Figure 4.

Wrapping phase diagram for fixed line tension or membrane tension. (A) Wrapping states of the system of a tip-first-oriented merozoite for fixed reduced line tension $\tilde{\gamma }$ = 0.20 and several values of effective adhesion strength and effective membrane tension: non wrapped merozoite (NW), partially wrapped merozoite with small (PW I) and high wrapping fractions (PW II), and completely wrapped/fully invaded merozoite (CW), see Fig. 1. The transition W₀ is a continuous transition, whereas the transitions W₁, W₂, and E are associated with energy barriers. The transition W₁ ends at a critical point where the difference between PW I and PW II vanishes. The terms in Eq. 2 can be rearranged, such that the spontaneous curvature c₀ can be combined with the membrane tension and the adhesion strength to an effective membrane tension, ${\tilde{\sigma }}_{\mathit{eff}}=\tilde{\sigma }+{\tilde{c}}_0^2/{\left(a{H}_0\right)}^2$, and an effective adhesion strength, ${\tilde{w}}_{eff}=\tilde{w}+{\tilde{c}}_0$, respectively. The critical point is indicated by a black point (•). (B) Wrapping states of the system of a tip-first-oriented merozoite for vanishing effective membrane tension, ${\tilde{\sigma }}_{\mathit{eff}}=0$, and several values of effective adhesion strength and line tension. The notation is analogous to A. Both phase diagrams with additional wrapping spinodals that indicate the values of the adhesion strength beyond which the energy barrier vanishes and spontaneous wrapping occurs, are shown in Fig. S3. However, the energy barriers may also be crossed by other mechanisms: arrow a indicates the effect of unstructured membrane secreted by the merozoite (Fig. S2B), arrow b shows the effect of favorable spontaneous curvature, arrow c the effect of increased adhesion strength, and arrow d the effect of increased line tension. To see this figure in color, go online.