Before the reaction can occur, charge is transported across this membrane, similar to charging a battery. This charge then allows the energy-producing reaction to happen. Since the reaction happens at the membrane surface, a folded membrane with increased surface area can produce more energy for the cell. They increase the surface area of the inner membrane, allowing there to be more proteins and more exchange of ions across the membrane, allowing the mitochondrion to do its job more quickly.
The function of the folds within the mitochondria is to increase the surface area of the mitochondrial membrane. Basically, the physical form of a structure can increase or decrease its surface area to volume ratio.
For instance, a sphere has the minimum surface area to volume ratio, whereas a pyramid has a larger surface area to volume ratio. For example, if you had a fixed volume of clay and made it into a sphere or a pyramid, the pyramid would have a larger surface area. The same concept applies to mitochondria that by having a highly folded structure, they increase the surface area of their membrane.
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