Periodic modulation of tubular vesicles induced by phase separation

We investigated changes in the shape of tubular ternary vesicles induced by phase separation into liquid-ordered and liquid-disordered phases. Tubular vesicles transform into two types of periodically modulated vesicles depending on the area fraction of the liquid-ordered phase. One type is a necklace of oblate subunits with two circular domains of the liquid-order phase, and the other is a periodically modulated tube with stripes of the liquid-order phase. The transition between the circular and striped domains is governed by the domain boundary energy, whereas the periodicity of modulated vesicles is determined geometrically based on the fixed volume and area constraints. The observed multidomain vesicles are kinetically trapped in metastable states, and all domains show budding to reduce the boundary energy.

Figure 1

Morphology diagram of phase-separated tubular vesicles in ${\varphi }_{\text{o}}$ $\left(m_{\text{chol}}\right)$ and $\xi$ space. The vesicles above the thick white line show typical shapes with large $\xi$ $\left(\sim 0.8\right)$. The white and black regions in the vesicles are the Ld and Lo phases, respectively. Scale bar is $5\mu \text{m}$.

Figure 2

(Color) Budding transition of multidomains on modulated tubular vesicles with a mole fraction of $\text{DPPC}/\text{DOPC}=1:1$ and Chol mole fractions of (a) 0.2, (b) 0.3, (c) 0.35, and (d) 0.4. The values of excess area in each vesicle are (a) 0.3, (b) 0.1, (c) 0.2, and (d) 0.6. The onset time of the budding transition is expressed as 0 s. Red (white) and green (black) regions indicate the Ld and Lo phases, respectively. Scale bars are (a)–(c) 5 and (d) $2\mu \text{m}$.

Figure 3

Geometrical spheroid models describing (a) an axisymmetric oblate vesicle with two circular Lo domains on both sides (OV2CD) and (b) an axisymmetric prolate vesicle with one striped Lo domain (PV1SD). The gray and black lines represent cross sections of the Ld and Lo phases, respectively.

Figure 4

(a) Normalized total free energy ($F/8\pi {\kappa }^{\text{d}}$, thick lines) and normalized line energy ($F_{\text{line}}/8\pi {\kappa }^{\text{d}}$, thin lines) curves of OV2CD (solid lines) and PV1SD (dotted lines) with $\xi =0.02$ as functions of the area fraction of the Lo phase, ${\varphi }_{\text{o}}$. Schematic representations show the geometries of OV2CD (upper side) and PV1SD (lower side) with different ${\varphi }_{\text{o}}=0.2$, 0.4, 0.6, and 0.8 (left to right). The gray regions represent Lo phases. (b) Normalized total free energy $\left(F/8\pi {\kappa }^{\text{d}}\right)$ for OV2CD (black lines) and PV1SD (gray lines) as a function of ${\varphi }_{\text{o}}$. Both vesicles have same excess areas $\xi =0.06$ (dashed lines), 0.03 (dotted lines), and 0 (solid lines).

Figure 5

Relationship between the number of subunits $N$ and excess area $\xi$ for periodically modulated vesicles with various ${\varphi }_{\text{o}}$’s. Necklace vesicles with ${\varphi }_{\text{o}}=0.35$ and ${\varphi }_{\text{o}}=0.45$ are composed of $N$ oblate subunits, and tubular vesicles with ${\varphi }_{\text{o}}=0.55$ have $N$ striped Lo domains. The solid line indicates the geometrical relationship $\xi +1=\left({\xi }_0+1\right)N^{1/6}$, with ${\xi }_0=0$.

Figure 6

Time evolution of domain growth on tubular vesicles with (a) ${\varphi }_{\text{o}}=0.35$, $\xi =0.1$; (b) ${\varphi }_{\text{o}}=0.35$, $\xi =0.3$; and (c) ${\varphi }_{\text{o}}=0.55$, $\xi =0.3$. The onset time of visible phase separation is expressed as 0 s. The white and black regions are the Ld and Lo phases, respectively. The scale bar is $5\mu \text{m}$.

Figure 7

Dimensionless wave number $k=2\pi r/\lambda$ of modulated vesicles (${\varphi }_{\text{o}}=0.35$: necklace of oblate subunits and ${\varphi }_{\text{o}}=0.55$: tubular vesicles with striped domains) as a function of the excess area $\xi$. The solid line indicates the geometrical relationship $\xi =-1+\left({\xi }_0+1\right){\left\{{\left(k/\pi \right)}^2{\left(3-2\pi /k\right)}^{-1}\right\}}^{1/6}$, with ${\xi }_0=0$.