The oxygen-carrying protein in muscle cells is myoglobin, which is very similar to the oxygen-carrying protein for the entire human body, hemoglobin. Hemoglobin carries oxygen to the muscle cells where it is handed off to myoglobin, which transports the oxygen within the muscle cells.
Myoglobin is a protein found mostly in muscle cells comprised of eight alpha-helices. The center of the protein is hydrophobic, meaning it does not react with water molecules. The outside of the protein is hydrophillic as it reacts with water molecules.
This makes the protein overall water soluble. Every myoblobin protein contains one heme group which is responsible for carrying oxygen. Every heme group contains one iron molecule. The oxygen atom attaches directly to the iron atom in the heme group.
The hydrophobic nature of the center of the myoglobin protein works to stabilize the attachment of the oxygen atom to the iron atom. This allows myoglobin to effectively transport the oxygen atom throughout the muscles without fear of it falling off and attaching itself to another protein or atom. Once the myoglobin protein reaches its destination with the attached oxygen, the oxygen is released from the iron atom and the myoglobin protein is free to attach to a different oxygen atom for further transport.