Application of different approaches to generate virtual patient populations for the quantitative systems pharmacology model of erythropoiesis.

In a standard situation, a quantitative systems pharmacology model describes a "reference patient," and the model parameters are fixed values allowing only the mean values to be described. However, the results of clinical trials include a description of variability in patients' responses to a drug, which is typically expressed in terms of conventional statistical parameters, such as standard deviations (SDs) from mean values. Therefore, in this study, we propose and compare four different approaches: (1) Monte Carlo Markov Chain (MCMC); (2) model fitting to Monte Carlo sample; (3) population of clones; (4) stochastically bounded selection to generate virtual patient populations based on experimentally measured mean data and SDs. We applied these approaches to generate virtual patient populations in the QSP model of erythropoiesis. According to the results of our research, stochastically bounded selection showed slightly better results than the other three methods as it allowed the description of any number of patients from clinical trials and could be applied in the case of complex models with a large number of variable parameters.

Comparison of asymptotic confidence sets for regression in small samples.

In case of small samples, asymptotic confidence sets may be inaccurate, with their actual coverage probability far from a nominal confidence level. In a single framework, we consider four popular asymptotic methods of confidence estimation. These methods are based on model linearization, F-test, likelihood ratio test, and nonparametric bootstrapping procedure. Next, we apply each of these methods to derive three types of confidence sets: confidence intervals, confidence regions, and pointwise confidence bands. Finally, to estimate the actual coverage of these confidence sets, we conduct a simulation study on three regression problems. A linear model and nonlinear Hill and Gompertz models are tested in conditions of different sample size and experimental noise. The simulation study comprises calculation of the actual coverage of confidence sets over pseudo-experimental datasets for each model. For confidence intervals, such metrics as width and simultaneous coverage are also considered. Our comparison shows that the F-test and linearization methods are the most suitable for the construction of confidence intervals, the F-test - for confidence regions and the linearization - for pointwise confidence bands.

Prediction of long-term treatment outcome in HCV following 24 day PEG-IFN alpha-2b therapy using population pharmacokinetic-pharmacodynamic mixture modeling and classification analysis.

Mathematical models have been widely used for understanding the dynamics of the hepatitis C virus (HCV). We propose a method to predict final clinical outcome for 24 HIV-HCV - coinfected patients with the help of a mathematical model based on the first two weeks of PEG-IFN therapy. Applying a pharmacokinetic-pharmacodynamic (PKPD) approach, together with mixture models, to the adapted model of viral dynamics developed by Neumann et al., we have analyzed the influence of PEG-IFN on the kinetics and interaction of target cells, infected cells and virus mRNA. It was found that PEG-IFN pharmacokinetic parameters were similar in sustained virological responders and nonresponders, while the plasma PEG-IFN concentration that decreases HCV production by 50% (EC50) and the rate of infected cell death were different. The treatment outcome depended mainly on the initial viral mRNA concentration and the rate of infected cell death. The population PKPD approach with a mixture model enabled the determination of individual PKPD parameters and showed high sensitivity (93.5%) and specificity (97.4%) for the prediction of the treatment outcome.

Receptor occupancy assessment and interpretation in terms of quantitative systems pharmacology: nivolumab case study.

Receptor occupancy assays applied in clinical studies provide insights into pharmacokinetic-pharmacodynamic relationships for therapeutic antibodies. When measured by different assays, however, receptor occupancy results can be controversial, as was observed for nivolumab, a monoclonal antibody targeting programmed cell death 1 (PD-1) receptor. We suggested an explanation of results obtained and a mechanistic approach based on specific features of the receptor occupancy assays: measurement of the free or bound receptor, normalized to the baseline or at each time point. The approach was evaluated against controversial clinical data on PD-1 receptor occupancy by nivolumab. It was shown that receptor occupancy measured by different assays might vary substantially if the internalization rate of the bound receptor is higher than the rate of degradation of the free receptor. Equations proposed in this work can be applied in quantitative systems pharmacology models to describe target receptor occupancy by different therapeutic antibodies.

CYTOCON: The manually curated database of human in vivo cell and molecule concentrations.

Cell and cYTOkine CONcentrations DataBase (CYTOCON DB) is a project undertaken by the InSysBio team and aimed at the development of a database that allows collecting, processing, and visualizing publicly available in vivo human data on baseline concentrations of cells, cytokines, chemokines, and other molecules. Besides manual curation, an important feature of CYTOCON is that most values found in papers are converted from a huge variety of original units (i.e., mg/ml and number of cells per mm2 of biopsy surface section) to unified units: "pM" for cytokine and "kcell/L" for cell concentration. These features of the database can help researchers facilitate the creation and calibration of quantitative systems pharmacology (QSP) models. Possible applications can be: estimation of the average value or variability of the cell, cytokine or chemokine concentrations for patient groups with different characteristics, such as age, gender, disease severity, disease subtype, etc.; and analysis of correlations among the cell, cytokine, or chemokine concentrations in patients with different characteristics, such as severity of the disease.

Monoclonal antibody therapy efficacy can be boosted by combinations with other treatments: Predictions using an integrated Alzheimer's Disease Platform.

For many years, clinical research in Alzheimer's disease (AD) has focused on attempts to identify the most explicit biomarker, namely amyloid beta. Unfortunately, the numerous therapies that have been developed have failed in clinical practice. AD arises as a consequence of multiple factors, and as such it requires a more mechanistic analytical approach than statistical modeling. Quantitative systems pharmacology modeling is a valuable tool for drug development. It utilizes in vitro data for the calibration of parameters, embeds them into physiologically based structures, and explores translation between animals and humans. Such an approach allows for a quantitative study of the dynamics of the interactions between multiple factors or variables. Here, we present an overview of the quantitative translational model in AD, which embraces current preclinical and clinical data. The previously published description of amyloid physiology has been updated and joined with a model for tau pathology and multiple intraneuronal processes responsible for cellular transport, metabolism, or proteostasis. In addition, several hypotheses regarding the best correlates of cognitive deterioration have been validated using clinical data. Here, the amyloid hypothesis was unable to predict the aducanumab clinical trial data, whereas simulations of cognitive impairment coupled with tau seeding or neuronal breakdown (expressed as caspase activity) matched the data. A satisfactory validation of the data from multiple preclinical and clinical studies was followed by an attempt to predict the results of combinatorial treatment with targeted immunotherapy and activation of autophagy using rapamycin. The combination is predicted to yield better efficacy than immunotherapy alone.

Kinetic modeling as a tool to integrate multilevel dynamic experimental data.

The metabolic networks are the most well-studied biochemical systems, with an abundance of in vitro and in vivo data available for quantitative estimation of its kinetic parameters. In this chapter, we present our approach to developing mathematical description of metabolic pathways. The model-based integration of reaction kinetics and the utilization of different types of experimental data including temporal dependencies have been described in detail. Software package DBSolve7 which allows us to develop kinetic model of the biochemical system and integrate experimental data has been presented.

The Edinburgh human metabolic network reconstruction and its functional analysis.

A better understanding of human metabolism and its relationship with diseases is an important task in human systems biology studies. In this paper, we present a high-quality human metabolic network manually reconstructed by integrating genome annotation information from different databases and metabolic reaction information from literature. The network contains nearly 3000 metabolic reactions, which were reorganized into about 70 human-specific metabolic pathways according to their functional relationships. By analysis of the functional connectivity of the metabolites in the network, the bow-tie structure, which was found previously by structure analysis, is reconfirmed. Furthermore, the distribution of the disease related genes in the network suggests that the IN (substrates) subset of the bow-tie structure has more flexibility than other parts.

Kinetic model of phosphofructokinase-1 from Escherichia coli.

This paper presents a kinetic model of phosphofructokinase-1 from Escherichia coli. A complete catalytic cycle has been reconstructed based on available information on the oligomeric structure of the enzyme and kinetic mechanism of its monomer. Applying the generalization of the Monod-Wyman-Changeux approach proposed by Popova and Sel'kov(35-37) to the reconstructed catalytic cycle rate equation has been derived. Dependence of the reaction rate on pH, magnesium, and effectors has been taken into account. Kinetic parameters have been estimated via fitting the rate equation against experimentally measured dependencies of initial rate on substrates, products, effectors, and pH available from the literature. The model of phosphofructokinase-1 predicts (1) cooperativity of binding both fructose-6-phosphate and ATPMg(2-), (2) significant inhibition of the enzyme resulting from an increase in total concentration of ATP under the condition of fixed concentration of Mg(2+) ions, and (3) dual effect of ADP consisting of allosteric activation and product inhibition of the enzyme. Moreover, the model developed can be used in the kinetic modeling of biochemical pathways containing phosphofructokinase-1.

Kinetic modeling of ace operon genetic regulation in Escherichia coli.

A family of kinetic models has been developed that takes into account available experimental information on the regulation of ace operon expression in Escherichia coli. This has allowed us to study and analyze possible versions of regulation of the ace operon and to test their possibilities. Based on literature analysis, we found that there is an ambiguity of properties of IclR (main repressor of ace operon). The main aspect of this ambiguity are two different forms of IclR purified from E. coli K strain and different coeffector sets for IclR purified from E. coli K and B strains. It has been shown that the full-length form of IclR is physiologically relevant and that IclR truncation is a result of purification of the protein from E. coli K strains. We also found that the IclR protein purified from E. coli B strain carries two coeffector binding sites. Using model-developed levels of steady state aceBAK expression against physiological ranges of coeffectors, concentration has been predicted.

A mathematical model of multisite phosphorylation of tau protein.

Abnormal tau metabolism followed by formation of tau deposits causes a number of neurodegenerative diseases called tauopathies including Alzheimer's disease. Hyperphosphorylation of tau protein precedes tau aggregation and is a topic of interest for the development of pharmacological interventions to prevent pathology progression at early stages. The development of a mathematical model of multisite phosphorylation of tau would be helpful for searching for the targets of pharmacological interventions and candidates for biomarkers of pathology progression. In the present study, we for the first time developed a model of multisite phosphorylation of tau protein and elucidated the relative contribution of kinases to phosphorylation of distinct sites. The model describes phosphorylation of tau or PKA-prephosphorylated tau by GSK3ß and CDK5 and dephosphorylation by PP2A, accurately reproducing the data for short-term kinetics of tau (de)phosphorylation. Our results suggest that kinase inhibition may more specifically prevent tau hyperphosphorylation, e.g., on PHF sites, which are key biomarkers of pathological changes in Alzheimer's disease. The main features of our model are partial phosphorylation of tau residues and merging of random and sequential mechanisms of multisite phosphorylation within the framework of the probability-based approach assuming independent phosphorylation events.

Correction: A mathematical model of multisite phosphorylation of tau protein.

[This corrects the article DOI: 10.1371/journal.pone.0192519.].

Studying the Progression of Amyloid Pathology and Its Therapy Using Translational Longitudinal Model of Accumulation and Distribution of Amyloid Beta.

Long-term effects of amyloid targeted therapy can be studied using a mechanistic translational model of amyloid beta (Aß) distribution and aggregation calibrated on published data in mouse and human species. Alzheimer disease (AD) pathology is modeled utilizing age-dependent pathological evolution for rate constants and several variants of explicit functions for Aß toxicity influencing cognitive outcomes (Adas-cog). Preventive Aß targeted therapies were simulated to minimize the Aß difference from healthy physiological levels. Therapeutic targeted simulations provided similar predictions for mouse and human studies. Our model predicts that: (1) at least 1 year (2 years for preclinical AD) of treatment is needed to observe cognitive effects; (2) under the hypothesis with functional importance of Aß, a 15% decrease in Aß (using an imaging biomarker) is related to 15-20% cognition improvement by immunotherapy. Despite negative outcomes in clinical trials, Aß continues to remain a prospective target demanding careful assessment of mechanistic effect and duration of trial design.

Comprehensive study of the drug delivery properties of poly(l-lactide)-poly(ethylene glycol) nanoparticles in rats and tumor-bearing mice.

Nanoparticles made of polylactide-poly(ethylene glycol) block-copolymer (PLA-PEG) are promising vehicles for drug delivery due to their biodegradability and controllable payload release. However, published data on the drug delivery properties of PLA-PEG nanoparticles are heterogeneous in terms of nanoparticle characteristics and mostly refer to low injected doses (a few mg nanoparticles per kg body weight). We have performed a comprehensive study of the biodistribution of nanoparticle formulations based on PLA-PEG nanoparticles of ~100nm size at injected doses of 30 to 140mg/kg body weight in healthy rats and nude tumor-bearing mice. Nanoparticle formulations differed by surface PEG coverage and by release kinetics of the encapsulated model active pharmaceutical ingredient (API). Increase in PEG coverage prolonged nanoparticle circulation half-life up to ~20h in rats and ~10h in mice and decreased retention in liver, spleen and lungs. Circulation half-life of the encapsulated API grew monotonously as the release rate slowed down. Plasma and tissue pharmacokinetics was dose-linear for inactive nanoparticles, but markedly dose-dependent for the model therapeutic formulation, presumably because of the toxic effects of released API. A mathematical model of API distribution calibrated on the data for inactive nanoparticles and conventional API form correctly predicted the distribution of the model therapeutic formulation at the lowest investigated dose, but for higher doses the toxic action of the released API had to be explicitly modelled. Our results provide a coherent illustration of the ability of controllable-release PLA-PEG nanoparticles to serve as an effective drug delivery platform to alter API biodistribution. They also underscore the importance of physiological effects of released drug in determining the biodistribution of therapeutic drug formulations at doses approaching tolerability limits.

Analysis of the efficacy of SGLT2 inhibitors using semi-mechanistic model.

The Renal sodium-dependent glucose co-transporter 2 (SGLT2) is one of the most promising targets for the treatment of type 2 diabetes. Two SGLT2 inhibitors, dapagliflozin, and canagliflozin, have already been approved for use in USA and Europe; several additional compounds are also being developed for this purpose. Based on the in vitro IC50 values and plasma concentration of dapagliflozin measured in clinical trials, the marketed dosage of the drug was expected to almost completely inhibit SGLT2 function and reduce glucose reabsorption by 90%. However, the administration of dapagliflozin resulted in only 30-50% inhibition of reabsorption. This study was aimed at investigating the mechanism underlying the discrepancy between the expected and observed levels of glucose reabsorption. To this end, systems pharmacology models were developed to analyze the time profile of dapagliflozin, canagliflozin, ipragliflozin, empagliflozin, and tofogliflozin in the plasma and urine; their filtration and active secretion from the blood to the renal proximal tubules; reverse reabsorption; urinary excretion; and their inhibitory effect on SGLT2. The model shows that concentration levels of tofogliflozin, ipragliflozin, and empagliflozin are higher than levels of other inhibitors following administration of marketed SGLT2 inhibitors at labeled doses and non-marketed SGLT2 inhibitors at maximal doses (approved for phase 2/3 studies). All the compounds exhibited almost 100% inhibition of SGLT2. Based on the results of our model, two explanations for the observed low efficacy of SGLT2 inhibitors were supported: (1) the site of action of SGLT2 inhibitors is not in the lumen of the kidney's proximal tubules, but elsewhere (e.g., the kidneys proximal tubule cells); and (2) there are other transporters that could facilitate glucose reabsorption under the conditions of SGLT2 inhibition (e.g., other transporters of SGLT family).

Modeling of celiac disease immune response and the therapeutic effect of potential drugs.

BACKGROUND: Celiac disease (CD) is an autoimmune disorder that occurs in genetically predisposed people and is caused by a reaction to the gluten protein found in wheat, which leads to intestinal villous atrophy. Currently there is no drug for treatment of CD. The only known treatment is lifelong gluten-free diet. The main aim of this work is to develop a mathematical model of the immune response in CD patients and to predict the efficacy of a transglutaminase-2 (TG-2) inhibitor as a potential drug for treatment of CD. RESULTS: A thorough analysis of the developed model provided the following results:1. TG-2 inhibitor treatment leads to insignificant decrease in antibody levels, and hence remains higher than in healthy individuals.2. TG-2 inhibitor treatment does not lead to any significant increase in villous area.3. The model predicts that the most effective treatment of CD would be the use of gluten peptide analogs that antagonize the binding of immunogenic gluten peptides to APC. The model predicts that the treatment of CD by such gluten peptide analogs can lead to a decrease in antibody levels to those of normal healthy people, and to a significant increase in villous area. CONCLUSIONS: The developed mathematical model of immune response in CD allows prediction of the efficacy of TG-2 inhibitors and other possible drugs for the treatment of CD: their influence on the intestinal villous area and on the antibody levels. The model also allows to understand what processes in the immune response have the strongest influence on the efficacy of different drugs. This model could be applied in the pharmaceutical R&D arena for the design of drugs against autoimmune small intestine disorders and on the design of their corresponding clinical trials.

Systems pharmacology of the nerve growth factor pathway: use of a systems biology model for the identification of key drug targets using sensitivity analysis and the integration of physiology and pharmacology.

The nerve growth factor (NGF) pathway is of great interest as a potential source of drug targets, for example in the management of certain types of pain. However, selecting targets from this pathway either by intuition or by non-contextual measures is likely to be challenging. An alternative approach is to construct a mathematical model of the system and via sensitivity analysis rank order the targets in the known pathway, with respect to an endpoint such as the diphosphorylated extracellular signal-regulated kinase concentration in the nucleus. Using the published literature, a model was created and, via sensitivity analysis, it was concluded that, after NGF itself, tropomyosin receptor kinase A (TrkA) was one of the most sensitive druggable targets. This initial model was subsequently used to develop a further model incorporating physiological and pharmacological parameters. This allowed the exploration of the characteristics required for a successful hypothetical TrkA inhibitor. Using these systems models, we were able to identify candidates for the optimal drug targets in the known pathway. These conclusions were consistent with clinical and human genetic data. We also found that incorporating appropriate physiological context was essential to drawing accurate conclusions about important parameters such as the drug dose required to give pathway inhibition. Furthermore, the importance of the concentration of key reactants such as TrkA kinase means that appropriate contextual data are required before clear conclusions can be drawn. Such models could be of great utility in selecting optimal targets and in the clinical evaluation of novel drugs.

Kinetic modelling of central carbon metabolism in Escherichia coli.

UNLABELLED: In the present study, we developed a detailed kinetic model of Escherichia coli central carbon metabolism. The main model assumptions were based on the results of metabolic and regulatory reconstruction of the system and thorough model verification with experimental data. The development and verification of the model included several stages, which allowed us to take into account both in vitro and in vivo experimental data and avoid the ambiguity that frequently occurs in detailed models of biochemical pathways. The choice of the level of detail for the mathematical description of enzymatic reaction rates and the evaluation of parameter values were based on available published data. Validation of the complete model of the metabolic pathway describing specific physiological states was based on fluxomics and metabolomics data. In particular, we developed a model that describes aerobic growth of E. coli in continuous culture with a limiting concentration of glucose. Such modification of the model was used to integrate experimental metabolomics data obtained in steady-state conditions for wild-type E. coli and genetically modified strains, e.g. knockout of the pyruvate kinase gene (pykA). Following analysis of the model behaviour, and comparison of the coincidence between predicted and experimental data, it was possible to investigate the functional and regulatory properties of E. coli central carbon metabolism. For example, a novel metabolic regulatory mechanism for 6-phosphogluconate dehydrogenase inhibition by phosphoenolpyruvate was hypothesized, and the flux ratios between the reactions catalysed by enzyme isoforms were predicted. DATABASE: The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/peskov/index.html

Regulation of leukotriene and 5oxoETE synthesis and the effect of 5-lipoxygenase inhibitors: a mathematical modeling approach.

BACKGROUND: 5-lipoxygenase (5-LO) is a key enzyme in the synthesis of leukotrienes and 5-Oxo-6E,8Z,11Z,14Z-eicosatetraenoic acid (oxoETE). These inflammatory signaling molecules play a role in the pathology of asthma and so 5-LO inhibition is a promising target for asthma therapy. The 5-LO redox inhibitor zileuton (Zyflo IR/CR(®)) is currently marketed for the treatment of asthma in adults and children, but widespread use of zileuton is limited by its efficacy/safety profile, potentially related to its redox characteristics. Thus, a quantitative, mechanistic description of its functioning may be useful for development of improved anti-inflammatory targeting this mechanism. RESULTS: A mathematical model describing the operation of 5-LO, phospholipase A2, glutathione peroxidase and 5-hydroxyeicosanoid dehydrogenase was developed. The catalytic cycles of the enzymes were reconstructed and kinetic parameters estimated on the basis of available experimental data. The final model describes each stage of cys-leukotriene biosynthesis and the reactions involved in oxoETE production. Regulation of these processes by substrates (phospholipid concentration) and intracellular redox state (concentrations of reduced glutathione, glutathione (GSH), and lipid peroxide) were taken into account. The model enabled us to reveal differences between redox and non-redox 5-LO inhibitors under conditions of oxidative stress. Despite both redox and non-redox inhibitors suppressing leukotriene A4 (LTA4) synthesis, redox inhibitors are predicted to increase oxoETE production, thus compromising efficacy. This phenomena can be explained in terms of the pseudo-peroxidase activity of 5-LO and the ability of lipid peroxides to transform 5-LO into its active form even in the presence of redox inhibitors. CONCLUSIONS: The mathematical model developed described quantitatively different mechanisms of 5-LO inhibition and simulations revealed differences between the potential therapeutic outcomes for these mechanisms.