The relationship between receptor-effector unit heterogeneity and the shape of the concentration-effect profile: pharmacodynamic implications

Evolution of optimal Hill coefficients in nonlinear public goods games

In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.

Dose-response curve slope helps predict therapeutic potency and breadth of HIV broadly neutralizing antibodies

A new generation of HIV broadly neutralizing antibodies (bnAbs) with remarkable potency, breadth and epitope diversity has rejuvenated interest in immunotherapeutic strategies. Potencies defined by in vitro IC₅₀ and IC₈₀ values (50 and 80% inhibitory concentrations) figure prominently into the selection of clinical candidates; however, much higher therapeutic levels will be required to reduce multiple logs of virus and impede escape. Here we predict bnAb potency at therapeutic levels by analysing dose–response curve slopes, and show that slope is independent of IC₅₀/IC₈₀ and specifically relates to bnAb epitope class. With few exceptions, CD4-binding site and V3-glycan bnAbs exhibit slopes >1, indicative of higher expected therapeutic effectiveness, whereas V2-glycan, gp41 membrane-proximal external region (MPER) and gp120–gp41 bnAbs exhibit less favourable slopes <1. Our results indicate that slope is one major predictor of both potency and breadth for bnAbs at clinically relevant concentrations, and may better coordinate the relationship between bnAb epitope structure and therapeutic expectations.

Potencies of HIV broadly neutralizing antibodies are usually defined by their in vitro IC₅₀ and IC₈₀ values, but much higher levels will be required for successful immunotherapies. Here, Webb et al. predict antibody potency at therapeutic levels by analyzing dose–response curve slopes, which correlate with epitope class.

Neutralization of Virus Infectivity by Antibodies: Old Problems in New Perspectives

Neutralizing antibodies (NAbs) can be both sufficient and necessary for protection against viral infections, although they sometimes act in concert with cellular immunity. Successful vaccines against viruses induce NAbs but vaccine candidates against some major viral pathogens, including HIV-1, have failed to induce potent and effective such responses. Theories of how antibodies neutralize virus infectivity have been formulated and experimentally tested since the 1930s; and controversies about the mechanistic and quantitative bases for neutralization have continually arisen. Soluble versions of native oligomeric viral proteins that mimic the functional targets of neutralizing antibodies now allow the measurement of the relevant affinities of NAbs. Thereby the neutralizing occupancies on virions can be estimated and related to the potency of the NAbs. Furthermore, the kinetics and stoichiometry of NAb binding can be compared with neutralizing efficacy. Recently, the fundamental discovery that the intracellular factor TRIM21 determines the degree of neutralization of adenovirus has provided new mechanistic and quantitative insights. Since TRIM21 resides in the cytoplasm, it would not affect the neutralization of enveloped viruses, but its range of activity against naked viruses will be important to uncover. These developments bring together the old problems of virus neutralization-mechanism, stoichiometry, kinetics, and efficacy-from surprising new angles.

Input-output relations in biological systems: measurement, information and the Hill equation

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system’s overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.

Reviewers

This article was reviewed by Eugene Koonin, Georg Luebeck and Sergei Maslov.

A model for educational simulation of the effect of oxytocin on uterine contractions

Fetal oxygenation is sometimes compromised due to hyperstimulation of uterine contractions (UC) following labor augmentation with oxytocin. We present a model for educational simulation that incorporates the pharmacokinetic-pharmacodynamic properties of oxytocin, reproducing the effect of this drug on UC features. Six UC tracings were generated, reflecting different relevant situations. Three independent experts identified correctly the simulated situations in all tracings and attributed an average realism score of 9.4 (0-10). The model presented for simulation of the effect of oxytocin on UC provides sufficiently realistic results to be used in healthcare education and can easily be adapted to different patients and educational scenarios.

A critical subset model provides a conceptual basis for the high antiviral activity of major HIV drugs

Control of HIV-1 replication was first achieved with regimens that included a nonnucleoside reverse transcriptase inhibitor (NNRTI) or a protease inhibitor (PI); however, an explanation for the high antiviral activity of these drugs has been lacking. Indeed, conventional pharmacodynamic measures like IC(50) (drug concentration causing 50% inhibition) do not differentiate NNRTIs and PIs from less active nucleoside reverse transcriptase inhibitors (NRTIs). Drug inhibitory potential depends on the slope of the dose-response curve (m), which represents how inhibition increases as a function of increasing drug concentration and is related to the Hill coefficient, a measure of intramolecular cooperativity in ligand binding to a multivalent receptor. Although NNRTIs and PIs bind univalent targets, they unexpectedly exhibit cooperative dose-response curves (m > 1). We show that this cooperative inhibition can be explained by a model in which infectivity requires participation of multiple copies of a drug target in an individual life cycle stage. A critical subset of these target molecules must be in the unbound state. Consistent with experimental observations, this model predicts m > 1 for NNRTIs and PIs and m = 1 in situations where a single drug target/virus mediates a step in the life cycle, as is the case with NRTIs and integrase strand transfer inhibitors. This model was tested experimentally by modulating the number of functional drug targets per virus, and dose-response curves for modulated virus populations fit model predictions. This model explains the high antiviral activity of two drug classes important for successful HIV-1 treatment and defines a characteristic of good targets for antiviral drugs in general, namely, intermolecular cooperativity.

Env-glycoprotein heterogeneity as a source of apparent synergy and enhanced cooperativity in inhibition of HIV-1 infection by neutralizing antibodies and entry inhibitors

We measured the inhibition of infectivity of HIV-1 isolates and derivative clones by combinations of neutralizing antibodies (NAbs) and other entry inhibitors in a single-cycle-replication assay. Synergy was analyzed both by the current linear and a new non-linear method. The new method reduced spurious indications of synergy and antagonism. Synergy between NAbs was overall weaker than between other entry inhibitors, and no stronger where one ligand is known to enhance the binding of another. However, synergy was stronger for a genetically heterogeneous HIV-1 R5 isolate than for its derivative clones. Enhanced cooperativity in inhibition by combinations, compared with individual inhibitors, correlated with increased synergy at higher levels of inhibition, while being less variable. Again, cooperativity enhancement was stronger for isolates than clones. We hypothesize that genetic, post-translational or conformational heterogeneity of the Env protein and of other targets for inhibitors can yield apparent synergy and increased cooperativity between inhibitors.

Integrated model for denosumab and ibandronate pharmacodynamics in postmenopausal women

This study aims to characterize the pharmacodynamic properties of denosumab, a RANK ligand inhibitor, and ibandronate, a bisphosphonate, using an integrated bone homeostasis model in postmenopausal women. Mean temporal profiles of denosumab, serum and urine N-telopeptide (sNTX, uNTX), lumbar spine bone mineral density (BMD) following denosumab administration, and urine C-telopeptide (uCTX) and lumbar spine BMD upon ibandronate administration were extracted from the literature. A mechanistic model was developed that integrates denosumab pharmacokinetics with binding to RANK ligand and ibandronate inhibition of osteoclast precursor differentiation to active osteoclasts (AOC). Biomarker concentrations were linked to the AOC pool. The BMD was characterized by a turnover model with stimulation of bone formation and degradation by AOB (active osteoblasts) and AOC pools. The estimated basal sNTX, uNTX and uCTX concentrations were 7.24 nm, 14.4 nmol/mmolCr and 31µg/mmolCr. The BMD degradation rate was 0.00161 day(-1) with stimulation constants associated with AOB and AOC of 1214 and 790 pm(-1) . The plasma ibandronate concentration producing 50% of maximum inhibition of osteoclast differentiation was 522 ng/l. The integrated model, which incorporates multiple pathways of therapeutic intervention, quantitatively describes changes in clinical biomarkers of bone turnover and BMD after denosumab and ibandronate exposures in postmenopausal women.

Dose-response curve slope sets class-specific limits on inhibitory potential of anti-HIV drugs

Highly active antiretroviral therapy (HAART) can control HIV-1 replication, but suboptimal treatment allows for the evolution of resistance and rebound viremia. A comparative measure of antiviral activity under clinically relevant conditions would guide drug development and the selection of regimens that maximally suppress replication. Here we show that current measures of antiviral activity, including IC(50) and inhibitory quotient, neglect a key dimension, the dose-response curve slope. Using infectivity assays with wide dynamic range, we show that this slope has noteworthy effects on antiviral activity. Slope values are class specific for antiviral drugs and define intrinsic limitations on antiviral activity for some classes. Nucleoside reverse transcriptase inhibitors and integrase inhibitors have slopes of approximately 1, characteristic of noncooperative reactions, whereas non-nucleoside reverse transcriptase inhibitors, protease inhibitors and fusion inhibitors unexpectedly show slopes >1. Instantaneous inhibitory potential (IIP), the log reduction in single-round infectivity at clinical drug concentrations, is strongly influenced by slope and varies by >8 logs for anti-HIV drugs. IIP provides a more accurate measure of antiviral activity and in general correlates with clinical outcomes. Only agents with slopes >1 achieve high-level inhibition of single-round infectivity, a finding with profound implications for drug and vaccine development.

Clinical trial simulation in drug development

The simulation of therapeutic models and clinical trial simulation have recently attracted attention as emerging techniques for developing new active molecules and the exploration of possible clinical trial results. Such approaches have benefited from fundamental progress in the development of 'in silico' models, as well as progress in nonlinear mixed-effect pharmacokinetic-pharmacodynamic models. Mixing the two approaches allows simulation of 'virtual' patients, who receive virtual treatments or placebo. These have various uses, such as proof of concept, decision analysis or experimental design optimisation. Also, the effect of departures from protocol on clinical trial results can easily be evaluated by the use of simulation. This technique is now implemented by the pharmaceutical industry for optimising phase II and III experimental designs when a good biomarker or a clinical outcome model is available, but the use of an in silico therapeutic model as a proof of concept is only just beginning. In order to see such methodologies used more widely in drug development, multidisciplinary efforts need to be initiated, new modelling and simulation tools developed, and sound modelling and simulation practice documents need to be adopted. A reduction in the number of failed clinical development projects, the number of negative phase II and III clinical trials, or in just their cost and duration, are among the expected benefits of modelling and simulation in clinical drug development.

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.

Power spectral analysis of heart rate variability in rats as a quantitative tool in the PK-PD analysis of the parasympatholytic activity of atropine

PURPOSE

To utilize power spectral analysis (PSA) of heart rate variability (HRV) as a pharmacodynamic (PD) measure of atropine parasympathetic effect, and to model the kinetics of action.

METHODS

Heart rate data was collected following atropine administration to rats and was analyzed off-line for high frequency peaks by PSA of HRV as a measure of parasympathetic tone. A temporal cumulative approach (TCA) detected transient changes in parasympathetic activity. The pharmacokinetics (PK) was analyzed and linked to both direct and indirect PK-PD models.

RESULTS

TCA enabled a quantitative measure of atropine parasympathetic activity. A simultaneous fit of the indirect PK-PD model to the experimental data of all three atropine doses successfully captured the experimental data.

CONCLUSIONS

TCA can be used as a quantitative measure of parasympathetic tone. Our work has established a preclinical model to investigate the kinetics of drug action on the autonomic nervous system.

Pharmacodynamic aspects of sustained release preparations

The sustained release (SR) mode of drug administration has certain features that have an important impact on the magnitude of the pharmacologic response: (a) it minimizes fluctuation in blood drug concentrations (i.e. between peak and trough). However, due to the pronounced non-linear relationship between drug concentration and pharmacologic effect (i.e. pharmacodynamics) the impact of this property differs considerably as a function of the shape of the pharmacodynamic profile and the position of the specific range of concentrations on the curve of this profile; (b) it produces a slow input rate which tends to minimize the body's counteraction to the drug's intervening effect on regulated physiological processes; and (c) it provides a continuous mode of drug administration. This important pharmacodynamic characteristic may produce, in certain cases, an opposite clinical effect than that attained by an intermittent (pulsatile) mode of administration of the same drug. For many drugs with non-concentration-dependent pharmacodynamics, the exposure time, rather than the AUC, is the relevant parameter and it can therefore be optimized by SR preparations. The slow input function may minimize hysteresis in cases where the site of action is not in a rapid equilibrium with the blood circulation. The pharmacodynamics of the desired effect(s) and/or adverse effect(s) may also be influenced by the site of administration, especially in cases where the drug is delivered directly to its site of action. These factors demonstrate the important influence of the mode of administration on the pharmacological and clinical outcomes. In addition, they highlight the need to include these pharmacodynamic considerations in all stages from drug development to the optimization of their clinical use.

Pharmacodynamic and pharmacokinetic rationales for the development of an oral controlled-release amoxicillin dosage form

The goal of this investigation was to develop an oral sustained-release formulation for amoxicillin that would maximize the duration of active drug concentration in the extracellular fluid, thus increasing the dosing interval while assuring antimicrobial activity. This rationale is based on the pharmacodynamic properties of the drug which is non- concentration dependent on the one hand, while requiring long exposure of the pathogen to the drug with minimal post-antibiotic effect on the other. Due to pharmacokinetic constraints, including short biological half-life and limited 'absorption window' (confined to the small intestine) with poor colonic absorption, the new matrix tablet formulation, composed of hydrophilic (hydroxypropyl methyl-cellulose) polymer, was designed to release 50% of its contents within the first 3 h and to complete the drug release process over 8 h (under in vitro conditions). The pharmacokinetics of the new formulation was evaluated in 12 healthy volunteers and compared to a conventional gelatin capsule with both formulations containing 500 mg amoxicillin. The plasma concentrations of active amoxicillin and penicilloic acid were determined by an HPLC method with a fluorometric detector. It was found that the area under the concentration-time curve and maximal serum amoxicillin concentrations following the sustained release preparation were lower than the immediate release formulation. However, the time over the required threshold concentrations, i.e. the minimal inhibitory concentration (MIC) as well as the more clinically relevant parameter--four times MIC of the drug against susceptible pathogens, was found to be maintained for significantly longer periods. The results suggest that in order to achieve a twice daily dosing regimen that will provide therapeutic concentrations for the whole 12 h dosing intervals, a larger dose of the new formulation should be given (e.g. 750 mg or even 1 g twice daily). This recommendation is based on the large interindividual differences of the extent of amoxicillin absorption found in this investigation, and is intended to assure that the 'poor' absorbers will also benefit from full antibiotic efficacy. This dosing regimen will lead to increased patient compliance and improved therapeutic outcome.

Characterization of a selective antagonist of neuropeptide Y at the Y2 receptor. Synthesis and pharmacological evaluation of a Y2 antagonist

Neuropeptide Y (NPY) is a potent inhibitor of neurotransmitter release through the Y2 receptor subtype. Specific antagonists for the Y2 receptors have not yet been described. Based on the concept of template-assembled synthetic proteins we have used a cyclic template molecule containing two beta-turn mimetics for covalent attachment of four COOH-terminal fragments RQRYNH2 (NPY 33-36), termed T4-[NPY(33-36)]4. This structurally defined template-assembled synthetic protein has been tested for binding using SK-N-MC and LN319 cell lines that express the Y1 and Y2 receptor, respectively. T4-[NPY(33-36)]4 binds to the Y2 receptor with high affinity (IC50 = 67.2 nM) and has poor binding to the Y1 receptor. This peptidomimetic tested on LN319 cells at concentrations up to 10 microM shows no inhibitory effect on forskolin-stimulated cAMP levels (IC50 for NPY = 2.5 nM). Furthermore, we used confocal microscopy to examine the NPY-induced increase in intracellular calcium in single LN319 cells. Preincubation of the cells with T4-[NPY(33-36)]4 shifted to the right the dose-response curves for intracellular mobilization of calcium induced by NPY at concentrations ranging from 0.1 nM to 10 microM. Finally, we assessed the competitive antagonistic properties of T4-[NPY(33-36)]4 at presynaptic peptidergic Y2 receptors modulating noradrenaline release. the compound T4-[NPY(33-36)]4 caused a marked shift to the right of the concentration-response curve of NPY 13-36, a Y2-selective fragment, yielding a pA2 value of 8.48. Thus, to our best knowledge, T4-[NPY(33-36)]4 represents the first potent and selective Y2 antagonist.