(25). Between Line 2 and Line 3, the substrate deforms strongly and it takes a concave shape with two inflection points, as displayed in Fig. 4(b) (phase II in Fig. 5). Between Line 3 and Line 4, the substrate possesses a convex morphology, corresponding to Fig. 4(d) (phase III in Fig. 5). Similar shapes can be verified by the finite element method in analysis of a droplet wrapped by a soft plate. [31]. Up Line 4, the valid shape of the vesicle-substrate system does not exist. Moreover, our findings can also set some illustrations of the opening angle of a soft membrane adhered by a droplet, which was controlled by the voltage [30]. It is found that when the voltage IDO inhibitor is zero, the opening angle has two

possible solutions, i.e. one is negative and the other is positive. In our model, we introduce the definition of opening angle of the substrate φ = 2ϕ0 − π, and the relationship between the opening angle and the reduced work of adhesion Erastin research buy with a fixed value of κ1/κ2 = 0.5 can be plotted in Fig. 6. From the figure we can see that there are two or three solution branches. In addition, the opening angle decreases with the increase of the work

of adhesion in a large range, which can be analogous to the droplet-membrane controlled by the electric voltage [30]. When w > 1.025, phase II (low branch) has lower energy and when 0.78 < w < 1.025, phase IV (green branch) has lower energy. When w < 0.78, there is only one solution. In the similar phenomenon, the voltage was input when the membrane-droplet is like phase I in Fig. 3, and the opening angle decreases with the increase of the voltage Vitamin B12 [30]. If the voltage is input to the droplet-membrane system like phase II in Fig. 3, shape saturation will occur and there is a sudden jump of the opening angle from point p to point p′. The developed model can certainly degenerate to the case of a vesicle adhering on a rigid substrate, where κ1/κ2 = 0. In this case, the function of the reduced free energy versus the reduced work of adhesion can be calculated, and the curve is demonstrated in Fig. 7. Clearly, the free energy of the system decreases

with the increase of the work of adhesion. This means that if a cell is deposited on a rigid substrate, it is prone to the position with strong adhesion capability. This result can provide some inspirations to control the moving direction of a living cell on a rigid substrate, by engineering some special materials with different surface energies. Fig. 8 shows the projected length as a function of the work of adhesion. The curve tells us that the projected length (as schematized in the figure) decreases with the increase of the work of adhesion, and this result is in agreement with the former experimental phenomenon [9]. In conclusion, a systematic analysis of a vesicle adhered to an elastic substrate was performed.