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

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.

Selecting Sensitive Parameter Subsets in Dynamical Models With Application to Biomechanical System Identification

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

Dynamical compensation and structural identifiability of biological models: 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. However, the original definition of dynamical compensation amounts to lack of structural identifiability. This is relevant if model parameters need to be estimated, as is often the case in biological modelling. 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.

A robust behaviour is a desirable feature in many biological systems. The study of mechanisms capable of maintaining the transient response unchanged despite environmental disturbances has recently motivated the introduction of a new concept: Dynamical Compensation (DC). However, the original definition of DC with respect to a parameter amounts to structural unidentifiability of that parameter, which means that it cannot be estimated by measuring the model output. Since most biological models have unknown parameters that need to be estimated, DC can be considered a negative property for the purpose of model identification. In this paper we reconcile these two conflicting views by proposing a new definition of DC that captures its intended biological meaning (i.e. robustness, which should be a systemic property, intrinsic to the dynamics) while making it distinct from structural unidentifiability (which is a modelling property that depends on decisions made by the modeller, such as the choice of model outputs or unknown parameters, and on experimental constraints). Our definition enables a model to have DC with respect to a structurally identifiable parameter, thus increasing the applicability of the concept.

Structural Identifiability of Dynamic Systems Biology Models

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 areas.