**4. Shape determination of CVs with complex composition**

If we take into account that the membrane is composed of more than one kind of constituents, the set of possible shapes with minimal energy is further expanded as the system has additional freedom by which it can adjust its configuration. The constituents may move to the regions of favorable curvature and additionally adjust their orientation. Allowing the system more freedom effectively increases its stability. To demonstrate the effect of the lateral distribution of constituents, **Figure 4B** shows two views on the shape with minimal free energy determined by the Monte Carlo simulation method. Two different isotropic constituents (favoring strong positive curvature and minute curvature, respectively) were considered. Red color denotes prevalence of the constituents that favor positive curvature and blue color denotes prevalence of the constituents that favor minute curvature; white color denotes the mixture of both kinds. Buds and undulated protrusions have formed largely from the constituents that favor strong positive curvature while the constituents that favor minute curvature organized themselves into a globule where the membrane is almost flat with respect to its thickness. Multiple buds recruit the constituents that favor strong positive curvature and span the almost flat parts to further minimize the energy. Agreement between the shapes observed in budding erythrocytes (**Figure 4A**) and shapes composed of two kinds of constituents does not reach the level evident in **Figure 1**. Budding erythrocyte undergoes detachment of the membrane skeleton at the top of the echinocyte spicules which is not taken into account in the theoretical consideration used to determine the shape shown in **Figure 4B**. Nevertheless, some aspects of the shape (i.e., multiple protrusions and rounded shape of the bud tips) can be noted.

Orientational ordering of the anisotropic constituents becomes evident in strongly anisotropically curved membrane parts such as in the necks and on the tubular parts (**Figure 5**). The variational problem of free energy minimization was solved by the expansion of the shape contour into the Fourier series [48]. Two kinds of constituents were considered—strongly anisotropically curved constituents and isotropic constituents that favor minute curvature. To enhance the formation of strongly anisotropically curved regions, a rod-like structure was imagined inside the vesicle by requiring a fixed length of the shape while the minimization took place. Longer rods induced

#### **Figure 4.**

*A: Budding erythrocytes. B: Shape of a vesicle with a two-component membrane, calculated by Monte Carlo simulation. Membrane nanodomains with high intrinsic curvature (red color) are accumulated in undulated membrane protrusions. A: From [34]. B: From [48].*

#### **Figure 5.**

*Shapes of vesicles that are composed of two types of constituents (anisotropic (red) and isotropic (blue)), calculated for different lengths of the rod-like structure inside the vesicle. Panels (a) - (e) show the effect of different lenght of the rod-like structure inside the vesicle as indicated in the figure. The color scale shows the proportion of the two kinds of constituents Φ. The average Φ over all vesicle membrane was 0.25. Orientation of the anisotropic constituents is denoted by short gray lines on the protrusions. From [48].*

longer and thinner tubular protrusions with well-ordered anisotropic constituents (**Figure 5**). The constituents redistributed into almost separate parts. Red color denotes prevalence of anisotropic constituents, blue color denotes prevalence of isotropic constituents while the rainbow between these two colors denotes a mixture of both kinds of constituents. It can be seen in **Figure 5** that the anisotropic constituents accumulated in the protrusion and underwent orientational ordering. While in thicker (conical or cylindrical) parts, the constituents ordered circumferentially (**Figure 5a**-**c**) the direction became tilted in thinner cylindrical parts toward the top of the shape (**Figure 5b**) and was almost uniform on longer tubular parts (**Figure 5d**-**f**).

Results shown in **Figures 4** and **5** indicate that the curvature induces sorting of membrane constituents to different extents determined by factors such as geometrical constraints and the intrinsic shape of the constituents.

*Morphology and Formation Mechanisms of Cellular Vesicles Harvested from Blood DOI: http://dx.doi.org/10.5772/intechopen.101639*
