Mathematical modeling of the microtubule detyrosination/tyrosination cycle for cell-based drug screening design

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.Author summary: Microtubules, cytoskeletal proteins, are involved in essential biological processes such as mitosis, cardiomyocyte contraction and cell motility. The tyrosination reaction, a microtubule post-translational modification is dysregulated in cancer, cardiomyopathies and neuronal diseases. Despite significant advances in recent years, the precise mechanisms regulating the tyrosination cycle and the microtubule dynamics still lack an integrative approach with predictive mathematical modeling. We present a mathematical model of the detyrosination/tyrosination cycle parameterized for neurons and proliferative cells using literature and image-based screening data. The model first explains the inability to increase the tyrosination status by activating the Tubulin Tyrosine Ligase enzyme in those cellular models, second captures the inhibition effect of the Tubulin Carboxy Peptidase enzyme, and third predicts the necessity to combine two drugs to increase the tyrosination status in living cells. Overall, our mathematical model enhances the early drug research by providing critical mechanistic insights and identifying promising targets.