The compound responsible for much of the umami taste in foods such as Parmesan and tomatoes is glutamate. It is the negatively charged form of glutamic acid and occurs naturally in many protein-rich or fermented foods.
Umami is often described as savory, brothy, or meaty. The human taste system detects glutamate through specialized receptors, including the T1R1/T1R3 receptor combination. Free glutamate—meaning glutamate not bound inside a protein—is especially important for the taste sensation.
Parmesan develops abundant free glutamate during aging as proteins break down. Ripe tomatoes also contain naturally occurring glutamate, which helps explain their savory depth. Other compounds, including inosinate and guanylate, can produce umami too and may intensify glutamate’s effect, especially in meat, fish, mushrooms, and seaweed. They are related contributors, but glutamate is the canonical answer for this question.