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.

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.

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.

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.

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.

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.

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.

Nicotinic acid timed to feeding reverses tissue lipid accumulation and improves glucose control in obese Zucker rats[S].

Nicotinic acid (NiAc) is a potent inhibitor of lipolysis, acutely reducing plasma free fatty acid (FFA) concentrations. However, a major FFA rebound is seen during rapid NiAc washout, and sustained exposure is associated with tolerance development, with FFAs returning to pretreatment levels. Our aim was to find a rational NiAc dosing regimen that preserves FFA lowering, sufficient to reverse nonadipose tissue lipid accumulation and improve metabolic control, in obese Zucker rats. We compared feeding-period versus fasting-period NiAc dosing for 5 days: 12 h subcutaneous infusion (programmable, implantable mini-pumps) terminated by gradual withdrawal. It was found that NiAc timed to feeding decreased triglycerides in liver (-47%; P < 0.01) and heart (-38%; P < 0.05) and reduced plasma fructosamine versus vehicle. During oral glucose tolerance test, plasma FFA levels were reduced with amelioration of hyperglycemia and hypertriglyceridemia. Furthermore, timing NiAc to feeding resulted in a general downregulation of de novo lipogenesis (DNL) genes in liver. By contrast, NiAc timed to fasting did not reduce tissue lipids, ameliorate glucose intolerance or dyslipidemia, or alter hepatic DNL genes. In conclusion, NiAc dosing regimen has a major impact on metabolic control in obese Zucker rats. Specifically, a well-defined NiAc exposure, timed to feeding periods, profoundly improves the metabolic phenotype of this animal model.

Modeling of free fatty acid dynamics: insulin and nicotinic acid resistance under acute and chronic treatments.

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc-FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague-Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional [Formula: see text] model. Insulin was incorporated in parallel with NiAc as the main endogenous co-variate of FFA dynamics. The model captured profound insulin resistance and complete drug resistance in obese rats. The efficacy of NiAc as an inhibitor of FFA release went from 1 to approximately 0 during sustained exposure in obese rats. The potency of NiAc as an inhibitor of insulin and of FFA release was estimated to be 0.338 and 0.436 [Formula: see text], respectively, in obese rats. A range of dosing regimens was analyzed and predictions made for optimizing NiAc delivery to minimize FFA exposure. Given the exposure levels of the experiments, the importance of washout periods in-between NiAc infusions was illustrated. The washout periods should be [Formula: see text]2 h longer than the infusions in order to optimize 24 h lowering of FFA in rats. However, the predicted concentration-response relationships suggests that higher AUC reductions might be attained at lower NiAc exposures.

Dosing profile profoundly influences nicotinic acid's ability to improve metabolic control in rats.

Acute nicotinic acid (NiAc) administration results in rapid reduction of plasma FFA concentrations. However, sustained NiAc exposure is associated with tolerance development resulting in return of FFA to pretreatment levels. The aim of this study was to determine whether a 12 h rectangular exposure profile (intermittent dose group) could avoid tolerance development and thereby reverse insulin resistance induced by lipid overload. FFA lowering was assessed in male Sprague Dawley (lean) and obese Zucker rats (obese) in response to a 5 h NiAc infusion, in either NiAc-naïve animals or after 5 days of continuous (24 h/day) or intermittent (12 h/day) NiAc dosing (via implantable, programmable minipump). We found that intermittent dosing over 5 days preserved NiAc-induced FFA lowering, comparable to dosing in NiAc-naïve animals. By contrast, following 5 days continuous administration, NiAc-induced FFA lowering was lost. The effect of intermittent NiAc infusion on insulin sensitivity was assessed in obese Zucker rats using hyperinsulinemic-isoglycemic clamps. The acute effect of NiAc to elevate glucose infusion rate (vs. saline control) was indeed preserved with intermittent dosing, while being lost upon continuous infusion. In conclusion, an intermittent but not continuous NiAc dosing strategy succeeded in retaining NiAc's ability to lower FFA and improve insulin sensitivity in obese Zucker rats.-Kroon, T., A. Kjellstedt, P. Thalén, J. Gabrielsson, and N. D. Oakes.

Modeling energy intake by adding homeostatic feedback and drug intervention.

Energy intake (EI) is a pivotal biomarker used in quantification approaches to metabolic disease processes such as obesity, diabetes, and growth disorders. Eating behavior is however under both short-term and long-term control. This control system manifests itself as tolerance and rebound phenomena in EI, when challenged by drug treatment or diet restriction. The paper describes a model with the capability to capture physiological counter-regulatory feedback actions triggered by energy imbalances. This feedback is general as it handles tolerance to both increases and decreases in EI, and works in both acute and chronic settings. A drug mechanism function inhibits (or stimulates) EI. The deviation of EI relative to a reference level (set-point) serves as input to a non-linear appetite control signal which in turn impacts EI in parallel to the drug intervention. Three examples demonstrate the potential usefulness of the model in both acute and chronic dosing situations. The model shifts the predicted concentration-response relationship rightwardly at lower concentrations, in contrast to models that do not handle functional adaptation. A fourth example further shows that the model may qualitatively explain differences in rate and extent of adaptation in observed EI and its concomitants in both rodents and humans.

Challenges of a mechanistic feedback model describing nicotinic acid-induced changes in non-esterified fatty acids in rats.

Previously, we developed a feedback model to describe the tolerance and oscillatory rebound of non-esterified fatty acid (NEFA) plasma concentrations in male Sprague Dawley rats after intravenous infusions of nicotinic acid (NiAc). This study challenges that model, using the following regimens of intravenous and oral NiAc dosing in male Sprague Dawley rats (n = 95) to create different patterns of exposure: (A) 30 min infusion at 0, 1, 5 or 20 µmol kg(-1) body weight; (B) 300 min infusion at 0, 5, 10 or 51 µmol kg(-1); (C) 30 min infusion at 5 µmol kg(-1), followed by a stepwise decrease in rate every 10 min for 180 min; (D) 30 min infusion at 5 µmol kg(-1), followed by a stepwise decrease in rate every 10 min for 180 min and another 30 min infusion at 5 µmol kg(-1) from 210 to 240 min; (E) an oral dose of 0, 24.4, 81.2 or 812 µmol kg(-1). Serial arterial blood samples were taken for measurement of plasma NiAc and NEFA concentrations. The gradual decrease in infusion rate in (C) and (D) were also designed to test the hypothesis that a gradual reduction in NiAc plasma concentration may be expected to reduce or prevent rebound. The absorption of NiAc was described by parallel linear and non-linear processes and the disposition of NiAc by a two-compartment model with endogenous turnover rate and two parallel capacity-limited elimination processes. NEFA (R) turnover, which was driven by the plasma concentration of NiAc via an inhibitory drug-mechanism function acting on NEFA formation, was described by a feedback model with a moderator distributed over a series of transit compartments, where the first compartment (M 1) inhibited the formation of R and the last compartment (M N ) stimulated the loss of R. All processes regulating the plasma NEFA concentration were assumed to be captured by the moderator function. Data were analyzed using non-linear mixed effects modeling (NONMEM). The potency IC 50 of NiAc was 68 nmol L(-1), the fractional turnover rate k out 0.27 L mmol(-1) min(-1), and the turnover rate of moderator k tol 0.023 min(-1). The lower physiological limit of NEFA, which was modeled as a NiAc-independent release (k cap ) of NEFA into plasma, was estimated to 0.023 mmol L(-1) min(-1). The parameter estimates derived in this study were consistent with our previous estimates, suggesting that the model may be used for prediction of the NEFA response time-course following different modes and routes administration of NiAc or NiAc analogues. In order to avoid NiAc-induced NEFA rebound, a slow decline in the NiAc exposure pattern is needed at or below IC (50).

Feedback modeling of non-esterified fatty acids in obese Zucker rats after nicotinic acid infusions.

This study investigates the impact of disease on nicotinic acid (NiAc)-induced changes in plasma concentrations of non-esterified fatty acids (NEFA). NiAc was given by constant intravenous infusion to normal Sprague-Dawley and obese Zucker rats, and arterial blood samples were taken for analysis of NiAc, NEFA, insulin and glucose plasma concentrations. The intravenous route was intentionally selected to avoid confounding processes, such as absorption, following extravascular administration. Data were analyzed using nonlinear mixed effects modeling (NONMEM, version VI). The disposition of NiAc in the normal rats was described by a two-compartment model with endogenous synthesis of NiAc and two parallel capacity-limited elimination processes. In the obese rats disposition was described by a one-compartment model with endogenous synthesis of NiAc and one capacity-limited elimination process. The plasma concentration of NiAc drove NEFA (R) turnover via an inhibitory drug-mechanism function acting on the formation of NEFA. NEFA turnover was described by a feedback model with a moderator distributed over a series of transit compartments, where the first compartment (M 1 ) inhibited the formation of R and the last compartment (M N ) stimulated the loss of R. All processes regulating plasma NEFA concentrations were assumed to be captured by the moderator function. Differences in the pharmacodynamic response of the two strains included, in the obese animals, an increased NEFA baseline, diminished rebound and post-rebound oscillation, and a more pronounced slowly developing tolerance during the period of constant drug exposure. The feedback model captured the NiAc-induced changes in NEFA response in both the normal and obese rats. Differences in the parameter estimates between the obese and normal rats included, in the former group, increases in R 0 , k in and p by 44, 41 and 78 %, respectively, and decreases in k out and γ by 64 and 84 %, respectively. The estimates of k tol and IC 50 were similar in both groups. The NiAc-NEFA concentration-response relationship at equilibrium was substantially different in the two groups, being shifted upwards and to the right, and being shallower in the obese rats. The extent of such shifts is important, as they demonstrate the impact of disease at equilibrium and, if ignored, will lead to erroneous dose predictions and, in consequence, poorly designed studies. The proposed models are primarily aimed at screening and selecting candidates with the highest potential of becoming a viable drug in man.

A modeling approach for compounds affecting body composition.

Body composition and body mass are pivotal clinical endpoints in studies of welfare diseases. We present a combined effort of established and new mathematical models based on rigorous monitoring of energy intake (EI) and body mass in mice. Specifically, we parameterize a mechanistic turnover model based on the law of energy conservation coupled to a drug mechanism model. Key model variables are fat-free mass (FFM) and fat mass (FM), governed by EI and energy expenditure (EE). An empirical Forbes curve relating FFM to FM was derived experimentally for female C57BL/6 mice. The Forbes curve differs from a previously reported curve for male C57BL/6 mice, and we thoroughly analyse how the choice of Forbes curve impacts model predictions. The drug mechanism function acts on EI or EE, or both. Drug mechanism parameters (two to three parameters) and system parameters (up to six free parameters) could be estimated with good precision (coefficients of variation typically <20 % and not greater than 40 % in our analyses). Model simulations were done to predict the EE and FM change at different drug provocations in mice. In addition, we simulated body mass and FM changes at different drug provocations using a similar model for man. Surprisingly, model simulations indicate that an increase in EI (e.g. 10 %) was more efficient than an equal lowering of EI. Also, the relative change in body mass and FM is greater in man than in mouse at the same relative change in either EI or EE. We acknowledge that this assumes the same drug mechanism impact across the two species. A set of recommendations regarding the Forbes curve, vehicle control groups, dual action on EI and loss, and translational aspects are discussed. This quantitative approach significantly improves data interpretation, disease system understanding, safety assessment and translation across species.

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.

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.

Feedback modeling of non-esterified fatty acids in rats after nicotinic acid infusions.

A feedback model was developed to describe the tolerance and oscillatory rebound seen in non-esterified fatty acid (NEFA) plasma concentrations following intravenous infusions of nicotinic acid (NiAc) to male Sprague-Dawley rats. NiAc was administered as an intravenous infusion over 30 min (0, 1, 5 or 20 µmol kg(-1) of body weight) or over 300 min (0, 5, 10 or 51 µmol kg(-1) of body weight), to healthy rats (n = 63), and serial arterial blood samples were taken for measurement of NiAc and NEFA plasma concentrations. Data were analyzed using nonlinear mixed effects modeling (NONMEM). The disposition of NiAc was described by a two-compartment model with endogenous turnover rate and two parallel capacity-limited elimination processes. The plasma concentration of NiAc was driving NEFA (R) turnover via an inhibitory drug-mechanism function acting on the formation of NEFA. The NEFA turnover was described by a feedback model with a moderator distributed over a series of transit compartments, where the first compartment (M (1)) inhibited the formation of R and the last compartment (M ( N )) stimulated the loss of R. All processes regulating plasma NEFA concentrations were assumed to be captured by the moderator function. The potency, IC (50), of NiAc was 45 nmol L(-1), the fractional turnover rate k ( out ) was 0.41 L mmol(-1) min(-1) and the turnover rate of moderator k ( tol ) was 0.027 min(-1). A lower physiological limit of NEFA was modeled as a NiAc-independent release (k ( cap )) of NEFA into plasma and was estimated to 0.032 mmol L(-1) min(-1). This model can be used to provide information about factors that determine the time-course of NEFA response following different modes, rates and routes of administration of NiAc. The proposed model may also serve as a preclinical tool for analyzing and simulating drug-induced changes in plasma NEFA concentrations after treatment with NiAc or NiAc analogues.

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.

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.