A set-point model with oscillatory behavior predicts the time course of 8-OH-DPAT-induced hypothermia

Delayed logistic indirect response models: realization of oscillating behavior

Indirect response (IDR) models are probably the most frequently applied tools relating the effect of a signal to a baseline response. A response modeled by such a classical IDR model will always return monotonously to its baseline after drug administration. We extend IDR models with a delay process, i.e. a retarded response state, that leads to oscillating response behavior. First, IDR models with a first-order production and second-order loss term based on the famous logistic equation are constructed. Second, a delay process similar to the delayed logistic equation is included. Relations of the classical IDR model with our extended IDR model concerning response and model parameters are revealed. Simulations of typical response profiles are presented and data fitting of a model for leptin and cholesterol dynamics after administration of methylprednisolone is performed. The influence of the delay parameter on the other model parameters is discussed.

Application of pharmacometrics and quantitative systems pharmacology to cancer therapy: The example of luminal a breast cancer

Breast cancer (BC) is the most common cancer in women, and the second most frequent cause of cancer-related deaths in women worldwide. It is a heterogeneous disease composed of multiple subtypes with distinct morphologies and clinical implications. Quantitative systems pharmacology (QSP) is an emerging discipline bridging systems biology with pharmacokinetics (PK) and pharmacodynamics (PD) leveraging the systematic understanding of drugs' efficacy and toxicity. Despite numerous challenges in applying computational methodologies for QSP and mechanism-based PK/PD models to biological, physiological, and pharmacological data, bridging these disciplines has the potential to enhance our understanding of complex disease systems such as BC. In QSP/PK/PD models, various sources of data are combined including large, multi-scale experimental data such as -omics (i.e. genomics, transcriptomics, proteomics, and metabolomics), biomarkers (circulating and bound), PK, and PD endpoints. This offers a means for a translational application from pre-clinical mathematical models to patients, bridging the bench to bedside paradigm. Not only can these models be applied to inform and advance BC drug development, but they also could aid in optimizing combination therapies and rational dosing regimens for BC patients. Here, we review the current literature pertaining to the application of QSP and pharmacometrics-based pharmacotherapy in BC including bottom-up and top-down modeling approaches. Bottom-up modeling approaches employ mechanistic signal transduction pathways to predict the behavior of a biological system. The ones that are addressed in this review include signal transduction and homeostatic feedback modeling approaches. Alternatively, top-down modeling techniques are bioinformatics reconstruction techniques that infer static connections between molecules that make up a biological network and include (1) Bayesian networks, (2) co-expression networks, and (3) module-based approaches. This review also addresses novel techniques which utilize the principles of systems biology, synthetic lethality and tumor priming, both of which are discussed in relationship to novel drug targets and existing BC therapies. By utilizing QSP approaches, clinicians may develop a platform for improved dose individualization for subpopulation of BC patients, strengthen rationale in treatment designs, and explore mechanism elucidation for improving future treatments in BC medicine.

Development of a mechanism-based pharmacokinetic/pharmacodynamic model to characterize the thermoregulatory effects of serotonergic drugs in mice

We have shown recently that concurrent harmaline, a monoamine oxidase-A inhibitor (MAOI), potentiates serotonin (5-HT) receptor agonist 5-methoxy-N,N-dimethyltryptamine (5-MeO-DMT)-induced hyperthermia. The objective of this study was to develop an integrated pharmacokinetic/pharmacodynamic (PK/PD) model to characterize and predict the thermoregulatory effects of such serotonergic drugs in mice. Physiological thermoregulation was described by a mechanism-based indirect-response model with adaptive feedback control. Harmaline-induced hypothermia and 5-MeO-DMT–elicited hyperthermia were attributable to the loss of heat through the activation of 5-HT_1A receptor and thermogenesis via the stimulation of 5-HT_2A receptor, respectively. Thus serotonergic 5-MeO-DMT–induced hyperthermia was readily distinguished from handling/injection stress-provoked hyperthermic effects. This PK/PD model was able to simultaneously describe all experimental data including the impact of drug-metabolizing enzyme status on 5-MeO-DMT and harmaline PK properties, and drug- and stress-induced simple hypo/hyperthermic and complex biphasic effects. Furthermore, the modeling results revealed a 4-fold decrease of apparent SC₅₀ value (1.88–0.496 µmol/L) for 5-MeO-DMT when harmaline was co-administered, providing a quantitative assessment for the impact of concurrent MAOI harmaline on 5-MeO-DMT–induced hyperthermia. In addition, the hyperpyrexia caused by toxic dose combinations of harmaline and 5-MeO-DMT were linked to the increased systemic exposure to harmaline rather than 5-MeO-DMT, although the body temperature profiles were mispredicted by the model. The results indicate that current PK/PD model may be used as a new conceptual framework to define the impact of serotonergic agents and stress factors on thermoregulation.

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.

Systems pharmacology - Towards the modeling of network interactions

Mechanism-based pharmacokinetic and pharmacodynamics (PKPD) and disease system (DS) models have been introduced in drug discovery and development research, to predict in a quantitative manner the effect of drug treatment in vivo in health and disease. This requires consideration of several fundamental properties of biological systems behavior including: hysteresis, non-linearity, variability, interdependency, convergence, resilience, and multi-stationarity. Classical physiology-based PKPD models consider linear transduction pathways, connecting processes on the causal path between drug administration and effect, as the basis of drug action. Depending on the drug and its biological target, such models may contain expressions to characterize i) the disposition and the target site distribution kinetics of the drug under investigation, ii) the kinetics of target binding and activation and iii) the kinetics of transduction. When connected to physiology-based DS models, PKPD models can characterize the effect on disease progression in a mechanistic manner. These models have been found useful to characterize hysteresis and non-linearity, yet they fail to explain the effects of the other fundamental properties of biological systems behavior. Recently systems pharmacology has been introduced as novel approach to predict in vivo drug effects, in which biological networks rather than single transduction pathways are considered as the basis of drug action and disease progression. These models contain expressions to characterize the functional interactions within a biological network. Such interactions are relevant when drugs act at multiple targets in the network or when homeostatic feedback mechanisms are operative. As a result systems pharmacology models are particularly useful to describe complex patterns of drug action (i.e. synergy, oscillatory behavior) and disease progression (i.e. episodic disorders). In this contribution it is shown how physiology-based PKPD and disease models can be extended to account for internal systems interactions. It is demonstrated how SP models can be used to predict the effects of multi-target interactions and of homeostatic feedback on the pharmacological response. In addition it is shown how DS models may be used to distinguish symptomatic from disease modifying effects and to predict the long term effects on disease progression, from short term biomarker responses. It is concluded that incorporation of expressions to describe the interactions in biological network analysis opens new avenues to the understanding of the effects of drug treatment on the fundamental aspects of biological systems behavior.

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.

PKPD modelling of the interrelationship between mean arterial BP, cardiac output and total peripheral resistance in conscious rats

BACKGROUND AND PURPOSE

The homeostatic control of arterial BP is well understood with changes in BP resulting from changes in cardiac output (CO) and/or total peripheral resistance (TPR). A mechanism-based and quantitative analysis of drug effects on this interrelationship could provide a basis for the prediction of drug effects on BP. Hence, we aimed to develop a mechanism-based pharmacokinetic-pharmacodynamic (PKPD) model in rats that could be used to characterize the effects of cardiovascular drugs with different mechanisms of action (MoA) on the interrelationship between BP, CO and TPR.

EXPERIMENTAL APPROACH

The cardiovascular effects of six drugs with diverse MoA, (amlodipine, fasudil, enalapril, propranolol, hydrochlorothiazide and prazosin) were characterized in spontaneously hypertensive rats. The rats were chronically instrumented with ascending aortic flow probes and/or aortic catheters/radiotransmitters for continuous recording of CO and/or BP. Data were analysed in conjunction with independent information on the time course of drug concentration using a mechanism-based PKPD modelling approach.

KEY RESULTS

By simultaneous analysis of the effects of six different compounds, the dynamics of the interrelationship between BP, CO and TPR were quantified. System-specific parameters could be distinguished from drug-specific parameters indicating that the model developed is drug-independent.

CONCLUSIONS AND IMPLICATIONS

A system-specific model characterizing the interrelationship between BP, CO and TPR was obtained, which can be used to quantify and predict the cardiovascular effects of a drug and to elucidate the MoA for novel compounds. Ultimately, the proposed PKPD model could be used to predict the effects of a particular drug on BP in humans based on preclinical data.

Saturable human neopterin response to interferon-α assessed by a pharmacokinetic-pharmacodynamic model

BACKGROUND

In this study, we developed a pharmacokinetic (PK)- pharmacodynamic (PD) model of a new sustained release formulation of interferon-α-2a (SR-IFN-α) using the blood concentration of IFN-α and neopterin in order to quantify the magnitude and saturation of neopterin production over time in healthy volunteers. The SR-IFN-α in this study is a solid microparticular formulation manufactured by spray drying of a feeding solution containing IFN-α, a biocompatible polymer (polyethylene glycol) and sodium hyaluronate.

METHODS

The full PK and PD (neopterin concentration) datasets from 24 healthy subjects obtained after single doses of 9, 18, 27 and 36 MIU of subcutaneous SR-IFN-α were used to build the mixed-effect model using NONMEM (version 7.2) with the GFORTRAN compiler.

RESULTS

A one-compartment model with first-order elimination and a mixture of zero- and first-order absorption was chosen to describe the PK of SR-IFN-α. The time-concentration profile of neopterin, the PD marker, was described by a turnover model combined with a single transit compartment. The saturable pattern of the neopterin response blurring the dose-response relationship of SR-IFN-α was addressed by introducing the concept of the EC50 increasing over time.

CONCLUSIONS

The PK-PD model of SR-IFN-α developed in this study has presented a quantitative tool to assess the time-course of a saturable neopterin response in 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).

Translation of drug effects from experimental models of neuropathic pain and analgesia to humans

Neuropathic pain research remains a challenging undertaking owing to: (i) the lack of understanding about the underlying disease processes; and (ii) poor predictive validity of the current models of evoked pain used for the screening of novel compounds. Common consensus is that experimental models replicate symptoms (i.e. have face validity but no construct validity). Another issue that requires attention is the sensitivity of endpoints to discriminate drug effects that are relevant to the disease in humans. In this paper we provide an overview of the pre-clinical models that can be used in conjunction with a model-based approach to facilitate the prediction of drug effects in humans. Our review strongly suggests that evidence of the concentration-effect relationship is necessary for translational purposes.

Quantitative analysis of rate and extent of tolerance of biomarkers: application to nicotinic acid-induced changes in non-esterified fatty acids in rats

In this paper we quantitatively evaluate two feedback systems with a focus on rate and extent of tolerance and rebound development. In the two feedback systems, the regulation of turnover of response is governed by one or several moderators. In the basic system, one single moderator inhibits the formation of response. This system has been applied to cortisol secretion and serotonin reuptake inhibition. The basic system has been extended to adequately describe nicotinic acid (NiAc)-induced changes in non-esterified fatty acids (NEFA). In the extended system, the feedback is described by a cascade of moderators where the first inhibits formation of response and the last stimulates loss of response. The objectives of this paper were to analyze these systems from a mathematical/analytical and quantitative point of view and to present simulations with different parameter settings and dosing regimens in order to highlight the intrinsic behaviour of these systems and to present expressions and graphs that are applicable for quantification of rate and extent of tolerance and rebound. The dynamics of the moderators (k(tol)) compared to the dynamics of the response (k(out)), was shown to be important for the behaviour of both systems. For instance, slow dynamics of the moderator compared to the response (k(tol)<<k(out)), resulted in overshoot and pronounced rebound. The extent of tolerance was studied over time at a single constant drug concentration and at steady state for different drug concentrations and was found to be largest at drug concentrations close to IC(50). An upper limit for the response could be identified and included in the quantification of extent of rebound. Especially, for the extended system, the duration of exposure was an important factor affecting size of rebound. The rate of tolerance development was addressed by quantitatively estimating the time to steady state for the two systems, in which the value of k(tol) and the length of the cascade were critical.

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 (M₁) 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, IC₅₀, 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.

Incorporating physiological and biochemical mechanisms into pharmacokinetic-pharmacodynamic models: a conceptual framework

The aim of this conceptual framework paper is to contribute to the further development of the modelling of effects of drugs or toxic agents by an approach which is based on the underlying physiology and pathology of the biological processes. In general, modelling of data has the purpose (1) to describe experimental data, (2a) to reduce the amount of data resulting from an experiment, e.g. a clinical trial and (2b) to obtain the most relevant parameters, (3) to test hypotheses and (4) to make predictions within the boundaries of experimental conditions, e.g. range of doses tested (interpolation) and out of the boundaries of the experimental conditions, e.g. to extrapolate from animal data to the situation in man. Describing the drug/xenobiotic-target interaction and the chain of biological events following the interaction is the first step to build a biologically based model. This is an approach to represent the underlying biological mechanisms in qualitative and also quantitative terms, thus being inherently connected in many aspects to systems biology. As the systems biology models may contain variables in the order of hundreds connected with differential equations, it is obvious that it is in most cases not possible to assign values to the variables resulting from experimental data. Reduction techniques may be used to create a manageable model which, however, captures the biologically meaningful events in qualitative and quantitative terms. Until now, some success has been obtained by applying empirical pharmacokinetic/pharmacodynamic models which describe direct and indirect relationships between the xenobiotic molecule and the effect, including tolerance. Some of the models may have physiological components built in the structure of the model and use parameter estimates from published data. In recent years, some progress toward semi-mechanistic models has been made, examples being chemotherapy-induced myelosuppression and glucose-endogenous insulin-antidiabetic drug interactions. We see a way forward by employing approaches to bridge the gap between systems biology and physiologically based kinetic and dynamic models. To be useful for decision making, the 'bridging' model should have a well founded mechanistic basis, but being reduced to the extent that its parameters can be deduced from experimental data, however capturing the biological/clinical essential details so that meaningful predictions and extrapolations can be made.

Model-based decision making in early clinical development: minimizing the impact of a blood pressure adverse event

We describe how modeling and simulation guided program decisions following a randomized placebo-controlled single-rising oral dose first-in-man trial of compound A where an undesired transient blood pressure (BP) elevation occurred in fasted healthy young adult males. We proposed a lumped-parameter pharmacokinetic-pharmacodynamic (PK/PD) model that captured important aspects of the BP homeostasis mechanism. Four conceptual units characterized the feedback PD model: a sinusoidal BP set point, an effect compartment, a linear effect model, and a system response. To explore approaches for minimizing the BP increase, we coupled the PD model to a modified PK model to guide oral controlled-release (CR) development. The proposed PK/PD model captured the central tendency of the observed data. The simulated BP response obtained with theoretical release rate profiles suggested some amelioration of the peak BP response with CR. This triggered subsequent CR formulation development; we used actual dissolution data from these candidate CR formulations in the PK/PD model to confirm a potential benefit in the peak BP response. Though this paradigm has yet to be tested in the clinic, our model-based approach provided a common rational framework to more fully utilize the limited available information for advancing the program.

A flexible nonlinear feedback system that captures diverse patterns of adaptation and rebound

An important approach to modeling tolerance and adaptation employs feedback mechanisms in which the response to the drug generates a counter-regulating action which affects the response. In this paper we analyze a family of nonlinear feedback models which has recently proved effective in modeling tolerance phenomena such as have been observed with SSRI's. We use dynamical systems methods to exhibit typical properties of the response-time course of these nonlinear models, such as overshoot and rebound, establish quantitive bounds and explore how these properties depend on the system and drug parameters. Our analysis is anchored in three specific in vivo data sets which involve different levels of pharmacokinetic complexity. Initial estimates for system (k(in), k(out), k(tol)) and drug (EC(50)/IC(50), E(max)/I(max), n) parameters are obtained on the basis of specific properties of the response-time course, identified in the context of exploratory (graphical) data analysis. Our analysis and the application of its results to the three concrete examples demonstrates the flexibility and potential of this family of feedback models.

A nonlinear feedback model capturing different patterns of tolerance and rebound

The objectives of the present analysis are to disect a class of turnover feedback models that have proven to be flexible from a mechanistic and empirical point of view, for the characterization of the onset, intensity and duration of response. Specifically, this class of models is designed so that it has the following properties: (I) Stimulation of the production term, which raises the steady state R(ss), causes an overshoot and a rebound upon return to baseline. (II) Stimulation of the loss term, which lowers the steady state R(ss), causes an overshoot which is negligible vis-a-vis the rebound upon the return to baseline. (III) Inhibition of the loss term, which raises the steady state R(ss), causes an overshoot which is larger than the rebound upon the return to the baseline. These models are then anchored in three datasets corresponding to the cases (I), (II) and (III). The objectives of this paper are to analyze the behavior of these turnover models from a mathematical/analytical point of view and to make simulations with different parameter settings and dosing regimens in order to highlight the intrinsic behavior of these models and draw some general conclusions. We also expand the analysis with two different extensions of the basic feedback model: one with a transduction step in the moderator and one which captures nonlinear phenomena (triggering mechanisms) caused by different drug input rates. A related objective is to come up with recommendations about experimental design and model building techniques in situations of feedback systems from a drug discovery point of view.

Allometric Scaling of Pharmacodynamic Responses: Application to 5-Ht1A Receptor Mediated Responses from Rat to Man

PURPOSE

The aim of the present study was to assess whether two widely used biomarkers for 5-HT(1A)-receptor mediated responses in the rat (hypothermia and corticosterone increase) could be scaled to man using allometric principles.

MATERIALS AND METHODS

Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) models were developed and characterized in rats for the standard 5-HT(1A)-receptor agonists, buspirone and flesinoxan. Allometric scaling was investigated on the basis of simulation taking into account the inter-individual variability and clinical study design. The model-predicted effects of both flesinoxan and buspirone were compared to those published in the literature.

RESULTS

The main finding of this analysis was that for both hypothermia and cortisol increase, the model could predict the extent of the pharmacological response in man adequately. For the hypothermic response, the time course of the response was also predicted with a high degree of accuracy. In contrast, in the case of the cortisol response, the observed time lag was, despite the fact that it fell within the model uncertainty, not predicted.

CONCLUSIONS

Based on these analyses, it is concluded that allometrically scaled mechanism based PK-PD models are promising as a means of predicting the pharmacodynamic responses in man. This approach provides for a novel way of interpreting and scaling pre-clinical pharmacological responses and ultimately facilitates the understanding and prediction of pharmacological responses in man.

Differential role of the 5-HT1A receptor in aggressive and non-aggressive mice: An across-strain comparison

Differential role of the 5-HT(1A) receptor in aggressive and non-aggressive mice: an across-strain comparison. PHYSIOL BEHAV 00(0) 000-000, 2006. According to the serotonin (5-HT)-deficiency hypothesis of aggression, highly aggressive individuals are characterized by low brain 5-HT neurotransmission. Key regulatory mechanisms acting on the serotonergic neuron involve the activation of the somatodendritic inhibitory 5-HT(1A) autoreceptor (short feedback loop) and/or the activation of postsynaptic 5-HT(1A) receptors expressed on neurons in cortico-limbic areas (long feedback loop). In this study, we examined whether low serotonin neurotransmission is associated with enhanced 5-HT(1A) (auto)receptor activity in highly aggressive animals. Male mice (SAL-LAL, TA-TNA, NC900-NC100) obtained through different artificial-selection breeding programs for aggression were observed in a resident-intruder test. The prefrontal cortex level of 5-HT and its metabolite 5-HIAA were determined by means of HPLC. The activity of the 5-HT(1A) receptors was assessed by means of the hypothermic response to the selective 5-HT(1A) agonists S-15535 (preferential autoreceptor agonist) and 8-OHDPAT (full pre- and postsynaptic receptor agonist). Highly aggressive mice had lower serotonin levels in the prefrontal cortex and two out of three aggressive strains had higher 5-HT(1A) (auto)receptor sensitivity. The results strengthen the validity of the serotonin-deficiency hypothesis of aggression and suggest that chronic exaggerated activity of the 5-HT(1A) receptor may be a causative link in the neural cascade of events leading to 5-HT hypofunction in aggressive individuals.

Mechanism-Based Pharmacokinetic-Pharmacodynamic Modeling: Biophase Distribution, Receptor Theory, and Dynamical Systems Analysis

Mechanism-based PK-PD models differ from conventional PK-PD models in that they contain specific expressions to characterize, in a quantitative manner, processes on the causal path between drug administration and effect. This includes target site distribution, target binding and activation, pharmacodynamic interactions, transduction, and homeostatic feedback mechanisms. As the final step, the effects on disease processes and disease progression are considered. Particularly through the incorporation of concepts from receptor theory and dynamical systems analysis, important progress has been made in the field of mechanism-based PK-PD modeling. This has yielded models with much-improved properties for extrapolation and prediction. These models constitute a theoretical basis for rational drug discovery and development.

Mechanistic model of acute autoinhibitory feedback action after administration of SSRIs in rats: Application to escitalopram-induced effects on brain serotonin levels

This study presents the development and evaluation of a feedback turnover model that mimics drug-induced effects on brain extracellular levels of serotonin (5-HT) after acute administration of the selective serotonin reuptake inhibitor (SSRI) escitalopram (S-citalopram) in rats. The extracellular 5-HT output in the hippocampus was continuously monitored by intracerebral microdialysis in conjunction with serial arterial blood sampling for evaluation of escitalopram pharmacokinetics. 5-HT levels were significantly increased following administration of 2.5, 5 and 10 mg/kg of escitalopram and the 5-HT levels gradually declined to its baseline value within 360 min. However, at 5 and 10 mg/kg, the response-time curves were almost identical. This might be explained by activation of serotonergic autoreceptors exerting negative feedback, leading to a reduced release of new 5-HT into the synapse. The dynamics of escitalopram-evoked changes of 5-HT response was characterized by a turnover model, which included an inhibitory feedback moderator component. Thus, the response acted linearly on the production of the moderator, which acted inversely on the production of response. The plasma kinetics served as input to an inhibitory function acting on the loss of response. Simultaneous fitting of the model after three constant rate infusions demonstrated the flexibility of the system. The efficacy (I(max)) and potency (IC(50)) of inhibition of reuptake were 0.9+/-0.03 and 4.4+/-1.4 ng/ml, respectively, corresponding to an EC(50) of escitalopram about 30 ng/ml. In conclusion, the model lends itself to 'what-if' predictions at different drug exposure scenarios, and has potential for extrapolation of the pharmacodynamics of SSRIs in man.

PKPD Model of Interleukin-21 Effects on Thermoregulation in Monkeys—Application and Evaluation of Stochastic Differential Equations

PURPOSE

To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling.

METHODS

A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM.

RESULTS

The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function.

CONCLUSIONS

The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

A dynamical systems analysis of the indirect response model with special emphasis on time to peak response

In this paper we present a mathematical analysis of the four classical indirect response models. We focus on characteristics such as the evolution of the response R(t) with time t, the time of maximal/minimal response T(max) and the area between the response and the baseline AUC(R), and the way these quantities depend on the drug dose, the dynamic parameters such as E(max) and EC50 and the ratio of the fractional turnover rate k(out) to the elimination rate constant k of drug in plasma. We find that depending on the model and on the drug mechanism function, T(max) may increase, decrease, decrease and then increase, or stay the same, as the drug dose is increased. This has important implications for using the shift in T(max) as a diagnostic tool in the selection of an appropriate model.

Pharmacokinetic-pharmacodynamic modelling: history and perspectives

A major goal in clinical pharmacology is the quantitative prediction of drug effects. The field of pharmacokinetic-pharmacodynamic (PK/PD) modelling has made many advances from the basic concept of the dose-response relationship to extended mechanism-based models. The purpose of this article is to review, from a historical perspective, the progression of the modelling of the concentration-response relationship from the first classic models developed in the mid-1960s to some of the more sophisticated current approaches. The emphasis is on general models describing key PD relationships, such as: simple models relating drug dose or concentration in plasma to effect, biophase distribution models and in particular effect compartment models, models for indirect mechanism of action that involve primarily the modulation of endogenous factors, models for cell trafficking and transduction systems. We show the evolution of tolerance and time-variant models, non- and semi-parametric models, and briefly discuss population PK/PD modelling, together with some example of more recent and complex pharmacodynamic models for control system and nonlinear HIV-1 dynamics. We also discuss some future possible directions for PK/PD modelling, report equations for general classes of novel semi-parametric models, as well as describing two new classes, additive or set-point, of regulatory, additive feedback models in their direct and indirect action variants.

A Pharmacodynamic Turnover Model Capturing Asymmetric Circadian Baselines of Body Temperature, Heart Rate and Blood Pressure in Rats: Challenges in Terms of Tolerance and Animal-handling Effects

This study presents development and behaviour of a feedback turnover model that mimics asymmetric circadian oscillations of body temperature, blood pressure and heart rate in rats. The study also includes an application to drug-induced hypothermia, tolerance and handling effects. Data were collected inn normotensive Sprague-Dawley rats, housed at 25 degrees C with a 12:12 hr light dark cycle (light on at 06:00 am) and with free access of food and water. The model consisted of two intertwined parallel compartments which captured a free-running rhythm with a period close to but not exactly 24 hrs. The free-running rhythm was synchronised to exactly 24 hrs by the environmental timekeeper (12:12 hr light on/off cycle) in experimental settings. The baseline model was fitted to a standardised 24-hr period derived from mean data of six animals over a period of nine consecutive days. The first-order rate constants related to the turnover of the baseline temperature, alpha and beta, were 0.026 min(-1) (+/-5%) and 0.0037 min(-1) (+/-3%). The alpha and beta parameters are approximately 2/transition time between day and night and 2/night time, respectively. The day:night timekeeper g(t), reference point T(ref) and amplitude were 0.053(+/-2%), 37.3(+/-0.02%) and 3.3% (+/-2%), respectively. Simulations with the baseline model revealed stable oscillations (free-running rhythm) in the absence of the timekeeper. This temperature-time profile was then symmetric and had a smaller amplitude, with a slightly shorter period and less pronounced temperature shift as compared to the profile in the presence of an external Timekeeper. Fitting the model to 96 hr mean profiles of blood pressure and heart rate from 10 control animals demonstrated the usefulness of the model. Simulations of the integrated temperature model succeeded in mimicking other modes of administration such as oral dosing.

A Mathematical Model for Paroxetine Antidepressant Effect Time Course and Its Interaction with Pindolol

Although selective 5-HT reuptake inhibitors (SSRIs) block monoamine uptake within hours of administration to patients, their full clinical effect does not appear until 2-4 weeks after treatment onset. Pindolol, a betablocker with weak partial 5-HT1A receptor agonist activity has been shown to produce a more rapid onset of antidepressant action of SSRIs. However, the optimal dosing schedule of pindolol remains controversial. Building on a set-point model described previously for the hypothermic effect of 5-HT agonists, we have developed a model based on the concept of homeostatic control mechanisms, in which SSRIs exert their antidepressant effect by increasing the transduction set-point of the postsynaptic 5-HT1A receptor, and pindolol exerts its effect by increasing the rate of feedback mechanisms. The predictive distribution of the proportion of responders at each day of measurement (based on population simulation from the model) was not significantly different from the proportions observed in two published clinical trials, one with fluoxetine, the other with paroxetine alone or combined with pindolol. The model was applied to the simulation of paroxetine response (clinical score) time course with or without pindolol, after administration of different doses of each drug. The simulated total scores on the MADR scale obtained after treatment with paroxetine alone (20 mg/day) or paroxetine (20 mg/day) with different doses of pindolol (1.5, 7.5 and 37.5 mg/day) support that the reason for inconstant pindolol efficacy is that the 7.5 mg dose is too low. The model might be useful as a basis for clinical trial simulation.

Disease System Analysis: Basic Disease Progression Models in Degenerative Disease

PURPOSE

To describe the disease status of degenerative diseases (i.e., type 2 diabetes mellitus, Parkinson's disease) as function of disease process and treatment effects, a family of disease progression models is introduced.

METHODS

Disease progression is described using a progression rate (Rdp) acting on the synthesis or elimination parameters of the indirect response model. Symptomatic effects act as disease-dependent or -independent effects on the synthesis or elimination parameters. Protective drug effects act as disease dependent or -independent effects on Rdp.

RESULTS

Simulations with the ten disease models show distinctly different signature profiles of treatment effects on disease status. Symptomatic effects result in improvement of disease status with a subsequent deterioration. Treatment cessation results in a disease status equal to the situation where treatment had not been applied. Protective effects result in a lasting reduction, or even reversal, of the disease progression rate and the resulting disease status during the treatment period. After cessation of treatment the natural disease course will continue from the disease status at that point.

CONCLUSION

Disease system analysis constitutes a scientific basis for the distinction between symptomatic versus protective drug effects in relation to specific disease processes as well as the identification of the exposure-response relationship during the time-course of disease.

Mechanism-Based Pharmacokinetic-Pharmacodynamic Modeling of 5-HT1AReceptor Agonists: Estimation of in Vivo Affinity and Intrinsic Efficacy on Body Temperature in Rats

The pharmacokinetic-pharmacodynamic (PK-PD) correlations of seven prototypical 5-HT(1A) agonists were analyzed on the basis of a recently proposed semi-mechanistic PK-PD model for the effect on body temperature. The resulting concentration-effect relationships were subsequently analyzed on the basis of the operational model of agonism to estimate the operational affinity (pK(A)) and efficacy (log tau) at the 5-HT(1A) receptor in vivo. The values obtained in this manner were compared with estimates of the affinity (pK(i)) and intrinsic efficacy (log[agonist ratio]) in a receptor-binding assay. Between 5-HT(1A) agonists wide differences in in vivo affinity and efficacy were observed, with values of the pK(A) ranging from 5.67 for flesinoxan to 8.63 for WAY-100,635 [N-(2-(4-(2-methoxyphenyl)-1-piperazinyl)ethyl)-N-2-pyridinyl-cyclohexanecarboxamide] and of the log tau ranging from -1.27 for WAY-100,135 [N-(1,1-dimethylethyl)-4-(2-methoxyphenyl)-alpha-phenyl-1-piperazine-propanamide] to 0.62 for R-(+)-8-hydroxy-2-[di-n-propylamino)tetralin. Poor correlations were observed between the in vivo receptor affinity (pK(A)) and the affinity estimates in the in vitro receptor binding assay (pK(i); r(2) = 0.55, P > 0.05), which could in part be explained by differences in blood-brain distribution. In contrast, a highly significant correlation was observed between the efficacy parameters in vivo (log tau) and in vitro (log [agonist ratio]; r(2) = 0.76, P < 0.05). Thus by combining the previously proposed semi-mechanistic PK-PD model for the effect on body temperature with the operational model of agonism, a full mechanistic PK-PD model for 5-HT(1A) receptor agonists has been obtained, which is highly predictive of the in vivo intrinsic efficacy.

Diversity of mechanism-based pharmacodynamic models

Pharmacodynamics is the study of the time course of pharmacological effects of drugs. The field of pharmacodynamic modeling has made many advances, due in part to the relatively recent development of basic and extended mechanism-based models. The purpose of this article is to describe the classic as well as contemporary approaches, with an emphasis on pertinent equations and salient model features. In addition, current methods of integrating various system complexities into these models are discussed. Future pharmacodynamic models will most likely reflect an assembly of the basic components outlined in this review.

Ambient temperature influences core body temperature response in rat lines bred for differences in sensitivity to 8-hydroxy-dipropylaminotetralin

Agonist-induced decrease in core body temperature has commonly been used as a measure of serotonin1A (5-HT(1A)) receptor sensitivity in mood disorder. The thermoregulatory basis for 5-HT(1A) receptor agonist-induced temperature responses in humans and rats remains unclear. Therefore, the influence of ambient temperature on 5-HT(1A) receptor-mediated decreases in core body temperature were measured in rat lines bred for high (HDS) or low (LDS) sensitivity to the selective 5-HT(1A) receptor agonist 8-hydroxy-dipropylaminotetralin (8-OH-DPAT). HDS and LDS rats were injected with either saline, 0.25 or 0.50 mg/kg 8-OH-DPAT at ambient temperatures of 10.5, 24, 30, or 37.5 degrees C, and core temperature was measured by radiotelemetry. For both lines, the thermic response to acute 8-OH-DPAT was greatest at 10.5 degrees C and decreased in magnitude as ambient temperature increased to 30 degrees C, consistent with hypothermia. HDS rats displayed a greater hypothermic response than LDS rats at 10.5, 24, and 30 degrees C. At 37.5 degrees C, LDS rats showed a lethal elevation of temperature in response to 0.50 mg/kg 8-OH-DPAT. All thermic responses to 8-OH-DPAT, including the lethality, were effectively blocked by pretreatment with the 5-HT(1A) receptor antagonist WAY100635, suggesting line differences in thermoregulatory circuits that are influenced by 5-HT(1A) receptor activation. Following repeated injection of 8-OH-DPAT, the magnitude of the hypothermic response decreased in both lines at 10.5 degrees C, but increased in HDS rats treated with 0.50 mg/kg 8-OH-DPAT at 30 and 37.5 degrees C. This pattern was reversed in HDS rats following 8-OH-DPAT challenge at 24 degrees C, suggesting that a compensatory thermoregulatory response accounts for changes in the hypothermic response to chronic 8-OH-DPAT.

Mechanism-based pharmacokinetic/pharmacodynamic modeling of the electroencephalogram effects of GABAA receptor modulators: in vitro-in vivo correlations

A mechanism-based pharmacokinetic-pharmacodynamic (PK/PD) model for neuroactive steroids, comprising a separate characterization of 1) the receptor activation process and 2) the stimulus-response relationship, was applied to various nonsteroidal GABAA receptor modulators. The EEG effects of nine prototypical GABAA receptor modulators (six benzodiazepines, one imidazopyridine, one cyclopyrrolone, and one beta-carboline) were determined in rats in conjunction with plasma concentrations. Population PK/PD modeling revealed monophasic concentration-EEG effect relationships with large differences in potency (EC50) and intrinsic activity between the compounds. The data were analyzed on the basis of the mechanism-based PK/PD model for (synthetic) neuroactive steroids on the assumption of a single and unique stimulus-response relationship. The model converged yielding estimates of both the apparent in vivo receptor affinity (KPD) and the in vivo intrinsic efficacy (ePD). The values of KPD ranged from 0.41 +/- 0 ng.ml(-1) for bretazenil to 436 +/- 72 ng.ml(-1) for clobazam and the values for e(PD) from -0.27 +/- 0 for methyl 6,7-dimethoxy-4-ethyl-beta-carboline-3-carboxylate to 0.54 +/- 0.02 for diazepam. Significant linear correlations were observed between KPD for unbound concentrations and the affinity in an in vitro receptor bioassay (r = 0.93) and between e(PD) and the GABA-shift in vitro (r = 0.95). The findings of this investigation show that the in vivo effects of nonsteroidal GABAA receptor modulators and (synthetic) neuroactive steroids can be described on the basis of a single unique transducer function. In this paradigm, the nonsteroidal GABAA receptor modulators behave as partial agonists relative to neuroactive steroids.

Pharmacokinetic-pharmacodynamic modeling of buspirone and its metabolite 1-(2-pyrimidinyl)-piperazine in rats

The objective of this investigation was to compare the in vivo potency and intrinsic activity of buspirone and its metabolite 1-(2-pyrimidinyl)-piperazine (1-PP) in rats by pharmacokinetic-pharmacodynamic modeling. Following intravenous administration of buspirone (5 or 15 mg/kg in 15 min) or 1-PP (10 mg/kg in 15 min), the time course of the concentrations in blood were determined in conjunction with the effect on body temperature. The pharmacokinetics of buspirone and 1-PP were analyzed based on a two-compartment model with metabolite formation. Differences in the pharmacokinetics of buspirone and 1-PP were observed with values for clearance of 13.1 and 8.2 ml/min and for terminal elimination half-life of 25 and 79 min, respectively. At least 26% of the administered dose of buspirone was converted into 1-PP. Complex hypothermic effects versus time profiles were observed, which were successfully analyzed on the basis of a physiological indirect response model with set-point control. Both buspirone and 1-PP behaved as partial agonists relative to R-(+)-8-hydroxy-2-(di-n-propylamino)tetralin (R-8-OH-DPAT) with values of the intrinsic activity of 0.465 and 0.312, respectively. Differences in the potency were observed with values of 17.6 and 304 ng/ml for buspirone and 1-PP, respectively. The results of this analysis show that buspirone and 1-PP behave as partial 5-hydroxytryptamine(1A) agonists in vivo and that following intravenous administration the amount of 1-PP formed is too small to contribute to the hypothermic effect.

Neuroactive steroids differ in potency but not in intrinsic efficacy at the GABA(A) receptor in vivo

The objective of the present investigation was to characterize the in vivo EEG effects of (synthetic) neuroactive steroids on the basis of a recently proposed mechanism-based pharmacokinetic/pharmacodynamic (PK/PD) model. After intravenous administration, the time course of the EEG effect of pregnanolone, 2beta-3alpha-5alpha-3-hydroxy-2-(2,2-dimethylmorpholin-4-yl)-pregnan-11,20-dione (ORG 21465), 2beta-3alpha-5alpha-21-chloro-3-hydroxy-2-(4-morpholinyl)-pregnan-20-one (ORG 20599), and alphaxalone was determined in conjunction with plasma concentrations in rats. For each neuroactive steroid the PK/PD correlation was described on the basis of a two-compartment pharmacokinetic model with an effect compartment to account for hysteresis. The observed concentration EEG effect relationships were biphasic and characterized with a mechanism-based pharmacodynamic model, which is based on a separation between the receptor activation process and the stimulus-response relationship. A single unique biphasic stimulus-response relationship could be identified for all neuroactive steroids, which was successfully described by a parabolic function. The receptor activation process was described by a hyperbolic function. Estimates for the maximum activation (e(PD)) were similar for the different neuroactive steroids but values of the potency estimate (K(PD)) ranged from 157 +/- 16 ng. ml(-1) for pregnanolone, 221 +/- 83 ng. ml(-1) for ORG 20599, and 483 +/- 42 ng. ml(-1) for alphaxalone to 1619 +/- 208 ng. ml(-1) for ORG 21465. A statistically significant correlation was observed between the in vivo potency and the IC(50) in an in vitro [(35)S]t-butylbicyclophosphorothionate binding assay (r = 0.91). It is concluded that the new PK/PD model constitutes a new mechanism-based approach to the quantification of the effects of (synthetic) neuroactive steroids in vivo effects. The results show that the neuroactive steroids differ in potency but not in intrinsic efficacy at the GABA(A) receptor in vivo.

Mechanism-based pharmacokinetic-pharmacodynamic modeling of concentration-dependent hysteresis and biphasic electroencephalogram effects of alphaxalone in rats

The neuroactive steroid alphaxalone reveals a complex biphasic concentration-effect relationship using the 11.5 to 30 Hz frequency band of the electroencephalogram (EEG) as biomarker. The purpose of the present investigation was to develop a mechanism-based pharmacokinetic-pharmacodynamic model to describe this observation. The proposed model is based on receptor theory and aims to separate the drug-receptor interaction from the transduction of the initial stimulus into the observed biphasic response. Individual concentration-time courses of alphaxalone were obtained in combination with continuous recording of the EEG parameter. Alphaxalone was administered intravenously in various dosages. The pharmacokinetics were described by a two-compartment model, and parameter estimates for clearance, intercompartmental clearance, volume of distribution 1 and 2 were 158 +/- 29 ml. min(-1). kg(-1), 143 +/- 31 ml. min(-1). kg(-1), 122 +/- 20 ml. kg(-1) and 606 +/- 48 ml. kg(-1), respectively. Concentration-effect relationships exhibited a biphasic pattern and delay in onset of effect. The hysteresis was described on the basis of an effect-compartment model with C(max) as covariate. The pharmacodynamic model consisted of a receptor model, featuring a monophasic saturable receptor activation model in combination with a biphasic stimulus-response model. The in vivo affinity (K(PD)) was estimated at 432 +/- 26 ng. ml(-1). Unique parameter estimates were obtained that were independent of the dose and the duration of the infusion. In conclusion, we have shown that this mechanism-based approach, which separates drug- and system-related properties in vivo, was successfully applied for the characterization of the biphasic effect versus time patterns of alphaxalone. The model should be of use in the characterization of other biphasic responses.