Force Generation by Curvature-Generating Molecules

Curvature-generating molecules (CGMs) are central to a variety of biological processes. In particular, proteins such as clathrin help provide bending forces and moments to drive endocytosis. We develop a discrete mechanical model of the shape of a small CGM-membrane complex that incorporates the effects of cell wall elasticity and high turgor pressure. We study the dependence of the force generated by the CGMs on several parameters, including the bending modulus, the complex size, and the turgor pressure. We find evidence of transitions as a function of external turgor pressure and intrinsic curvature. This work also compares the discrete model to previous continuous models of CGM forces, finding that the distribution of the forces depends on the strength of the turgor pressure relative to the bending energy. The forces are localized at the edges for high turgor pressure, and more widely distributed for low turgor pressure. In addition, the energy exhibits a minimum at small numbers of molecules. Further, for realistic values of the bending rigidity and curvature, CGMs alone are insufficient to initiate endocytosis against turgor pressure, in agreement with previous findings.