Model-based dose optimization framework for bedaquiline, pretomanid and linezolid for the treatment of drug-resistant tuberculosis.

AIMS: Bedaquiline, pretomanid and linezolid (BPaL) combination treatment against Mycobacterium tuberculosis is promising, yet safety and adherence concerns exist that motivate exploration of alternative dosing regimens. We developed a mechanistic modelling framework to compare the efficacy of the current and alternative BPaL treatment strategies. METHODS: Pharmacodynamic models for each drug in the BPaL combination treatment were developed using in vitro time-kill data. These models were combined with pharmacokinetic models, incorporating body weight, lesion volume, site-of-action distribution, bacterial susceptibility and pharmacodynamic interactions to assemble the framework. The model was qualified by comparing the simulations against the observed clinical data. Simulations were performed evaluating bedaquiline and linezolid approved (bedaquiline 400 mg once daily [QD] for 14 days followed by 200 mg three times a week, linezolid 1200 mg QD) and alternative dosing regimens (bedaquiline 200 mg QD, linezolid 600 mg QD). RESULTS: The framework adequately described the observed antibacterial activity data in patients following monotherapy for each drug and approved BPaL dosing. The simulations suggested a minor difference in median time to colony forming unit (CFU)-clearance state with the bedaquiline alternative compared to the approved dosing and the linezolid alternative compared to the approved dosing. Median time to non-replicating-clearance state was predicted to be 15 days from the CFU-clearance state. CONCLUSIONS: The model-based simulations suggested that comparable efficacy can be achieved using alternative bedaquiline and linezolid dosing, which may improve safety and adherence in drug-resistant tuberculosis patients. The framework can be utilized to evaluate treatment optimization approaches, including dosing regimen and duration of treatment predictions to eradicate both replicating- and non-replicating bacteria from lung and lesions.

Computational neurosciences and quantitative systems pharmacology: a powerful combination for supporting drug development in neurodegenerative diseases.

Successful clinical development of new therapeutic interventions is notoriously difficult, especially in neurodegenerative diseases, where predictive biomarkers are scarce and functional improvement is often based on patient's perception, captured by structured interviews. As a consequence, mechanistic modeling of the processes relevant to therapeutic interventions in CNS disorders has been lagging behind other disease indications, probably because of the perceived complexity of the brain. However in this report, we develop the argument that a combination of Computational Neurosciences and Quantitative Systems Pharmacology (QSP) modeling of molecular pathways is a powerful simulation tool to enhance the probability of successful drug development for neurodegenerative diseases. Computational Neurosciences aims to predict action potential dynamics and neuronal circuit activation that are ultimately linked to behavioral changes and clinically relevant functional outcomes. These processes can not only be affected by the disease state, but also by common genotype variants on neurotransmitter-related proteins and the psycho-active medications often prescribed in these patient populations. Quantitative Systems Pharmacology (QSP) modeling of molecular pathways allows to simulate key pathological drivers of dementia, such as protein aggregation and neuroinflammatory responses. They often impact neurotransmitter homeostasis and voltage-gated ion-channels or lead to mitochondrial dysfunction, ultimately leading to changes in action potential dynamics and clinical readouts. Combining these two modeling approaches can lead to better actionable understanding of the many non-linear pharmacodynamic processes active in the human diseased brain. Practical applications include a rational selection of the optimal doses in combination therapies, identification of subjects more likely to respond to treatment, a more balanced stratification of treatment arms in terms of comedications, disease status and common genotype variants and re-analysis of small clinical trials to uncover a possible clinical signal. Ultimately this will lead to a higher success rate of bringing new therapeutics to the right patient populations.

Using a Network-Based Analysis Approach to Investigate the Involvement of S. aureus in the Pathogenesis of Granulomatosis with Polyangiitis.

Chronic nasal carriage of Staphylococcus aureus (SA) has been shown to be significantly higher in GPA patients when compared to healthy subjects, as well as being associated with increased endonasal activity and disease relapse. The aim of this study was to investigate SA involvement in GPA by applying a network-based analysis (NBA) approach to publicly available nasal transcriptomic data. Using these data, our NBA pipeline generated a proteinase 3 (PR3) positive ANCA associated vasculitis (AAV) disease network integrating differentially expressed genes, dysregulated transcription factors (TFs), disease-specific genes derived from GWAS studies, drug-target and protein-protein interactions. The PR3+ AAV disease network captured genes previously reported to be dysregulated in AAV associated. A subnetwork focussing on interactions between SA virulence factors and enriched biological processes revealed potential mechanisms for SA's involvement in PR3+ AAV. Immunosuppressant treatment reduced differential expression and absolute TF activities in this subnetwork for patients with inactive nasal disease but not active nasal disease symptoms at the time of sampling. The disease network generated identified the key molecular signatures and highlighted the associated biological processes in PR3+ AAV and revealed potential mechanisms for SA to affect these processes.

Quantitative Systems Pharmacology Modeling Framework of Autophagy in Tuberculosis: Application to Adjunctive Metformin Host-Directed Therapy.

Quantitative systems pharmacology (QSP) modeling of the host immune response against Mycobacterium tuberculosis can inform the rational design of host-directed therapies (HDTs). We aimed to develop a QSP framework to evaluate the effects of metformin-associated autophagy induction in combination with antibiotics. A QSP framework for autophagy was developed by extending a model for host immune response to include adenosine monophosphate-activated protein kinase (AMPK)-mTOR-autophagy signaling. This model was combined with pharmacokinetic-pharmacodynamic models for metformin and antibiotics against M. tuberculosis. We compared the model predictions to mice infection experiments and derived predictions for the pathogen- and host-associated dynamics in humans treated with metformin in combination with antibiotics. The model adequately captured the observed bacterial load dynamics in mice M. tuberculosis infection models treated with metformin. Simulations for adjunctive metformin therapy in newly diagnosed patients suggested a limited yet dose-dependent effect of metformin on reduction of the intracellular bacterial load when the overall bacterial load is low, late during antibiotic treatment. We present the first QSP framework for HDTs against M. tuberculosis, linking cellular-level autophagy effects to disease progression and adjunctive HDT treatment response. This framework may be extended to guide the design of HDTs against M. tuberculosis.

Modelling inflammatory biomarker dynamics in a human lipopolysaccharide (LPS) challenge study using delay differential equations.

Clinical studies in healthy volunteers challenged with lipopolysaccharide (LPS), a constituent of the cell wall of Gram-negative bacteria, represent a key model to characterize the Toll-like receptor 4 (TLR4)-mediated inflammatory response. Here, we developed a mathematical modelling framework to quantitatively characterize the dynamics and inter-individual variability of multiple inflammatory biomarkers in healthy volunteer LPS challenge studies. Data from previously reported LPS challenge studies were used, which included individual-level time-course data for tumour necrosis factor α (TNF-α), interleukin 6 (IL-6), interleukin 8 (IL-8) and C-reactive protein (CRP). A one-compartment model with first-order elimination was used to capture the LPS kinetics. The relationships between LPS and inflammatory markers was characterized using indirect response (IDR) models. Delay differential equations were applied to quantify the delays in biomarker response profiles. For LPS kinetics, our estimates of clearance and volume of distribution were 35.7 L h-1 and 6.35 L, respectively. Our model adequately captured the dynamics of multiple inflammatory biomarkers. The time delay for the secretion of TNF-α, IL-6 and IL-8 were estimated to be 0.924, 1.46 and 1.48 h, respectively. A second IDR model was used to describe the induced changes of CRP in relation to IL-6, with a delayed time of 4.2 h. The quantitative models developed in this study can be used to inform design of clinical LPS challenge studies and may help to translate preclinical LPS challenge studies to humans.

A Quantitative Systems Pharmacology Perspective on the Importance of Parameter Identifiability.

There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no "gold standard" for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges.

A quantitative systems pharmacology model for simulating OFF-Time in augmentation trials for Parkinson's disease: application to preladenant.

The clinical impact of therapeutic interventions in Parkinson's disease is often measured as a reduction in OFF-time when the beneficial effects of the standard-of-care L-DOPA formulations wanes off. We investigated the pharmacodynamic interactions of augmentation therapy to standard-of-care using a quantitative systems pharmacology (QSP) model of the basal ganglia motor circuit, essentially a computer model of neuronal firing in the different subregions with anatomically informed connectivity, cell-specific expression of 17 different G-protein coupled receptors and corresponding coupling to voltage-gated ion channel effector proteins based on experimentally observed intracellular signaling. The calculated beta/gamma (b/g) power spectrum of the local field potentials in the subthalamic nucleus was previously calibrated on the clinically relevant Unified Parkinson's Disease Rating Scale (UPDRS). When combining this QSP model with PK modeling of different formulations of L-DOPA, we calculated the b/g fluctuations over a 16 h awake period and used a weighted distance from a specific threshold to determine the cumulative liability of OFF-Time. Prediction of OFF-time with clinical observations of different L-DOPA formulations showed a significant correlation. Simulations show that augmentation with the adenosine A2A antagonist preladenant reduces OFF-time with 6 min for carbidopa/levodopa 950 mg 5-times daily to 37 min for 100 mg L-DOPA - 3 or 5 times daily. Exploring delays between preladenant and L-DOPA intake did not improve the outcome. Hypothetical A2A antagonists with an ideal PK and pharmacology profile can achieve OFF-Time reductions ranging from 9.5 min with DuoDopa to 55 min with low dose L-DOPA formulations. Combination of the QSP model with PK modeling can predict the anticipated OFF-Time reduction of novel A2A antagonists with standard of care. With the large number of GPCR in the model, this combination can support both the design of clinical trials with new therapeutic agents and the optimization of combination therapy in clinical practice.

A system pharmacology Boolean network model for the TLR4-mediated inflammatory response in early sepsis.

Sepsis is a life-threatening condition driven by the dysregulation of the host immune response to an infection. The complex and interacting mechanisms underlying sepsis remain not fully understood. By integrating prior knowledge from literature using mathematical modelling techniques, we aimed to obtain a deeper mechanistic insight into sepsis pathogenesis and to evaluate promising novel therapeutic targets, with a focus on Toll-like receptor 4 (TLR4)-mediated pathways. A Boolean network of regulatory relationships was developed for key immune components associated with sepsis pathogenesis after TLR4 activation. Perturbation analyses were conducted to identify therapeutic targets associated with organ dysfunction or antibacterial activity. The developed model consisted of 42 nodes and 183 interactions. Perturbation analyses suggest that over-expression of tumour necrosis factor alpha (TNF-α) or inhibition of soluble receptor sTNF-R, tissue factor, and inflammatory cytokines (IFN-γ, IL-12) may lead to a reduced activation of organ dysfunction related endpoints. Over-expression of complement factor C3b and C5b led to an increase in the bacterial clearance related endpoint. We identified that combinatory blockade of IFN-γ and IL-10 may reduce the risk of organ dysfunction. Finally, we found that combining antibiotic treatment with IL-1ß targeted therapy may have the potential to decrease thrombosis. In summary, we demonstrate how existing biological knowledge can be effectively integrated using Boolean network analysis for hypothesis generation of potential treatment strategies and characterization of biomarker responses associated with the early inflammatory response in sepsis.

Minimal brain PBPK model to support the preclinical and clinical development of antibody therapeutics for CNS diseases.

There are several antibody therapeutics in preclinical and clinical development, industry-wide, for the treatment of central nervous system (CNS) disorders. Due to the limited permeability of antibodies across brain barriers, the quantitative understanding of antibody exposure in the CNS is important for the design of antibody drug characteristics and determining appropriate dosing regimens. We have developed a minimal physiologically-based pharmacokinetic (mPBPK) model of the brain for antibody therapeutics, which was reduced from an existing multi-species platform brain PBPK model. All non-brain compartments were combined into a single tissue compartment and cerebral spinal fluid (CSF) compartments were combined into a single CSF compartment. The mPBPK model contains 16 differential equations, compared to 100 in the original PBPK model, and improved simulation speed approximately 11-fold. Area under the curve ratios for minimal versus full PBPK models were close to 1 across species for both brain and plasma compartments, which indicates the reduced model simulations are similar to those of the original model. The minimal model retained detailed physiological processes of the brain while not significantly affecting model predictability, which supports the law of parsimony in the context of balancing model complexity with added predictive power. The minimal model has a variety of applications for supporting the preclinical development of antibody therapeutics and can be expanded to include target information for evaluating target engagement to inform clinical dose selection.

Model informed quantification of the feed-forward stimulation of growth hormone by growth hormone-releasing hormone.

AIMS: Growth hormone (GH) secretion is pulsatile and secretion varies highly between individuals. To understand and ultimately predict GH secretion, it is important to first delineate and quantify the interaction and variability in the biological processes underlying stimulated GH secretion. This study reports on the development of a population nonlinear mixed effects model for GH stimulation, incorporating individual GH kinetics and the stimulation of GH by GH-releasing hormone (GHRH). METHODS: Literature data on the systemic circulation, the median eminence, and the anterior pituitary were included as system parameters in the model. Population parameters were estimated on data from 8 healthy normal weight and 16 obese women who received a 33 µg recombinant human GH dose. The next day, a bolus injection of 100 µg GHRH was given to stimulate GH secretion. RESULTS: The GH kinetics were best described with the addition of 2 distribution compartments with a bodyweight dependent clearance (increasing linearly from 24.7 L/h for a 60-kg subject to 32.1 L/h for a 100-kg subject). The model described the data adequately with high parameter precision and significant interindividual variability on the GH clearance and distribution volume. Additionally, high variability in the amount of secreted GH, driven by GHRH receptor activation, was identified (coefficient of variation = 90%). CONCLUSION: The stimulation of GH by GHRH was quantified and significant interindividual variability was identified on multiple parameters. This model sets the stage for further development of by inclusion of additional physiological components to quantify GH secretion in humans.

Mathematical Modelling of Alternative Pathway of Complement System.

The complement system (CS) is an integral part of innate immunity and can be activated via three different pathways. The alternative pathway (AP) has a central role in the function of the CS. The AP of complement system is implicated in several human disease pathologies. In the absence of triggers, the AP exists in a time-invariant resting state (physiological steady state). It is capable of rapid, potent and transient activation response upon challenge with a trigger. Previous models of AP have focused on the activation response. In order to understand the molecular machinery necessary for AP activation and regulation of a physiological steady state, we built parsimonious AP models using experimentally supported kinetic parameters. The models further allowed us to test quantitative roles played by negative and positive regulators of the pathway in order to test hypotheses regarding their mechanisms of action, thus providing more insight into the complex regulation of AP.

Quantification of the endogenous growth hormone and prolactin lowering effects of a somatostatin-dopamine chimera using population PK/PD modeling.

A phase 1 clinical trial in healthy male volunteers was conducted with a somatostatin-dopamine chimera (BIM23B065), from which information could be obtained on the concentration-effect relationship of the inhibition of pulsatile endogenous growth hormone and prolactin secretion. Endogenous growth hormone profiles were analyzed using a two-step deconvolution-analysis-informed population pharmacodynamic modeling approach, which was developed for the analyses of pulsatile profiles. Prolactin concentrations were modelled using a population pool model with a circadian component on the prolactin release. During treatment with BIM23B065, growth hormone secretion was significantly reduced (maximal effect [EMAX] = - 64.8%) with significant reductions in the pulse frequency in two out of three multiple ascending dose cohorts. A circadian component in prolactin secretion was identified, modelled using a combination of two cosine functions with 24 h and 12 h periods. Dosing of BIM23B065 strongly inhibited (EMAX = - 91%) the prolactin release and demonstrated further reduction of prolactin secretion after multiple days of dosing. This study quantified the concentration-effect relationship of BIM23B065 on the release of two pituitary hormones, providing proof of pharmacology of the chimeric actions of BIM23B065.

Use of translational modeling and simulation for quantitative comparison of PF-06804103, a new generation HER2 ADC, with Trastuzumab-DM1.

A modeling and simulation approach was used for quantitative comparison of a new generation HER2 antibody drug conjugate (ADC, PF-06804103) with trastuzumab-DM1 (T-DM1). To compare preclinical efficacy, the pharmacokinetic (PK)/pharmacodynamic (PD) relationship of PF-06804103 and T-DM1 was determined across a range of mouse tumor xenograft models, using a tumor growth inhibition model. The tumor static concentration was assigned as the minimal efficacious concentration. PF-06804103 was concluded to be more potent than T-DM1 across cell lines studied. TSCs ranged from 1.0 to 9.8 µg/mL (n = 7) for PF-06804103 and from 4.7 to 29 µg/mL (n = 5) for T-DM1. Two experimental models which were resistant to T-DM1, responded to PF-06804103 treatment. A mechanism-based target mediated drug disposition (TMDD) model was used to predict the human PK of PF-06804103. This model was constructed and validated based on T-DM1 which has non-linear PK at doses administered in the clinic, driven by binding to shed HER2. Non-linear PK is predicted for PF-06804103 in the clinic and is dependent upon circulating HER2 extracellular domain (ECD) concentrations. The models were translated to human and suggested greater efficacy for PF-06804103 compared to T-DM1. In conclusion, a fit-for-purpose translational PK/PD strategy for ADCs is presented and used to compare a new generation HER2 ADC with T-DM1.

Mechanistic and Quantitative Understanding of Pharmacokinetics in Zebrafish Larvae through Nanoscale Blood Sampling and Metabolite Modeling of Paracetamol.

Zebrafish larvae are increasingly used for pharmacological research, but internal drug exposure is often not measured. Understanding pharmacokinetics is necessary for reliable translation of pharmacological results to higher vertebrates, including humans. Quantification of drug clearance and distribution requires measurements of blood concentrations. Additionally, measuring drug metabolites is of importance to understand clearance in this model organism mechanistically. We therefore mechanistically studied and quantified pharmacokinetics in zebrafish larvae, and compared this to higher vertebrates, using paracetamol (acetaminophen) as a paradigm compound. A method was developed to sample blood from zebrafish larvae 5 days post fertilization. Blood concentrations of paracetamol and its major metabolites, paracetamol-glucuronide and paracetamol-sulfate, were measured. Blood concentration data were combined with measured amounts in larval homogenates and excreted amounts and simultaneously analyzed through nonlinear mixed-effects modeling, quantifying absolute clearance and distribution volume. Blood sampling from zebrafish larvae was most successful from the posterior cardinal vein, with a median volume (interquartile range) of 1.12 nl (0.676-1.66 nl) per blood sample. Samples were pooled (n = 15-35) to reach measurable levels. Paracetamol blood concentrations at steady state were only 10% of the external paracetamol concentration. Paracetamol-sulfate was the major metabolite, and its formation was quantified using a time-dependent metabolic formation rate. Absolute clearance and distribution volume correlated well with reported values in higher vertebrates, including humans. Based on blood concentrations and advanced data analysis, the mechanistic and quantitative understanding of paracetamol pharmacokinetics in zebrafish larvae has been established. This will improve the translational value of this vertebrate model organism in drug discovery and development. SIGNIFICANCE STATEMENT: In early phases of drug development, new compounds are increasingly screened in zebrafish larvae, but the internal drug exposure is often not taken into consideration. We developed innovative experimental and computational methods, including a blood-sampling technique, to measure the paradigm drug paracetamol (acetaminophen) and its major metabolites and quantify pharmacokinetics (absorption, distribution, elimination) in zebrafish larvae of 5 days post fertilization with a total volume of only 300 nl. These parameter values were scaled to higher vertebrates, including humans.

The Pharmacodynamic Effects of a Dopamine-Somatostatin Chimera Agonist on the Cardiovascular System.

The quantification of the effect of pharmacological treatment on the cardiovascular system is complicated because of the high level of interindividual and circadian variability. Recently, a dopamine-somatostatin chimera, BIM23B065, was under investigation to concurrently target the somatostatin and dopamine D2 receptors for the treatment of neuroendocrine tumors. However, both dopamine and somatostatin interact with different components of the cardiovascular system. This study established the response of the heart rate and the systolic blood pressure after administration of BIM23B065 in healthy male volunteers by analysis of the rate-pressure product (RPP), in a model-informed analysis. The RPP in the supine position of placebo-treated subjects showed a clear circadian component, best described by 2 cosine functions. The pharmacokinetics of BIM23B065 and its metabolite were best described using 2-compartment models with different forms of elimination kinetics. The administration of BIM23B065 gave a statistically significant reduction in the RPP, after which the effect diminished because of the tolerance to the cardiovascular effects after prolonged exposure to BIM23B065. This model provided insight in the circadian rhythm of the RPP in the supine position and the level of interindividual variability in healthy male volunteers. The developed population pharmacokinetic/pharmacodynamic model quantified the interaction between BIM23B065 and the RPP, informing on the clinical pharmacological properties of BIM23B065.

Drug disposition in obesity: toward evidence-based dosing.

Obesity and morbid obesity are associated with many physiological changes affecting pharmacokinetics, such as increased blood volume, cardiac output, splanchnic blood flow, and hepatic blood flow. In obesity, drug absorption appears unaltered, although recent evidence suggests that this conclusion may be premature. Volume of distribution may vary largely, but the magnitude and direction of changes seem difficult to predict, with extrapolation on the basis of total body weight being the best approach to date. Changes in clearance may be smaller than in distribution, whereas there is growing evidence that the influence of obesity on clearance can be predicted on the basis of reported changes in the metabolic or elimination pathways involved. For obese children, we propose two methods to distinguish between developmental and obesity-related changes. Future research should focus on the characterization of physiological concepts to predict the optimal dose for each drug in the obese population.

How are growth hormone and insulin-like growth factor-1 reported as markers for drug effectiveness in clinical acromegaly research? A comprehensive methodologic review.

OBJECTIVE: In rare disease research, most randomized prospective clinical trials can only use limited number of patients and are comprised of highly heterogeneous populations. Therefore, it is crucial to report the results in such a manner that it allows for comparison of treatment effectiveness and biochemical control between studies. The aim of this review was to investigate the current methods that are being applied to measure and report growth hormone (GH) and insulin-like growth factor-1 (IGF-1) as markers for drug effectiveness in clinical acromegaly research. SEARCH STRATEGY: A systematic search of recent prospective and retrospective studies, published between 2012 and 2017, that studied the effects of somatostatin analogues or dopamine agonists in acromegaly patients was performed. The markers of interest were GH, IGF-1, and the suppression of GH after an oral glucose tolerance test (OGTT). Additionally, the use of pharmacokinetic (PK) measurements in these studies was analyzed. The sampling design, cut-off for biochemical control, reported units, and used summary statistics were summarized. RESULTS: A total of 49 articles were selected out of the 263 screened abstracts. IGF-1 concentrations were measured in all 49 studies, GH in 45 studies, and an OGTT was performed in 11 studies. A wide range of different cut-off values and sampling designs were used to determine biochemical control in acromegaly patients. The summary statistics were reported in various ways, with the percentage of biochemical control most frequently used. Nine studies sampled the PK at one or more time points. Non-compartmental analyses were commonly performed on the available PK data. CONCLUSIONS: The way GH and IGF-1 are measured and reported in acromegaly research varies considerably. A consensus on how to report study results would enable better comparisons between studies, thereby improving evidence based decision making to optimize treatment in acromegaly.

Model reduction in mathematical pharmacology : Integration, reduction and linking of PBPK and systems biology models.

In this paper we present a framework for the reduction and linking of physiologically based pharmacokinetic (PBPK) models with models of systems biology to describe the effects of drug administration across multiple scales. To address the issue of model complexity, we propose the reduction of each type of model separately prior to being linked. We highlight the use of balanced truncation in reducing the linear components of PBPK models, whilst proper lumping is shown to be efficient in reducing typically nonlinear systems biology type models. The overall methodology is demonstrated via two example systems; a model of bacterial chemotactic signalling in Escherichia coli and a model of extracellular regulatory kinase activation mediated via the extracellular growth factor and nerve growth factor receptor pathways. Each system is tested under the simulated administration of three hypothetical compounds; a strong base, a weak base, and an acid, mirroring the parameterisation of pindolol, midazolam, and thiopental, respectively. Our method can produce up to an 80% decrease in simulation time, allowing substantial speed-up for computationally intensive applications including parameter fitting or agent based modelling. The approach provides a straightforward means to construct simplified Quantitative Systems Pharmacology models that still provide significant insight into the mechanisms of drug action. Such a framework can potentially bridge pre-clinical and clinical modelling - providing an intermediate level of model granularity between classical, empirical approaches and mechanistic systems describing the molecular scale.

Modelling the delay between pharmacokinetics and EEG effects of morphine in rats: binding kinetic versus effect compartment models.

Drug-target binding kinetics (as determined by association and dissociation rate constants, kon and koff) can be an important determinant of the kinetics of drug action. However, the effect compartment model is used most frequently instead of a target binding model to describe hysteresis. Here we investigate when the drug-target binding model should be used in lieu of the effect compartment model. The utility of the effect compartment (EC), the target binding kinetics (TB) and the combined effect compartment-target binding kinetics (EC-TB) model were tested on either plasma (ECPL, TBPL and EC-TBPL) or brain extracellular fluid (ECF) (ECECF, TBECF and EC-TBECF) morphine concentrations and EEG amplitude in rats. It was also analyzed when a significant shift in the time to maximal target occupancy (TmaxTO) with increasing dose, the discriminating feature between the TB and EC model, occurs in the TB model. All TB models assumed a linear relationship between target occupancy and drug effect on the EEG amplitude. All three model types performed similarly in describing the morphine pharmacodynamics data, although the EC model provided the best statistical result. The analysis of the shift in TmaxTO (∆TmaxTO) as a result of increasing dose revealed that ∆TmaxTO is decreasing towards zero if the koff is much smaller than the elimination rate constant or if the target concentration is larger than the initial morphine concentration. The results for the morphine PKPD modelling and the analysis of ∆TmaxTO indicate that the EC and TB models do not necessarily lead to different drug effect versus time curves for different doses if a delay between drug concentrations and drug effect (hysteresis) is described. Drawing mechanistic conclusions from successfully fitting one of these two models should therefore be avoided. Since the TB model can be informed by in vitro measurements of kon and koff, a target binding model should be considered more often for mechanistic modelling purposes.

Correction to: Modelling the delay between pharmacokinetics and EEG effects of morphine in rats: binding kinetic versus effect compartment models.

The original version of this article was published open access. Unfortunately, due to a technical issue, the copyright holder name in the online version (HTML and XML) is incorrectly published as "Springer Science+Business Media, LLC, part of Springer Nature 2018". Instead, it should be "The Author(s) 2018".