The same factor that increases the rate of ADP + phosphate ATP will also increase the rate of the converse reaction, ADP + phosphate → ATP. The rate of the ATP → ADP + phosphate reaction won't be affected by the catalyst.
An enzyme can be thought of as a catalyst that quickens a reaction. Enzymes play a key role in accelerating reactions by lowering the activation energy.
In this scenario, the same factor that speeds up the formation of adenosine triphosphate from the dissociation of adenosine triphosphate into adenosine diphosphate and inorganic phosphate (ATP ADP + phosphate) will also speed up the formation of adenosine triphosphate from the combination of adenosine diphosphate and inorganic phosphate (ADP + phosphate ATP).
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