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Triosephosphate isomerase (TIM) catalyzes the reaction to convert dihydroxyacetone phosphate into glyceraldehyde 3-phosphate, and vice versa. In most organisms, its functional oligomeric state is a homodimer; however, tetramer formation in hyperthermophiles is required for functional activity. The tetrameric TIM structure also provides added stability to the structure, enabling it to function at more extreme temperatures. We apply Principal Component Analysis to find that the TIM structure space is clearly divided into two groups--the open and the closed TIM structures. The distribution of the structures in the open set is much sparser than that in the closed set, showing a greater conformational diversity of the open structures. We also apply the Elastic Network Model to four different TIM structures--an engineered monomeric structure, a dimeric structure from a mesophile--Trypanosoma brucei, and two tetrameric structures from hyperthermophiles Thermotoga maritima and Pyrococcus woesei. We find that dimerization not only stabilizes the structures, it also enhances their functional dynamics. Moreover, tetramerization of the hyperthermophilic structures increases their functional loop dynamics, enabling them to function in the destabilizing environment of extreme temperatures. Computations also show that the functional loop motions, especially loops 6 and 7, are highly coordinated. In summary, our computations reveal the underlying mechanism of the allosteric regulation of the functional loops of the TIM structures, and show that tetramerization of the structure as found in the hyperthermophilic organisms is required to maintain the coordination of the functional loops at a level similar to that in the dimeric mesophilic structure.