TY - JOUR AB - Background Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the ?-cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the ?-cell cycle for the development of diabetes mellitus. Methods This paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the ?-cell cycle. The interplay of glucose, insulin and ?-cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability. Results Our model shows the connection of glucose and insulin concentrations to the ?-cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the ?-cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose-insulin regulatory system showed in biological experiments. Conclusions This work focusses on modeling the physiological situation of the glucose-insulin regulatory system with a detailed consideration of the $eta$-cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes. AU - Gallenberger, M. AU - zu Castell, W. AU - Hense, B.A. AU - Kuttler, C.* C1 - 11797 C2 - 30815 TI - Dynamics of glucose and insulin concentration connected to the β-cell cycle: Model development and analysis. JO - Theor. Biol. Med. Model. VL - 9 IS - 1 PB - Biomed Central PY - 2012 ER - TY - JOUR AB - BACKGROUND: Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to coordinate gene expression and behaviour in groups, based on population densities. MODEL: We mathematically model quorum sensing and EPS production in a growing biofilm under various environmental conditions, to study how a developing biofilm impacts quorum sensing, and conversely, how a biofilm is affected by quorum sensing-regulated EPS production. We investigate circumstances when using quorum-sensing regulated EPS production is a beneficial strategy for biofilm cells. RESULTS: We find that biofilms that use quorum sensing to induce increased EPS production do not obtain the high cell populations of low-EPS producers, but can rapidly increase their volume to parallel high-EPS producers. Quorum sensing-induced EPS production allows a biofilm to switch behaviours, from a colonization mode (with an optimized growth rate), to a protection mode.CONCLUSIONS: A biofilm will benefit from using quorum sensing-induced EPS production if bacteria cells have the objective of acquiring a thick, protective layer of EPS, or if they wish to clog their environment with biomass as a means of securing nutrient supply and outcompeting other colonies in the channel, of their own or a different species. AU - Frederick, M.R.* AU - Kuttler, C.* AU - Hense, B.A. AU - Eberl, H.J.* C1 - 6832 C2 - 29337 TI - A mathematical model of quorum sensing regulated EPS production in biofilm communities. JO - Theor. Biol. Med. Model. VL - 8 PB - BioMed Central Ltd PY - 2011 ER - TY - JOUR AB - Background It is commonly accepted that embryonic segmentation of vertebrates is regulated by a segmentation clock, which is induced by the cycling genes Hes1 and Hes7. Their products form dimers that bind to the regulatory regions and thereby repress the transcription of their own encoding genes. An increase of the half-life of Hes7 protein causes irregular somite formation. This was shown in recent experiments by Hirata et al. In the same work, numerical simulations from a delay differential equations model, originally invented by Lewis, gave additional support. For a longer half-life of the Hes7 protein, these simulations exhibited strongly damped oscillations with, after few periods, severely attenuated the amplitudes. In these simulations, the Hill coefficient, a crucial model parameter, was set to 2 indicating that Hes7 has only one binding site in its promoter. On the other hand, Bessho et al. established three regulatory elements in the promoter region. Results We show that – with the same half life – the delay system is highly sensitive to changes in the Hill coefficient. A small increase changes the qualitative behaviour of the solutions drastically. There is sustained oscillation and hence the model can no longer explain the disruption of the segmentation clock. On the other hand, the Hill coefficient is correlated with the number of active binding sites, and with the way in which dimers bind to them. In this paper, we adopt response functions in order to estimate Hill coefficients for a variable number of active binding sites. It turns out that three active transcription factor binding sites increase the Hill coefficient by at least 20% as compared to one single active site. Conclusion Our findings lead to the following crucial dichotomy: either Hirata's model is correct for the Hes7 oscillator, in which case at most two binding sites are active in its promoter region; or at least three binding sites are active, in which case Hirata's delay system does not explain the experimental results. Recent experiments by Chen et al. seem to support the former hypothesis, but the discussion is still open.   AU - Zeiser, S. AU - Liebscher, H.V.* AU - Tiedemann, H.* AU - Rubio-Aliaga, I. AU - Przemeck, G.K.H. AU - Hrabě de Angelis, M. AU - Winkler, G. C1 - 2834 C2 - 23546 SP - 11 TI - Number of active transcription factor binding sites is essential for the Hes7 oscillator. JO - Theor. Biol. Med. Model. VL - 3 PY - 2006 ER -