: Conceptually, why does creatine increase muscle size? Muscle contractions are powered by ATP losing a phosphate and becoming ADP. Creatine can give away one phosphate to convert ADP back to ATP. With more ATP, muscles are

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It will increase it indirectly. Creatine draws more water and nutrients to muscle, so if your nutrition is good, more protein will come to muscle and build into it. Also creatine gives more power and improves recovery time, so again, it indirectly helps our muscle grow by helping us with our gym training without witch there is no muscle growth.

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Creatine increases the high energy phosphate diffusion between the mitochondria and myosine heads. Furthermore it works as a buffer for pH changes, which can improve cellulair homeostasis. And a decreased PCr level stimulates phosphofructokinase, an enzyme which limits glycolysis, and thus replenishment of this will lead to an improved glycolysis which also leads to a faster ATP reproduction. The following reviews explore this in more detail:

Sports Med. 1999 Jul;28(1):49-60. Review.

Sports Med. 2002;32(14):903-44. Review.

Physiol Rev. 2000 Jul;80(3):1107-213. Review.

Edit:
As a reaction on Ivo I'll try to provide a more basic explanation of how creatine works.

With the execution of a physical effort, your body uses energy. This energy comes from ATP (Adenosine Tri-Phosphate). ATP is the primary energy source. When ATP is used, ADP (Adenosine Di-Phosphate) arises and a phosphate ion. The energy which comes free with this reaction, is used by your body to execute the effort. Unfortunately the muscle cells only contain a small pool of ATP. This pool is only enough to supply energy for a few seconds of intense physical effort (1). But fortunately your body does everything it can to regenerate the ATP. Your body uses another pool (creatine phosphate, PCr), to regenerate the ATP. And this is where creatine supplementation gets interesting. After intake of creatine it gets absorbed by the intestine-wall and the Creatine Transporter (CT) pulls creatine into the muscle cell. When there is enough ATP (during rest), the enzym Creatine Kinase (CK) extracts the phosphate ion from the ATP, and binds it to the creatine, forming PCr. When you exercise after, and you utilise your ATP, ADP arises and this reaction works the other way around, CK binds PCr to ADP and generates ATP. The main goal of creatine supplementation is to raise PCr and Cr levels within the muscle cell, so ATP regenerates faster. And this is exactly what happens when you supplement creatine. (I don't think I need to provide any sources for this, there are numerous of publications reporting an increase of PCr and Cr levels during creatine supplementation).

References

Biochem J. 1992 Jan 1;281 ( Pt 1):21-40.