Fig 1.
Schematic outline of our mechanistic model building method.
(A) Influence diagram of the detyrosination/tyrosination cycle. (B) Chemical Reaction Network of the detyrosination/tyrosination cycle in BIOCHAM syntax with either mass action law kinetics (MA) or Michaelis-Menten kinetics (MM), plus initial concentrations. (C) Parametric Ordinary Differential Equation (ODE) derived from the Chemical Reaction Network. (D) Unperturbed numerical simulation of the computational model CDTN, parameterized with kinetics values taken from the literature and hypothesis.
Fig 2.
Parameterization of the computational model CDTP with HCI quantification combined with BIOCHAM parameter optimization procedures.
(A) Representative images of immunostaining of tyrosinated tubulin (Tyr) in green, detyrosinated tubulin (Detyr) in red in MEF cells and hTERT RPE-1 cells (left). Cells were co-stained with Hoechst. Scale bars: 20 μm. (B) Quantification of the tyrosination status by high-content imaging (Right). Tubulin and microtubule are predominantly observed in tyrosinated form (Z’-factor > 0.5). The plotted values are the average of single-cells values ± SD. (C) Best satisfaction degree obtained by the parameter search procedure by varying only one kinetic parameter independently, showing failure to reproduce the observed behaviour. The BIOCHAM command used is: search_parameters(F(Time == 5 /\ Tyr = factor1 * Detyr /\ F(Time == 20 /\ Tyr = factor2 * Detyr)), [0 <= p <= 100], [factor1 -> 10, factor2 -> 10]) where p is the kinetic parameter to optimize. (D) Best satisfaction degree obtained by the parameter search procedure by varying couples of two kinetic parameters simultaneously, showing perfect satisfaction of the specification with one couple of parameters only: (Vm2, km1). The BIOCHAM command used is: search_parameters(F(Time == 5 /\ Tyr = factor1 * Detyr /\ F(Time == 20 /\ Tyr = factor2 * Detyr)), [0 <= p1 <= 100, 0 <= p2<= 100], [factor1 -> 10, factor2 -> 10]) where p1 and p2 are two kinetic parameters to optimize. (E) Landscape of the satisfaction degree obtained by scanning the parameter values of the couple (Vm2, km1). The BIOCHAM command used to obtain the landscape is: scan_parameters(F(Time == 5 /\ Tyr = factor1 * Detyr /\ F(Time == 20 /\ Tyr = factor2 * Detyr)), (0 <= Vm2 <= 15), (0 <= km1 <= 30), [factor1 -> 10, factor2 -> 10], resolution:30). (F) Unperturbed numerical simulation of the CDTP model showing the maintenance of a high level of tyrosination. The FO-LTL formulae used to infer the new parameter values for has been updated to infer new parameters with minimal difference from their original values from the CDTN model: search_parameters(F(Time == 5 /\ Vm2 = VarVm2 /\ km1 = Varkm1 /\ Tyr = factor1 * Detyr /\ F(Time == 20 /\ Tyr = factor2 * Detyr)), [0 <= Vm2 <= 15, 0 <= km1 <= 30], [VarVm2 -> 0.2, Varkm1 -> 0.478, factor1 -> 10, factor2 -> 10]).
Table 1.
Parameter values of the computational models.
Fig 3.
Mathematical model predictions of the tyrosination reaction activation in proliferative and neuronal cells explaining failures of compound screening.
(A) Sensitivity analysis of the equilibrium value of TyrDetyr obtained for different coefficients of variation of the kinetic parameter Vm2 in the computational model CDTP, indicating a tolerance of five hundred percent for the parameter Vm2 before TyrDetyr deviates from its equilibrium state by eighty percent. The BIOCHAM command used is: sensitivity(F(G(TyrDetyr = x)), [Vm2], [x -> 10], robustness_coeff_var: c), where c is the robustness coefficient value. (B) Similar sensitivity analysis in the computational model CDTN, indicating a tolerance of five hundred percent for the parameter Vm2 before TyrDetyr deviates from its equilibrium state by fifteen percent. The BIOCHAM command used is: sensitivity(F(G(TyrDetyr = x)), [Vm2], [x -> 0.065386], robustness_coeff_var: c) where c is the robustness coefficient value. (C) Perturbed numerical simulation in the model CDTP. The tyrosination rate constant Vm2 is increased at 20 units of time (min) by a factor ten. The numerical simulation shows that the tyrosination status do not increase. (D) Perturbed numerical simulation in the model CDTN. The tyrosination rate constant Vm2 is increased at time 60 (min) by a factor ten. The numerical simulation shows that tyrosinated species slightly increase but are not greater than detyrosinated species at steady state.
Fig 4.
Mathematical model predictions of the detyrosination inhibition with experimental validation in proliferative cells.
(A) Sensitivity analysis of the equilibrium value of TyrDetyr obtained for different coefficients of variation of the kinetic parameter k1 in the computational model CDTP, indicating that the equilibrium value of TyrDetyr is sensitive for strong variation of k1. The BIOCHAM command used is: sensitivity(F(G(TyrDetyr = x)), [k1], [x -> 10], robustness_coeff_var: c). where c is the robustness coefficient value. (B) Dose response diagram from the CDTP model by varying the kinetic parameter k1. The BIOCHAM commands used are: change_parameter_to_variable(k1), dose_response(k1, 0, 10, time:100, show:TyrDetyr). The BIOCHAM command draws a dose-response diagram by linear variation of the initial concentration (the dose) of the input object, here k1, and plotting the output object (the response), here the molecular species: Tyr, Detyr and TyrDetyr, showing an increase of the tyrosination status with a decrease of k1. (C) Compounds screening in dose response of the chemical compound parthenolide. Representative images showing immunostaining of Tyr (green) and Detyr (red) on MEF cells pretreated with or without paclitaxel. Compound concentrations: Parthenolide (1.2 μM (log)), Paclitaxel (5 μM), Parthenolide + Paclitaxel (1.2 μM (log) + 5 μM). Cells were co-stained with Hoechst. Scale bars represent 20 μm. There was no extraction for free tubulin and the visualization of co-localization is potentially impacted. (D) Dose response diagrams of the tyrosination status from 4 conditions: DMSO, Paclitaxel, Parthenolide and Parthenolide+Paclitaxel, showing that the tyrosination status increase by inhibiting the detyrosination reaction. Parthenolide concentrations are indicated on the x-axis. Paclitaxel concentration is fixed to 5 μM. We observe that the parthenolide and DMSO error bars overlap at concentrations above 1.5 μM (log). At this parthenolide concentration, the cell morphologies are indeed altered, cytoplasms are reduced, and the cells appear to be highly stressed.
Fig 5.
Prediction of drug combinations for potential new screen for neurodegenerative disorders.
(A) Perturbed numerical simulation in the model CDTN. The detyrosinated microtubule depolymerization rate constant km1 is increased by a factor ten at 60 units of time (min). The numerical simulation shows a slight increase of tyrosinated species suggesting that when the system reached its steady state, increasing the detyrosinated microtubule depolymerization reaction alone does not enable an increase of the tyrosination status. (B) Perturbed numerical simulation in the model CDTN. The detyrosinated microtubule depolymerization rate constant km1 and the tyrosination rate constant Vm2 are increased at 60 units of time (min) by a factor ten. The numerical simulation shows that the level of tyrosinated species become quickly larger than detyrosinated species. Increasing in synergy the tyrosination and detyrosinated microtubule depolymerization reactions is predicted to be sufficient to trigger a significant increase of the tyrosinated species. (C) Prediction of drug combinations combining an increase of the tyrosination rate constant (Vm2) and the detyrosinated microtubule depolymerization rate constant (km1) by different factors showing a synergistic effect to increase the tyrosination status. (D) Perturbed numerical simulation in the model CDTN. The detyrosination rate constant k1 is decreased by a factor one hundred at 60 units of time (min). The numerical simulation shows that tyrosinated species slowly increase and become predominant at steady state.