Does the mitochondria have a relationship to any other biomolecules?

Typically, when respiration is considered, we consider the catabolism of glucose to produce ATP. In eukaryotes (organisms with nucleus-containing cells) this process begins in the cytoplasm of the cell with glycolysis. Glycolysis breaks down a 6-carbon glucose into two 3-carbon pyruvic acid molecules, 2 NADH, and 2 ATP (4 are produced, but 2 are used).  

The pyruvic acid molecules are then oxidized to produce 2 acetyl CoA molecules which can enter the Kreb's cycle (also known as the citric acid cycle or the TCA cycle) which takes place within the mitochondria. The cycle is completed twice for each original glucose molecule. This cycle, per original glucose, produces 6 NADH, 2 ATP, 2 FADH2, and 4 CO2.

The electron carriers (NADH and FADH2) produced during the previous 2 steps then go on to the electron transport chain embedded within the inner mitochondrial membrane. Proteins within the chain are reduced by the electron carriers as they take the electrons that they are carrying. The electrons are then passed from protein to protein along a chain of increasing electronegativity until the final electron acceptor, water, accepts the electrons to form water. As the electrons are transported, the energy is used to pump protons into the intermembrane space, creating a proton gradient. The only place where these protons can diffuse down their concentration gradient is through ATP synthase. As they do, the movement of the enzyme results in the production of ATP.

Glucose (a carbohydrate) is not the only macromolecule that can be broken down to produce ATP. Lipids and proteins can also be used. The fatty acid chains of lipids, such as triglycerides, can be broken apart 2 carbons at a time to produce acetyl CoA molecules. This process is called beta oxidation. These acetyl CoA molecules can then enter the Kreb's cycle with the same result as acetyl CoAs resulting from glucose catabolism.

Proteins are broken down into their component amino acids building blocks during digestive processes. Once this occurs, energy can be obtained from amino acids. Amino acids can be converted to Kreb's cycle intermediates and then enter the Kreb's cycle. For example, arginine, glutamate, histidine, and proline can be converted to alpha ketoglutarate, an intermediate in the cycle. Once they are inserted, the cycle continues as it does with glucose.