Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available

Structural identifiability of dynamic systems biology models

22 páginas, 5 figuras, 2 tablas.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areasAFV acknowledges funding from the Galician government (Xunta de Galiza, Consellería de Cultura, Educación e Ordenación Universitaria http://www.edu.xunta.es/portal/taxonomy/term/206) through the I2C postdoctoral program, fellowship ED481B2014/133-0. AB and AFV were partially supported by grant DPI2013-47100-C2-2-P from the Spanish Ministry of Economy and Competitiveness (MINECO). AFV acknowledges additional funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (CanPathPro). AP was partially supported through EPSRC projects EP/M002454/1 and EP/J012041/1.Peer reviewe

Mechanistic modelling of in vitro transporter processes to improve drug-drug interaction predictions

There is currently a need to evaluate the interaction of drugs in the liver and at the liver membrane, to determine whether the potential for a drug-drug interaction in the clinic could adversely affect a patients prognosis. The interactions of drugs or probe substrates with liver membrane transporters are currently poorly understood at a molecular level, and there is strong interest in terms of the pharmacology of the transporters and how we can examine and understand these interactions through mathematical models. Currently the dynamics of interactions through the use of micro-rate constants, where steady-state assumptions are not implied in data analysis are less favoured. Whilst modelling and data analysis conducted using Michaelis-Menten type kinetics (defined as macro-rate constant mechanistic models), under the assumption of rapid equilibration of substrate with the transporter (association with the transporter is almost instantaneous) are more common. The aim of this thesis is to improve the determination of transporter mediated drug-drug interactions (TrDDIs) in in vitro liver specific cellular systems through the use of structurally identifiable mechanistic models describing the dynamics of the interaction between substrates and inhibitors. This was done by the design of experiments to optimise the data collected for substrate and inhibitors for use within the mechanistic models across different cellular systems (human cell lines, rat and human hepatocytes) under different inhibition conditions. Mechanistic models were developed to obtain robust model fits that adequately described the interaction between substrates and inhibitors, whilst gaining an insight in terms of model selectivity, given the data available. The structural identifiability of the mechanistic models was assessed to ensure that the unknown parameters in the model could be estimated from the experimental data. The mode of inhibition was determined through the use of mechanistic models for each experimental chapter and compared with conclusions drawn in the in literature. The potential for a clinical TrDDI was evaluated for the experimental work in cryopreserved human hepatocytes (Chapter 5), through a worst case scenario static xviii drug interaction model at the entrance to the liver using an \R value", and through the use of a semi-quantitative physiologically based pharmacokinetic (PBPK) model. All the micro-rate constant mechanistic models were at least structurally locally identifiable with no parameters unknown. Conversely, the macro-rate constant mechanistic were only structurally locally identifiable if both substrate and inhibitor were measured (see Chapter 5). Otherwise one to two parameters had to be known for the macro-rate constant mechanistic models to be structurally locally identifiable. Concurrent with the structural identifiability analysis results, in each of the experimental chapters, the use of micro-rate constant mechanistic models were always the best fitting model to the experimental data based on goodness of fit statistics compared to the use of Michaelis-Menten macro-rate constant mechanistic models. Both the micro-rate constant and macro-rate constant mechanistic models were in agreement with regards to the mechanism of inhibition in all experimental cases, whilst the steady-state assumptions required for the use of the Michaelis-Menten equation were only valid for the micro-rate constants derived in Chapter 5. This supported the use of scaled micro-rate constant parameters in Chapter 5 to Michaelis-Menten parameters in the semi-quantitative mechanistic PBPK model in Chapter 6, where there was a potential for a clinical TrDDI given the in vitro data, which was at odds with the determined R value. In conclusion, this work strongly supports the use of micro-rate constants in mechanistic modelling of in vitro TrDDIs to formally test steady-state assumptions through more robust, structurally identifiable parameter estimates

A mechanistic modelling approach for the determination of the mechanisms of inhibition by cyclosporine on the uptake and metabolism of atorvastatin in rat hepatocytes using a high throughput uptake method

(1) Determine the inhibition mechanism through which cyclosporine inhibits the uptake and metabolism of atorvastatin in fresh rat hepatocytes using mechanistic models applied to data generated using a high throughput oil spin method. (2) Atorvastatin was incubated in fresh rat hepatocytes (0.05–150 nmol/ml) with or without 20 min pre-incubation with 10 nmol/ml cyclosporine and sampled over 0.25–60 min using a high throughput oil spin method. Micro-rate constant and macro-rate constant mechanistic models were ranked based on goodness of fit values. (3) The best fitting model to the data was a micro-rate constant mechanistic model including non-competitive inhibition of uptake and competitive inhibition of metabolism by cyclosporine (Model 2). The association rate constant for atorvastatin was 150-fold greater than the dissociation rate constant and 10-fold greater than the translocation into the cell. The association and dissociation rate constants for cyclosporine were 7-fold smaller and 10-fold greater, respectively, than atorvastatin. The simulated atorvastatin-transporter-cyclosporine complex derived using the micro-rate constant parameter estimates increased in line with the incubation concentration of atorvastatin. (4) The increased amount of data generated with the high throughput oil spin method, combined with a micro-rate constant mechanistic model helps to explain the inhibition of uptake by cyclosporine following pre-incubation

Prediction of clinical transporter‐mediated drug–drug interactions via comeasurement of pitavastatin and eltrombopag in human hepatocyte Models

A structurally identifiable micro‐rate constant mechanistic model was used to describe the interaction between pitavastatin and eltrombopag, with improved goodness‐of‐fit values through comeasurement of pitavastatin and eltrombopag. Transporter association and dissociation rate constants and passive rates out of the cell were similar between pitavastatin and eltrombopag. Translocation into the cell through transporter‐mediated uptake was six times greater for pitavastatin, leading to pronounced inhibition of pitavastatin uptake by eltrombopag. The passive rate into the cell was 91 times smaller for pitavastatin compared with eltrombopag. A semimechanistic physiologically‐based pharmacokinetic (PBPK) model was developed to evaluate the potential for clinical drug–drug interactions (DDIs). The PBPK model predicted a twofold increase in the pitavastatin peak blood concentration and area under the concentration‐time curve in the presence of eltrombopag in simulated healthy volunteers. The use of structural identifiability supporting experimental design combined with robust micro‐rate constant parameter estimates and a semimechanistic PBPK model gave more informed predictions of transporter‐mediated DDIs

A mechanistic modelling approach for the determination of the mechanisms of inhibition by cyclosporine on the uptake and metabolism of atorvastatin in rat hepatocytes using a high throughput uptake method

Determine the inhibition mechanism through which cyclosporine inhibits the uptake and metabolism of atorvastatin in fresh rat hepatocytes using mechanistic models applied to data generated using a high throughput oil spin method. Atorvastatin was incubated in fresh rat hepatocytes (0.05–150 nmol/ml) with or without 20 min pre-incubation with 10 nmol/ml cyclosporine and sampled over 0.25–60 min using a high throughput oil spin method. Micro-rate constant and macro-rate constant mechanistic models were ranked based on goodness of fit values. The best fitting model to the data was a micro-rate constant mechanistic model including non-competitive inhibition of uptake and competitive inhibition of metabolism by cyclosporine (Model 2). The association rate constant for atorvastatin was 150-fold greater than the dissociation rate constant and 10-fold greater than the translocation into the cell. The association and dissociation rate constants for cyclosporine were 7-fold smaller and 10-fold greater, respectively, than atorvastatin. The simulated atorvastatin-transporter-cyclosporine complex derived using the micro-rate constant parameter estimates increased in line with the incubation concentration of atorvastatin. The increased amount of data generated with the high throughput oil spin method, combined with a micro-rate constant mechanistic model helps to explain the inhibition of uptake by cyclosporine following pre-incubation

Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Estudio de la contribución de los factores genéticos a la variabilidad farmacocinética y farmacodinámica de los inhibidores de la HMG-CoA reductasa en voluntarios sanos

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Medicina. Departamento de Farmacología y Terapéutica. Fecha de lectura: 20 de Abril de 201