Apoptosis is an important physiological process crucially involved in development and homeostasis of multicellular organisms. Although the major signaling pathways have been unraveled, a detailed mechanistic understanding of the complex underlying network remains elusive. We have translated here the current knowledge of the molecular mechanisms of the deathreceptor-activated caspase cascade into a mathematical model. A reduction down to the apoptotic core machinery enables the application of analytical mathematical methods to evaluate the system behavior within a wide range of parameters. Using parameter values from the literature, the model reveals an unstable status of survival indicating the need for further control. Based on recent publications we tested one additional regulatory mechanism at the level of initiator caspase activation and demonstrated that the resulting system displays desired characteristics such as bistability. In addition, the results from our model studies allowed us to reconcile the fast kinetics of caspase 3 activation observed at the single cell level with the much slower kinetics found at the level of a cell population.Apoptosis is a genetically defined major form of programmed cell death enabling the organism to remove unwanted cells, e.g. during embryonal development and after immune responses, to select educated immune cells and to eliminate virally infected and transformed cells (1, 2). Enhanced or inhibited apoptotic cell death can be involved in severe pathological alterations, including developmental defects, autoimmune diseases, neurodegeneration, or cancer. Extrinsic and intrinsic apoptotic pathways can be distinguished, although partly employing overlapping signal transduction pathways. A hallmark of the ongoing apoptotic process is the activation of a family of aspartatedirected cysteine proteases, the caspases. Caspases are produced as proenzymes and become activated upon cleavage (3). Activation of caspases finally dismantles the cells via the cleavage of important regulatory and structural proteins and enables phagocytic removal of the dying cell (4). A simplified outline of the extrinsic pathway of apoptosis induction after death receptor stimulation is depicted in Fig. 1.Mathematical modeling and systems theory can provide valuable tools to get insight into complex dynamical systems, to test hypotheses, and to identify weak points (5, 6). Previous modeling approaches in apoptosis focused on the extrinsically triggered pathways, resulting in complex models (7,8). The model parameters were fitted to data derived from cell population studies showing caspase activation in a range from 30 min to several hours. These models can describe and nicely illustrate certain aspects of the signal transduction pathway. However, more recent experimental results performed at the single cell level show that the majority of caspases are activated within a very short time interval (Ͻ15 min) (9 -12).Obviously, the single cell level is relevant for a mechanistic understanding. With the focus...

The aim of this tutorial is to introduce the fundamental concepts of physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling with a special focus on their practical implementation in a typical PBPK model building workflow. To illustrate basic steps in PBPK model building, a PBPK model for ciprofloxacin will be constructed and coupled to a pharmacodynamic model to simulate the antibacterial activity of ciprofloxacin treatment.

The presented results facilitate the integration of pregnancy-dependent changes in anatomy and physiology into mechanistic population physiologically based pharmacokinetic models. Such models can ultimately provide a valuable tool to investigate the pharmacokinetics during pregnancy in silico and support informed decision making regarding optimal dosing regimens in this vulnerable special population.

Today, in silico studies and trial simulations already complement experimental approaches in pharmaceutical R&D and have become indispensable tools for decision making and communication with regulatory agencies. While biology is multiscale by nature, project work, and software tools usually focus on isolated aspects of drug action, such as pharmacokinetics at the organism scale or pharmacodynamic interaction on the molecular level. We present a modeling and simulation software platform consisting of PK-Sim® and MoBi® capable of building and simulating models that integrate across biological scales. A prototypical multiscale model for the progression of a pancreatic tumor and its response to pharmacotherapy is constructed and virtual patients are treated with a prodrug activated by hepatic metabolization. Tumor growth is driven by signal transduction leading to cell cycle transition and proliferation. Free tumor concentrations of the active metabolite inhibit Raf kinase in the signaling cascade and thereby cell cycle progression. In a virtual clinical study, the individual therapeutic outcome of the chemotherapeutic intervention is simulated for a large population with heterogeneous genomic background. Thereby, the platform allows efficient model building and integration of biological knowledge and prior data from all biological scales. Experimental in vitro model systems can be linked with observations in animal experiments and clinical trials. The interplay between patients, diseases, and drugs and topics with high clinical relevance such as the role of pharmacogenomics, drug–drug, or drug–metabolite interactions can be addressed using this mechanistic, insight driven multiscale modeling approach.

According to current US Food and Drug Administration (FDA) and European Medicines Agency (EMA) guidance documents, physiologically based pharmacokinetic (PBPK) modeling is a powerful tool to explore and quantitatively predict drug‐drug interactions (DDIs) and may offer an alternative to dedicated clinical trials. This study provides whole‐body PBPK models of rifampicin, itraconazole, clarithromycin, midazolam, alfentanil, and digoxin within the Open Systems Pharmacology (OSP) Suite. All models were built independently, coupled using reported interaction parameters, and mutually evaluated to verify their predictive performance by simulating published clinical DDI studies. In total, 112 studies were used for model development and 57 studies for DDI prediction. 93% of the predicted area under the plasma concentration‐time curve (AUC) ratios and 94% of the peak plasma concentration (Cmax) ratios are within twofold of the observed values. This study lays a cornerstone for the qualification of the OSP platform with regard to reliable PBPK predictions of enzyme‐mediated and transporter‐mediated DDIs during model‐informed drug development. All presented models are provided open‐source and transparently documented.