Indirect pharmacodynamic models for responses with circadian removal

Early erythroferrone levels can predict the long-term haemoglobin responses to erythropoiesis-stimulating agents

BACKGROUND AND PURPOSE

Our previous study reported that erythroferrone (ERFE), a newly identified hormone produced by erythroblasts, responded to recombinant human erythropoietin (rHuEPO) sensitively but its dynamics was complicated by double peaks and circadian rhythm. This study intends to elucidate the underlying mechanisms for the double peaks of ERFE dynamics and further determine whether early ERFE measurements can predict haemoglobin responses to rHuEPO.

EXPERIMENTAL APPROACH

By using the purified recombinant rat ERFE protein and investigating its deposition in rats, the production of ERFE was deconvoluted. To explore the role of iron in ERFE production, we monitored short-term changes of iron status after injection of rHuEPO or deferiprone. Pharmacokinetic/pharmacodynamic (PK/PD) modelling was used to confirm the mechanisms and examine the predictive ability of ERFE for long-term haemoglobin responses.

KEY RESULTS

The rRatERFE protein was successfully purified. The production of ERFE was deconvoluted and showed two independent peaks (2 and 8 h). Transient iron decrease was observed at 4 h after rHuEPO injection and deferiprone induced significant increases of ERFE. Based on this mechanism, the PK/PD model could characterize the complex dynamics of ERFE. In addition, the model predictions further revealed a stronger correlation between ERFE and haemoglobin peak values than that for observed values.

CONCLUSIONS AND IMPLICATIONS

The complex dynamics of ERFE should be composited by an immediate release and transient iron deficiency-mediated secondary production of ERFE. The early peak values of ERFE, which occur within a few hours, can predict haemoglobin responses several weeks after ESA treatment.

The Physiological and Pharmacological Significance of the Circadian Timing of the HPA Axis: A Mathematical Modeling Approach

As a potent endogenous regulator of homeostasis, the circadian time-keeping system synchronizes internal physiology to periodic changes in the external environment to enhance survival. Adapting endogenous rhythms to the external time is accomplished hierarchically with the central pacemaker located in the suprachiasmatic nucleus (SCN) signaling the hypothalamus-pituitary-adrenal (HPA) axis to release hormones, notably cortisol, which help maintain the body's circadian rhythm. Given the essential role of HPA-releasing hormones in regulating physiological functions, including immune response, cell cycle, and energy metabolism, their daily variation is critical for the proper function of the circadian timing system. In this review, we focus on cortisol and key fundamental properties of the HPA axis and highlight their importance in controlling circadian dynamics. We demonstrate how systems-driven, mathematical modeling of the HPA axis complements experimental findings, enhances our understanding of complex physiological systems, helps predict potential mechanisms of action, and elucidates the consequences of circadian disruption. Finally, we outline the implications of circadian regulation in the context of personalized chronotherapy. Focusing on the chrono-pharmacology of synthetic glucocorticoids, we review the challenges and opportunities associated with moving toward personalized therapies that capitalize on circadian rhythms.

Pharmacodynamic Models of Indirect Effects and Irreversible Inactivation with Turnover: Applicability to Mechanism-Based Modeling of Gene Silencing and Targeted Protein Degradation

Indirect response (IDR) and turnover with inactivation (TI) comprise two arrays of mechanism-based pharmacodynamic (PD) models widely used to describe delayed drug effects. IDR Model-IV (stimulation of response loss) and TI (irreversible loss) have been described with discerning "signature" profiles; classical IDR-IV response-time profiles display slow declines where peak response shifts later with increasing dose, whereas TI profiles feature steep response declines with earlier-shifting nadirs. Herein, we demonstrate mathematical convergence of IDR-IV and TI models upon implementation with identical linear versus nonlinear pharmacologic effect terms. Time of peak response in IDR-IV can in fact shift earlier or later depending on PK or PD parameters (e.g., kel, Smax) and effect type. A generalized dynamic model linking mRNA and protein turnover is proposed. Applicability of IDR-IV and TI, with either linear or nonlinear terms acting on degradation/catabolism/loss of response, is demonstrated through model-fitting PK-PD effects of three proteolysis-targeting chimeras (PROTACs) and two ligand-conjugated small interfering RNAs (siRNA). This work clarifies mathematical properties, convergence, and expected responses of IDR-IV and TI, demonstrates their applicability for targeted gene-silencing and protein-degrading agents, and illustrates how well-designed in vivo studies covering broad dose ranges with richly sampled time-points can influence PK-PD model structure and parameter resolution.

Dosing time optimization of antihypertensive medications by including the circadian rhythm in pharmacokinetic-pharmacodynamic models

Blood pressure (BP) follows a circadian variation, increasing during active hours, showing a small postprandial valley and a deeper decrease during sleep. Nighttime reduction of 10–20% relative to daytime BP is defined as a dipper pattern, and a reduction of less than 10%, as a non-dipper pattern. Despite this BP variability, hypertension’s diagnostic criteria and therapeutic objectives are usually based on BP average values. Indeed, studies have shown that chrono-pharmacological optimization significantly reduces long-term cardiovascular risk if a BP dipper pattern is maintained. Changes in the effect of antihypertensive medications can be explained by circadian variations in their pharmacokinetics (PK) and pharmacodynamics (PD). Nevertheless, BP circadian variation has been scarcely included in PK-PD models of antihypertensive medications to date. In this work, we developed PK-PD models that include circadian rhythm to find the optimal dosing time (Ta) of first-line antihypertensive medications for dipper and non-dipper patterns. The parameters of the PK-PD models were estimated using global optimization, and models were selected according to the lowest corrected Akaike information criterion value. Simultaneously, sensitivity and identifiability analysis were performed to determine the relevance of the parameters and establish those that can be estimated. Subsequently, Ta parameters were optimized to maximize the effect on BP average, BP peaks, and sleep-time dip. As a result, all selected models included at least one circadian PK component, and circadian parameters had the highest sensitivity. Furthermore, Ta with which BP>130/80 mmHg and a dip of 10–20% are achieved were proposed when possible. We show that the optimal Ta depends on the therapeutic objective, the medication, and the BP profile. Therefore, our results suggest making chrono-pharmacological recommendations in a personalized way.

Circadian rhythms: influence on physiology, pharmacology, and therapeutic interventions

Circadian rhythms are ubiquitous phenomena that recur daily in a self-sustaining, entrainable, and oscillatory manner, and orchestrate a wide range of molecular, physiological, and behavioral processes. Circadian clocks are comprised of a hierarchical network of central and peripheral clocks that generate, sustain, and synchronize the circadian rhythms. The functioning of the peripheral clock is regulated by signals from autonomic innervation (from the central clock), endocrine networks, feeding, and other external cues. The critical role played by circadian rhythms in maintaining both systemic and tissue-level homeostasis is well established, and disruption of the rhythm has direct consequence for human health, disorders, and diseases. Circadian oscillations in both pharmacokinetics and pharmacodynamic processes are known to affect efficacy and toxicity of several therapeutic agents. A variety of modeling approaches ranging from empirical to more complex systems modeling approaches have been applied to characterize circadian biology and its influence on drug actions, optimize time of dosing, and identify opportunities for pharmacological modulation of the clock mechanisms and their downstream effects. In this review, we summarize current understanding of circadian rhythms and its influence on physiology, pharmacology, and therapeutic interventions, and discuss the role of chronopharmacometrics in gaining new insights into circadian rhythms and its applications in chronopharmacology.

Circadian Effects of Drug Responses

Circadian rhythms describe physiological systems that repeat themselves with a cycle of approximately 24 h. Our understanding of the cellular and molecular origins of these oscillations has improved dramatically, allowing us to appreciate the significant role these oscillations play in maintaining physiological homeostasis. Circadian rhythms allow living organisms to predict and efficiently respond to a dynamically changing environment, set by repetitive day/night cycles. Since circadian rhythms underlie almost every aspect of human physiology, it is unsurprising that they also influence the response of a living organism to disease, stress, and therapeutics. Therefore, not only do the mechanisms that maintain health and disrupt homeostasis depend on our internal circadian clock, but also the way drugs are perceived and function depends on these physiological rhythms. We present a holistic view of the therapeutic process, discussing components such as disease state, pharmacokinetics, and pharmacodynamics, as well as adverse reactions that are critically affected by circadian rhythms. We outline challenges and opportunities in moving toward personalized medicine approaches that explore and capitalize on circadian rhythms for the benefit of the patient.

Mathematical modeling of mammalian circadian clocks affecting drug and disease responses

To align with daily environmental changes, most physiological processes in mammals exhibit a time-of-day rhythmicity. This circadian control of physiology is intrinsically driven by a cell-autonomous clock gene network present in almost all cells of the body that drives rhythmic expression of genes that regulate numerous molecular and cellular processes. Accordingly, many aspects of pharmacology and toxicology also oscillate in a time-of-day manner giving rise to diverse effects on pharmacokinetics and pharmacodynamics. Genome-wide studies and mathematical modeling are available tools that have significantly improved our understanding of these nonlinear aspects of physiology and therapeutics. In this manuscript current literature and our prior work on the model-based approaches that have been used to explore circadian genomic systems of mammals are reviewed. Such basic understanding and having an integrative approach may provide new strategies for chronotherapeutic drug treatments and yield new insights for the restoration of the circadian system when altered by diseases.

The rhythm of a preterm neonate's life: ultradian oscillations of heart rate, body temperature and sleep cycles

The objectives are to characterize oscillations of physiological functions such as heart rate and body temperature, as well as the sleep cycle from behavioral states in generally stable preterm neonates during the first 5 days of life. Heart rate, body temperature as well as behavioral states were collected during a daily 3-h observation interval in 65 preterm neonates within the first 5 days of life. Participants were born before 32 weeks of gestational age or had a birth weight below 1500 g; neonates with asphyxia, proven sepsis or malformation were excluded. In total 263 observation intervals were available. Heart rate and body temperature were analyzed with mathematical models in the context of non-linear mixed effects modeling, and the sleep cycles were characterized with signal processing methods. The average period length of an oscillation in this preterm neonate population was 159 min for heart rate, 290 min for body temperature, and the average sleep cycle duration was 19 min. Oscillation of physiological functions as well as sleep cycles can be characterized in very preterm neonates within the first few days of life. The observed parameters heart rate, body temperature and sleep are running in a seemingly uncorrelated pace at that stage of development. Knowledge about such oscillations may help to guide nursing and medical care in these neonates as they do not yet follow a circadian rhythm.

Transitioning from Basic toward Systems Pharmacodynamic Models: Lessons from Corticosteroids

Technology in bioanalysis, -omics, and computation have evolved over the past half century to allow for comprehensive assessments of the molecular to whole body pharmacology of diverse corticosteroids. Such studies have advanced pharmacokinetic and pharmacodynamic (PK/PD) concepts and models that often generalize across various classes of drugs. These models encompass the "pillars" of pharmacology, namely PK and target drug exposure, the mass-law interactions of drugs with receptors/targets, and the consequent turnover and homeostatic control of genes, biomarkers, physiologic responses, and disease symptoms. Pharmacokinetic methodology utilizes noncompartmental, compartmental, reversible, physiologic [full physiologically based pharmacokinetic (PBPK) and minimal PBPK], and target-mediated drug disposition models using a growing array of pharmacometric considerations and software. Basic PK/PD models have emerged (simple direct, biophase, slow receptor binding, indirect response, irreversible, turnover with inactivation, and transduction models) that place emphasis on parsimony, are mechanistic in nature, and serve as highly useful "top-down" methods of quantitating the actions of diverse drugs. These are often components of more complex quantitative systems pharmacology (QSP) models that explain the array of responses to various drugs, including corticosteroids. Progressively deeper mechanistic appreciation of PBPK, drug-target interactions, and systems physiology from the molecular (genomic, proteomic, metabolomic) to cellular to whole body levels provides the foundation for enhanced PK/PD to comprehensive QSP models. Our research based on cell, animal, clinical, and theoretical studies with corticosteroids have provided ideas and quantitative methods that have broadly advanced the fields of PK/PD and QSP modeling and illustrates the transition toward a global, systems understanding of actions of diverse drugs. SIGNIFICANCE STATEMENT: Over the past half century, pharmacokinetics (PK) and pharmacokinetics/pharmacodynamics (PK/PD) have evolved to provide an array of mechanism-based models that help quantitate the disposition and actions of most drugs. We describe how many basic PK and PK/PD model components were identified and often applied to the diverse properties of corticosteroids (CS). The CS have complications in disposition and a wide array of simple receptor-to complex gene-mediated actions in multiple organs. Continued assessments of such complexities have offered opportunities to develop models ranging from simple PK to enhanced PK/PD to quantitative systems pharmacology (QSP) that help explain therapeutic and adverse CS effects. Concurrent development of state-of-the-art PK, PK/PD, and QSP models are described alongside experimental studies that revealed diverse CS actions.