FtsZ is the first protein recruited to the bacterial division site, where it forms the cytokinetic Z ring. We have determined the functional energetics of FtsZ assembly, employing FtsZ from the thermophilic Archaea Methanococcus jannaschii bound to GTP, GMPCPP, GDP, or GMPCP, under different solution conditions. FtsZ oligomerizes in a magnesium-insensitive manner. FtsZ cooperatively assembles with magnesium and GTP or GMPCPP into large polymers, following a nucleated condensation polymerization mechanism, under nucleotide hydrolyzing and non-hydrolyzing conditions. The effect of temperature on the critical concentration indicates polymer elongation with an apparent heat capacity change of -800 +/- 100 cal mol-1 K-1 and positive enthalpy and entropy changes, compatible with axial hydrophobic contacts of each FtsZ in the polymer, and predicts optimal polymer stability near 75 degrees C. Assembly entails the binding of one medium affinity magnesium ion and the uptake of one proton per FtsZ. Interestingly, GDP- or GMPCP-liganded FtsZ cooperatively form helically curved polymers, with an elongation only 1-2 kcal mol-1 more unfavorable than the straight polymers formed with nucleotide triphosphate, suggesting a physiological requirement for FtsZ polymerization inhibitors. This GTP hydrolysis switch should provide the basic properties for FtsZ polymer disassembly and its functional dynamics.