Sensitivity analysis on a physiologically-based pharmacokinetic and pharmacodynamic model for diisopropylfluorophosphate-induced toxicity in mice and rats

Abstract

A physiologically-based pharmacokinetic and pharmacodynamic (PBPK/PD) model was recently developed to study the effect of diisopropylfluorophosphate (DFP) on acetylcholinesterase (AChE) activity in mouse and rat. That model takes into account relatively complex interactions involving many parameters, some of which may be uncertain and/or highly variable, especially those characterizing AChE activity after DFP intoxication. The primary objective of this study was to identify parameters that contribute most to the variability of AChE dynamics for model optimization against data. For this purpose, the influence of the variability of the rate constants for synthesis (K_syn) and degradation (K_deg) of AChE, and regeneration (K_reg) and aging (K_age) of inhibited AChE on the variability of AChE activity in mice and rat venous blood and brain was first calculated by a global sensitivity analysis. Next, the mouse PBPK/PD model was calibrated by optimizing the values of K_syn, K_deg, K_reg and K_age. Thereafter, scale-up of the DFP-induced AChE activity was performed from mouse to rat. Validation of the rat model was performed by comparing the time course of venous blood and brain AChE activities from a Monte Carlo analysis to those obtained in vivo. Sensitivity analysis on the verified models showed that K_reg and K_syn were the most influential factors of AChE activity at shorter and longer durations, respectively, after DFP challenge. Scale-up of the AChE dynamics from mouse to rat was also successful, as evidenced by significant overlapping between the predicted 95^th percentile confidence intervals and the experimental data.

Keywords::

• Acetylcholinesterase
• allometric scaling
• diisopropylfluorophosphate
• physiologically-based pharmacokinetic and pharmacodynamic model
• sensitivity analysis

Acknowledgements

We thank Dr Jeffery M. Gearhart for his insightful discussion in developing the revised model. We are grateful for Dr Eu Jin Teoh and Douglas Goh for assistance in implementing initial versions of the model equations. This work was supported through a grant from the Singapore Ministry of Defence.

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.

Appendix

Equation Tracking DFP concentration (with DFP hydrolysis by A-esterase (A-EST))—different from that reported by Gearhart et al. (1990; 1994):

where C_DFP,ART = Concentration of DFP in the ART compartment (μM); C_DFP,BR = Concentration of DFP in the BR compartment (μM); C_IAChE,BR = Concentration of AChE-DFP complex in the BR compartment (μM); C_IBuChE,BR = Concentration of BuChE-DFP complex in the BR compartment (μM); C_IChE,BR = Concentration of CaE-DFP complex in the BR compartment (μM); C_TAChE,BR = Total concentration of AChE in the BR compartment (μM); C_TBuChE,BR = Total concentration of BuChE in the BR compartment (μM); C_TChE,BR = Total concentration of CaE in the BR compartment (μM); K_AChE,BR = Bimolecular rate constant for DFP reaction with AChE in BR (μM/h); K_BuChE,BR = Bimolecular rate constant for DFP reaction with BuChE in BR (μM/h); K_ChE,BR = Bimolecular rate constant for DFP reaction with CaE in BR (μM/h); K_M,BR = Michaelis-Menten constant for DFP hydrolysis in brain (mg/L); MW = Molecular weight of DFP (mg/μmole); P_BR = Brain/blood partition coefficient of DFP; Q_BR = Rate of blood flow to the BR compartment (L/h); V_BR = Volume of the BR compartment (L); and V_max,BR = Maximum rate of DFP hydrolysis (mg/L).

This equation was also used to simulate DFP kinetics in the KI, LI, HE, RPT, VEN and ART compartments.

Equation Tracking DFP concentration (without DFP hydrolysis by A-EST)—different from that reported by Gearhart et al. (1990; 1994):

where C_DFP,ART = Concentration of DFP in the ART compartment (μM); C_DFP,SPT = Concentration of DFP in the SPT compartment (μM); C_IAChE,SPT = Concentration of AChE-DFP complex in the SPT compartment (μM); C_IBuChE,SPT = Concentration of BuChE-DFP complex in the SPT compartment (μM); C_IChE,SPT = Concentration of CaE-DFP complex in the SPT compartment (μM); C_TAChE,SPT = Total concentration of AChE in the SPT compartment (μM); C_TBuChE,SPT = Total concentration of BuChE in the SPT compartment (μM); C_TChE,SPT = Total concentration of CaE in the SPT compartment (μM); K_AChE,SPT = Bimolecular rate constant for DFP reaction with AChE in SPT (μM/h); K_BuChE,SPT = Bimolecular rate constant for DFP reaction with BuChE in SPT (μM/h); K_ChE,SPT = Bimolecular rate constant for DFP reaction with CaE in SPT (μM/h); MW = Molecular weight of DFP (mg/μmole); P_SPT = SPT/blood partition coefficient of DFP; Q_SPT = Rate of blood flow to the SPT compartment (L/h); and V_SPT = Volume of the SPT compartment (L).

This equation was also used to simulate DFP kinetics in the LU and DIAP compartments.

Equation Tracking DFP concentration in the AD compartment:

where C_DFP,ART = Concentration of DFP in the ART compartment (μM); C_DFP,AD = Concentration of DFP in the AD compartment (μM); P_AD = AD/blood partition coefficient of DFP; Q_AD = Rate of blood flow to the AD compartment (L/h); and V_AD = Volume of the AD compartment (L).

Equation Tracking inhibited AChE concentration:

where C_DFP,BR = Concentration of DFP in the BR compartment (μM); C_IAChE,BR = Concentration of AChE-DFP complex in the BR compartment (μM); C_TAChE,BR = Total concentration of AChE in the BR compartment (μM); K_AChE,BR = Bimolecular rate constant for DFP reaction with AChE in BR (μM/h); K_age,BR = Unimolecular rate constant for aging of AChE-DFP complex in BR (1/h); and K_reg,BR = Unimolecular rate constant for regeneration of AChE by breakdown of AChE-DFP complex in BR (1/h).

Equation Tracking total AChE (free + inhibited) concentration—not present in the model of Gearhart et al. (1990; 1994):

where C_IAChE,BR = Concentration of AChE-DFP complex in the BR compartment (μM); C_TAChE,BR = Total concentration of AChE in the BR compartment (μM); K_AChE,BR = Bimolecular rate constant for DFP reaction with AChE in BR (μM/h); K_deg,BR = Unimolecular rate constant for degradation of free AChE in BR (1/h); K_syn,BR = Zeroth-order rate constant for synthesis of free AChE in BR (μmole/h); and V_BR = Volume of brain compartment (L).