In vitro PK/PD modeling of tyrosine kinase inhibitors in non-small cell lung cancer cell lines.

Tyrosine kinase inhibitors (TKIs) are routinely prescribed for the treatment of non-small cell lung cancer (NSCLC). As with all medications, patients can experience adverse events due to TKIs. Unfortunately, the relationship between many TKIs and the occurrence of certain adverse events remains unclear. There are limited in vivo studies which focus on TKIs and their effects on different regulation pathways. Many in vitro studies, however, that investigate the effects of TKIs observe additional changes, such as changes in gene activations or protein expressions. These studies could potentially help to gain greater understanding of the mechanisms for TKI induced adverse events. However, in order to utilize these pathways in a pharmacokinetic/pharmacodynamic (PK/PD) framework, an in vitro PK/PD model needs to be developed, in order to characterize the effects of TKIs in NSCLC cell lines. Through the use of ordinary differential equations, cell viability data and nonlinear mixed effects modeling, an in vitro TKI PK/PD model was developed with estimated PK and PD parameter values for the TKIs alectinib, crizotinib, erlotinib, and gefitinib. The relative standard errors for the population parameters are all less than 25%. The inclusion of random effects enabled the model to predict individual parameter values which provided a closer fit to the observed response. It is hoped that this model can be extended to include in vitro data of certain pathways that may potentially be linked with adverse events and provide a better understanding of TKI-induced adverse events.

Parameter estimation of a model describing the human fingers.

The goal of this paper is twofold: firstly, to provide a novel mathematical model that describes the kinematic chain of motion of the human fingers based on Lagrangian mechanics with four degrees of freedom and secondly, to estimate the model parameters using data from able-bodied individuals. In the literature there are a variety of mathematical models that have been developed to describe the motion of the human finger. These models offer little to no information on the underlying mechanisms or corresponding equations of motion. Furthermore, these models do not provide information as to how they scale with different anthropometries. The data used here is generated using an experimental procedure that considers the free response motion of each finger segment with data captured via a motion capture system. The angular data collected are then filtered and fitted to a linear second-order differential approximation of the equations of motion. The results of the study show that the free response motion of the segments is underdamped across flexion/extension and ad/abduction.

The ingredients for an antimicrobial mathematical modelling broth.

Mathematical modelling has made significant contributions to the optimization of the use of antimicrobial treatments. This article discusses the key processes that such mathematical modelling should attempt to capture. In particular, this article highlights that the response of the host immune system requires quantification, and this is illustrated with a novel model structure.

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.

Substrate and Stereochemical Control of Peptidoglycan Cross-Linking by Transpeptidation by Escherichia coli PBP1B.

Penicillin binding proteins (PBPs) catalyzing transpeptidation reactions that stabilize the peptidoglycan component of the bacterial cell wall are the targets of ß-lactams, the most clinically successful antibiotics to date. However, PBP-transpeptidation enzymology has evaded detailed analysis, because of the historical unavailability of kinetically competent assays with physiologically relevant substrates and the previously unappreciated contribution of protein cofactors to PBP activity. By re-engineering peptidoglycan synthesis, we have constructed a continuous spectrophotometric assay for transpeptidation of native or near native peptidoglycan precursors and fragments by Escherichia coli PBP1B, allowing us to (a) identify recognition elements of transpeptidase substrates, (b) reveal a novel mechanism of stereochemical editing within peptidoglycan transpeptidation, (c) assess the impact of peptidoglycan substrates on ß-lactam targeting of transpeptidation, and (d) demonstrate that both substrates have to be bound before transpeptidation occurs. The results allow characterization of high molecular weight PBPs as enzymes and not merely the targets of ß-lactam acylation.

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.

Parameter Identification for a Model of Neonatal Fc Receptor-Mediated Recycling of Endogenous Immunoglobulin G in Humans.

Salvage of endogenous immunoglobulin G (IgG) by the neonatal Fc receptor (FcRn) is implicated in many clinical areas, including therapeutic monoclonal antibody kinetics, patient monitoring in IgG multiple myeloma, and antibody-mediated transplant rejection. There is a clear clinical need for a fully parameterized model of FcRn-mediated recycling of endogenous IgG to allow for predictive modeling, with the potential for optimizing therapeutic regimens for better patient outcomes. In this paper we study a mechanism-based model incorporating nonlinear FcRn-IgG binding kinetics. The aim of this study is to determine whether parameter values can be estimated using the limited in vivo human data, available in the literature, from studies of the kinetics of radiolabeled IgG in humans. We derive mathematical descriptions of the experimental observations-timecourse data and fractional catabolic rate (FCR) data-based on the underlying physiological model. Structural identifiability analyses are performed to determine which, if any, of the parameters are unique with respect to the observations. Structurally identifiable parameters are then estimated from the data. It is found that parameter values estimated from timecourse data are not robust, suggesting that the model complexity is not supported by the available data. Based upon the structural identifiability analyses, a new expression for the FCR is derived. This expression is fitted to the FCR data to estimate unknown parameter values. Using these parameter estimates, the plasma IgG response is simulated under clinical conditions. Finally a suggestion is made for a reduced-order model based upon the newly derived expression for the FCR. The reduced-order model is used to predict the plasma IgG response, which is compared with the original four-compartment model, showing good agreement. This paper shows how techniques for compartmental model analysis-structural identifiability analysis, linearization, and reparameterization-can be used to ensure robust parameter identification.

Best Practices to Maximize the Use and Reuse of Quantitative and Systems Pharmacology Models: Recommendations From the United Kingdom Quantitative and Systems Pharmacology Network.

The lack of standardization in the way that quantitative and systems pharmacology (QSP) models are developed, tested, and documented hinders their reproducibility, reusability, and expansion or reduction to alternative contexts. This in turn undermines the potential impact of QSP in academic, industrial, and regulatory frameworks. This article presents a minimum set of recommendations from the UK Quantitative and Systems Pharmacology Network (UK QSP Network) to guide QSP practitioners seeking to maximize their impact, and stakeholders considering the use of QSP models in their environment.

Three novel approaches to structural identifiability analysis in mixed-effects models.

BACKGROUND AND OBJECTIVE: Structural identifiability is a concept that considers whether the structure of a model together with a set of input-output relations uniquely determines the model parameters. In the mathematical modelling of biological systems, structural identifiability is an important concept since biological interpretations are typically made from the parameter estimates. For a system defined by ordinary differential equations, several methods have been developed to analyse whether the model is structurally identifiable or otherwise. Another well-used modelling framework, which is particularly useful when the experimental data are sparsely sampled and the population variance is of interest, is mixed-effects modelling. However, established identifiability analysis techniques for ordinary differential equations are not directly applicable to such models. METHODS: In this paper, we present and apply three different methods that can be used to study structural identifiability in mixed-effects models. The first method, called the repeated measurement approach, is based on applying a set of previously established statistical theorems. The second method, called the augmented system approach, is based on augmenting the mixed-effects model to an extended state-space form. The third method, called the Laplace transform mixed-effects extension, is based on considering the moment invariants of the systems transfer function as functions of random variables. RESULTS: To illustrate, compare and contrast the application of the three methods, they are applied to a set of mixed-effects models. CONCLUSIONS: Three structural identifiability analysis methods applicable to mixed-effects models have been presented in this paper. As method development of structural identifiability techniques for mixed-effects models has been given very little attention, despite mixed-effects models being widely used, the methods presented in this paper provides a way of handling structural identifiability in mixed-effects models previously not possible.

Learning pharmacokinetic models for in vivo glucocorticoid activation.

To understand trends in individual responses to medication, one can take a purely data-driven machine learning approach, or alternatively apply pharmacokinetics combined with mixed-effects statistical modelling. To take advantage of the predictive power of machine learning and the explanatory power of pharmacokinetics, we propose a latent variable mixture model for learning clusters of pharmacokinetic models demonstrated on a clinical data set investigating 11ß-hydroxysteroid dehydrogenase enzymes (11ß-HSD) activity in healthy adults. The proposed strategy automatically constructs different population models that are not based on prior knowledge or experimental design, but result naturally as mixture component models of the global latent variable mixture model. We study the parameter of the underlying multi-compartment ordinary differential equation model via identifiability analysis on the observable measurements, which reveals the model is structurally locally identifiable. Further approximation with a perturbation technique enables efficient training of the proposed probabilistic latent variable mixture clustering technique using Estimation Maximization. The training on the clinical data results in 4 clusters reflecting the prednisone conversion rate over a period of 4 h based on venous blood samples taken at 20-min intervals. The learned clusters differ in prednisone absorption as well as prednisone/prednisolone conversion. In the discussion section we include a detailed investigation of the relationship of the pharmacokinetic parameters of the trained cluster models for possible or plausible physiological explanation and correlations analysis using additional phenotypic participant measurements.

Extending existing structural identifiability analysis methods to mixed-effects models.

The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system's observation function(s). By considering the uniqueness of the analytical statistical moments of the derived functions of the random variables, the structural identifiability of the corresponding mixed-effects model can be determined. The two methods are applied to a set of examples of mixed-effects models to illustrate how they work in practice.

Input Estimation for Extended-Release Formulations Exemplified with Exenatide.

Estimating the in vivo absorption profile of a drug is essential when developing extended-release medications. Such estimates can be obtained by measuring plasma concentrations over time and inferring the absorption from a model of the drug's pharmacokinetics. Of particular interest is to predict the bioavailability-the fraction of the drug that is absorbed and enters the systemic circulation. This paper presents a framework for addressing this class of estimation problems and gives advice on the choice of method. In parametric methods, a model is constructed for the absorption process, which can be difficult when the absorption has a complicated profile. Here, we place emphasis on non-parametric methods that avoid making strong assumptions about the absorption. A modern estimation method that can address very general input-estimation problems has previously been presented. In this method, the absorption profile is modeled as a stochastic process, which is estimated using Markov chain Monte Carlo techniques. The applicability of this method for extended-release formulation development is evaluated by analyzing a dataset of Bydureon, an injectable extended-release suspension formulation of exenatide, a GLP-1 receptor agonist for treating diabetes. This drug is known to have non-linear pharmacokinetics. Its plasma concentration profile exhibits multiple peaks, something that can make parametric modeling challenging, but poses no major difficulties for non-parametric methods. The method is also validated on synthetic data, exploring the effects of sampling and noise on the accuracy of the estimates.

Analysis of a Compartmental Model of Endogenous Immunoglobulin G Metabolism with Application to Multiple Myeloma.

Immunoglobulin G (IgG) metabolism has received much attention in the literature for two reasons: (i) IgG homeostasis is regulated by the neonatal Fc receptor (FcRn), by a pH-dependent and saturable recycling process, which presents an interesting biological system; (ii) the IgG-FcRn interaction may be exploitable as a means for extending the plasma half-life of therapeutic monoclonal antibodies, which are primarily IgG-based. A less-studied problem is the importance of endogenous IgG metabolism in IgG multiple myeloma. In multiple myeloma, quantification of serum monoclonal immunoglobulin plays an important role in diagnosis, monitoring and response assessment. In order to investigate the dynamics of IgG in this setting, a mathematical model characterizing the metabolism of endogenous IgG in humans is required. A number of authors have proposed a two-compartment nonlinear model of IgG metabolism in which saturable recycling is described using Michaelis-Menten kinetics; however it may be difficult to estimate the model parameters from the limited experimental data that are available. The purpose of this study is to analyse the model alongside the available data from experiments in humans and estimate the model parameters. In order to achieve this aim we linearize the model and use several methods of model and parameter validation: stability analysis, structural identifiability analysis, and sensitivity analysis based on traditional sensitivity functions and generalized sensitivity functions. We find that all model parameters are identifiable, structurally and taking into account parameter correlations, when several types of model output are used for parameter estimation. Based on these analyses we estimate parameter values from the limited available data and compare them with previously published parameter values. Finally we show how the model can be applied in future studies of treatment effectiveness in IgG multiple myeloma with simulations of serum monoclonal IgG responses during treatment.

Personalized Medication Response Prediction for Attention-Deficit Hyperactivity Disorder: Learning in the Model Space vs. Learning in the Data Space.

Attention-Deficit Hyperactive Disorder (ADHD) is one of the most common mental health disorders amongst school-aged children with an estimated prevalence of 5% in the global population (American Psychiatric Association, 2013). Stimulants, particularly methylphenidate (MPH), are the first-line option in the treatment of ADHD (Reeves and Schweitzer, 2004; Dopheide and Pliszka, 2009) and are prescribed to an increasing number of children and adolescents in the US and the UK every year (Safer et al., 1996; McCarthy et al., 2009), though recent studies suggest that this is tailing off, e.g., Holden et al. (2013). Around 70% of children demonstrate a clinically significant treatment response to stimulant medication (Spencer et al., 1996; Schachter et al., 2001; Swanson et al., 2001; Barbaresi et al., 2006). However, it is unclear which patient characteristics may moderate treatment effectiveness. As such, most existing research has focused on investigating univariate or multivariate correlations between a set of patient characteristics and the treatment outcome, with respect to dosage of one or several types of medication. The results of such studies are often contradictory and inconclusive due to a combination of small sample sizes, low-quality data, or a lack of available information on covariates. In this paper, feature extraction techniques such as latent trait analysis were applied to reduce the dimension of on a large dataset of patient characteristics, including the responses to symptom-based questionnaires, developmental health factors, demographic variables such as age and gender, and socioeconomic factors such as parental income. We introduce a Bayesian modeling approach in a "learning in the model space" framework that combines existing knowledge in the literature on factors that may potentially affect treatment response, with constraints imposed by a treatment response model. The model is personalized such that the variability among subjects is accounted for by a set of subject-specific parameters. For remission classification, this approach compares favorably with conventional methods such as support vector machines and mixed effect models on a range of performance measures. For instance, the proposed approach achieved an area under receiver operator characteristic curve of 82-84%, compared to 75-77% obtained from conventional regression or machine learning ("learning in the data space") methods.

Parameter Identifiability of Fundamental Pharmacodynamic Models.

Issues of parameter identifiability of routinely used pharmacodynamics models are considered in this paper. The structural identifiability of 16 commonly applied pharmacodynamic model structures was analyzed analytically, using the input-output approach. Both fixed-effects versions (non-population, no between-subject variability) and mixed-effects versions (population, including between-subject variability) of each model structure were analyzed. All models were found to be structurally globally identifiable under conditions of fixing either one of two particular parameters. Furthermore, an example was constructed to illustrate the importance of sufficient data quality and show that structural identifiability is a prerequisite, but not a guarantee, for successful parameter estimation and practical parameter identifiability. This analysis was performed by generating artificial data of varying quality to a structurally identifiable model with known true parameter values, followed by re-estimation of the parameter values. In addition, to show the benefit of including structural identifiability as part of model development, a case study was performed applying an unidentifiable model to real experimental data. This case study shows how performing such an analysis prior to parameter estimation can improve the parameter estimation process and model performance. Finally, an unidentifiable model was fitted to simulated data using multiple initial parameter values, resulting in highly different estimated uncertainties. This example shows that although the standard errors of the parameter estimates often indicate a structural identifiability issue, reasonably "good" standard errors may sometimes mask unidentifiability issues.

Input estimation for drug discovery using optimal control and Markov chain Monte Carlo approaches.

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery.

PKPD modelling of PR and QRS intervals in conscious dogs using standard safety pharmacology data.

INTRODUCTION: Pharmacokinetic-pharmacodynamic (PKPD) modelling can improve safety assessment, but few PKPD models describing drug-induced QRS and PR prolongations have been published. This investigation aims to develop and evaluate PKPD models for describing QRS and PR effects in routine safety studies. METHODS: Exposure and telemetry data from safety pharmacology studies in conscious beagle dogs were acquired. Mixed effects baseline and PK-QRS/PR models were developed for the anti-arrhythmic compounds AZD1305, flecainide, quinidine and verapamil and the anti-muscarinic compounds AZD8683 and AZD9164. RR interval correction and circadian rhythms were investigated for predicting baseline variability. Individual PK predictions were used to drive the pharmacological effects evaluating linear and non-linear direct and effect compartment models. RESULTS: Conduction slowing induced by the tested anti-arrhythmics was direct and proportional at low exposures, whilst time delays and non-linear effects were evident for the tested anti-muscarinics. AZD1305, flecainide and quinidine induced QRS widening with 4.2, 10 and 5.6% µM(-1) unbound drug. AZD1305 and flecainide also prolonged PR with 13.5 and 11.5% µM(-1). PR prolongations induced by the anti-muscarinics and verapamil were best described by Emax models with maximal effects ranging from 55 to 95%. RR interval correction and circadian rhythm improved PR but not QRS modelling. However, circadian rhythm had minor impact on estimated drug effects. DISCUSSION: Baseline and drug-induced effects on QRS and PR intervals can be effectively described with PKPD models using routine data, providing quantitative safety information to support drug discovery and development.

Dose-response-time modelling: Second-generation turnover model with integral feedback control.

This study presents a dose-response-time (DRT) analysis based on a large preclinical biomarker dataset on the interaction between nicotinic acid (NiAc) and free fatty acids (FFA). Data were collected from studies that examined different rates, routes, and modes of NiAc provocations on the FFA time course. All information regarding the exposure to NiAc was excluded in order to demonstrate the utility of a DRT model. Special emphasis was placed on the selection process of the biophase model. An inhibitory Imax-model, driven by the biophase amount, acted on the turnover rate of FFA. A second generation NiAc/FFA model, which encompasses integral (slow buildup of tolerance - an extension of the previously used NiAc/FFA turnover models) and moderator (rapid and oscillatory) feedback control, was simultaneously fitted to all time courses in normal rats. The integral feedback control managed to capture an observed 90% adaptation (i.e., almost a full return to baseline) when 10 days constant-rate infusion protocols of NiAc were used. The half-life of the adaptation process had a 90% prediction interval between 3.5-12 in the present population. The pharmacodynamic parameter estimates were highly consistent when compared to an exposure-driven analysis, partly validating the DRT modelling approach and suggesting the potential of DRT analysis in areas where exposure data are not attainable. Finally, new numerical algorithms, which rely on sensitivity equations to robustly and efficiently compute the gradients in the parameter optimization, were successfully used for the mixed-effects approach in the parameter estimation.

Observation of the time-course for peptidoglycan lipid intermediate II polymerization by Staphylococcus aureus monofunctional transglycosylase.

The polymerization of lipid intermediate II by the transglycosylase activity of penicillin-binding proteins (PBPs) represents an important target for antibacterial action, but limited methods are available for quantitative assay of this reaction, or screening potential inhibitors. A new labelling method for lipid II polymerization products using Sanger's reagent (fluoro-2,4-dinitrobenzene), followed by gel permeation HPLC analysis, has permitted the observation of intermediate polymerization products for Staphylococcus aureus monofunctional transglycosylase MGT. Peak formation is inhibited by 6 µM ramoplanin or enduracidin. Characterization by mass spectrometry indicates the formation of tetrasaccharide and octasaccharide intermediates, but not a hexasaccharide intermediate, suggesting a dimerization of a lipid-linked tetrasaccharide. Numerical modelling of the time-course data supports a kinetic model involving addition to lipid-linked tetrasaccharide of either lipid II or lipid-linked tetrasaccharide. Observation of free octasaccharide suggests that hydrolysis of the undecaprenyl diphosphate lipid carrier occurs at this stage in peptidoglycan transglycosylation.