Impact of plasma-protein binding on receptor occupancy: an analytical description

PET Imaging of the Serotonin 1A Receptor in Major Depressive Disorder: Hierarchical Multivariate Analysis of [11C]WAY100635 Overcomes Outcome Measure Discrepancies

The serotonin 1A receptor has been linked to both the pathophysiology of major depressive disorder (MDD) and the antidepressant action of serotonin reuptake inhibitors. Most PET studies of the serotonin 1A receptor in MDD used the receptor antagonist radioligand, [carbonyl-11C]WAY100635; however the interpretation of the combined results has been contentious owing to reports of higher or lower binding in MDD with different outcome measures. The reasons for these divergent results originate from several sources, including properties of the radiotracer itself, which complicate its quantification and interpretation; as well as from previously reported differences between MDD and healthy volunteers in both reference tissue binding and plasma free fraction, which are typically assumed not to differ. Recently, we have developed two novel hierarchical multivariate methods which we validated for the quantification and analysis of [11C]WAY100635, which show better accuracy and inferential efficiency compared to standard analysis approaches. Importantly, these new methods should theoretically be more resilient to many of the factors thought to have caused the discrepancies observed in previous studies. We sought to apply these methods in the largest [11C]WAY100635 sample to date, consisting of 160 individuals, including 103 MDD patients, of whom 50 were not-recently-medicated and 53 were antidepressant-exposed, as well as 57 healthy volunteers. While the outcome measure discrepancies were substantial using conventional univariate analysis, our multivariate analysis techniques instead yielded highly consistent results across PET outcome measures and across pharmacokinetic models, with all approaches showing higher serotonin 1A autoreceptor binding potential in the raphe nuclei of not-recently-medicated MDD patients relative to both healthy volunteers and antidepressant-exposed MDD patients. Moreover, with the additional precision of estimates afforded by this approach, we can show that while binding is also higher in projection areas in this group, these group differences are approximately half of those in the raphe nuclei, which are statistically distinguishable from one another. These results are consistent with the biological role of the serotonin 1A autoreceptor in the raphe nuclei in regulating serotonin neuron firing and release, and with preclinical and clinical evidence of deficient serotonin activity in MDD due to over expression of autoreceptors resulting from genetic and/or epigenetic effects. These results are also consistent with downregulation of autoreceptors as a mechanism of action of selective serotonin reuptake inhibitors. In summary, the results using multivariate analysis approaches therefore demonstrate both face and convergent validity, and may serve to provide a resolution and consensus interpretation for the disparate results of previous studies examining the serotonin 1A receptor in MDD.

Building optimal 3-drug combination chemotherapy regimens to eradicate Mycobacterium tuberculosis in its slow growth acid phase

Mycobacterium tuberculosis (Mtb) metabolic state affects the response to therapy. Quantifying the effect of antimicrobials in the acid- and nonreplicating-metabolic phases of Mtb growth will help to optimize therapy for tuberculosis. As a brute-force approach to all possible drug combinations against Mtb in all different metabolic states is impossible, we have adopted a model-informed strategy to accelerate the discovery. Using multiple concentrations of each drug in time kill studies, we examined single-, two- and three-drug combinations of pretomanid, moxifloxacin, and bedaquiline plus its active metabolite against Mtb in its acid-phase metabolic state. We used a nonparametric modeling approach to generate full distributions of interaction terms between pretomanid and moxifloxacin for susceptible and less-susceptible populations. From the model, we could predict the 95% confidence interval of the simulated total bacterial population decline due to the 2-drug combination regimen of pretomanid and moxifloxacin and compare this to observed declines with 3 drug regimens. We found that the combination of pretomanid and moxifloxacin at concentrations equivalent to average or peak human concentrations effectively eradicated Mtb in its acid growth phase and prevented emergence of less susceptible isolates. The addition of bedaquiline as a third drug shortened time to total and less susceptible bacterial suppression by 8 days compared to the 2-drug regimen, which was significantly faster than the 2-drug kill.

Estimating drug potency in the competitive target mediated drug disposition (TMDD) system when the endogenous ligand is included

Predictions for target engagement are often used to guide drug development. In particular, when selecting the recommended phase 2 dose of a drug that is very safe, and where good biomarkers for response may not exist (e.g. in immuno-oncology), a receptor occupancy prediction could even be the main determinant in justifying the approved dose, as was the case for atezolizumab. The underlying assumption in these models is that when the drug binds its target, it disrupts the interaction between the target and its endogenous ligand, thereby disrupting downstream signaling. However, the interaction between the target and its endogenous binding partner is almost never included in the model. In this work, we take a deeper look at the in vivo system where a drug binds to its target and disrupts the target's interaction with an endogenous ligand. We derive two simple steady state inhibition metrics (SSIMs) for the system, which provides intuition for when the competition between drug and endogenous ligand should be taken into account for guiding drug development.

Consideration of the Unbound Drug Concentration in Enzyme Kinetics

The study of enzyme kinetics in drug metabolism involves assessment of rates of metabolism and inhibitory potencies over a suitable concentration range. In all but the very simplest in vitro system, these drug concentrations can be influenced by a variety of nonspecific binding reservoirs that can reduce the available concentration to the enzyme system(s) under investigation. As a consequence, the apparent kinetic parameters, such as K_m or K_i, that are derived can deviate from the true values. There are a number of sources of these nonspecific binding depots or barriers, including membrane permeation and partitioning, plasma or serum protein binding, and incubational binding. In the latter case, this includes binding to the assay apparatus as well as biological depots, depending on the characteristics of the in vitro matrix being used. Given the wide array of subcellular, cellular, and recombinant enzyme systems utilized in drug metabolism, each of these has different components which can influence the free drug concentration. The physicochemical properties of the test compound are also paramount in determining the influential factors in any deviation between true and apparent kinetic behavior. This chapter describes the underlying mechanisms determining the free drug concentration in vitro and how these factors can be accounted for in drug metabolism studies, illustrated with case studies from the literature.

Practical approaches to evaluating and optimizing brain exposure in early drug discovery

Developing drugs for CNS related diseases continues to be one of the most challenging endeavors in drug discovery. This is at least in part related to the existence of the Blood Brain Barrier (BBB), a complex multicellular organization that provides selective access to required nutrients and hormones, while removing waste and restricting exposure to potential harmful toxins, pathogens, and xenobiotics. Consequently, designing and selecting molecules that can overcame this protection system are unique and critical aspects of the CNS drug discovery. Here we review modern CNS pharmacokinetic concepts and methods suitable for early drug discovery, and medicinal chemistry strategies towards molecules with optimal CNS exposure.

Stability analysis of drug dynamics model: A mathematical approach

In this paper, a mathematical model of drug release from polymeric matrix and consequent intracellular drug transport is proposed and analyzed. Modeling of drug release is done through solubilization dynamics of drug particles, diffusion of the solubilized drug through the polymeric matrix in addition to reversible dissociation/recrystallization process. The interaction between drug-receptor, drug-plasma proteins along with other intracellular endosomal events is modeled. This leads to a mixed system of partial and ordinary differential equations with associated pertinent set of initial and boundary conditions. Furthermore, besides the stability of the proposed model, several sub-models are also studied for their stability criteria. Prominence is provided to the reduced model system having requisite relevance to the original system where quasi steady state approximation (QSSA) theory is utilized. For the model to be potent enough to generate appropriate predictive results for drug delivery, the stability properties of equilibrium in the mathematical model are analyzed both analytically and numerically. Numerical simulation in the embodiment of graphical representations speaks about various vital characteristics of the underlying physical phenomena along with the importance and sensitized impact of the model parameters controlling significant biological functions. Probed new therapies and clinical procedures could be assessed considering the present mathematical model and its analysis as the basis framework in order to effectively enhance therapeutic efficacy and improved patient compliance. The present study confirms the necessity of stability analysis study so that advocated mathematical model can effectively complement the real physiological behavior of pharmacokinetics.

Impact of soft protein interactions on the excretion, extent of receptor occupancy and tumor accumulation of ultrasmall metal nanoparticles: a compartmental model simulation

Ultrasmall metal nanoparticles (NPs) are next-generation nano-based platforms for in vivo disease diagnosis and treatment. Due to their small size below the kidney filtration threshold and marked resistance to nonspecific serum protein adsorption, ultrasmall NPs can be rapidly excreted through the kidneys and escape liver uptake. However, although ultrasmall particles may be deemed highly resistant to protein adsorption, the real extent of this resistance is not known. Here, a simple compartmental model simulation was therefore implemented to understand how NP behavior in vivo could be modulated by soft, transient NP–plasma protein interactions characterized by dissociation constants in the millimolar range. In Model 1, ultrasmall NPs functionalized with a targeting probe, plasma proteins and target receptors were assumed to co-exist within a single compartment. Simulations were performed to understand the synergistic effect of soft interactions, systemic clearance and NP size on receptor occupancy in the single compartment. The results revealed the existence of a narrow range of ultraweak affinities and optimal particle sizes leading to greater target occupancy. In Model 2, simulations were performed to understand the impact of soft interactions on NP accumulation into a peripheral (tumor) compartment. The results revealed that soft interactions – but not active targeting – enhanced tumor uptake levels when tumor accumulation was limited by ‘fast’ plasma clearance and ‘slow’ vascular extravasation. The simple model presented here provides a basic framework to quantitatively understand the blood and tumor pharmacokinetics of ultrasmall NPs under the influence of transient protein interactions.

A compartmental model simulation shows that the blood and tumor pharmacokinetics of ultrasmall metal nanoparticles can be modulated by soft interactions with plasma proteins.

Mathematical modelling of liposomal drug release to tumour

The primary aim of liposomal drug delivery is to wisely modulate the drug delivery system in order to target diseased tissues. Temperature-sensitive liposomes function as a prospective weapon to combat toxic side effects corresponding to direct infusion of anticancer drugs. The main objective of the present study is to model liposomal drug release, subsequent drug transport in solid tumour along with integrated actions of tumour cell surface and endosomal events. Generalized mathematical model for liposomal drug delivery is proposed in which vital physical phenomena, such as kinetics of liposome-encapsulated drug, free drug release from liposomes, transport of both liposomal drug and free drug into the tumour compartment, plasma clearance, protein-drug interactions, drug-tumour cell receptor interactions, internalization of drug through endocytosis along with corresponding endosomal events. The model is expressed through a system of coupled partial differential equations along with appropriate set of initial, interface and boundary conditions which is solved numerically. Simulated results are compared with respective existing experimental data to demonstrate the potency and reliability of the proposed model. Graphical representations of time variant concentration profiles are illustrated to understand the underlying phenomena in details. Moreover, the model speaks for the sensitivity of important drug kinetic parameters, such as advection coefficients, drug release coefficient, plasma clearance rate and internalization parameters through graphical portrayals. The proposed model and the simulated results act as a tool in designing a more effective drug delivery system for cancerous tumours.

Mathematical analysis and drug exposure evaluation of pharmacokinetic models with endogenous production and simultaneous first-order and Michaelis-Menten elimination: the case of single dose

Drugs with an additional endogenous source often exhibit simultaneous first-order and Michaelis-Menten elimination and are becoming quite common in pharmacokinetic modeling. In this paper, we investigate the case of single dose intravenous bolus administration for the one-compartment model. Relying on a formerly introduced transcendent function, we were able to analytically express the concentration time course of this model and provide the pharmacokinetic interpretation of its components. Using the concept of the corrected concentration, the mathematical expressions for the partial and total areas under the concentration time curve (AUC) were also given. The impact on the corrected concentration and AUC is discussed as well as the relative contribution of the exogenous part in presence of endogenous production. The present findings theoretically elucidate several pharmacokinetic issues for the considered drug compounds and provide guidance for the rational estimation of their pharmacokinetic parameters.

Impact of saturable distribution in compartmental PK models: dynamics and practical use

We explore the impact of saturable distribution over the central and the peripheral compartment in pharmacokinetic models, whilst assuming that back flow into the central compartiment is linear. Using simulations and analytical methods we demonstrate characteristic tell-tale differences in plasma concentration profiles of saturable versus linear distribution models, which can serve as a guide to their practical applicability. For two extreme cases, relating to (i) the size of the peripheral compartment with respect to the central compartment and (ii) the magnitude of the back flow as related to direct elimination from the central compartment, we derive explicit approximations which make it possible to give quantitative estimates of parameters. In three appendices we give detailed explanations of how these estimates are derived. They demonstrate how singular perturbation methods can be successfully employed to gain insight in the dynamics of multi-compartment pharmacokinetic models. These appendices are also intended to serve as an introductory tutorial to these ideas.

Understanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study

In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase‐planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor‐pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not.

Consideration of the unbound drug concentration in enzyme kinetics

The study of enzyme kinetics in drug metabolism involves assessment of rates of metabolism and inhibitory potencies over a suitable concentration range. In all but the very simplest in vitro system, these drug concentrations can be influenced by a variety of nonspecific binding reservoirs that can reduce the available concentration to the enzyme system under investigation. As a consequence, the apparent kinetic parameters that are derived, such as K m or K i, can deviate from the true values. There are a number of sources of these nonspecific binding depots or barriers, including membrane permeation and partitioning, plasma or serum protein binding, and incubational binding. In the latter case, this includes binding to the assay apparatus, as well as biological depots, depending on the characteristics of the in vitro matrix being used. Given the wide array of subcellular, cellular, and recombinant enzyme systems utilized in drug metabolism, each of these has different components that can influence the free drug concentration. The physicochemical properties of the test compound are also paramount in determining the influential factors in any deviation between true and apparent kinetic behavior. This chapter describes the underlying mechanisms determining the free drug concentration in vitro and how these factors can be accounted for in drug metabolism studies, illustrated with case studies from the literature.

Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification

In this paper we present a mathematical analysis of the basic model for target mediated drug disposition (TMDD). Assuming high affinity of ligand to target, we give a qualitative characterisation of ligand versus time graphs for different dosing regimes and derive accurate analytic approximations of different phases in the temporal behaviour of the system. These approximations are used to estimate model parameters, give analytical approximations of such quantities as area under the ligand curve and clearance. We formulate conditions under which a suitably chosen Michaelis-Menten model provides a good approximation of the full TMDD-model over a specified time interval.

Coping with time scales in disease systems analysis: application to bone remodeling

In this study we demonstrate the added value of mathematical model reduction for characterizing complex dynamic systems using bone remodeling as an example. We show that for the given parameter values, the mechanistic RANK-RANKL-OPG pathway model proposed by Lemaire et al. (J Theor Biol 229:293-309, 2004) can be reduced to a simpler model, which can describe the dynamics of the full Lemaire model to very good approximation. The response of both models to changes in the underlying physiology and therapeutic interventions was evaluated in four physiologically meaningful scenarios: (i) estrogen deficiency/estrogen replacement therapy, (ii) Vitamin D deficiency, (iii) ageing, and (iv) chronic glucocorticoid treatment and its cessation. It was found that on the time scale of disease progression and therapeutic intervention, the models showed negligible differences in their dynamic properties and were both suitable for characterizing the impact of estrogen deficiency and estrogen replacement therapy, Vitamin D deficiency, ageing, and chronic glucocorticoid treatment and its cessation on bone forming (osteoblasts) and bone resorbing (osteoclasts) cells. It was also demonstrated how the simpler model could help in elucidating qualitative properties of the observed dynamics, such as the absence of overshoot and rebound, and the different dynamics of onset and washout.

Preclinical prediction of human brain target site concentrations: considerations in extrapolating to the clinical setting

The development of drugs for central nervous system (CNS) disorders has encountered high failure rates. In part, this has been due to the sole focus on blood-brain barrier permeability of drugs, without taking into account all other processes that determine drug concentrations at the brain target site. This review deals with an overview of the processes that determine the drug distribution into and within the CNS, followed by a description of in vivo techniques that can be used to provide information on CNS drug distribution. A plea follows for the need for more mechanistic understanding of the mechanisms involved in brain target site distribution, and the condition-dependent contributions of these mechanisms to ultimate drug effect. As future direction, such can be achieved by performing integrative cross-compare designed studies, in which mechanisms are systematically influenced (e.g., inhibition of an efflux transporter or induction of pathological state). With the use of advanced mathematical modeling procedures, we may dissect contributions of individual mechanisms in animals as links to the human situation.

The effect of plasma protein binding on in vivo efficacy: misconceptions in drug discovery

Data from in vitro plasma protein binding experiments that determine the fraction of protein-bound drug are frequently used in drug discovery to guide structure design and to prioritize compounds for in vivo studies. However, we consider that these practices are usually misleading, because in vivo efficacy is determined by the free (unbound) drug concentration surrounding the therapeutic target, not by the free drug fraction. These practices yield no enhancement of the in vivo free drug concentration. So, decisions based on free drug fraction could result in the wrong compounds being advanced through drug discovery programmes. This Perspective provides guidance on the application of plasma protein binding information in drug discovery.

Binding kinetics and mechanism of action: toward the discovery and development of better and best in class drugs

Binding kinetics (BK), an often overlooked key aspect of the broader concept of drug mechanism of action (MOA), is increasingly recognized as a springboard from pharmacokinetics (PK) to pharmacodynamics, and as a critical differentiator and predictor for drug efficacy and safety. Just as greater attention to PK issues has helped reduce the attrition of drugs tested in clinical trials, the emerging paradigm shift from primarily affinity/potency-emphasized to a more holistic BK-perceptive and MOA-informed approach is expected to further enhance the success of drug discovery and development. This perspective attempts to envision what this new approach looks like when proper emphasis is placed on BK and MOA in designing better and best in class drugs.

Impact of protein binding on receptor occupancy: a two-compartment model

In this paper we analyse the impact of protein-, lipid- and receptor-binding on receptor occupancy in a two-compartment system, with proteins in both compartments and lipids and receptors in the peripheral compartment only. We do this for two manners of drug administration: a bolus administration and a constant rate infusion, both into the central compartment. We derive explicit approximations for the time-curves of the different compounds valid for a wide range of realistic values of rate constants and initial concentrations of proteins, lipids, receptors and the drug. These approximations are used to obtain both qualitative and quantitative insight into such critical properties as the distribution of the drug over the two compartments, the maximum receptor occupancy and the area under the drug-receptor complex curve. In particular we focus on assessing the impact of the dissociation constants, K(P), K(L) and K(R) of the drug with, respectively, the proteins, the lipids and the receptors, the permeability and the surface area of the membrane between compartments, and the rate the drug is eliminated from the system.

Estimation of binding rate constants using a simultaneous mixed-effects method: application to monoamine transporter reuptake inhibitor reboxetine

BACKGROUND AND PURPOSE

Reboxetine is a clinically used antidepressant and is a racemic mixture of two enantiomers, SS- and RR-reboxetine. The aim of the work described in this manuscript was to determine the kinetics of binding of the RR- and SS-reboxetine to the human noradrenaline transporter (hNET).

EXPERIMENTAL APPROACH

We have applied a simultaneous mixed-effects method to the analysis of the transient kinetics of binding of SS-, RR- and racemic reboxetine to hNET. This method allowed simultaneous modelling of multiple datasets, taking into account inter-experiment variability, thereby facilitating robust parameter estimation and minimizing the assumptions made.

KEY RESULTS

The mixed-effects method proved simple and robust. SS-reboxetine bound to hNET according to a one-step binding model with the SS-enantiomer having 130-fold higher steady state affinity than the RR-enantiomer (K(d)= 0.076 +/- 0.009 nM vs. 9.7 +/- 0.8 nM respectively). The k(on) for SS-reboxetine was c. 1.4 x 10(5) M(-1).s(-1) and k(off) 1.05 x 10(-5) s(-1) (t(1/2) approximately 18 h). The k(on) for RR-reboxetine was c. 4.3 x 10(5) M(-1).s(-1) and k(off) 4.2 x 10(-3) s(-1) (t(1/2) approximately 3 min). The racemate behaved as expected for an equimolar mixture of RR- and SS-reboxetine, assuming mutually exclusive binding.

CONCLUSIONS AND IMPLICATIONS

These data will be useful for the interpretation of the behaviour of reboxetine and its enantiomers in man and the method used could be applied to other candidate drugs.

Dynamics of target-mediated drug disposition

We present a mathematical analysis of the basic model underlying target-mediated drug disposition (TMDD) in which a ligand is supplied through an initial bolus or through a constant rate infusion and forms a complex with a receptor (target), which is supplied and removed continuously. Ligand and complex may be eliminated according to first-order processes. We assume that the total receptor pool (free and bound) is constant in time and we give a geometrical description of the evolution of the concentrations of ligand, receptor and receptor-ligand complex which offers a transparent way to compare the full model with simpler models such as the quasi-steady-state (QSS) model, the quasi-equilibrium (QE) model and the empirical Michaelis-Menten (MM) model; we also give precise conditions on the parameters in the TMDD model for the validity of these reduced models. We relate characteristic properties of time courses to parameter regimes and, in particular, we identify and explain non-monotone dependence of the time-to-steady-state on the infusion rate. Finally, we discuss how the volume of the central compartment may be overestimated because of singular initial behaviour of the time course of the ligand concentration.