Bending energy

The energy stored in a membrane doesn't depend just on how much it is stretched (its size or area) but also on how bent or curved it is. Just as stretching a spring takes energy, bending takes energy too. Consider the effort it takes to bend a bamboo stick -- ask any panda!

Just as we considered the stretching of an amphiphilic membrane in terms of springs between the molecules, we can consider bending with the same model (and with the same caution).

In the diagram it is clear that bending the membrane stretches the springs in the top layer and compresses the bonds in the lower layer. Now, both compressing and stretching a spring take energy so we see that bending the membrane will take energy. So we see that just in the same way that a spring has en equilibrium length the membrane will have an equilibrium amount of curve (called its spontaneuous curvature). If both sides are the same then we will expect the equilibium shape to be flat. This is because it is the shape with the lowest energy. We can say that the membrane will have a certain rigidity (*), or resistance to bending, because it takes energy to bend it.