Chains of enzyme reactions in a cell that regulate enzyme activity and energy flow are

centrioles

metabolic pathways

activators

inhibitors

Correct  METABOLIC PATHWAYS

According to dictionary definition, metabolic pathways are sequences of biochemical reactions in living cells, driven along by enzymes, that mainly involve the exchange of energy and chemicals.

Metabolic studies were initiated as far back in history as the 13th century.  Ibn al-Nafis (1213-1288), an Arab doctor in Damascus, observed that "the body and its parts are in a continuous state of dissolution and nourishment, so they are inevitably undergoing permanent change."

As for the specific discovery of metabolic pathways and enzyme involvement, we can look to Louis Pasteur in the 19th century, who noted that yeast changed sugar into alcohol by the catalyst of substances within the yeast cells that he termed "ferments."  (Thus we speak of "fermentation.")  In addition to Pasteur's  discovery, Friedrich Wöhler published work in 1828 regarding the chemical synthesis of urea, which he discovered when he was trying to synthesize ammonium cyanate.  These scientists were documenting the chemical reactions found in cells that we now refer to as  metabolic pathways.  

In the 20th century, Eduard Buchner furthered knowledge of metabolic pathways by the discovery of enzymes.  This showed that studying the chemical reactions of metabolism was different from the biological study of cells.