Abstract
Aqueous two-phase systems and water-in-water emulsions have attracted much recent interest. Here, we theoretically study the interactions of such systems with biomimetic membranes and giant unilamellar vesicles (GUVs). For partial wetting, the water-water interface and the membrane form a three-phase contact line that partitions the membrane into two distinct segments with different tensions and different curvature-elastic properties. On the nanometer scale, the capillary forces arising from the water-water interface lead to a smoothly curved membrane that forms an intrinsic contact angle with the interface. The corresponding balance conditions are derived here for general curvature-elastic parameters of the two membrane segments. On the micrometer scale, the capillary forces deform the membrane segments into spherical caps with an apparent kink along the contact line. A new computational method is introduced by which these piece-wise spherical vesicle shapes can be analyzed in a systematic manner. The method is based on a general relationship that is reminiscent of Neumann's triangle but depends explicitly on the curvatures of the membrane segments. For certain regions of the parameter space, corresponding to small or large spontaneous curvatures, the force balance along the apparent contact line can be described in a self-consistent manner and then leads to curvature-independent relationships that involve the total membrane tensions. The different relationships can be used to determine the material parameters of the droplet-vesicle system from the observed morphologies of the GUVs. The approach described here is quite general and can be applied to different membrane compositions and aqueous two-phase systems. The same computational approach can also be used to elucidate the response of biological membranes to the recently discovered membrane-less, droplet-like organelles.
Highlights
We examine the energy of the spherical cap segments and derive tension−angle relationships that apply to certain regions of the parameter space and describe the force balance along the apparent contact line
Xjγ ≡ Wjγ + σjγ and Yjγ ≡ −2κjγmjγ. When we insert these expressions for the effective tensions Σjeγff into the relationships (41)−(43), we see that these relationships contain three different types of quantities: (i) the mean curvatures of the spherical membrane segments and the apparent contact angles, two types of geometric quantities that can be directly deduced from the microscopy images; (ii) the material parameters Xjγ and Yjγ; and (iii) the lateral membrane stress Σ that depends on the size and shape of the giant unilamellar vesicles (GUVs) and represents a hidden variable from the experimental point of view
Partial wetting morphologies of giant vesicles exposed to aqueous two-phase systems as depicted in Figure 1a and Figure 6a for in- and out-wetting, respectively, are characterized by a three-phase contact line that partitions the vesicle membrane into two segments, an αγ or γα segment in contact with the aqueous α phase, and a βγ or γβ segment in contact with the aqueous β phase
Summary
Aqueous two-phase systems, called aqueous biphasic systems, have been used for a long time in biochemical analysis and biotechnology and are intimately related to water-in-water emulsions.[1,2] Renewed interest in these systems arose from several recent developments such as the use of ionic liquids,[3] improved control of the biphasic partitioning of biomolecules,[4,5] the production and handling in microfluidic devices,[6] and the Pickering stabilization of water-in-water droplets by various types of particles.[7−10] Aqueous two-phase systems based on biopolymers such as PEG and dextran undergo phase separation when the weight fractions of the polymers exceed a few percent. The effective tensions Σαefγf as given by (35) can be rewritten in the form When we insert these expressions for the effective tensions Σjeγff into the relationships (41)−(43), we see that these relationships contain three different types of quantities: (i) the mean curvatures of the spherical membrane segments and the apparent contact angles, two types of geometric quantities that can be directly deduced from the microscopy images; (ii) the material parameters Xjγ and Yjγ; and (iii) the lateral membrane stress Σ that depends on the size and shape of the GUVs and represents a hidden variable from the experimental point of view. From three different γβ segments with three distinct mean curvatures Mγ(nβ), we can obtain the two parameter combinations (Σ + Wγβ + σγβ)/Σαβ and κγβmγβ/Σαβ that determine the tension ratios Σγ(nβ)/Σαβ
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