Model-based assessment of combination therapies - ranking of radiosensitizing agents in oncology.

BACKGROUND: To increase the chances of finding efficacious anticancer drugs, improve development times and reduce costs, it is of interest to rank test compounds based on their potential for human use as early as possible in the drug development process. In this paper, we present a method for ranking radiosensitizers using preclinical data. METHODS: We used data from three xenograft mice studies to calibrate a model that accounts for radiation treatment combined with radiosensitizers. A nonlinear mixed effects approach was utilized where between-subject variability and inter-study variability were considered. Using the calibrated model, we ranked three different Ataxia telangiectasia-mutated inhibitors in terms of anticancer activity. The ranking was based on the Tumor Static Exposure (TSE) concept and primarily illustrated through TSE-curves. RESULTS: The model described data well and the predicted number of eradicated tumors was in good agreement with experimental data. The efficacy of the radiosensitizers was evaluated for the median individual and the 95% population percentile. Simulations predicted that a total dose of 220 Gy (5 radiation sessions a week for 6 weeks) was required for 95% of tumors to be eradicated when radiation was given alone. When radiation was combined with doses that achieved at least 8 [Formula: see text] of each radiosensitizer in mouse blood, it was predicted that the radiation dose could be decreased to 50, 65, and 100 Gy, respectively, while maintaining 95% eradication. CONCLUSIONS: A simulation-based method for calculating TSE-curves was developed, which provides more accurate predictions of tumor eradication than earlier, analytically derived, TSE-curves. The tool we present can potentially be used for radiosensitizer selection before proceeding to subsequent phases of the drug discovery and development process.

Turn On, Tune In, Turnover! Target Biology Impacts In Vivo Potency, Efficacy, and Clearance.

Even though significant efforts have been spent in recent years to understand and define the determinants of in vivo potency and clearance, important pieces of information are still lacking. By introducing target turnover into the reasoning, we open up to further the understanding of central factors important to the optimization of translational dose-concentration-response predictions. We describe (i) new (open model) expressions of the in vivo potency and efficacy parameters, which embody target turnover, binding, and complex kinetics, also capturing full, partial, and inverse agonism and antagonism; (ii) a detailed examination of open models to show what potency and efficacy parameters have in common and how they differ; and (iii) a comprehensive literature review showing that target turnover rate varies with age, species, tissue/subregion, treatment, disease state, hormonal and nutritional state, and day-night cycle. The new open model expression, which integrates system and drug properties, shows the following. Fractional turnover rates rather than the absolute target or ligand-target complex expression determine necessary drug exposure via in vivo potency. Absolute ligand-target expression determines the need of a drug, based on the transduction ρ and in vivo efficacy parameters. The free enzyme concentration determines clearance and maximum metabolic rate. The fractional turnover rate determines time to equilibrium between substrate, free enzyme, and complex.The properties of substrate, target, and the complex demonstrate nonsaturable metabolic behavior at equilibrium. Nonlinear processes, previously referred to as capacity- and time-dependent kinetics, may occasionally have been disequilibria. Finally, the open model may pinpoint why some subjects differ in their demand of drug. SIGNIFICANCE STATEMENT: Understanding the target turnover is a central tenet in many translational dose-concentration-response predictions. New open model expressions of in vivo potency, efficacy parameter, and clearance are derived and anchored onto a comprehensive literature review showing that target turnover rate varies with age, species, tissue/subregion, treatment, disease, hormonal and nutritional state, day-night cycle, and more. Target turnover concepts will therefore significantly impact fundamental aspects of pharmacodynamics and pharmacokinetics, thereby also the basics of drug discovery, development, and optimization of clinical dosing.

Impact of enzyme turnover on the dynamics of the Michaelis-Menten model.

Enzymatic (metabolic rate) processes are traditionally modelled by means of Michaelis-Menten type reactions. The experimental setup is usually performed in vitro also denoted as a 'closed system'. In this paper we explore the impact of enzyme turnover on the classical Michaelis-Menten model by modifying it to include enzyme turnover, specifically through zeroth-order synthesis and first-order degeneration of the enzyme. It is shown how enzyme turnover significantly alters the dynamics of substrate, free- and bound enzyme, and impacts the rate with which substrate is converted to a metabolite P. Qualitative and quantitative estimates are derived for the effect of the parameters ksyn, kdeg and kcat on the dynamics of substrate, and free- and bound enzyme. The model integrates four distinct processes, each characterised with its own parameter(s): (i) substrate-enzyme binding, characterised by kon and koff; (ii) the catalytic process, characterised by kcat; (iii) simultaneous re-generation of free enzyme; and (iv) turnover of free enzyme, characterised by kdeg. The properties of the open Michaelis-Menten model have a direct bearing on the drug discovery process, the translation of data to the human situation and on explaining deviating clinical metabolic observations.

Exposure-response modeling improves selection of radiation and radiosensitizer combinations.

A central question in drug discovery is how to select drug candidates from a large number of available compounds. This analysis presents a model-based approach for comparing and ranking combinations of radiation and radiosensitizers. The approach is quantitative and based on the previously-derived Tumor Static Exposure (TSE) concept. Combinations of radiation and radiosensitizers are evaluated based on their ability to induce tumor regression relative to toxicity and other potential costs. The approach is presented in the form of a case study where the objective is to find the most promising candidate out of three radiosensitizing agents. Data from a xenograft study is described using a nonlinear mixed-effects modeling approach and a previously-published tumor model for radiation and radiosensitizing agents. First, the most promising candidate is chosen under the assumption that all compounds are equally toxic. The impact of toxicity in compound selection is then illustrated by assuming that one compound is more toxic than the others, leading to a different choice of candidate.

Comparisons of basic target-mediated drug disposition (TMDD) and ligand facilitated target removal (LFTR).

In the well-known model for basic Target-Mediated Drug Disposition (TMDD), drug binds to the target and the resulting drug-target complex is removed by a first order process, leading to loss of both drug and target. In the present note we study what happens when, instead, drug is returned to the free drug pool so that it can a new target molecule. What results is a mechanism in which the drug, here referred to as the ligand, facilitates the removal of the target,and then returns to the free ligand pool. Accordingly the process will be referred to as Ligand-Facilitated Target Removal (LFTR). It is shown through simulations and mathematical analysis how the two models differ and how their signature profiles typically appear. We also derive a useful parameter of both models, the in vivo potency EC50 (L50) which contains both ligand-target binding properties (kon,koff), target turnover (kdeg) and ligand-target complex kinetics (ke(RL)). Thus, this parameter contains a conglomerate of properties and is therefore potentially more informative about relevant (clinical) exposure than the binding affinity (Kd) alone. The derived potency parameter EC50 may therefore be used as a more robust ranking parameter among small and large drug molecules in drug discovery. Subsequently the LFTR model is applied to experimentally obtained literature data and the relevant parameters are estimated.

An Integrative Approach for Improved Assessment of Cardiovascular Safety Data.

Cardiovascular adverse effects in drug development are a major source of compound attrition. Characterization of blood pressure (BP), heart rate (HR), stroke volume (SV), and QT-interval prolongation are therefore necessary in early discovery. It is, however, common practice to analyze these effects independently of each other. High-resolution time courses are collected via telemetric techniques, but only low-resolution data are analyzed and reported. This ignores codependencies among responses (HR, BP, SV, and QT-interval) and separation of system (turnover properties) and drug-specific properties (potencies, efficacies). An analysis of drug exposure-time and high-resolution response-time data of HR and mean arterial blood pressure was performed after acute oral dosing of ivabradine, sildenafil, dofetilide, and pimobendan in Han-Wistar rats. All data were modeled jointly, including different compounds and exposure and response time courses, using a nonlinear mixed-effects approach. Estimated fractional turnover rates [h-1, relative standard error (%RSE) within parentheses] were 9.45 (15), 30.7 (7.8), 3.8 (13), and 0.115 (1.7) for QT, HR, total peripheral resistance, and SV, respectively. Potencies (nM, %RSE within parentheses) were IC 50 = 475 (11), IC 50 = 4.01 (5.4), EC 50 = 50.6 (93), and IC 50 = 47.8 (16), and efficacies (%RSE within parentheses) were I max = 0.944 (1.7), Imax = 1.00 (1.3), E max = 0.195 (9.9), and Imax = 0.745 (4.6) for ivabradine, sildenafil, dofetilide, and pimobendan. Hill parameters were estimated with good precision and below unity, indicating a shallow concentration-response relationship. An equilibrium concentration-biomarker response relationship was predicted and displayed graphically. This analysis demonstrates the utility of a model-based approach integrating data from different studies and compounds for refined preclinical safety margin assessment. SIGNIFICANCE STATEMENT: A model-based approach was proposed utilizing biomarker data on heart rate, blood pressure, and QT-interval. A pharmacodynamic model was developed to improve assessment of high-resolution telemetric cardiovascular safety data driven by different drugs (ivabradine, sildenafil, dofetilide, and pimobondan), wherein system- (turnover rates) and drug-specific parameters (e.g., potencies and efficacies) were sought. The model-predicted equilibrium concentration-biomarker response relationships and was used for safety assessment (predictions of 20% effective concentration, for example) of heart rate, blood pressure, and QT-interval.

Does In Vitro Potency Predict Clinically Efficacious Concentrations?

The in vitro affinity of a compound for its target is an important feature in drug discovery, but what remains is how predictive in vitro properties are of in vivo therapeutic drug exposure. We assessed the relationship between in vitro potency and clinically efficacious concentrations for marketed small molecule drugs (n = 164) and how they may differ depending on therapeutic indication, mode of action, receptor type, target localization, and function. Approximately 70% of compounds had a therapeutic unbound plasma exposure lower than in vitro potency; the median ratio of exposure in relation to in vitro potency was 0.32, and 80% had ratios within the range of 0.007 to 8.7. We identified differences in the in vivo-to-in vitro potency ratio between indications, mode of action, target type, and matrix localization, and whether or not the drugs had active metabolites. The in vitro-assay variability contributions appeared to be the smallest; within the same drug target and mode of action the within-variability was slightly broader; but both were substantially less compared with the overall distribution of ratios. These data suggest that in vitro potency conditions, estimated in vivo potency, required level of receptor occupancy, and target turnover are key components for further understanding the link between clinical drug exposure and in vitro potency.

Modeling long-term tumor growth and kill after combinations of radiation and radiosensitizing agents.

PURPOSE: Radiation therapy, whether given alone or in combination with chemical agents, is one of the cornerstones of oncology. We develop a quantitative model that describes tumor growth during and after treatment with radiation and radiosensitizing agents. The model also describes long-term treatment effects including tumor regrowth and eradication. METHODS: We challenge the model with data from a xenograft study using a clinically relevant administration schedule and use a mixed-effects approach for model-fitting. We use the calibrated model to predict exposure combinations that result in tumor eradication using Tumor Static Exposure (TSE). RESULTS: The model is able to adequately describe data from all treatment groups, with the parameter estimates taking biologically reasonable values. Using TSE, we predict the total radiation dose necessary for tumor eradication to be 110 Gy, which is reduced to 80 or 30 Gy with co-administration of 25 or 100 mg kg-1 of a radiosensitizer. TSE is also explored via a heat map of different growth and shrinkage rates. Finally, we discuss the translational potential of the model and TSE concept to humans. CONCLUSIONS: The new model is capable of describing different tumor dynamics including tumor eradication and tumor regrowth with different rates, and can be calibrated using data from standard xenograft experiments. TSE and related concepts can be used to predict tumor shrinkage and eradication, and have the potential to guide new experiments and support translations from animals to humans.

Challenge model of TNFα turnover at varying LPS and drug provocations.

A mechanism-based biomarker model of TNFα-response, including different external provocations of LPS challenge and test compound intervention, was developed. The model contained system properties (such as kt, kout), challenge characteristics (such as ks, kLPS, Km, LPS, Smax, SC50) and test-compound-related parameters (Imax, IC50). The exposure to test compound was modelled by means of first-order input and Michaelis-Menten type of nonlinear elimination. Test compound potency was estimated to 20 nM with a 70% partial reduction in TNFα-response at the highest dose of 30 mg·kg-1. Future selection of drug candidates may focus the estimation on potency and efficacy by applying the selected structure consisting of TNFα system and LPS challenge characteristics. A related aim was to demonstrate how an exploratory (graphical) analysis may guide us to a tentative model structure, which enables us to better understand target biology. The analysis demonstrated how to tackle a biomarker with a baseline below the limit of detection. Repeated LPS-challenges may also reveal how the rate and extent of replenishment of TNFα pools occur. Lack of LPS exposure-time courses was solved by including a biophase model, with the underlying assumption that TNFα-response time courses, as such, contain kinetic information. A transduction type of model with non-linear stimulation of TNFα release was finally selected. Typical features of a challenge experiment were shown by means of model simulations. Experimental shortcomings of present and published designs are identified and discussed. The final model coupled to suggested guidance rules may serve as a general basis for the collection and analysis of pharmacological challenge data of future studies.

Modelling of oscillatory cortisol response in horses using a Bayesian population approach for evaluation of dexamethasone suppression test protocols.

Cortisol is a steroid hormone relevant to immune function in horses and other species and shows a circadian rhythm. The glucocorticoid dexamethasone suppresses cortisol in horses. Pituitary pars intermedia dysfunction (PPID) is a disease in which the cortisol suppression mechanism through dexamethasone is challenged. Overnight dexamethasone suppression test (DST) protocols are used to test the functioning of this mechanism and to establish a diagnosis for PPID. However, existing DST protocols have been recognized to perform poorly in previous experimental studies, often indicating presence of PPID in healthy horses. This study uses a pharmacokinetic/pharmacodynamic (PK/PD) modelling approach to analyse the oscillatory cortisol response and its interaction with dexamethasone. Two existing DST protocols were then scrutinized using model simulations with particular focus on their ability to avoid false positive outcomes. Using a Bayesian population approach allowed for quantification of uncertainty and enabled predictions for a broader population of horses than the underlying sample. Dose selection and sampling time point were both determined to have large influence on the number of false positives. Advice on pitfalls in test protocols and directions for possible improvement of DST protocols were given. The presented methodology is also easily extended to other clinical test protocols.

Challenging the dose-response-time data approach: Analysis of a complex system.

This study presents an extensive dose-response-time (DRT) meta-analysis of the nicotinic acid-induced inhibition of free fatty acids and insulin release. The purpose was to quantify the implications of lacking exposure data when analysing complex pharmacodynamic systems. The DRT model successfully characterised various response behaviours-including time-delays, rebound, feedback mechanisms, and adaptation-on both the individual and the population level. Comparing the fitted DRT model to an exposure-driven reference analysis showed that bias and uncertainty were introduced in the parameter estimates. However, most estimates were within one standard error from the reference. In both approaches, a few parameters suffered from practical identifiability issues, likely due to large differences in half-lives of the different rate processes. Moreover, the optimal dosing strategies predicted by the DRT model differed slightly from those of the exposure-driven analysis, having a lower optimal steady-state reduction of free fatty acids exposure.

Dose-Response-Time Data Analysis: An Underexploited Trinity.

The most common approach to in vivo pharmacokinetic and pharmacodynamic analyses involves sequential analysis of the plasma concentration- and response-time data, such that the plasma kinetic model provides an independent function, driving the dynamics. However, in situations when plasma sampling may jeopardize the effect measurements or is scarce, nonexistent, or unlinked to the effect (e.g., in intensive care units, pediatric or frail elderly populations, or drug discovery), focusing on the response-time course alone may be an adequate alternative for pharmacodynamic analyses. Response-time data inherently contain useful information about the turnover characteristics of response (target turnover rate, half-life of response), as well as the drug's biophase kinetics (biophase availability, absorption half-life, and disposition half-life) pharmacodynamic properties (potency, efficacy). The use of pharmacodynamic time-response data circumvents the need for a direct assay method for the drug and has the additional advantage of being applicable to cases of local drug administration close to its intended targets in the immediate vicinity of target, or when target precedes systemic plasma concentrations. This review exemplifies the potential of biophase functions in pharmacodynamic analyses in both preclinical and clinical studies, with the purpose of characterizing response data and optimizing subsequent study protocols. This article illustrates crucial determinants to the success of modeling dose-response-time (DRT) data, such as the dose selection, repeated dosing, and different input rates and routes. Finally, a literature search was also performed to gauge how frequently this technique has been applied in preclinical and clinical studies. This review highlights situations in which DRT should be carefully scrutinized and discusses future perspectives of the field.

Michaelis-Menten from an In Vivo Perspective: Open Versus Closed Systems.

After a century of applications of the seminal Michaelis-Menten equation since its advent it is timely to scrutinise its principal parts from an in vivo point of view. Thus, the Michaelis-Menten system was revisited in which enzymatic turnover, i.e. synthesis and elimination was incorporated. To the best of our knowledge, previous studies of the Michaelis-Menten system have been mainly based on the assumption that the total pool of enzyme, free and bound, is constant. However, in fact this may not always be the case, particularly for chronic indications. Chronic (periodic) administration of drugs is often related to induction or inhibition of enzymatic processes and even changes in the free enzymatic load per se. This may account for the fact that translation of in vitro metabolism data have shown to give systematic deviations from experimental in vivo data. Interspecies extrapolations of metabolic data are often challenged by poor predictability due to insufficient power of applied functions and methods. By incorporating enzyme turnover, a more mechanistic expression of substrate, free enzyme and substrate-enzyme complex concentrations is derived. In particular, it is shown that whereas in closed systems there is a threshold for chronic dosing beyond which the substrate concentration keeps rising, in open systems involving enzyme turnover this is no longer the case. However, in the presence of slow enzyme turnover, after an initial period of adjustment which may be quite long, the relation between substrate concentration and dose rate reduces to a linear expression. This new open framework is also applicable to transporter systems.

Evaluation and translation of combination therapies in oncology - A quantitative approach.

Quantitative techniques improve our understanding of tumor volume data for combination treatments and its translation across in vivo models and species. The focus of this paper is therefore on understanding in vivo data, highlighting key structural elements of pharmacodynamic tumor models, and challenging these methods from a translational point of view. We introduce the concept of Tumor Static Exposure (TSE) both for single and multiple combined anticancer agents. The TSE curve separates all possible exposure combinations into regions of tumor growth and tumor shrinkage. Moreover, the degree of curvature of the TSE curve indicates the degree of synergy or antagonism. We demonstrate the TSE approach by two case studies. The first examines a combination of the drugs cetuximab and cisplatin. The TSE curve associated with this combination reveals a weak synergistic effect, suggesting only modest gains from combination therapy. The second case study examines combinations of ionizing radiation and a radiosensitizing agent. In this case, the TSE curve exhibits a pronounced curvature, indicating a strong synergistic effect; tumor regression can be achieved at significantly lower exposure levels and/or radiation doses. Finally, an allometric approach to human dose prediction demonstrates the translational power of the model and the TSE concept. We conclude that the TSE approach, which embodies model-based measures of both drug (potency) and target properties (tumor growth rate), has a strong potential for ranking of compounds, supporting compound selection, and translating preclinical findings to humans.

Lost in translation: What's in an EC50? Innovative PK/PD reasoning in the drug development context.

Translation across species and from in vitro to in vivo is a central tenet in drug discovery pharmacology. Successful implementation requires proper assessment of both in vivo potency and efficacy. This notwithstanding, in vivo data is typically defined mostly in terms of ligand-to-target binding affinity, similar to in vitro studies. As in vivo potency and efficacy involve a combination not only of drug, but also partitioning, target, and drug-target-complex events and processes, ignoring some of the central differences between in vivo and in vitro may result in serious miscalculations of in vivo efficacious exposure for translational predictions. We compare potency measures derived from two basic pharmacodynamic model situations: A 'closed' in vitro system defining target binding of a ligand when both concentrations remain essentially static, and an 'open' in vivo system where target turnover dynamics and elimination of the drug-target complex are also included. Corresponding equilibrium (steady-state) expressions in the central pharmacokinetic compartment are derived and presented. Three representative variants of 'open' in vivo systems are discussed, showing relationships for ligand-target complex and ligand for each of the systems and graphically illustrating corresponding shapes. The examples include i) two ligands competing for one target, ii) two targets competing for one ligand (/drug), and iii) target-ligand (/drug) interactions in a peripheral PK compartment. The expanded in vivo potency EC50 expression emphasises the contribution from target-related biology parameters that need accounting for, and particularly that 'closed' system (in vitro) properties should not be first choice when ranking compounds in vivo ('open' system).

New Equilibrium Models of Drug-Receptor Interactions Derived from Target-Mediated Drug Disposition.

In vivo analyses of pharmacological data are traditionally based on a closed system approach not incorporating turnover of target and ligand-target kinetics, but mainly focussing on ligand-target binding properties. This study incorporates information about target and ligand-target kinetics parallel to binding. In a previous paper, steady-state relationships between target- and ligand-target complex versus ligand exposure were derived and a new expression of in vivo potency was derived for a circulating target. This communication is extending the equilibrium relationships and in vivo potency expression for (i) two separate targets competing for one ligand, (ii) two different ligands competing for a single target and (iii) a single ligand-target interaction located in tissue. The derived expressions of the in vivo potencies will be useful both in drug-related discovery projects and mechanistic studies. The equilibrium states of two targets and one ligand may have implications in safety assessment, whilst the equilibrium states of two competing ligands for one target may cast light on when pharmacodynamic drug-drug interactions are important. The proposed equilibrium expressions for a peripherally located target may also be useful for small molecule interactions with extravascularly located targets. Including target turnover, ligand-target complex kinetics and binding properties in expressions of potency and efficacy will improve our understanding of within and between-individual (and across species) variability. The new expressions of potencies highlight the fact that the level of drug-induced target suppression is very much governed by target turnover properties rather than by the target expression level as such.

Impact of mathematical pharmacology on practice and theory: four case studies.

Drug-discovery has become a complex discipline in which the amount of knowledge about human biology, physiology, and biochemistry have increased. In order to harness this complex body of knowledge mathematics can play a critical role, and has actually already been doing so. We demonstrate through four case studies, taken from previously published data and analyses, what we can gain from mathematical/analytical techniques when nonlinear concentration-time courses have to be transformed into their equilibrium concentration-response (target or complex) relationships and new structures of drug potency have to be deciphered; when pattern recognition needs to be carried out for an unconventional response-time dataset; when what-if? predictions beyond the observational concentration-time range need to be made; or when the behaviour of a semi-mechanistic model needs to be elucidated or challenged. These four examples are typical situations when standard approaches known to the general community of pharmacokineticists prove to be inadequate.

Model-Based Evaluation of Radiation and Radiosensitizing Agents in Oncology.

Radiotherapy is one of the major therapy forms in oncology, and combination therapies involving radiation and chemical compounds can yield highly effective tumor eradication. In this paper, we develop a tumor growth inhibition model for combination therapy with radiation and radiosensitizing agents. Moreover, we extend previous analyses of drug combinations by introducing the tumor static exposure (TSE) curve. The TSE curve for radiation and radiosensitizer visualizes exposure combinations sufficient for tumor regression. The model and TSE analysis are then tested on xenograft data. The calibrated model indicates that the highest dose of combination therapy increases the time until tumor regrowth 10-fold. The TSE curve shows that with an average radiosensitizer concentration of 1.0 µg/mL the radiation dose can be decreased from 2.2 Gy to 0.7 Gy. Finally, we successfully predict the effect of a clinically relevant treatment schedule, which contributes to validating both the model and the TSE concept.

In vivo potency revisited - Keep the target in sight.

Potency is a central parameter in pharmacological and biochemical sciences, as well as in drug discovery and development endeavors. It is however typically defined in terms only of ligand to target binding affinity also in in vivo experimentation, thus in a manner analogous to in in vitro studies. As in vivo potency is in fact a conglomerate of events involving ligand, target, and target-ligand complex processes, overlooking some of the fundamental differences between in vivo and in vitro may result in serious mispredictions of in vivo efficacious dose and exposure. The analysis presented in this paper compares potency measures derived from three model situations. Model A represents the closed in vitro system, defining target binding of a ligand when total target and ligand concentrations remain static and constant. Model B describes an open in vivo system with ligand input and clearance (Cl(L)), adding in parallel to the turnover (ksyn, kdeg) of the target. Model C further adds to the open in vivo system in Model B also the elimination of the target-ligand complex (ke(RL)) via a first-order process. We formulate corresponding equations of the equilibrium (steady-state) relationships between target and ligand, and complex and ligand for each of the three model systems and graphically illustrate the resulting simulations. These equilibrium relationships demonstrate the relative impact of target and target-ligand complex turnover, and are easier to interpret than the more commonly used ligand-, target- and complex concentration-time courses. A new potency expression, labeled L50, is then derived. L50 is the ligand concentration at half-maximal target and complex concentrations and is an amalgamation of target turnover, target-ligand binding and complex elimination parameters estimated from concentration-time data. L50 is then compared to the dissociation constant Kd (target-ligand binding affinity), the conventional Black & Leff potency estimate EC50, and the derived Michaelis-Menten parameter Km (target-ligand binding and complex removal) across a set of literature data. It is evident from a comparison between parameters derived from in vitro vs. in vivo experiments that L50 can be either numerically greater or smaller than the Kd (or Km) parameter, primarily depending on the ratio of kdeg-to-ke(RL). Contrasting the limit values of target R and target-ligand complex RL for ligand concentrations approaching infinity demonstrates that the outcome of the three models differs to a great extent. Based on the analysis we propose that a better understanding of in vivo pharmacological potency requires simultaneous assessment of the impact of its underlying determinants in the open system setting. We propose that L50 will be a useful parameter guiding predictions of the effective concentration range, for translational purposes, and assessment of in vivo target occupancy/suppression by ligand, since it also encompasses target turnover - in turn also subject to influence by pathophysiology and drug treatment. Different compounds may have similar binding affinity for a target in vitro (same Kd), but vastly different potencies in vivo. L50 points to what parameters need to be taken into account, and particularly that closed-system (in vitro) parameters should not be first choice when ranking compounds in vivo (open system).

Pharmacokinetic Steady-States Highlight Interesting Target-Mediated Disposition Properties.

In this paper, we derive explicit expressions for the concentrations of ligand L, target R and ligand-target complex RL at steady state for the classical model describing target-mediated drug disposition, in the presence of a constant-rate infusion of ligand. We demonstrate that graphing the steady-state values of ligand, target and ligand-target complex, we obtain striking and often singular patterns, which yield a great deal of insight and understanding about the underlying processes. Deriving explicit expressions for the dependence of L, R and RL on the infusion rate, and displaying graphs of the relations between L, R and RL, we give qualitative and quantitive information for the experimentalist about the processes involved. Understanding target turnover is pivotal for optimising these processes when target-mediated drug disposition (TMDD) prevails. By a combination of mathematical analysis and simulations, we also show that the evolution of the three concentration profiles towards their respective steady-states can be quite complex, especially for lower infusion rates. We also show how parameter estimates obtained from iv bolus studies can be used to derive steady-state concentrations of ligand, target and complex. The latter may serve as a template for future experimental designs.