Open Access
Filtern
Dokumenttyp
- Wissenschaftlicher Artikel (1)
- Postprint (1)
Sprache
- Englisch (2)
Gehört zur Bibliographie
- ja (2)
Schlagworte
- mathematical model (2) (entfernen)
Institut
Background
Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/ β-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/ β-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells.
Results
Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/ β-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength.
Conclusions
Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter- and intracellular processes, such as Dkk feedback, diffusion and Wnt/ β-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression.
A mathematical model of working-memory capacity limits is proposed on the key assumption of mutual interference between items in working memory. Interference is assumed to arise from overwriting of features shared by these items. The model was fit to time-accuracy data of memory-updating tasks from four experiments using nonlinear mixed effect (NLME) models as a framework. The model gave a good account of the data from a numerical and a spatial task version. The performance pattern in a combination of numerical and spatial updating could be explained by variations in the interference parameter: assuming less feature overlap between contents from different domains than between contents from the same domain, the model can account for double dissociations of content domains in dual-task experiments. Experiment 3 extended this idea to similarity within the verbal domain. The decline of memory accuracy with increasing memory load was steeper with phonologically similar than with dissimilar material, although processing speed was faster for the similar material. The model captured the similarity effects with a higher estimated interference parameter for the similar than for the dissimilar condition. The results are difficult to explain with alternative models, in particular models incorporating time-based decay and models assuming limited resource pools.