Apoptosis in response to the ligand CD95L (also known as Fas ligand) is initiated by caspase-8, which is activated by dimerization and self-cleavage at death-inducing signaling complexes (DISCs). Previous work indicated that the degree of substrate cleavage by caspase-8 determines whether a cell dies or survives in response to a death stimulus. To determine how a death ligand stimulus is effectively translated into caspase-8 activity, we assessed this activity over time in single cells with compartmentalized probes that are cleaved by caspase-8, and used multiscale modeling to simultaneously describe single-cell and population data with an ensemble of single-cell models. We derived and experimentally validated a minimal model in which cleavage of caspase-8 in the enzymatic domain occurs in an interdimeric manner through interaction between DISCs, whereas prodomain cleavage sites are cleaved in an intradimeric manner within DISCs. Modeling indicated that sustained membrane-bound caspase-8 activity is followed by transient cytosolic activity, which can be interpreted as a molecular timer mechanism reflected by a limited lifetime of active caspase-8. The activation of caspase-8 by combined intra- and interdimeric cleavage ensures weak signaling at low concentrations of CD95L and strongly accelerated activation at higher ligand concentrations, thereby contributing to precise control of apoptosis.

The model captures the experimental findings very well and confirms the hypothesis that low abundance of HMA4 produces a radial gradient in zinc concentration. Surprisingly, transpiration was found also to be a key parameter. The model suggests that ZIP regulation takes place on a comparable timescale as symplastic transport.

In yeast (Saccharomyces cerevisiae) and plant roots (Arabidopsis thaliana) zinc enters the cells via influx transporters of the ZIP family. Since zinc is both essential for cell function and toxic at high concentrations, tight regulation is essential for cell viability. We provide new insight into the underlying mechanisms, starting from a general model based on ordinary differential equations and adapting it to the specific cases of yeast and plant root cells. In yeast, zinc is transported by the transporters ZRT1 and ZRT2, which are both regulated by the zinc-responsive transcription factor ZAP1. Using biological data, parameters were estimated and analyzed, confirming the different affinities of ZRT1 and ZRT2 reported in the literature. Furthermore, our model suggests that the positive feedback in ZAP1 production has a stabilizing function at high influx rates. In plant roots, various ZIP transporters play a role in zinc uptake. Their regulation is largely unknown, but bZIP transcription factors are thought to be involved. We set up three putative models based on: an activator only, an activator with dimerization and an activator-inhibitor pair. These were fitted to measurements and analyzed. Simulations show that the activator-inhibitor model outperforms the other two in providing robust and stable homeostasis at reasonable parameter ranges.

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.