Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. In this study, we present nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with a modified Brusselator model that is one of the simplest reaction-diffusion models. Two proteins (curvature-inducing and regulatory proteins) bind to the membrane. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis [1]. Temporal oscillation of the protein concentration can be changed into Turing pattern (stable spatial patterns). Budding and multi-spindle shapes are also induced by Turing patterns as shown in Fig. 1.

Fig. 1. Snapshots of vesicles with Turing patterns. Top panel: multi-spindle shapes. Bottom panel: budded vesicles. Color indicates the concentration of the curvature-inducing protein.

We also found that the propagating wave patterns change into non-propagating patterns and spiral wave patterns due to the mechanochemical effects [2]. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins as shown in Fig. 2. This agrees with the experimental observation of GUVs with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

Fig. 2. Sequential snapshots of a shape-oscillation vesicle. Budding repeatedly occurs, accompanied by the propagation wave. Color indicates the concentration of the curvature-inducing protein.

References

• [1] N. Tamemoto and H. Noguchi, Sci. Rep. 10, 19582 (2020).
• [2] N. Tamemoto and H. Noguchi, Soft Matter 17, 6589 (2021).

Authors

• N. Tamemoto and H. Noguchi