Machine learning framework to predict pharmacokinetic profile of small molecule drugs based on chemical structure.

Accurate prediction of a new compound's pharmacokinetic (PK) profile is pivotal for the success of drug discovery programs. An initial assessment of PK in preclinical species and humans is typically performed through allometric scaling and mathematical modeling. These methods use parameters estimated from in vitro or in vivo experiments, which although helpful for an initial estimation, require extensive animal experiments. Furthermore, mathematical models are limited by the mechanistic underpinning of the drugs' absorption, distribution, metabolism, and elimination (ADME) which are largely unknown in the early stages of drug discovery. In this work, we propose a novel methodology in which concentration versus time profile of small molecules in rats is directly predicted by machine learning (ML) using structure-driven molecular properties as input and thus mitigating the need for animal experimentation. The proposed framework initially predicts ADME properties based on molecular structure and then uses them as input to a ML model to predict the PK profile. For the compounds tested, our results demonstrate that PK profiles can be adequately predicted using the proposed algorithm, especially for compounds with Tanimoto score greater than 0.5, the average mean absolute percentage error between predicted PK profile and observed PK profile data was found to be less than 150%. The suggested framework aims to facilitate PK predictions and thus support molecular screening and design earlier in the drug discovery process.

A minimal physiologically based pharmacokinetic model to study the combined effect of antibody size, charge, and binding affinity to FcRn/antigen on antibody pharmacokinetics.

Protein therapeutics have revolutionized the treatment of a wide range of diseases. While they have distinct physicochemical characteristics that influence their absorption, distribution, metabolism, and excretion (ADME) properties, the relationship between the physicochemical properties and PK is still largely unknown. In this work we present a minimal physiologically-based pharmacokinetic (mPBPK) model that incorporates a multivariate quantitative relation between a therapeutic's physicochemical parameters and its corresponding ADME properties. The model's compound-specific input includes molecular weight, molecular size (Stoke's radius), molecular charge, binding affinity to FcRn, and specific antigen affinity. Through derived and fitted empirical relationships, the model demonstrates the effect of these compound-specific properties on antibody disposition in both plasma and peripheral tissues using observed PK data in mice and humans. The mPBPK model applies the two-pore hypothesis to predict size-based clearance and exposure of full-length antibodies (150 kDa) and antibody fragments (50-100 kDa) within a onefold error. We quantitatively relate antibody charge and PK parameters like uptake rate, non-specific binding affinity, and volume of distribution to capture the relatively faster clearance of positively charged mAb as compared to negatively charged mAb. The model predicts the terminal plasma clearance of slightly positively and negatively charged antibody in humans within a onefold error. The mPBPK model presented in this work can be used to predict the target-mediated disposition of a drug when compound-specific and target-specific properties are known. To our knowledge, a combined effect of antibody weight, size, charge, FcRn, and antigen has not been incorporated and studied in a single mPBPK model previously. By conclusively incorporating and relating a multitude of protein's physicochemical properties to observed PK, our mPBPK model aims to contribute as a platform approach in the early stages of drug development where many of these properties can be optimized to improve a molecule's PK and ultimately its efficacy.

A multi-model approach to predict efficacious clinical dose for an anti-TGF-ß antibody (GC2008) in the treatment of osteogenesis imperfecta.

Osteogenesis imperfecta (OI) is a heterogeneous group of inherited bone dysplasias characterized by reduced skeletal mass and bone fragility. Although the primary manifestation of the disease involves the skeleton, OI is a generalized connective tissue disorder that requires a multidisciplinary treatment approach. Recent studies indicate that application of a transforming growth factor beta (TGF-ß) neutralizing antibody increased bone volume fraction (BVF) and strength in an OI mouse model and improved bone mineral density (BMD) in a small cohort of patients with OI. In this work, we have developed a multitiered quantitative pharmacology approach to predict human efficacious dose of a new anti-TGF-ß antibody drug candidate (GC2008). This method aims to translate GC2008 pharmacokinetic/pharmacodynamic (PK/PD) relationship in patients, using a number of appropriate mathematical models and available preclinical and clinical data. Compartmental PK linked with an indirect PD effect model was used to characterize both pre-clinical and clinical PK/PD data and predict a GC2008 dose that would significantly increase BMD or BVF in patients with OI. Furthermore, a physiologically-based pharmacokinetic model incorporating GC2008 and the body's physiological properties was developed and used to predict a GC2008 dose that would decrease the TGF-ß level in bone to that of healthy individuals. By using multiple models, we aim to reveal information for different aspects of OI disease that will ultimately lead to a more informed dose projection of GC2008 in humans. The different modeling efforts predicted a similar range of pharmacologically relevant doses in patients with OI providing an informed approach for an early clinical dose setting.

Current Approaches for Predicting Human PK for Small Molecule Development Candidates: Findings from the IQ Human PK Prediction Working Group Survey.

Accurate prediction of human clearance (CL) and volume of distribution at steady state (Vd,ss) for small molecule drug candidates is an essential component of assessing likely efficacious dose and clinical safety margins. In 2021, the IQ Consortium Human PK Prediction Working Group undertook a survey of IQ member companies to understand the current PK prediction methods being used to estimate these parameters across the pharmaceutical industry. The survey revealed a heterogeneity in approaches being used across the industry (e.g., the use of allometric approaches, differing incorporation of binding terms, and inconsistent use of empirical correction factors for in vitro-in vivo extrapolation, IVIVE), which could lead to different PK predictions with the same input data. Member companies expressed an interest in improving human PK predictions by identifying the most appropriate compound-class specific methods, as determined by physiochemical properties and knowledge of CL pathways. Furthermore, there was consensus that increased understanding of the uncertainty inherent to the compound class-dependent prediction would be invaluable in aiding communication of human PK and dose uncertainty at the time of candidate nomination for development. The human PK Prediction Working Group is utilizing these survey findings to help interrogate clinical IV datasets from across the IQ consortium member companies to understand PK prediction accuracy and uncertainty from preclinical datasets.

Machine Learning guided early drug discovery of small molecules.

Machine learning (ML) approaches have been widely adopted within the early stages of the drug discovery process, particularly within the context of small-molecule drug candidates. Despite this, the use of ML is still limited in the pharmacokinetic/pharmacodynamic (PK/PD) application space. Here, we describe recent progress and the role of ML used in preclinical drug discovery. We summarize the advances and current strategies used to predict ADME (absorption, distribution, metabolism and, excretion) properties of small molecules based on their structures, and predict structures based on the desired properties for molecular screening and optimization. Finally, we discuss the use of ML to predict PK to rank the ability of drug candidates to achieve appropriate exposures and hence provide important insights into safety and efficacy.

Pathway-level analysis of genome-wide circadian dynamics in diverse tissues in rat and mouse.

A computational framework is developed to enable the characterization of genome-wide, multi-tissue circadian dynamics at the level of "functional groupings of genes" defined in the context of signaling, cellular/genetic processing and metabolic pathways in rat and mouse. Our aim is to identify how individual genes come together to generate orchestrated rhythmic patterns and how these may vary within and across tissues. We focus our analysis on four tissues (adipose, liver, lung, and muscle). A genome-wide pathway-centric analysis enables us to develop a comprehensive picture on how the observed circadian variation at the individual gene level, orchestrates functional responses at the pathway level. Such pathway-based "meta-data" analysis enables the rational integration and comparison across platforms and/or experimental designs evaluating emergent dynamics, as opposed to comparisons of individual elements. One of our key findings is that when considering the dynamics at the pathway level, a complex behavior emerges. Our work proposes that tissues tend to coordinate gene's circadian expression in a way that optimizes tissue-specific pathway activity, depending of each tissue's broader role in homeostasis.

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.

ATLAS mPBPK: A MATLAB-Based Tool for Modeling and Simulation of Minimal Physiologically-Based Pharmacokinetic Models.

Minimal physiologically-based pharmacokinetic (mPBPK) models are frequently used to model plasma pharmacokinetic (PK) data and utilize and yield physiologically relevant parameters. Compared with classical compartment and whole-body physiologically-based pharmacokinetic modeling approaches, mPBPK models maintain a structure of intermediate physiological complexity that can be adequately informed by plasma PK data. In this tutorial, we present a MATLAB-based tool for the modeling and simulation of mPBPK models (ATLAS mPBPK) of small and large molecules. This tool enables the users to perform the following: (i) PK data visualization, (ii) simulation, (iii) parameter optimization, and (iv) local sensitivity analysis of mPBPK models in a simple and efficient manner. In addition to the theoretical background and implementation of the different tool functionalities, this tutorial includes simulation and sensitivity analysis showcases of small and large molecules with and without target-mediated drug disposition.

Population Pharmacokinetics of Vamorolone (VBP15) in Healthy Men and Boys With Duchenne Muscular Dystrophy.

Duchenne muscular dystrophy (DMD) is an inherited neuromuscular disorder occurring in boys and caused by mutations in the dystrophin gene. Vamorolone is a first-generation delta-9,11 compound that has favorable efficacy and side effect profiles relative to classical glucocorticoids. The pharmacokinetics (PK) of oral vamorolone were assessed in parallel-group studies in healthy men (phase 1, n = 86) and boys with DMD (phase 2a, n = 48) during 14 days of once-daily dosing with a range of doses. Vamorolone exhibited moderate variability in PK, with the maximum plasma concentration usually occurring at 2-4 hours and a half-life of approximately 2 hours for all doses and days examined. Population PK modeling of all data together indicated that the PK of vamorolone can be well described by a 1-compartment model with zero-order absorption. Both men and boys showed a dose-linearity of PK parameters for the doses examined, with no accumulation of the drug during daily dosing. Ingestion with food resulted in markedly enhanced absorption of the drug, as tested in healthy men. There were similar PK of vamorolone in healthy men and DMD boys with apparent clearance averaging 2.0 L/h/kg in men and 1.7 L/h/kg in boys. Overall, vamorolone exhibited well-behaved linear PK, with similar profiles in healthy men and boys with DMD, moderate variability in PK parameters, and absorption and disposition profiles similar to those of classical glucocorticoids.

On the unphysical hypotheses in pharmacokinetics and oral drug absorption: Time to utilize instantaneous rate coefficients instead of rate constants.

This work aims to explore the unphysical assumptions associated with i) the homogeneity of the well mixed compartments of pharmacokinetics and ii) the diffusion limited model of drug dissolution. To this end, we i) tested the homogeneity hypothesis using Monte Carlo simulations for a reaction and a diffusional process that take place in Euclidean and fractal media, ii) re-considered the flip-flop kinetics assuming that the absorption rate for a one-compartment model is governed by an instantaneous rate coefficient instead of a rate constant, and, iii) re-considered the extent of drug absorption as a function of dose using an in vivo reaction limited model of drug dissolution with integer and non-integer stoichiometry values. We found that drug diffusional processes and reactions are slowed down in heterogeneous media and the environmental heterogeneity leads to increased fluctuations of the measurable quantities. Highly variable experimental literature data with measurements in intrathecal space and gastrointestinal fluids were explained accordingly. Next, by applying power law and Weibull input functions to a one-compartment model of disposition we show that the shape of concentration-time curves is highly dependent on the time exponent of the input functions. Realistic examples based on PK data of three compounds known to exhibit flip-flop kinetics are analyzed. The need to use time dependent coefficients instead of rate constants in PBPK modeling and virtual bioequivalence is underlined. Finally, the shape of the fraction absorbed as a function of dose plots, using an in vivo reaction limited model of drug dissolution were found to be dependent on the stoichiometry value and the solubility of drug. Ascending and descending limbs were observed for the higher stoichiometries (2.0 and 1.5) with the low solubility drug. In contrast, for the more soluble drug, a continuous increase of fraction absorbed as a function of dose is observed when the higher stoichiometries are used (2.0 and 1.5). For both drugs, the fraction absorbed for the lower values of stoichiometry (0.7 and 1.0) exhibit a non-dependency on dose profile. Our results give an insight into the complex picture of in vivo drug dissolution since diffusion-limited and reaction-limited processes seem to operate under in vivo conditions concurrently.

Phase IIa trial in Duchenne muscular dystrophy shows vamorolone is a first-in-class dissociative steroidal anti-inflammatory drug.

We report a first-in-patient study of vamorolone, a first-in-class dissociative steroidal anti-inflammatory drug, in Duchenne muscular dystrophy. This 2-week, open-label Phase IIa multiple ascending dose study (0.25, 0.75, 2.0, and 6.0 mg/kg/day) enrolled 48 boys with Duchenne muscular dystrophy (4 to <7 years), with outcomes including clinical safety, pharmacokinetics and pharmacodynamic biomarkers. The study design included pharmacodynamic biomarkers in three contexts of use: 1. Secondary outcomes for pharmacodynamic safety (insulin resistance, adrenal suppression, bone turnover); 2. Exploratory outcomes for drug mechanism of action; 3. Exploratory outcomes for expanded pharmacodynamic safety. Vamorolone was safe and well-tolerated through the highest dose tested (6.0 mg/kg/day) and pharmacokinetics of vamorolone were similar to prednisolone. Using pharmacodynamic biomarkers, the study demonstrated improved safety of vamorolone versus glucocorticoids as shown by reduction of insulin resistance, beneficial changes in bone turnover (loss of increased bone resorption and decreased bone formation only at the highest dose level), and a reduction in adrenal suppression. Exploratory biomarkers of pharmacodynamic efficacy showed an anti-inflammatory mechanism of action and a beneficial effect on plasma membrane stability, as demonstrated by a dose-responsive decrease in serum creatine kinase activity. With an array of pre-selected biomarkers in multiple contexts of use, we demonstrate the development of the first dissociative steroid that preserves anti-inflammatory efficacy and decreases steroid-associated safety concerns. Ongoing extension studies offer the potential to bridge exploratory efficacy biomarkers to clinical outcomes.

Modeling circadian variability of core-clock and clock-controlled genes in four tissues of the rat.

Circadian clocks, present in almost all cells of the body, are entrained to rhythmic changes in the environment (e.g. light/dark cycles). Genes responsible for this timekeeping are named core-clock genes, which through transcriptional feedback interactions mediated by transcription factor binding to Ebox/RRE/Dbox elements can generate oscillatory activity of their expression. By regulating the transcription of other clock-controlled genes (CCGs) circadian information is transmitted to tissue and organ levels. Recent studies have indicated that there is a considerable variability of clock-controlled gene expression between tissues both with respect to the circadian genes that are regulated and to their phase lags. In this work, a mathematical model was adapted to explore the dynamics of core-clock and clock-controlled genes measured in four tissues of the rat namely liver, muscle, adipose, and lung. The model efficiently described the synchronous rhythmicity of core-clock genes and further predicted that their phases are mainly regulated by Per2 and Cry1 transcriptional delays and Rev-Erba and Cry1 degradation rates. Similarly, after mining databases for potential Ebox/RRE/Dbox elements in the promoter region of clock-controlled genes, the phase variabilities of the same genes between different tissues were described. The analysis suggests that inter-tissue circadian variability of the same clock-controlled genes is an inherent component of homeostatic function and may arise due to different transcription factor activities on Ebox/RRE/Dbox elements.

Daily variation of gene expression in diverse rat tissues.

Circadian information is maintained in mammalian tissues by a cell-autonomous network of transcriptional feedback loops that have evolved to optimally regulate tissue-specific functions. An analysis of daily gene expression in different tissues, as well as an evaluation of inter-tissue circadian variability, is crucial for a systems-level understanding of this transcriptional circuitry. Affymetrix gene chip measurements of liver, muscle, adipose, and lung tissues were obtained from a rich time series light/dark experiment, involving 54 normal rats sacrificed at 18 time points within the 24-hr cycle. Our analysis revealed a high degree of circadian regulation with a variable distribution of phases among the four tissues. Interestingly, only a small number of common genes maintain circadian activity in all tissues, with many of them consisting of "core-clock" components with synchronous rhythms. Our results suggest that inter-tissue circadian variability is a critical component of homeostatic body function and is mediated by diverse signaling pathways that ultimately lead to highly tissue-specific transcription regulation.

Development and validation of a physiology-based model for the prediction of pharmacokinetics/toxicokinetics in rabbits.

The environmental fates of pharmaceuticals and the effects of crop protection products on non-target species are subjects that are undergoing intense review. Since measuring the concentrations and effects of xenobiotics on all affected species under all conceivable scenarios is not feasible, standard laboratory animals such as rabbits are tested, and the observed adverse effects are translated to focal species for environmental risk assessments. In that respect, mathematical modelling is becoming increasingly important for evaluating the consequences of pesticides in untested scenarios. In particular, physiologically based pharmacokinetic/toxicokinetic (PBPK/TK) modelling is a well-established methodology used to predict tissue concentrations based on the absorption, distribution, metabolism and excretion of drugs and toxicants. In the present work, a rabbit PBPK/TK model is developed and evaluated with data available from the literature. The model predictions include scenarios of both intravenous (i.v.) and oral (p.o.) administration of small and large compounds. The presented rabbit PBPK/TK model predicts the pharmacokinetics (Cmax, AUC) of the tested compounds with an average 1.7-fold error. This result indicates a good predictive capacity of the model, which enables its use for risk assessment modelling and simulations.

Circadian characteristics of permissive and suppressive effects of cortisol and their role in homeostasis and the acute inflammatory response.

In this work we explore a semi-mechanistic model that considers cortisol's permissive and suppressive effects through the regulation of cytokine receptors and cytokines respectively. Our model reveals the proactive role of cortisol during the resting period and its reactive character during the body's activity phase. Administration of an acute LPS dose during the night, when cortisol's permissive effects are higher than suppressive, leads to increased cytokine levels compared to LPS administration at morning when cortisol's suppressive effects are higher. Interestingly, our model presents a hysteretic behavior where the relative predominance of permissive or suppressive effects results not only from cortisol levels but also from the previous states of the model. Therefore, for the same cortisol levels, administration of an inflammatory stimulus at cortisol's ascending phase, that follows a time period where cytokine receptor expression is elevated ultimately sensitizing the body for the impending stimulus, leads to higher cytokine expression compared to administration of the same stimulus at cortisol's descending phase.

Mathematical modeling of light-mediated HPA axis activity and downstream implications on the entrainment of peripheral clock genes.

In this work we propose a semimechanistic model that describes the photic signal transduction to the hypothalamic-pituitary-adrenal (HPA) axis that ultimately regulates the synchronization of peripheral clock genes (PCGs). Our HPA axis model predicts that photic stimulation induces a type-1 phase response curve to cortisol's profile with increased cortisol sensitivity to light exposure in its rising phase, as well as the shortening of cortisol's period as constant light increases (Aschoff's first rule). Furthermore, our model provides insight into cortisol's phase and amplitude dependence on photoperiods and reveals that cortisol maintains highest amplitude variability when it is entrained by a balanced schedule of light and dark periods. Importantly, by incorporating the links between HPA axis and PCGs we were able to investigate how cortisol secretion impacts the entrainment of a population of peripheral cells and show that disrupted light schedules, leading to blunted cortisol secretion, fail to synchronize a population of PCGs which further signifies the loss of circadian rhythmicity in the periphery of the body.

Translational applications of evaluating physiologic variability in human endotoxemia.

Dysregulation of the inflammatory response is a critical component of many clinically challenging disorders such as sepsis. Inflammation is a biological process designed to lead to healing and recovery, ultimately restoring homeostasis; however, the failure to fully achieve those beneficial results can leave a patient in a dangerous persistent inflammatory state. One of the primary challenges in developing novel therapies in this area is that inflammation is comprised of a complex network of interacting pathways. Here, we discuss our approaches towards addressing this problem through computational systems biology, with a particular focus on how the presence of biological rhythms and the disruption of these rhythms in inflammation may be applied in a translational context. By leveraging the information content embedded in physiologic variability, ranging in scale from oscillations in autonomic activity driving short-term heart rate variability to circadian rhythms in immunomodulatory hormones, there is significant potential to gain insight into the underlying physiology.

Modeling physiologic variability in human endotoxemia.

The control and management of inflammation is a key aspect of clinical care for critical illnesses such as sepsis. In an ideal reaction to injury, the inflammatory response provokes a strong enough response to heal the injury and then restores homeostasis. When inflammation becomes dysregulated, a persistent inflammatory state can lead to significant deleterious effects and clinical challenges. Thus, gaining a better biological understanding of the mechanisms driving the inflammatory response is of the utmost importance. In this review, we discuss our work with the late Stephen F. Lowry to investigate systemic inflammation through systems biology of human endotoxemia. We present our efforts in modeling the human endotoxemia response with a particular focus on physiologic variability. Through modeling, with a focus ultimately on translational applications, we obtain more fundamental understanding of relevant physiological processes. And by taking advantage of the information embedded in biological rhythms, ranging in time scale from high-frequency autonomic oscillations reflected in heart rate variability to circadian rhythms in inflammatory mediators, we gain insight into the underlying physiology.

Entrainment of peripheral clock genes by cortisol.

Circadian rhythmicity in mammals is primarily driven by the suprachiasmatic nucleus (SCN), often called the central pacemaker, which converts the photic information of light and dark cycles into neuronal and hormonal signals in the periphery of the body. Cells of peripheral tissues respond to these centrally mediated cues by adjusting their molecular function to optimize organism performance. Numerous systemic cues orchestrate peripheral rhythmicity, such as feeding, body temperature, the autonomic nervous system, and hormones. We propose a semimechanistic model for the entrainment of peripheral clock genes by cortisol as a representative entrainer of peripheral cells. This model demonstrates the importance of entrainer's characteristics in terms of the synchronization and entrainment of peripheral clock genes, and predicts the loss of intercellular synchrony when cortisol moves out of its homeostatic amplitude and frequency range, as has been observed clinically in chronic stress and cancer. The model also predicts a dynamic regime of entrainment, when cortisol has a slightly decreased amplitude rhythm, where individual clock genes remain relatively synchronized among themselves but are phase shifted in relation to the entrainer. The model illustrates how the loss of communication between the SCN and peripheral tissues could result in desynchronization of peripheral clocks.

Modeling autonomic regulation of cardiac function and heart rate variability in human endotoxemia.

Heart rate variability (HRV), the quantification of beat-to-beat variability, has been studied as a potential prognostic marker in inflammatory diseases such as sepsis. HRV normally reflects significant levels of variability in homeostasis, which can be lost under stress. Much effort has been placed in interpreting HRV from the perspective of quantitatively understanding how stressors alter HRV dynamics, but the molecular and cellular mechanisms that give rise to both homeostatic HRV and changes in HRV have received less focus. Here, we develop a mathematical model of human endotoxemia that incorporates the oscillatory signals giving rise to HRV and their signal transduction to the heart. Connections between processes at the cellular, molecular, and neural levels are quantitatively linked to HRV. Rhythmic signals representing autonomic oscillations and circadian rhythms converge to modulate the pattern of heartbeats, and the effects of these oscillators are diminished in the acute endotoxemia response. Based on the semimechanistic model developed herein, homeostatic and acute stress responses of HRV are studied in terms of these oscillatory signals. Understanding the loss of HRV in endotoxemia serves as a step toward understanding changes in HRV observed clinically through translational applications of systems biology based on the relationship between biological processes and clinical outcomes.