dependence on salt concentration or initial temperature, which is direct evidence against spontaneous adhesion.

The theoretical treatment of mutual adhesion induced by lateral tension is difficult because of the simultaneous action of bending rigidity and lateral tension. We have tried to explain the experimental data in terms of undulatory repulsion, partially suppressed by tension, and attraction through a 1/ z² Van der Waals potential [14-16]. This approach leads to the scaling laws

(2)

and

  (3)

where s is the lateral tension and g_ad the adhesion energy between membranes per unit area of adhesive contact. A derivation of the same scaling laws, but for a different regime near the critical point of unbinding where the spacings are large, has been given by Lipowsky and Seifert [18]. Both (2) and (3) agree with the experimental data, a coincidence regarded at first [14] as proof that the membranes are driven apart by the usual thermal undulations. However, a comparison of the values of the adhesion energy obtained from two different formulas, the Young equation and another energy balance, revealed discrepancies of two orders of magnitude. They forced us to postulate that at very low tensions (ca. 10^-5 mN/m) the membranes store several times the excess area that is expected to reside in the undulations. This anomalous membrane roughness, in turn, requires for its support a membrane superstructure. In the meantime we have searched with more direct experimental methods for both superstructure and roughness.

The following is a review of our experiments on induced adhesion and their theoretical interpretation. There seems to be no similar work by other authors in the literature. At the end of the article we will compile additional evidence, direct or circumstantial, for a superstructure, an anomalous roughness or, generally, anomalous behavior of the lipid membranes investigated.

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