What is the name of a protein that can exist in multiple shapes depending on the binding of a molecule?

The correct term for a protein that can adopt multiple shapes depending on the binding of a specific molecule is an allosteric protein. Allosteric proteins have distinct binding sites where effectors or ligands can attach, causing a conformational change in the protein's structure. This alteration can enhance or inhibit the protein's activity, making them crucial in various regulatory processes within cells.

In contrast, hemoglobin is a specific type of allosteric protein that binds oxygen, but it doesn't represent the broader category of proteins exhibiting this property. An enzyme is a specialized type of protein that catalyzes biochemical reactions, and while many enzymes can undergo conformational changes, not all enzymes are considered allosteric. Lastly, globular proteins refer to a shape of proteins that is more compact and soluble, but the term does not convey the multiple shape characteristics associated with allosteric proteins. Hence, the concept of allosteric regulation precisely captures the dynamic nature of proteins that change shape upon binding.