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[Display omitted] • Optimization of enzyme kinetic flexibility is performed for the four-state enzyme reaction. • Maximal kinetic flexibility results in the global optimal enzyme state. • Kinetic flexibility is linked to entropy production and Shannon information entropy. • Maximal kinetic flexibility results in maxima of entropy production and of Shannon information entropy. • Kinetic flexibility of the enzymatic structure plays a crucial role in the natural enzyme design. We investigate the relations between the enzyme kinetic flexibility, the rate of entropy production, and the Shannon information entropy in a steady-state enzyme reaction. All these quantities are maximized with respect to enzyme rate constants. We show that the steady-state, which is characterized by the most flexible enzymatic transitions between the enzyme conformational states, coincides with the global maxima of the Shannon information entropy and the rate of entropy production. This steady-state of an enzyme is referred to as globally optimal. This theoretical approach is then used for the analysis of the kinetic and the thermodynamic performance of the enzyme triose-phosphate isomerase. The analysis reveals that there exist well-defined maxima of the kinetic flexibility, the rate of entropy production, and the Shannon information entropy with respect to any arbitrarily chosen rate constant of the enzyme and that these maxima, calculated from the measured kinetic rate constants for the triose-phosphate isomerase are lower, however of the same order of magnitude, as the maxima of the globally optimal state of the enzyme. This suggests that the triose-phosphate isomerase could be a well, but not fully evolved enzyme, as it was previously claimed. Herein presented theoretical investigations also provide clear evidence that the flexibility of enzymatic transitions between the enzyme conformational states is a requirement for the maximal Shannon information entropy and the maximal rate of entropy production. [ABSTRACT FROM AUTHOR]