Parameter estimation for sigmoid Emax models in exposure-response relationship

Physiologically based toxicokinetic and toxicodynamic (PBTK-TD) modelling of cis-bifenthrin in Carassius auratus and Xenopus laevis accounting for reproductive toxicity

Pyrethroid insecticides are a class of endocrine disruptors and are believed to exhibit reproductive toxicity to aquatic organisms. Pyrethroids are widely detected in aquatic environments and can accumulate in aquatic organisms, but studies on their accumulation and the associated reproductive toxicity in aquatic organisms are still limited. We utilized Carassius auratus and Xenopus laevis as models for fish and amphibians, respectively, and developed and validated a physiologically based toxicokinetic and toxicodynamic (PBTK-TD) model for adult fish and frogs exposed to typical pyrethroid pesticides cis-bifenthrin (cis-BF). The model includes the brain, kidney, liver, gonads, gills/lungs, well-perfused tissue, and poorly-perfused tissue, which are interconnected by blood circulation in the PBTK process. There are also dynamic relationships between target organ concentrations and reproductive-related endpoints in the TD process. Results showed that the PBTK sub-model accurately described and predicted the uptake, distribution, and disposition kinetics in fish and frogs. In fish, the kidney exhibited the fastest accumulation rate, while in frogs, the skin showed the fastest accumulation rate, followed by the kidney. Sensitivity analysis indicated that parameters such as blood flow and blood distribution coefficients had significant effects on chemical concentrations. A sigmoid Emax model was employed to describe the relationship between the reproductive toxicity effects of cis-BF and its dose-concentration variations. We found that testosterone (T) exhibited the highest correlation coefficient, suggesting that T could serve as an effective biomarker for cis-BF reproductive toxicity. The PBTK-TD model established in this study is beneficial for predicting the toxicological effects of pyrethroids in fish and amphibians.

Population pharmacokinetic, pharmacodynamic and efficacy modeling of SB12 (proposed eculizumab biosimilar) and reference eculizumab

PURPOSE

To describe, compare similarity of pharmacokinetic (PK), pharmacodynamic (PD) and efficacy of SB12 and reference eculizumab (ECU) and find clinically significant covariate relationships.

METHODS

The PK, PD (terminal complement activity) and efficacy (LDH) data of SB12 and ECU were obtained from 289 subjects from phase I and phase III studies. One- and two-compartment PK models with first-order elimination were evaluated for SB12 and ECU. For PD and efficacy, both direct and indirect models were tested. The impact of covariates on PK, PD and efficacy parameters was assessed. Relationship between PK/PD and PD/efficacy was characterized. This modeling was performed using NONMEM version 7.4 (Icon Development Solutions, Ellicott City, MD, USA).

RESULTS

The two-compartment model adequately described the PK of SB12 and ECU, and the subject's weight was chosen as a clinically significant covariate affecting drugs' clearance and central volume of distribution. Treatment group was not a significant covariate affecting clearance. The direct response model using inhibitory sigmoid Emax and sigmoid Emax relationship well described the PK/PD relationship and PD/efficacy relationship of SB12 and ECU, respectively. Through this modeling, the relationships between PK, PD and efficacy were characterized. There were no differences in PK, PD and efficacy parameters between SB12 and ECU in pooled populations of healthy subjects and paroxysmal nocturnal haemoglobinuria (PNH) patients.

CONCLUSION

The population modeling showed PK, PD and efficacy similarities between SB12 and ECU in pooled population of healthy subjects and PNH patients, supporting the totality of evidence on biosimilarity for SB12.

Formulation and Validation of an Extended Sigmoid Emax Model in Pharmacodynamics

PURPOSE OR OBJECTIVE

Drug concentration-response curves (DRCs) are crucial in pharmacology for assessing the drug effects on biological systems. The widely used sigmoid Emax model, which accounts for response saturation, relies heavily on the effective drug concentration ( E D 50 ). This reliance can lead to validation errors and inaccuracies in model fitting. The Emax model cannot generate multiple DRCs, raising concerns about whether the dataset is fully utilized.

METHODS

This study formulates an extended Emax (eEmax) model designed to overcome these limitations. The eEmax model generates multiple DRCs from a single dataset by using various estimatedα ' s ∈ 0,100 , while keeping E D α fixed, rather than estimating an E D 50 value as in the Emax model.

RESULTS

This model effectively captures a broader range of concentration-response behavior, including non-sigmoidal patterns, thus providing greater flexibility and accuracy compared to the Emax model. Validation using various drug-response data and PKPD frameworks demonstrates the eEmax model's improved accuracy and versatility in handling concentration-response data.

CONCLUSIONS

The eEmax model provides a robust and flexible method for drug concentration-response analysis, facilitating the generation of multiple DRCs from a single dataset and reducing the possibility of validation errors. This model is particularly valuable for its ease of use and its capability to fully utilize datasets, providing its potential in PKPD modeling and drug discovery.

Investigations on In Vivo Pharmacokinetic/Pharmacodynamic Determinants of Fosfomycin in Murine Thigh and Kidney Infection Models

Background: Amidst the era of widespread resistance, there has been a renewed interest in older antibiotics such as fosfomycin, owing to its activity against certain resistant Gram-negative pathogens, including multidrug-resistant variants expressing extended spectrum β-lactamases or carbapenemases. The goal of the study was to investigate pharmacokinetic/pharmacodynamic (PK/PD) index and PK/PD targets of fosfomycin in murine thigh and kidney infection models, employing clinical isolates of Escherichia coli (E. coli) and Klebsiella pneumoniae (K. pneumoniae). Methods: Seven isolates of E. coli (one wild-type and six clinical isolates) and five isolates of K. pneumoniae (one wild-type and four clinical isolates) were utilized for in vivo PK/PD studies. Single-dose plasma PK studies were conducted in infected mice by subcutaneous route. PD index was determined from exposure-response analysis employing 24-hr dose fractionation studies in neutropenic murine thigh infection model, while pharmacodynamic targets (PDTs) were derived from both thigh and kidney infection models. Results: Dose fractionation studies demonstrated that in vivo efficacy of fosfomycin best correlated with AUC/MIC for E. coli (R² = 0.9227) and K. pneumoniae (R² = 0.8693). The median AUC/MIC linked to 1 log10 kill effects were 346.2 and 745.2 in thigh infection model and 244.1 and 425.4 in kidney infection model for E. coli and K. pneumoniae, respectively. The mice plasma protein binding of fosfomycin was estimated to be 5.4%. Conclusions: The in vivo efficacy of fosfomycin against Enterobacterales was best described by AUC/MIC. The PDTs derived from this study may help define the coverage potential of fosfomycin at the clinical doses approved.

Inhibitory effect of proteinase K against dermatophyte biofilms: an alternative for increasing the antifungal effects of terbinafine and griseofulvin

This study aimed to evaluate the effect of proteinase K on mature biofilms of dermatophytes, by assays of metabolic activity and biomass. In addition, the proteinase K-terbinafine and proteinase K-griseofulvin interactions against these biofilms were investigated by the checkerboard assay and scanning electron and confocal microscopy. The biofilms exposed to 32 µg ml^-1 of proteinase K had lower metabolic activity and biomass, by 39% and 38%, respectively. Drug interactions were synergistic, with proteinase K reducing the minimum inhibitory concentration of antifungals against dermatophyte biofilms at a concentration of 32 µg ml^-1 combined with 128-256 µg ml^-1 of terbinafine and griseofulvin. Microscopic images showed a reduction in biofilms exposed to proteinase K, proteinase K-terbinafine and proteinase K-griseofulvin combinations. These findings demonstrate that proteinase K has activity against biofilms of dermatophytes, and the interactions of proteinase K with terbinafine and griseofulvin improve the activity of drugs against mature dermatophyte biofilms.

Design and application of hybrid cyclic-linear peptide-doxorubicin conjugates as a strategy to overcome doxorubicin resistance and toxicity

Doxorubicin (Dox) is used for breast cancer, leukemia, and lymphoma treatment as an effective chemotherapeutic agent. However, Dox use is restricted due to inherent and acquired resistance and an 8-fold increase in the risk of potentially fatal cardiotoxicity. Hybrid cyclic-linear peptide [R₅K]W₇A and linear peptide R₅KW₇A were conjugated with Dox through a glutarate linker to afford [R₅K]W₇A-Dox and R₅KW₇A-Dox conjugates to generate Dox derivatives. Alternatively, [R₅K]W₇C was conjugated with Dox via a disulfide linker to generate [R₅K]W₇C-S-S-Dox conjugate, where S-S is a disulfide bond. Comparative antiproliferative assays between conjugates [R₅K]W₇A-Dox, [R₅K]W₇C-S-S-Dox, linear R₅KW₇A-Dox, the corresponding physical mixtures of the peptides, and Dox were performed in normal and cancer cells. [R₅K]W₇A-Dox conjugate was 2-fold more efficient than R₅KW₇A-Dox, and [R₅K]W₇C-S-S-Dox conjugates in inhibiting the cell proliferation of human leukemia cells (CCRF-CEM). Therefore, hybrid cyclic-linear [R₅K]W₇A-Dox conjugate was selected for further studies and inhibited the cell viability of CCRF-CEM (84%), ovarian adenocarcinoma (SK-OV-3, 39%), and gastric carcinoma (AGS, 73%) at a concentration of 5 μM after 72 h of incubation, which was comparable to Dox (5 μM) efficacy (CCRF-CEM (85%), SK-OV-3 (33%), and AGS (87%)). While [R₅K]W₇A-Dox had a significant effect on the viability of cancer cells, it exhibited minimal cytotoxicity to normal kidney (LLC-PK1, 5-7%) and heart cells (H9C2, <9%) at concentrations of 5-10 μM (compared to free Dox at 5 μM that reduced the viability of kidney and heart cells by 85% and 44%, respectively). The fluorescence microscopy images were consistent with the cytotoxicity studies, indicating minimal uptake of the cyclic-linear [R₅K]W₇A-Dox (5 μM) in H9C2 cells. In comparison, Dox (5 μM) showed significant uptake, reduced cell viability, and changed the morphology of the cells after 24 h. [R₅K]W₇A-Dox showed 16-fold and 9.5-fold higher activity against Dox-resistant cells MDA231R and MES-SA/MX2 (lethal dose for 50% cell death or LC₅₀ of 2.3 and 4.3 μM, respectively) compared to free Dox (LC₅₀ of 36-41 μM, respectively). These data, along with the results obtained from the cell viability tests, indicate comparable efficiency of [R₅K]W₇A-Dox to free Dox in leukemia, ovarian, and gastric cancer cells, significantly reduced toxicity in normal kidney LLC-PK1 and heart H9C2 cells, and significantly higher efficiency in Dox-resistant cells. A number of endocytosis inhibitors did not affect the cellular uptake of [R₅K]W₇A-Dox.

Control Theory and Cancer Chemotherapy: How They Interact

Control theory arises in most modern real-life applications, not least in biological and medical applications. In particular, in biological and medical contexts, the role of control theory began to take shape in the early 1980s when the first works appeared on the application of control theory in models of pharmacokinetics and pharmacodynamics for antitumor therapies. Forty years after those first works, the theory of control continues to be considered a mathematical analysis tool of extreme importance and usefulness, but the challenges it must overcome in order to manage the complexity of biological processes are in fact not yet overcome. In this article, we introduce the reader to the basic ideas of control theory, its aims and its mathematical formalization, and we review its use in cell phase-specific models for cancer chemotherapy. We discuss strengths and limitations of the control theory approach to the analysis pharmacokinetics and pharmacodynamics models, and we will see that most of them are strongly related to data availability and mathematical form of the model. We propose some future research directions that could prove useful in overcoming the these limitations and we indicate the crucial steps preliminary to a useful and informative application of control theory to cancer chemotherapy modeling.

Impact of Sampling Period on Population Pharmacokinetic Analysis of Antibiotics: Why do You Take Blood Samples Following the Fourth Dose?

To date, many population pharmacokinetic models of antibiotics have been developed using blood sampling data after the fourth or fifth dose, which represents steady-state levels. However, if a model developed using blood sampled after the first dose is equivalent to that using blood sampled after the fourth dose, it would be advantageous to utilize the former. The aim of this study was to investigate the effect of blood sampling after the first and/or fourth drug administration on the accuracy and precision of parameter estimates. A previously reported robust, two-compartment model of vancomycin was used for simulation to evaluate the performances of the parameter estimates. The parameter estimation performances were assessed using relative bias and relative root mean square error. Performance was investigated in 72 scenarios consisting of a combination of two blood sampling periods (the first and fourth dose), two total clearances, three infusion times, and four sample sizes. The population pharmacokinetic models from data collected at the first dose and those collected at the fourth dose produced parameter estimates that were similar in accuracy and precision. This study will contribute to increasing the efficiency and simplicity of antibiotic pharmacokinetic studies.

Usefulness of mizoribine administration in children with frequently relapsing nephrotic syndrome, and the relationship between pharmacokinetic parameters and efficacy: a multicenter prospective cohort study in China

BACKGROUND

Mizoribine (MZR) is an immunosuppressant used to treat adult nephropathy. There is little experience with the drug in treating Chinese children with frequently relapsing nephrotic syndrome (FRNS). We investigated the efficacy and safety for treating MZR with FRNS. Furthermore, the relationship between efficacy and serum concentration was investigated.

METHODS

A prospective multicenter observational 12-month study was performed for evaluating the usefulness of MZR with FRNS. Serum MZR concentration was measured, and the relationships between pharmacokinetic parameters (C_max, AUC), number of relapses, and urinary protein were evaluated.

RESULTS

Eighty-two pediatric patients from four hospitals were treated with MZR and prednisone. MZR treatment significantly reduced the number of relapses and steroid doses. A correlation between pharmacokinetic parameters and relapses was observed, which fits well with the sigmoidal E_max model. Even in the relationship between pharmacokinetic parameters and urinary proteins, it was recognized that there was a threshold in the pharmacokinetic parameters for the therapeutic effect similar to the results obtained with the sigmoidal E_max model. Eleven patients (13.4%) experienced mild adverse events.

CONCLUSIONS

MZR therapy was effective in reducing the number of relapses and steroid doses. No severe adverse reactions were observed. Therapeutically effective serum concentrations were estimated to be C_max ≥ about 2 μg/mL or AUC ≥ about 10 μg h/mL. MZR and steroid treatment were effective and safe for pediatric FRNS.