Dynamics of Growth and Form in Prebiotic Vesicles

The growth, form, and division of prebiotic vesicles, membraneous bags of fluid of varying components and shapes is hypothesized to have served as the substrate for the origin of life. The dynamics of these out-of-equilibrium structures is controlled by physicochemical processes that include the intercalation of amphiphiles into the membrane, fluid flow across the membrane, and elastic deformations of the membrane. To understand prebiotic vesicular forms and their dynamics, we construct a minimal model that couples membrane growth, deformation, and fluid permeation, ultimately couched in terms of two dimensionless parameters that characterize the relative rate of membrane growth and the membrane permeability. Numerical simulations show that our model captures the morphological diversity seen in extant precursor mimics of cellular life, and might provide simple guidelines for the synthesis of these complex shapes from simple ingredients.

Figure 1

(top) Different morphologies observed during growth in synthetic giant vesicles and $L$-form bacteria: (a) symmetric division, adapted from Ref. [11], (b) budding adapted from Refs. [10, 13], (c) tubulation adapted from Ref. [13], (d) vesiculation adapted from Refs. [10, 13] (Scale bars represent $3\mu \mathrm{m}$). Our minimal model leads to shapes that are similar to those observed experimentally, using the following dimensionless parameters: (a) ${\mathrm{\Pi }}_1=0.01$, ${\mathrm{\Pi }}_2=2.5$, (b) ${\mathrm{\Pi }}_1=0.15$, ${\mathrm{\Pi }}_2=5$, (c) ${\mathrm{\Pi }}_1=0.02$, ${\mathrm{\Pi }}_2=5$, and (d) ${\mathrm{\Pi }}_1=0.15$, ${\mathrm{\Pi }}_2=-2.5$ (see text for details). (e) A schematic of our vesicle model that uses a 3D triangulated lattice with bending rigidity $B$ immersed in a fluid with viscosity $\mu$, with area that grows with homogeneous expansion of the triangle size at a rate $\gamma$ and volume whose evolution is controlled by the wall permeability $K$.

Figure 2

Morphospace of vesicle shapes as a function of the dimensionless mechanical relaxation ${\mathrm{\Pi }}_1$ and the dimensionless spontaneous curvature ${\mathrm{\Pi }}_2$. For ${\mathrm{\Pi }}_2=-2.5$ the shapes also visualize the interior of the vesicles where vesiculation occurs. Configurations correspond to vesicle shapes immediately prior to division or fission, with snapshots of the vesicle just before a topological transition associated with fission.

Figure 3

Scaled elastic energy and vesicle shapes as a function of scaled time for two different modes of growth. (Top) When ${\mathrm{\Pi }}_1=0.05$ and ${\mathrm{\Pi }}_2=2.5$, the formation of a skinny neck between symmetric lobes provides a likely mechanism of homeostatic division in three dimensions. The slow growth allows the vesicle to deform through quasiequilibrated shapes with roughly constant elastic energy, and with a drop in the energy corresponding to neck formation. (Bottom) When ${\mathrm{\Pi }}_1=0.25$ and ${\mathrm{\Pi }}_2=-2.5$, fast surface growth and negative curvature lead to multiple sites of inward vesiculation. The buildup in elastic energy is a signature of fast nonequilibrated growth. The shapes along the curve also show the interior of the vesicles.