Physicochemical characterization and phase II metabolic profiling of echinochrome A, a bioactive constituent from sea urchin, and its physiologically based pharmacokinetic modeling in rats and humans.

Echinochrome A, a natural naphthoquinone pigment found in sea urchins, is increasingly being investigated for its nutritional and therapeutic value associated with antioxidant, anticancer, antiviral, antidiabetic, and cardioprotective activities. Although several studies have demonstrated the biological effects and therapeutic potential of echinochrome A, little is known regarding its biopharmaceutical behaviors. Here, we aimed to investigate the physicochemical properties and metabolic profiles of echinochrome A and establish a physiologically-based pharmacokinetic (PBPK) model as a useful tool to support its clinical applications. We found that the lipophilicity, color variability, ultraviolet/visible spectrometry, and stability of echinochrome A were markedly affected by pH conditions. Moreover, metabolic and pharmacokinetic profiling studies demonstrated that echinochrome A is eliminated primarily by hepatic metabolism and that four possible metabolites, i.e., two glucuronidated and two methylated conjugates, are formed in rat and human liver preparations. A whole-body PBPK model incorporating the newly identified hepatic phase II metabolic process was constructed and optimized with respect to chemical-specific parameters. Furthermore, model simulations suggested that echinochrome A could exhibit linear disposition profiles without systemic and local tissue accumulation in clinical settings. Our proposed PBPK model of echinochrome A could be a valuable tool for predicting drug interactions in previously unexplored scenarios and for optimizing dosage regimens and drug formulations.

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model.

The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

Extended transit compartment model to describe tumor delay using Coxian distribution.

The measured response of cell population is often delayed relative to drug injection, and individuals in a population have a specific age distribution. Common approaches for describing the delay are to apply transit compartment models (TCMs). This model reflects that all damaged cells caused by drugs suffer transition processes, resulting in death. In this study, we present an extended TCM using Coxian distribution, one of the phase-type distributions. The cell population attacked by a drug is described via age-structured models. The mortality rate of the damaged cells is expressed by a convolution of drug rate and age density. Then applying to Erlang and Coxian distribution, we derive Erlang TCM, representing the existing model, and Coxian TCMs, reflecting sudden death at all ages. From published data of drug and tumor, delays are compared after parameter estimations in both models. We investigate the dynamical changes according to the number of the compartments. Model robustness and equilibrium analysis are also performed for model validation. Coxian TCM is an extended model considering a realistic case and captures more diverse delays.

Development and application of a physiologically based pharmacokinetic model for entrectinib in rats and scale-up to humans: Route-dependent gut wall metabolism.

Entrectinib (Rozlytrek®) is an oral antineoplastic agent approved by the U.S. Food and Drug Administration in 2019 for the treatment of c-ros oncogene 1 (ROS1)-positive non-small cell lung cancer and neurotrophic tyrosine receptor kinase (NTRK) fusion-positive solid tumors. Although there have been a few studies on the pharmacokinetics of entrectinib, the relative contributions of several kinetic factors determining the oral bioavailability and systemic exposure of entrectinib are still worthy of investigation. Experimental data on the intestinal absorption and disposition of entrectinib in rats were acquired from studies on in vitro protein binding/tissue S9 metabolism, in situ intestinal perfusion, and in vivo dose-escalation/hepatic extraction. Using these datasets, an in-house whole-body physiologically based pharmacokinetic (PBPK) model incorporating the QGut model concepts and segregated blood flow in the gut was constructed and optimized with respect to drug-specific parameters. The established rat PBPK model was further extrapolated to humans through relevant physiological scale-up and parameter optimization processes. The optimized rat and human PBPK models adequately captured the impact of route-dependent gut metabolism on the systemic exposure to entrectinib and closely mirrored various preclinical and clinical observations. Our proposed PBPK model could be useful in optimizing dosage regimens and predicting drug interaction potential in various clinical conditions, after partial modification and validation.

A Tumor-Immune Interaction Model for Synergistic Combinations of Anti PD-L1 and Ionizing Irradiation Treatment.

Combination therapy with immune checkpoint blockade and ionizing irradiation therapy (IR) generates a synergistic effect to inhibit tumor growth better than either therapy does alone. We modeled the tumor-immune interactions occurring during combined IT and IR based on the published data from Deng et al. The mathematical model considered programmed cell death protein 1 and programmed death ligand 1, to quantify data fitting and global sensitivity of critical parameters. Fitting of data from control, IR and IT samples was conducted to verify the synergistic effect of a combination therapy consisting of IR and IT. Our approach using the model showed that an increase in the expression level of PD-1 and PD-L1 was proportional to tumor growth before therapy, but not after initiating therapy. The high expression level of PD-L1 in T cells may inhibit IT efficacy. After combination therapy begins, the tumor size was also influenced by the ratio of PD-1 to PD-L1. These results highlight that the ratio of PD-1 to PD-L1 in T cells could be considered in combination therapy.

Recent advances in physiologically based pharmacokinetic and pharmacodynamic models for anticancer nanomedicines.

Nanoparticles (NPs) have distinct pharmacokinetic (PK) properties and can potentially improve the absorption, distribution, metabolism, and elimination (ADME) of small-molecule drugs loaded therein. Owing to the unwanted toxicities of anticancer agents in healthy organs and tissues, their precise delivery to the tumor is an essential requirement. There have been numerous advancements in the development of nanomedicines for cancer therapy. Physiologically based PK (PBPK) models serve as excellent tools for describing and predicting the ADME properties and the efficacy and toxicity of drugs, in combination with pharmacodynamic (PD) models. The recent preliminary application of these modeling approaches to NPs demonstrated their potential benefits in research and development processes relevant to the ADME and pharmacodynamics of NPs and nanomedicines. Here, we comprehensively review the pharmacokinetics of NPs, the developed PBPK models for anticancer NPs, and the developed PD model for anticancer agents.

Modeling to capture bystander-killing effect by released payload in target positive tumor cells.

BACKGROUND: Antibody-drug conjugates (ADCs) are intended to bind to specific positive target antigens and eradicate only tumor cells from an intracellular released payload through the lysosomal protease. Payloads, such as MMAE, have the capacity to kill adjacent antigen-negative (Ag-) tumor cells, which is called the bystander-killing effect, as well as directly kill antigen-positive (Ag+) tumor cells. We propose that a dose-response curve should be independently considered to account for target antigen-positive/negative tumor cells. METHODS: A model was developed to account for the payload in Ag+/Ag- cells and the associated parameters were applied. A tumor growth inhibition (TGI) effect was explored based on an ordinary differential equation (ODE) after substituting the payload concentration in Ag+/Ag- cells into an Emax model, which accounts for the dose-response curve. To observe the bystander-killing effects based on the amount of Ag+/Ag- cells, the Emax model is used independently. TGI models based on ODE are unsuitable for describing the initial delay through a tumor-drug interaction. This was solved using an age-structured model based on the stochastic process. RESULTS: ß∈(0,1] is a fraction parameter that determines the proportion of cells that consist of Ag+/Ag- cells. The payload concentration decreases when the ratio of efflux to influx increases. The bystander-killing effect differs with varying amounts of Ag+ cells. The larger ß is, the less bystander-killing effect. The decrease of the bystander-killing effect becomes stronger as Ag+ cells become larger than the Ag- cells. Overall, the ratio of efflux to influx, the amount of released payload, and the proportion of Ag+ cells determine the efficacy of the ADC. The tumor inhibition delay through a payload-tumor interaction, which goes through several stages, may be solved using an age-structured model. CONCLUSIONS: The bystander-killing effect, one of the most important topics of ADCs, has been explored in several studies without the use of modeling. We propose that the bystander-killing effect can be captured through a mathematical model when considering the Ag+ and Ag- cells. In addition, the TGI model based on the age-structure can capture the initial delay through a drug interaction as well as the bystander-killing effect.

Qualitative and Sensitivity Analysis of the Effect of Electronic Cigarettes on Smoking Cessation.

Recently, the role of the electronic cigarettes (e-cigarettes) in a way to reduce smoking is increasing. E-cigarettes are a device that delivers only the nicotine, and its use is considered less harmful to health compared with tobacco cigarettes. Smokers frequently make use of e-cigarettes as one of the nonsmoking aid devices. In this work, we propose a mathematical model to analyze the effect of e-cigarettes on smoking cessation. The stability and the bifurcation of the model have been discussed. The parameter estimations from the observed data are drawn, and using the parameters, a reasonable smoking model has been designed. Moreover, by considering the sensitivity results depending on the basic reproduction number R0, the effective strategies that reduce the smokers are investigated. Numerical simulations of the model show that e-cigarettes may somewhat diminish the numbers of smokers, but it does not reduce the number of quitters ultimately.

Mathematical modeling of antibody drug conjugates with the target and tubulin dynamics to predict AUC.

Antibody drug conjugates (ADCs)are one of the most recently developed chemotherapeutics to treat some types of tumor cells. They consist of monoclonal antibodies (mAbs), linkers, and potent cytotoxic drugs. Unlike common chemotherapies, ADCs combine selectively with a target at the surface of the tumor cell, and a potent cytotoxic drug (payload) effectively prevents microtubule polymerization. In this work, we construct an ADC model that considers both the target of antibodies and the receptor (tubulin) of the cytotoxic payloads. The model is simulated with brentuximab vedotin, one of ADCs, and used to investigate the pharmacokinetic (PK) characteristics of ADCs in vivo. It also predicts area under the curve (AUC) of ADCs and the payloads by identifying the half-life. The results show that dynamical behaviors fairly coincide with the observed data and half-life and capture AUC. Thus, the model can be used for estimating some parameters, fitting experimental observations, predicting AUC, and exploring various dynamical behaviors of the target and the receptor.

Optimal treatment strategy for a tumor model under immune suppression.

We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer.

Stability analysis and optimal vaccination of an SIR epidemic model.

Almost all mathematical models of diseases start from the same basic premise: the population can be subdivided into a set of distinct classes dependent upon experience with respect to the relevant disease. Most of these models classify individuals as either a susceptible individual S, infected individual I or recovered individual R. This is called the susceptible-infected-recovered (SIR) model. In this paper, we describe an SIR epidemic model with three components; S, I and R. We describe our study of stability analysis theory to find the equilibria for the model. Next in order to achieve control of the disease, we consider a control problem relative to the SIR model. A percentage of the susceptible populations is vaccinated in this model. We show that an optimal control exists for the control problem and describe numerical simulations using the Runge-Kutta fourth order procedure. Finally, we describe a real example showing the efficiency of this optimal control.