An essential aspect of protein science is to determine the deductive relationship between structure, dynamics, and various sets of functions. The role of dynamics is currently challenging our understanding of protein functions, both experimentally and theoretically. To verify the internal fluctuations and dynamics correlations in an enzyme protein undergoing conformational transitions, we have applied a coarse-grained dynamics algorithm using the elastic network model for adenylate kinase. Normal mode analysis reveals possible dynamical and allosteric pathways for the transition between the open and the closed states of adenylate kinase. As the ligands binding induces significant flexibility changes of the nucleotides monophosphate (NMP) domain and adenosine triphosphate (ATP) domain, the diagonalized correlation between different structural transition states shows that most correlated motions occur between the NMP domain and the helices surrounding the ATP domain. The simultaneous existence of positive and negative correlations indicates that the conformational changes of adenylate kinase take place in an allosteric manner. Analyses of the cumulated normal mode overlap coefficients and long-range correlated motion provide new insights of operating mechanisms and dynamics of adenylate kinase. They also suggest a quantitative dynamics criterion for determining the allosteric cooperativity, which may be applicable to other proteins.