The soure of energy for these reactions is stuff like ATP and GTP.
Nope.
Today's organisms use three types of energy sources: fermentation, photosynthesis and respiration. None of these energy sources has been linked directly to the origin of life. A fourth energy source, ”thermosynthesis,’ free energy gain from thermal cycling, was proposed in a theoretical model for the emergence of the chemiosmotic machinery ...
http://www.arxiv.org/pdf/q-bio.PE/0501013
Of course modern ATP synthase didn't exist back then. Nobody's claiming it did. Except you, I mean.
Furthermore. The polymerization was probably catalyzed. Catalyzation of this sort has been done in the lab. The catalyzed polymerization rate was greater than the uncatalyzed polymerization rate by a factor of 10e9. (Gosh darn it! What's the code for "superscript"? I hate this whole 10e9 business.) Anyway. That's a billion to you and me.
The catalyzed polymerization rate is
really thermodynamically favored. That means that the reaction is going to be "pushed" in the direction of polymerization. ATP is not necessary. Actually, nothing else is necessary. It's like putting a ball on the side of a mountain. It's gonna roll down hill. The energy state of the ball at the bottom of the hill is lower than the energy state of the ball on the side of the mountain. So it will happen.
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