Skin pattern formation is an early process during the embryogenesis and
happens before the cells fully differentiate. Experimental data indicates
a hierarchical system, where cell chemotaxis is guided by a Turing system.
We aim at developing mathematical models to describe the underlying
biological processes leading to skin patterning, especially the
interaction of chemotaxis with reaction-diffusion (Turing) systems. We
study the parameter-dependence of the model using linear stability
analysis,  and possible model structures, and their impact on the pattern
forming process. Using a numerical approach for the PDE system, we develop
a framework to study quantitatively how chemotaxis and Turing systems are
related and the coupling impact on the patterning process. We analyse the
spatial regularity of the patterns for increasing chemosensitivity for
parameters inside and outside Turing's pattern space.

Visualizing cells and their organelles is central to modern life science. Fluorescence microscopy can reveal the subcellular structure of many organelles; however, this approach is slow, expensive and fatally damages the cell. Furthermore, it is highly limited in the number of simultaneous labels due to spectral overlap. In this project we implement a deep learning approach that predicts florescent labels of different organelles from transmitted-light images in silico. First, we train a UNet model to binary segment the nucleus. This simple model achieves results similar to state-of-the-art (intersection over union = 0.95). We then further develop the model’s architecture to segment continuous fluorescent labels of the endoplasmic reticulum. To predict this organelle’s fine tubular structure, we enhance the common UNet architecture with residual and attention units among others. Currently this model achieves a correlation between the predicted and observed fluorescent labels of r = 0.68. As the labeling happens in silico, this method allows to reduce the costs and damages to the cells, as well as a prediction of different labels simultaneously.

Background: During the mammalian preimplantation phase, cells undergo two subsequent cell fate decisions. During the first cell fate decision, cells become either part of an outer trophectoderm or part of the inner cell mass. Subsequently, the inner cell mass (ICM) segregates into the epiblast and the primitive endoderm, giving rise to the embryo and the placenta respectively. Recently, ICM organoids have been published as an in vitro model system towards preimplantational development. ICM organoids mimic the second cell fate decision taking place in the in vivo mouse embryos. In a previous study, the spatial pattern of the different cell lineage types was investigated. The study revealed that cells of the same fate tend to cluster stronger than expected for the currently hypothesised purely random cell fate distribution. Three major processes are hypothesised to contribute to the final cell fate arrangements at the mid and late blastocysts or 24 h old and 48 h old ICM organoids, respectively: 1) intra- and intercellular chemical signalling; 2) a cell sorting process; 3) cell proliferation.

Methods & Results: In order to quantify the influence of cell proliferation on the emergence of the observed cell lineage type clustering behaviour, an agent-based model was developed. The model accounts for mechanical cell-cell interactions, cell growth and cell division and was applied to compare several current assumptions of how ICM neighbourhood structures are generated. The model supports the hypothesis that initial cell fate acquisition is a stochastically driven process, taking place in the early development of inner cell mass organoids. The model further shows that the observed neighbourhood structures can emerge due to cell fate heredity during cell division and allows the inference of a time point for the cell fate decision.

Discussion: Simulations based on the model show that cell divisions involving cell fate heredity seem sufficient to lead to the local clustering observed in 24 h old ICM organoids, and that the initial cell differentiation process takes place only during a small time window, during or prior to ICM organoid composition. Our results leave little room for extracellular signalling believed to be important in cell fate decision, therefore we are discussing an alternative role of chemical signalling in this process. 

References

[1] Liebisch, T., A. Drusko, B. Mathew, E. H. Stelzer, S. C. Fischer, and F. Matthäus. Cell Fate Clusters in ICM Organoids Arise from Cell Fate Heredity & Division–a Modelling Approach. bioRxiv 698928, 2019

[2] Mathew, B., S. Munoz-Descalzo, E. Corujo-Simon, C. Schröter, E. H. Stelzer, and S. C. Fischer. Mouse ICM organoids reveal three-dimensional cell fate clustering. Biophysical journal 116:127–141, 2019

Recent experimental studies show substantial ongoing changes of both synaptic connections and neuronal population activity. It is, however, unclear, how the changes in neuronal activity can be linked to changes in the underlying synaptic connections. 
To shed light on these phenomena we study a simple neural network model of randomly connected neurons.
In a regime, that reproduces key characteristics of experimentally measured neuronal activity, we find that gradual changes of synaptic strength can result in periods of stable responses which are interrupted by abrupt transitions towards new responses. To understand the mechanism underlying these transitions, we compute the fixed points of this network model. Analyzing how the fixed points of a network change during ongoing, random synaptic drift reveals that abrupt transitions of response patterns coincide with topological changes in the structure of fixed points and not just a rerouting of response trajectories due to the displacement of unstable fixed points.
We conclude, that even slow ongoing synaptic drift can lead to abrupt transitions in stimulus responses, which can be understood by monitoring the fixed point structure of the underlying network.

COVID-19 has been the major cause of morbidity and mortality worldwide in
the past couple of months. It has paralysed our societies, leading to self
isolation and quarantine for several months. A COVID-19 vaccine remains a
critical element in the eventual solution to this public health crisis.
From 52 candidate COVID-19 vaccines in clinical trials, some vaccines are
already being mass produced and available to the general public. Here, we
develop an epidemiological network model able to represent COVID-19
epidemic dynamics. Stochastic computational simulations identify the
necessary number of vaccines and vaccine efficacy thresholds capable of
preventing an epidemic whilst adhering to lockdown guidelines. Simulation
results suggest that the "Ring of Vaccination" strategy, vaccinating
susceptible contact and contact of contacts, would be more tractable in
preventing new waves of COVID -19 with the requirement that a high
percentage of the population is vaccinated.

Neutron stars are the remnants of supernova explosions of massive stars at the end of their lifetime. The masses of those stars can be observed relatively precisely so that we know they can reach values up to 2 solar masses. The calculation of neutron stars and their masses on the other hand using a simplistic model leads to a maximal possible mass of 0.7 solar masses, way below the observed values. Since this model only takes into account neutrons for the composition of those stars, in order to compensate the mass gap between theory and observation, established models add different particles and interactions, leading to the right, observed masses. But what if we - instead of adding new interactions - could stay with our simplistic model and still reach high enough masses? In this talk, I will show how a modified neutron mass could solve the problem of the mass gap while still using one of the simplest assumptions for the calculation of a neutron star.