The use of mathematical models has become increasingly prevalent in pharmacological fields, particularly in drug development processes. These models are instrumental in tasks such as designing clinical trials and assessing factors like efficacy, toxicity, and clinical practice. Various types of models have been developed and documented. Nevertheless, emphasizing the reliability of parameter values is crucial, as they play a pivotal role in shaping the behavior of the system. In some instances, parameter values reported previously are treated as fixed values, which can lead to convergence towards values that deviate substantially from those found in actual biological systems. This is especially true when parameter values are determined through fitting to limited observations. To mitigate this risk, the reuse of parameter values from previous reports should be approached with a critical evaluation of their validity. Currently, there is a proposal for a simultaneous search for plausible values for all parameters using comprehensive search algorithms in both pharmacokinetic and pharmacodynamic or systems pharmacological models. Implementing these methodologies can help address issues related to parameter determination. Furthermore, integrating these approaches with methods developed in the field of machine-learning field has the potential to enhance the reliability of parameter values and the resulting model outputs.

Omalizumab is the first approved anti-immunoglobulin E (IgE) agent for the treatment of moderate to severe persistent inadequately controlled allergic asthma in adults and adolescents (≥ 12 years old). In 2016, it was approved in pediatric patients (6-11 years old). The objective of this study was to quantitatively characterize the relationship between serum free IgE and pulmonary function (as measured by forced expiratory volume in 1 s [FEV1]) in pediatrics using a population-based pharmacodynamic model. Data collected during the steroid-stable period (first 24 weeks) of an omalizumab trial with pediatric asthma patients (Study IA05) were used to build the pediatric IgE-FEV1 model. The previously developed population IgE-FEV1 model in adults/adolescents was adapted to characterize the FEV1 and IgE relationship in pediatrics with different magnitude and onset of response. The pediatric IgE-FEV1 model adequately characterized the IgE-FEV1 relationship in pediatrics, particularly at the extremes of the observed body weights (i.e., ≤ 30 kg) and IgE values at screening (i.e., > 700 IU/mL). The estimated sigmoidal free IgE-FEV1 curves were similar in shape and maximum effect, but the estimated free IgE concentration leading to 50% maximum effect (IC50) in pediatric patients (39.4, 95% confidence interval [CI] 24.3-63.9 ng/mL) was higher than estimated in adults (19.8, 95% CI 15.1-24.5 ng/mL). The model further confirmed that the current omalizumab dosing rationale based on the mean target free IgE level of 25 ng/ml was appropriate. The pediatric model can be used to predict population FEV1 response for omalizumab when combined with an omalizumab pharmacokinetic-IgE model.

Pseudomonas aeruginosa can develop resistance. Therefore, it is necessary to design proper treatment for it. Pseudomonas aeruginosa can develop resistance against levofloxacin due to the development of efflux pumps. However, the development of these efflux pumps cannot develop resistance against imipenem. Additionally, the MexCDOprJ efflux system which is responsible for the resistance of Pseudomonas aeruginosa to levofloxacin is highly susceptible to imipenem. The objective of the study was to evaluate the emergence of resistance of Pseudomonas aeruginosa against 750 mg levofloxacin, 250 mg imipenem, and a combination of 750 mg levofloxacin and 250 mg imipenem. An in vitro pharmacodynamic model was selected for the evaluation of the emergence of resistance. Pseudomonas aeruginosa strain 236, Pseudomonas aeruginosa strain GB2, and Pseudomonas aeruginosa strain GB65 were selected. Susceptibility testing of both antibiotics was done by agar dilution methodology. A disk diffusion bioassay was performed for antibiotics. RT-PCR measurement was done for the evaluation of expressions of Pseudomonas aeruginosa genes. Samples were tested at 2 h, 4 h, 6 h, 8 h, 12 h, 16 h, 24 h, and 30 h. Levofloxacin and imipenem both individually reported a decrease in colony-forming unit per milliliter of strength in the initial stage but in the later stage both develop resistance individually. Levofloxacin with imipenem had no resistance to Pseudomonas aeruginosa during 30 h. Time after the start of development of resistance or decrease in clinical efficacy was higher for levofloxacin and imipenem combination in all strains. The concentration of Pseudomonas aeruginosa at the time after the start of development of resistance or decrease in clinical efficacy was fewer for levofloxacin and imipenem combination. Levofloxacin with imipenem is recommended for the treatment of infection due to Pseudomonas aeruginosa.

Escherichia coli (E. coli) infections are becoming increasingly difficult to treat, as antibiotic-resistant variants proliferate. Studies on novel methods to combat the spread of resistance and improve the performance of current antibiotics are vital. We aimed to boost the efficacy of the antibiotic orbifloxacin (ORB) against E. coli by combining it with a phenolic component, propyl gallate (PG). The minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) of ORB against the E. coli KVCC 1423 resistant strain were 128 μg/ml and 256 μg/ml, respectively. However, the MIC of ORB for the remaining E. coli strains was 0.5 μg/ml-2 μg/ml. For the combination of PG and ORB, the lowest fractional inhibitory concentration (FIC) index was less than 0.5, and the combination decreased the MIC of both drugs by 74%. The time-kill assay revealed the killing properties of both the drugs and the pharmacodynamic model (PD model) confirmed the strong killing properties of the combination as compared to the individual activities of the drugs. The ratio between MIC and mutant prevention concentration of ORB against E. coli 1400306 and 1,423 were 1:32 and 1:8, respectively. The combination of ORB and PG showed strong biofilm eradication and inhibited the motility of bacteria. The cell viability of the combination was > 80%. Therefore, we believe that ORB and PG in combination could be a possible antibacterial candidate that could minimize resistance and improve antibiotic potential.

Objective: This study aimed to establish a pharmacodynamic model and to screen reasonable covariates to quantitatively describe the efficacy of poly (ADP-ribose) polymerase inhibitors (PARPis) as maintenance treatment for recurrent ovarian cancer (ROC). Methods: The log normal hazard function model was established by using progression-free survival (PFS) data of 1,169 patients from published randomized trials on FDA-approved PARP inhibitors (olaparib, niraparib, and rucaparib). Monte Carlo simulation was used to compare PFS values in different scenarios, such as monotherapy (administered alone) and combination therapy (PARPis combined with chemo- or target-therapies), different biomarker statuses, and different PARP inhibitors. PFS was also estimated. Results: The study showed that the median PFS was 8.5 months with monotherapy and 16.0 months with combination therapy. The median PFS of patients with the BRCA mutation, BRCA wild-type, and HRD-positivity were 11.0, 7.5, and 9.0 months in monotherapy, respectively, and 23.0, 14.0 and 17.5 months, in combination therapy, respectively. In addition, the median PFS of olaparib, niraparib, and rucaparib monotherapy were about 9.5, 10.5, and 12.0 months, respectively, and about 19.0, 20.0, and 25 months, respectively, in combination therapy. The median PFS values in combination with cediranib, bevacizumab, and chemotherapy were approximately 17.0, 12.5 and 19.5 months, respectively. Conclusion: PARPi combination therapy is more effective as maintenance treatment for ROC than monotherapy, and the efficacy of PARPis in combination with chemotherapy is higher than that of the combination with antiangiogenic drugs. We found that the PFS of BRCA wild-type was similar to that of HRD-positive patients, and there was no significant difference in PFS between olaparib, niraparib, and rucaparib, which provides necessary quantitative information for the clinical practice of PARPis in the treatment of ROC.

Tuberculosis has been described as a global health crisis since the 1990s, with an estimated 1.4 million deaths in the last year. Herein, a series of 20 1H-indoles were synthesized and evaluated as in vitro inhibitors of Mycobacterium tuberculosis (Mtb) growth. Furthermore, the top hit compounds were active against multidrug-resistant strains, without cross-resistance with first-line drugs. Exposing HepG2 and Vero cells to the molecules for 72 h showed that one of the evaluated structures was devoid of apparent toxicity. In addition, this 3-phenyl-1H-indole showed no genotoxicity signals. Finally, time-kill and pharmacodynamic model analyses demonstrated that this compound has bactericidal activity at concentrations close to the Minimum Inhibitory Concentration, coupled with a strong time-dependent behavior. To the best of our knowledge, this study describes the activity of 3-phenyl-1H-indole against Mtb for the first time.

The success of antimicrobial treatment is threatened by the evolution of drug resistance. Population genetic models are an important tool in mitigating that threat. However, most such models consider resistance emergence via a single mutational step. Here, we assembled experimental evidence that drug resistance evolution follows two patterns: (i) a single mutation, which provides a large resistance benefit, or (ii) multiple mutations, each conferring a small benefit, which combine to yield high-level resistance. Using stochastic modeling, we then investigated the consequences of these two patterns for treatment failure and population diversity under various treatments. We find that resistance evolution is substantially limited if more than two mutations are required and that the extent of this limitation depends on the combination of drug type and pharmacokinetic profile. Further, if multiple mutations are necessary, adaptive treatment, which only suppresses the bacterial population, delays treatment failure due to resistance for a longer time than aggressive treatment, which aims at eradication.
The rise in antibiotic resistance is threatening our ability to treat bacterial infections. Bacteria often evolve resistance by acquiring new genetic mutations during the treatment period. Understanding how resistance emerges and spreads through a bacterial population is crucial to prevent antibiotic drugs from failing. Mathematical models are a useful tool for exploring how bacteria will respond to antibiotics and assessing the risk of resistance. Usually, these models only consider instances where bacteria acquire one genetic mutation that makes them virtually impervious to treatment. But, in nature, this is not the only possibility. Although some mutations do give bacteria a high level of resistance, numerous others only provide small amounts of protection against the drug. If these mutations accumulate in the same bacterial cell, their effects can combine to make the strain highly resistant to treatment. But it was unclear how the emergence of multiple mutations affects the risk of treatment failure and the diversity of the bacterial population. To answer this question, Igler et al. devised a mathematical model in which each bacterium is able to mutate multiple times during the treatment period. The model revealed that if one mutation provides a high level of resistance on its own, the risk of bacteria surviving treatment is very high. But, if it takes more than two mutations to achieve a high level of resistance, the risk drops to almost nothing. Igler et al. also found that the chance of bacteria evolving high enough resistance is affected by the type of antibiotics used and how fast the drug decays. With low-level resistance mutations, adapting treatment to maintain an acceptable number of sensitive bacteria as competitors for (a small number of) resistant bacteria was more effective at delaying treatment failure than trying to kill all the bacteria at once. These findings suggest that adjusting the treatment strategy used for bacterial infections according to the proportion of low- and high-level resistance mutations could slow down the evolution of resistance. To apply these models in the real world, it will be important to measure the level of resistance conferred by single mutations. The type of models used here could also predict the response of other diseases that resist treatment, such as cancer.

BACKGROUND: Rhubarb (Rhei Radix et Rhizoma) is a traditional Chinese medicine, has been used as a strong astringent in China to treat inflammation-related diseases, such as acute pancreatitis, acute cholecystitis, appendicitis and so on. Rhein, emodin and aloe-emodin are the important active anthraquinone in rhubarb, and are considered to be the main ingredients contributing to anti-inflammatory.
OBJECTIVE: Rhein, emodin and aloe-emodin, anthraquinones with the same parent structure that are found in rhubarb, have beneficial anti-inflammatory effects in vitro and in vivo. Anthraquinone derivatives also have important clinical roles. However, their pharmacodynamic differences and the structure-activity relationships associated with their anti-inflammatory properties have not been systematically explored. The present study was designed to quantify the effects of three rhubarb anthraquinones on inflammation and to explore the structure-activity relationships of these compounds.
METHODS: In this study, we detected NF-κB phosphorylation, iNOS protein expression, and IL-6 and NO production in LPS-stimulated RAW264.7 cells and then calculated median effect equations and built a dynamic pharmacodynamic model to quantitatively evaluate the efficacy of these three anthraquinones. Additionally, to determine the structure-activity relationships, we investigated the physicochemical properties and molecular electrostatic potentials of the drug molecules.
RESULTS: We found that rhein, emodin, and aloe-emodin exerted at least dual-target (NF-κB, iNOS) inhibition of LPS-induced inflammatory responses. Compared with rhein and emodin, aloe-emodin had a stronger anti-inflammatory effect, and its inhibition of iNOS protein expression was approximately twice that of NF-κB phosphorylation. In addition, aloe-emodin had the strongest hydrophobic effect among the three anthraquinones.
CONCLUSIONS: Overall, we concluded that the receptor binding the rhubarb anthraquinones had a hydrophobic pocket. Anthraquinone molecules with stronger hydrophobic effects had higher affinity for the receptor, resulting in greater anti-inflammatory activity. These results suggest that the addition of a hydrophobic group is a potential method for structural modification to design anti-inflammatory anthraquinone derivatives with enhanced potency.

BACKGROUND: Multiagent therapies, due to their ability to delay or overcome resistance, are a hallmark of treatment in multiple myeloma (MM). The growing number of therapeutic options in MM requires high-throughput combination screening tools to better allocate treatment, and facilitate personalized therapy.
METHODS: A second-order drug response model was employed to fit patient-specific ex vivo responses of 203 MM patients to single-agent models. A novel pharmacodynamic model, developed to account for two-way combination effects, was tested with 130 two-drug combinations. We have demonstrated that this model is sufficiently parameterized by single-agent and fixed-ratio combination responses, by validating model estimates with ex vivo combination responses for different concentration ratios, using a checkerboard assay. This new model reconciles ex vivo observations from both Loewe and BLISS synergy models, by accounting for the dimension of time, as opposed to focusing on arbitrary time-points or drug effect. Clinical outcomes of patients were simulated by coupling patient-specific drug combination models with pharmacokinetic data.
RESULTS: Combination screening showed 1 in 5 combinations (21.43% by LD50, 18.42% by AUC) were synergistic ex vivo with statistical significance (P < 0.05), but clinical synergy was predicted for only 1 in 10 combinations (8.69%), which was attributed to the role of pharmacokinetics and dosing schedules.
CONCLUSIONS: The proposed framework can inform clinical decisions from ex vivo observations, thus providing a path toward personalized therapy using combination regimens.
BACKGROUND: This research was funded by the H. Lee Moffitt Cancer Center Physical Sciences in Oncology (PSOC) Grant (1U54CA193489-01A1) and by H. Lee Moffitt Cancer Center\'s Team Science Grant. This work has been supported in part by the PSOC Pilot Project Award (5U54CA193489-04), the Translational Research Core Facility at the H. Lee Moffitt Cancer Center & Research Institute, an NCI-designated Comprehensive Cancer Center (P30-CA076292), the Pentecost Family Foundation, and Miles for Moffitt Foundation.

Use of pharmacodynamic in vitro models provides more clinically relevant information about the activities of antibiotics than static endpoints. Several models are used to simulate pharmacokinetics by dilution of the medium. It is discussed whether this procedure would result in a washout of bacteria, particularly if profiles with a short half-life are simulated. Methods have been developed to minimise the washout of bacteria. Bacteria are retained in the system either by centrifugation and resuspension, use of filters, a capillary unit, dialysis tubing or mathematical correction, versus systems with an unprotected outflow allowing a continuous washout of bacteria. None of these eight models has been directly compared with another. Therefore, an interlaboratory study was performed to address the question of whether or not washout matters. All laboratories used identical batches of media, bacteria, antibiotics and simulated pharmacokinetic profiles with a short or long half-life. Values of area under the bacterial kill-time curve (AUBKC), single-point kill rate and time to 3-log10 reduction of inoculum were calculated. These parameters did not differ significantly between the models. Differences were noted if the inoculum was prepared from the early logarithmic growth phase compared with the late logarithmic or stationary growth phase, resulting either in a pronounced or reduced antibacterial activity. Thus, preparation of inocula affects the results generated, whereas washout of bacteria has apparently a negligible impact on antibacterial activities.