Hepatocyte lipid and glucose metabolism is regulated not only by major hormones like insulin and glucagon but also by many other factors, including calcium ions. Recently, mitochondria-associated membrane (MAM) dysfunction combined with incorrect IP3-receptor regulation has been shown to result in abnormal calcium signaling in hepatocytes. This dysfunction could further lead to hepatic metabolism pathology. However, the exact contribution of MAM dysfunction, incorrect IP3-receptor regulation and insulin resistance to the calcium-insulin-glucagon interplay is not understood yet. In this work, we analyze the role of abnormal calcium signaling and insulin dysfunction in hepatocytes by proposing a model of hepatocyte metabolic regulatory network with a detailed focus on the model construction details besides the biological aspect. In this work, we analyze the role of abnormal calcium signaling and insulin dysfunction in hepatocytes by proposing a model of hepatocyte metabolic regulatory network. We focus on the model construction details, model validation, and predictions. We describe the dynamic regulation of signaling processes by sigmoid Hill function. In particular, we study the effect of both the Hill function slope and the distance between Hill function extremes on metabolic processes in hepatocytes as a model of nonspecific insulin dysfunction. We also address the significant time difference between characteristic time of glucose hepatic processing and a typical calcium oscillation period in hepatocytes. Our modeling results show that calcium signaling dysfunction results in an abnormal increase in postprandial glucose levels, an abnormal glucose decrease in fasting, and a decreased amount of stored glycogen. An insulin dysfunction of glucose phosphorylation, glucose dephosphorylation, and glycogen breakdown also cause a noticeable effect. We also get some insight into the so-called hepatic insulin resistance paradox, confirming the hypothesis regarding indirect insulin action on hepatocytes via dysfunctional adipocyte lipolysis.

Polymeric nanoparticles are highly tunable drug delivery systems that show promise in targeting therapeutics to specific sites within the body. Rational nanoparticle design can make use of mathematical models to organize and extend experimental data, allowing for optimization of nanoparticles for particular drug delivery applications. While rational nanoparticle design is attractive from the standpoint of improving therapy and reducing unnecessary experiments, it has yet to be fully realized. The difficulty lies in the complexity of nanoparticle structure and behavior, which is added to the complexity of the physiological mechanisms involved in nanoparticle distribution throughout the body. In this review, we discuss the most important aspects of rational design of polymeric nanoparticles. Ultimately, we conclude that many experimental datasets are required to fully model polymeric nanoparticle behavior at multiple scales. Further, we suggest ways to consider the limitations and uncertainty of experimental data in creating nanoparticle design optimization schema, which we call quantitative nanoparticle design frameworks.

Compared with traditional oral and injection administration, the transdermal administration of traditional Chinese medicine has distinctive characteristics and advantages, which can avoid the \"first pass effect\" of the liver and the destruction of the gastrointestinal tract, maintain a stable blood concentration, and prolong drug action time. However, the basic theory and technology research in transdermal drug delivery are relatively limited at present, especially regarding research on new carriers of transdermal drug delivery and pharmacokinetic studies of the skin, which has become a bottleneck of transdermal drug delivery development. Triptolide is one of the main active components of Tripterygium wilfordii, which displays activities against mouse models of polycystic kidney disease and pancreatic cancer but its physical properties and severe toxicity limit its therapeutic potential. Due to the previously mentioned advantages of transdermal administration, in this study, we performed a detail analysis of the pharmacokinetics of a new transdermal triptolide delivery system. Triptolide nanoemulsion gels were prepared and served as new delivery systems, and the ex vivo characteristics were described. The metabolic characteristics of the different triptolide transdermal drug delivery formulations were investigated via skin-blood synchronous microdialysis combined with LC/MS. A multiscale modeling framework, molecular dynamics and finite element modeling were adopted to simulate the transport process of triptolide in the skin and to explore the pharmacokinetics and mathematical patterns. This study shows that the three-layer model can be used for transdermal drug delivery system drug diffusion research. Therefore, it is profitable for transdermal drug delivery system design and the optimization of the dosage form. Based on the drug concentration of the in vivo microdialysis measurement technology, the diffusion coefficient of drugs in the skin can be more accurately measured, and the numerical results can be verified. Therefore, the microdialysis technique combined with mathematical modeling provides a very good platform for the further study of transdermal delivery systems. This research will provide a new technology and method for the study of the pharmacokinetics of traditional Chinese medicine transdermal drug delivery. It has important theoretical and practical significance in clarifying the metabolic transformation of percutaneous drug absorption and screening for appropriate drugs and dosage forms of transdermal drug delivery.

Paxlovid is a promising, orally bioavailable novel drug for SARS-CoV-2 with excellent safety profiles. Our main goal here is to explore the pharmacometric features of this new antiviral. To provide a detailed assessment of Paxlovid, we propose a hybrid multiscale mathematical approach. We demonstrate that the results of the present in silico evaluation match the clinical expectations remarkably well: on the one hand, our computations successfully replicate the outcome of an actual in vitro experiment; on the other hand, we verify both the sufficiency and the necessity of Paxlovid\'s two main components (nirmatrelvir and ritonavir) for a simplified in vivo case. Moreover, in the simulated context of our computational framework, we visualize the importance of early interventions and identify the time window where a unit-length delay causes the highest level of tissue damage. Finally, the results\' sensitivity to the diffusion coefficient of the virus is explored in detail.

BACKGROUND: Neurogenesis in the murine cerebral cortex involves the coordinated divisions of two main types of progenitor cells, whose numbers, division modes and cell cycle durations set up the final neuronal output. To understand the respective roles of these factors in the neurogenesis process, we combine experimental in vivo studies with mathematical modeling and numerical simulations of the dynamics of neural progenitor cells. A special focus is put on the population of intermediate progenitors (IPs), a transit amplifying progenitor type critically involved in the size of the final neuron pool.
RESULTS: A multiscale formalism describing IP dynamics allows one to track the progression of cells along the subsequent phases of the cell cycle, as well as the temporal evolution of the different cell numbers. Our model takes into account the dividing apical progenitors (AP) engaged into neurogenesis, both neurogenic and proliferative IPs, and the newborn neurons. The transfer rates from one population to another are subject to the mode of division (proliferative, or neurogenic) and may be time-varying. The model outputs are successfully fitted to experimental cell numbers from mouse embryos at different stages of cortical development, taking into account IPs and neurons, in order to adjust the numerical parameters. We provide additional information on cell kinetics, such as the mitotic and S phase indexes, and neurogenic fraction.
CONCLUSIONS: Applying the model to a mouse mutant for Ftm/Rpgrip1l, a gene involved in human ciliopathies with severe brain abnormalities, reveals a shortening of the neurogenic period associated with an increased influx of newborn IPs from apical progenitors at mid-neurogenesis. Our model can be used to study other mouse mutants with cortical neurogenesis defects and can be adapted to study the importance of progenitor dynamics in cortical evolution and human diseases.