Immune responses are regulated by diffusible mediators, the cytokines, which act at sub-nanomolar concentrations. The spatial range of cytokine communication is a crucial, yet poorly understood, functional property. Both containment of cytokine action in narrow junctions between immune cells (immunological synapses) and global signaling throughout entire lymph nodes have been proposed, but the conditions under which they might occur are not clear. Here we analyze spatially three-dimensional reaction-diffusion models for the dynamics of cytokine signaling at two successive scales: in immunological synapses and in dense multicellular environments. For realistic parameter values, we observe local spatial gradients, with the cytokine concentration around secreting cells decaying sharply across only a few cell diameters. Focusing on the well-characterized T-cell cytokine interleukin-2, we show how cytokine secretion and competitive uptake determine this signaling range. Uptake is shaped locally by the geometry of the immunological synapse. However, even for narrow synapses, which favor intrasynaptic cytokine consumption, escape fluxes into the extrasynaptic space are expected to be substantial (≥20% of secretion). Hence paracrine signaling will generally extend beyond the synapse but can be limited to cellular microenvironments through uptake by target cells or strong competitors, such as regulatory T cells. By contrast, long-range cytokine signaling requires a high density of cytokine producers or weak consumption (e.g., by sparsely distributed target cells). Thus in a physiological setting, cytokine gradients between cells, and not bulk-phase concentrations, are crucial for cell-to-cell communication, emphasizing the need for spatially resolved data on cytokine signaling.

Our aim is to find the optimal shape of periodically distributed microstructures on surfaces of swimming bodies in order to reduce their drag. The model describes the flow in the viscous sublayer of the boundary layer of a turbulent flow. The microscopic optimization problem is reduced applying homogenization. In the reduced so-called macroscopic optimization problem we minimize the Navier constant subject to the boundary layer equations which are solved in a very small part of the original domain. Under the assumptions that the microstructures can be represented as smooth functions the sensitivity can be determined analytically. The optimization problem is then solved by a sensitivity based method (steepest descent with optimal step size) and the state equations are solved in each iteration with an external software. Our reduced model is validated by comparing the results from the homogenized model with those obtained by simulating the whole rough channel. An improved shape is found and a drag reduction up to 10% can be shown. (2000). Primary 35B27; secondary 76D10, 76D55, 49Q12. Mathematics Subject Classification

Among other approaches, differential equations are used for a deterministic quantitative description of time-dependent biological processes. For intracellular systems, such as signaling pathways, most existing models are based on ordinary differential equations. These models describe temporal processes, while they neglect spatial aspects. We present a model for the SMAD signaling pathway, which gives a temporal and spatial description on the basis of reaction diffusion equations to answer the question whether cell geometry plays a role in signaling. In this article we simulate the ordinary differential equations as well as partial differential equations of parabolic type with suile numerical methods, the latter on different cell geometries. In addition to manual construction of idealized cells, we also construct meshes from microscopy images of real cells. The main focus of the paper is to compare the results of the model without and with spatial aspects to answer the addressed question. The results show that diffusion in the model can lead to significant intracellular gradients of signaling molecules and changes the level of response to the signal transduced by the signaling pathway. In particular, the extent of these observations depends on the geometry of the cell.

The pregnane X receptor (PXR) is a drug/xenobiotic-activated transcription factor of crucial importance for major cytochrome P450 xenobiotic-metabolizing enzymes (CYP) expression and regulation in the liver and the intestine. One of the major target genes regulated by PXR is the cytochrome P450 enzyme (CYP3A4), which is the most important human drug-metabolizing enzyme. In addition, PXR is supposed to be involved both in basal and/or inducible expression of many other CYPs, such as CYP2B6, CYP2C8, 2C9 and 2C19, CYP3A5, CYP3A7, and CYP2A6. Interestingly, the dynamics of PXR-mediated target genes regulation has not been systematically studied and we have only a few mechanistic mathematical and biologically based models describing gene expression dynamics after PXR activation in cellular models. Furthermore, few indirect mathematical PKPD models for prediction of CYP3A metabolic activity in vivo have been built based on compartmental models with respect to drug–drug interactions or hormonal crosstalk. Importantly, several negative feedback loops have been described in PXR regulation. Although current mathematical models propose these adaptive mechanisms, a comprehensive mathematical model based on sufficient experimental data is still missing. In the current review, we summarize and compare these models and address some issues that should be considered for the improvement of PXR-mediated gene regulation modelling as well as for our better understanding of the quantitative and spatial dynamics of CYPs expression.

In this laboratory study, we assessed the resistance to microvacuole (glistening) formation in hydrophobic intraocular lenses (IOLs). Glistenings were induced in five lenses each of five different hydrophobic acrylic IOL models, using an established in vitro laboratory model: 800C (Rayner, Worthing, UK), AcrySof SN60WF (Alcon, Fort Worth, USA), Tecnis ZCB00 (Johnson & Johnson Vision, Santa Ana, USA), Vivinex XY1 (Hoya, Tokyo, Japan) and CT Lucia 611P (Zeiss, Oberkochen, Germany). We evaluated the number of microvacuoles per square millimeter (MV/mm2) in the central part of each IOL. Results were analyzed statistically, and mean glistening numbers were ranked, with the highest in the SN60WF which had 66.0 (±45.5) MVs/mm, followed by the 611P with 30.7 (±8.4) MVs/mm2. The 800C and XY1 showed comparable values of 2.0 (±3.6) and 2.7 (±2.4) MVs/mm2, respectively. ZCB00 had the lowest number with 0.9 (±0.6) MVs/mm2. This study shows that the resistance to glistening formation differs depending on the hydrophobic acrylic copolymer composition of the IOL material. Some IOLs from current clinical use are still prone to develop glistenings whereas others, including the ZCB00, 800C and XY1 show high resistance to microvacuole formation.