We study the structural fluctuations of triosephosphate isomerase (TIM) by an elastic model, namely, the Gaussian network model (GNM), to identify a network of coupled motions in the allosteric communication between its deamidation and catalytic sites, and the promoting motions for the deamidation activity. For this, three TIM structures have been studied: one crystal structure and two model structures designed to describe different putative models for the deamidation reaction taking place at the subunit interface. The structural fluctuations have been mapped on the functional properties; then the differences in the fluctuations between the two models in relation to the deamidation reaction have been considered. The results demonstrate that the qualitative picture of the mean-square fluctuations and the correlations between the fluctuations are similar in both, but the differences may affect the observed barrier height of the deamidation reaction. The higher packing density at regions close to deamidation sites, reflected by the high-frequency fluctuating residues in the respective regions, the stronger positive correlation between the fluctuations of the deamidation sites, and enhanced positive correlation of the primary deamidation site with the extended vicinity of the catalytic region on the juxtaposed unit promote the probability of the deamidation reaction. The results in general emphasize the importance of structural fluctuations in enzyme reactions, as well as proposing the present methodology as a plausible approach for studies on the network of coupled promoting motions in protein functions.