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Microtubules and their post-translational modifications are involved in major cellular processes. In severe diseases such as neurodegenerative disorders, tyrosinated tubulin and tyrosinated microtubules are in lower concentration. We present here a mechanistic mathematical model of the microtubule tyrosination cycle combining computational modeling and high-content image analyses to understand the key kinetic parameters governing the tyrosination status in different cellular models. That mathematical model is parameterized, firstly, for neuronal cells using kinetic values taken from the literature, and, secondly, for proliferative cells, by a change of two parameter values obtained, and shown minimal, by a continuous optimization procedure based on temporal logic constraints to formalize experimental high-content imaging data. In both cases, the mathematical models explain the inability to increase the tyrosination status by activating the Tubulin Tyrosine Ligase enzyme. The tyrosinated tubulin is indeed the product of a chain of two reactions in the cycle: the detyrosinated microtubule depolymerization followed by its tyrosination. The tyrosination status at equilibrium is thus limited by both reaction rates and activating the tyrosination reaction alone is not effective. Our computational model also predicts the effect of inhibiting the Tubulin Carboxy Peptidase enzyme which we have experimentally validated in MEF cellular model. Furthermore, the model predicts that the activation of two particular kinetic parameters, the tyrosination and detyrosinated microtubule depolymerization rate constants, in synergy, should suffice to enable an increase of the tyrosination status in living cells.