Cells are able to control membrane curvature by modulating the lipid composition within their membrane. This is through the use of membrane rafts, flippases, and other enzymes to control the composition.
Lipids are unable to move between the two leaflets of a biological membrane without the assistance of a flippase - this is due to the energy cost of moving being very high. Therefore, this allows the maintenance of different proportions across the two leaflets.
Some lipids, such as phosphatidylethanolamine, have large tail groups. This causes a concave curvature in the membrane. However, phosphatidylcholine is a much more rectangular molecule, having a fairly even diameter along its length. This gives a more flat membrane shape.
By modulating the composition of membrane lipids, including sphingomyelin, phosphatidylinositol, and other molecules (including cholesterol (which modulates the fluidity and thickness of the membrane while not being a lipid)), it is possible to induce a desired curvature into the membrane.
Flippase enzymes can be used to modulate lipid composition, transferring lipids from one leaflet to the other. This can be used to ensure the curvature of the membrane is correct. The presentation of phosphatidylserine on the cytosolic face of the membrane can be an indicator that apoptosis is being induced - this is caused by flippases.