Natural killer (NK) cells belong to the first line of host defense against infection and cancer. Cytokines, including interleukin-15 (IL-15), critically regulate NK cell activity, resulting in recognition and direct killing of transformed and infected target cells. NK cells have to adapt and respond in inflamed and often hypoxic areas. Cellular stabilization and accumulation of the transcription factor hypoxia-inducible factor-1α (HIF-1α) is a key mechanism of the cellular hypoxia response. At the same time, HIF-1α plays a critical role in both innate and adaptive immunity. While the HIF-1α hydroxylation and degradation pathway has been recently described with the help of mathematical methods, less is known concerning the mechanistic mathematical description of processes regulating the levels of HIF-1α mRNA and protein. In this work we combine mathematical modeling with experimental laboratory analysis and examine the dynamic relationship between HIF-1α mRNA, HIF-1α protein, and IL-15-mediated upstream signaling events in NK cells from human blood. We propose a system of non-linear ordinary differential equations with positive and negative feedback loops for describing the complex interplay of HIF-1α regulators. The experimental design is optimized with the help of mathematical methods, and numerical optimization techniques yield reliable parameter estimates. The mathematical model allows for the investigation and prediction of HIF-1α stabilization under different inflammatory conditions and provides a better understanding of mechanisms mediating cellular enrichment of HIF-1α. Thanks to the combination of in vitro experimental data and in silico predictions we identified the mammalian target of rapamycin (mTOR), the nuclear factor-κB (NF-κB), and the signal transducer and activator of transcription 3 (STAT3) as central regulators of HIF-1α accumulation. We hypothesize that the regulatory pathway proposed here for NK cells can be extended to other types of immune cells. Understanding the molecular mechanisms involved in the dynamic regulation of the HIF-1α pathway in immune cells is of central importance to the immune cell function and could be a promising strategy in the design of treatments for human inflammatory diseases and cancer.
An ef®cient modeling technique for multibody systems, which extends the concept of natural coordinates with closed kinematic loops is presented. By establishing a local coordinate system in each body a system with constant mass matrix is set up. The propagation of topological information into the model leads to the application of a block-oriented rational Cholesky decomposition of the system matrix. The overall algorithm shows linear complexity in the number of bodies for systems with a constant number of kinematic loops. To handle rank-de®cient constraint Jacobians arising from loop closing conditions the concept of constraint partitioning during decomposition is outlined. Restriction of the partitioning decision based on the topology information minimizes the monitoring effort and avoids disadvantages experienced in other partitioning methods. Numerical results for the 6-bar-mechanism proof the algorithm to run ef®ciently with projection stabilized index-1 integration methods.
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