GUV shape and membrane tension analysis

A single vesicle is isolated from the chamber in which the GUVs are suspended in. The vesicle is held via pipette-aspiration under constant pressure (details in SI), protected from dehydration via a transfer capillary¹⁸, and moved from this suspension to a chamber containing a microparticle suspension with otherwise identical solution conditions, i.e., 800 mM glucose and 10 mM PBS; this allows us to study microparticle migration without interference from other vesicles in the field of view.

Once the GUV is introduced into the chamber, particles begin to adhere to the membrane. Concomitantly, the GUV is deformed using a large, clean, glass bead of radius 10-30 μm glued to a second micropipette. Using micro-manipulators, the bead is tapped gently against the GUV to promote adhesion to the membrane, and gently retracted to elongate the GUV into a lemon-like shape (Fig. 2 (A)). The entire arrangement is then held fixed. The micropipettes are configured so that the elongated vesicle shape is axisymmetric. A GUV aspirated by the pipette, shown in Fig. 2 (B), consists of two parts: a part outside of the pipette that is elongated by pulling, and a part inside the pipette with a shape that can be roughly approximated by a cylinder with a spherical cap of radius R_P at its end.

(A) Schematic of an aspirated GUV being elongated by two micro-manipulated micropipettes in a liquid chamber with suspended particles. One micropipette holds the aspirated area reservoir. A bead, affixed to the other micropipette, adheres to the GUV and is used to impose elongation. (B) Bright field microscopy image of an elongated GUV. The yellow dashed lines are the contours with constant H; black lines underneath the dashed lines are the contour found by tracking the shape of the membrane; the blue line is the calculated axis of symmetry. Scale bar: 10 μm (C) Deviatoric curvature (upper panel) and gradient of deviatoric curvature with respect to arc length (lower panel) are plotted against arc length, s.

The contour of the elongated part of the GUV was tracked from both confocal and bright field images using ImageJ and Matlab. A typical contour imaged via confocal fluorescence microscopy is shown in Fig. 2 (B). We define a coordinate (R,Z) with Z=0 located at the large bead, and R=0 on the axis of symmetry. The meridional arc length s along the contour is measured from the bead, as well. After elongation, we observe that the GUV has constant mean curvature H. By minimizing an objective function characterizing the difference between the experimental contour (black line in Fig. 2 (B)) and numerically generated curves, the location for the axis of symmetry (blue line in Fig. 2 (B)), values for H and values the principle curvatures of the membrane along the contour were determined ^19,20. The fitted profile (yellow dashed line, Fig. 2 (B)) agrees well with the experimental contour. The axis of symmetry is a line that is found to be located at equal distance from both sides of the GUV contour. (See SI for discussion of fitting error).

The pressure drop across the aspiration pipette was controlled by the height of a water reservoir connected to the pipette. The height of the water reservoir was monitored by a pressure transducer measuring the hydrostatic pressure of the water reservoir (DP-1520, Validyne, Northridge CA). We measure the pressure drop between inside and outside of the pipette, P_out − P_in, where P_in and P_out are the pressures inside of the pipette and in the bulk solution external to the aspiration pipette, respectively. We measure the radius of the aspirated cap, R_P, and the mean curvature of the elongated GUV, H, from image analysis as mentioned. Applying the Young-Laplace equation to the portion of vesicle in the aspirated cap, and to the elongated vesicle yields two equations with two unknowns, the membrane tension σ, and the pressure inside the GUV. We can therefore calculate the membrane tension from the relationship ²¹:

While H is constant along the deformed GUV, the deviatoric curvature Δc, defined by the difference between the principal curvatures (such that Δc > 0), varies with arc length s. Gradients in Δc are zero near the middle of the GUV, and are steepest near the bead and micropipette (Fig. 2 (C)). Below, we show that particle migration is related to this quantity. To probe particle migrations on tense vesicles, tensions are varied over the range 0.24 mN/m < σ < 0.69 mN/m. To probe for migration at very low tension, we also run the same experiment under a tension of 0.05 mN/m.