@phdthesis{Schardt2023,
  author    = {Schardt, Simon},
  title     = {Agent-based modeling of cell differentiation in mouse ICM organoids},
  doi       = {10.25972/OPUS-30194},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-301940},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2023},
  abstract  = {Mammalian embryonic development is subject to complex biological relationships that need to be understood. However, before the whole structure of development can be put together, the individual building blocks must first be understood in more detail. One of these building blocks is the second cell fate decision and describes the differentiation of cells of the inner cell mass of the embryo into epiblast and primitive endoderm cells. These cells then spatially segregate and form the subsequent bases for the embryo and yolk sac, respectively. In organoids of the inner cell mass, these two types of progenitor cells are also observed to form, and to some extent to spatially separate. This work has been devoted to these phenomena over the past three years. Plenty of studies already provide some insights into the basic mechanics of this cell differentiation, such that the first signs of epiblast and primitive endoderm differentiation, are the expression levels of transcription factors NANOG and GATA6. Here, cells with low expression of GATA6 and high expression of NANOG adopt the epiblast fate. If the expressions are reversed, a primitive endoderm cell is formed. Regarding the spatial segregation of the two cell types, it is not yet clear what mechanism leads to this. A common hypothesis suggests the differential adhesion of cell as the cause for the spatial rearrangement of cells. In this thesis however, the possibility of a global cell-cell communication is investigated. The approach chosen to study these phenomena follows the motto "mathematics is biology's next microscope". Mathematical modeling is used to transform the central gene regulatory network at the heart of this work into a system of equations that allows us to describe the temporal evolution of NANOG and GATA6 under the influence of an external signal. Special attention is paid to the derivation of new models using methods of statistical mechanics, as well as the comparison with existing models. After a detailed stability analysis the advantages of the derived model become clear by the fact that an exact relationship of the model parameters and the formation of heterogeneous mixtures of two cell types was found. Thus, the model can be easily controlled and the proportions of the resulting cell types can be estimated in advance. This mathematical model is also combined with a mechanism for global cell-cell communication, as well as a model for the growth of an organoid. It is shown that the global cell-cell communication is able to unify the formation of checkerboard patterns as well as engulfing patterns based on differently propagating signals. In addition, the influence of cell division and thus organoid growth on pattern formation is studied in detail. It is shown that this is able to contribute to the formation of clusters and, as a consequence, to breathe some randomness into otherwise perfectly sorted patterns.},
  subject      = {Mathematische Modellierung},
  language  = {en}
}
@article{FischerSchardtLilaoGarzonetal.2023,
  author    = {Fischer, Sabine C. and Schardt, Simon and Lilao-Garz{\´o}n, Joaqu{\´i}n and Mu{\~n}oz-Descalzo, Silvia},
  title     = {The salt-and-pepper pattern in mouse blastocysts is compatible with signaling beyond the nearest neighbors},
  series = {iScience},
  volume    = {26},
  journal   = {iScience},
  number    = {11},
  doi       = {10.1016/j.isci.2023.108106},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-350184},
  year      = {2023},
  abstract  = {Summary Embryos develop in a concerted sequence of spatiotemporal arrangements of cells. In the preimplantation mouse embryo, the distribution of the cells in the inner cell mass evolves from a salt-and-pepper pattern to spatial segregation of two distinct cell types. The exact properties of the salt-and-pepper pattern have not been analyzed so far. We investigate the spatiotemporal distribution of NANOG- and GATA6-expressing cells in the ICM of the mouse blastocysts with quantitative three-dimensional single-cell-based neighborhood analyses. A combination of spatial statistics and agent-based modeling reveals that the cell fate distribution follows a local clustering pattern. Using ordinary differential equations modeling, we show that this pattern can be established by a distance-based signaling mechanism enabling cells to integrate information from the whole inner cell mass into their cell fate decision. Our work highlights the importance of longer-range signaling to ensure coordinated decisions in groups of cells to successfully build embryos. Highlights • The local cell neighborhood and global ICM population composition correlate • ICM cells show characteristics of local clustering in early and mid mouse blastocysts • ICM patterning requires integration of signals from cells beyond the first neighbors},
  language  = {en}
}
@article{DirkFischerSchardtetal.2023,
  author    = {Dirk, Robin and Fischer, Jonas L. and Schardt, Simon and Ankenbrand, Markus J. and Fischer, Sabine C.},
  title     = {Recognition and reconstruction of cell differentiation patterns with deep learning},
  series = {PLoS Computational Biology},
  volume    = {19},
  journal   = {PLoS Computational Biology},
  number    = {10},
  doi       = {10.1371/journal.pcbi.1011582},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-350167},
  year      = {2023},
  abstract  = {Abstract Cell lineage decisions occur in three-dimensional spatial patterns that are difficult to identify by eye. There is an ongoing effort to replicate such patterns using mathematical modeling. One approach uses long ranging cell-cell communication to replicate common spatial arrangements like checkerboard and engulfing patterns. In this model, the cell-cell communication has been implemented as a signal that disperses throughout the tissue. On the other hand, machine learning models have been developed for pattern recognition and pattern reconstruction tasks. We combined synthetic data generated by the mathematical model with spatial summary statistics and deep learning algorithms to recognize and reconstruct cell fate patterns in organoids of mouse embryonic stem cells. Application of Moran's index and pair correlation functions for in vitro and synthetic data from the model showed local clustering and radial segregation. To assess the patterns as a whole, a graph neural network was developed and trained on synthetic data from the model. Application to in vitro data predicted a low signal dispersion value. To test this result, we implemented a multilayer perceptron for the prediction of a given cell fate based on the fates of the neighboring cells. The results show a 70\% accuracy of cell fate imputation based on the nine nearest neighbors of a cell. Overall, our approach combines deep learning with mathematical modeling to link cell fate patterns with potential underlying mechanisms. Author summary Mammalian embryo development relies on organized differentiation of stem cells into different lineages. Particularly at the early stages of embryogenesis, cells of different fates form three-dimensional spatial patterns that are difficult to identify by eye. Pattern quantification and mathematical modeling have produced first insights into potential mechanisms for the cell fate arrangements. However, these approaches have relied on classifications of the patterns such as inside-out or random, or used summary statistics such as pair correlation functions or cluster radii. Deep neural networks allow characterizing patterns directly. Since the tissue context can be readily reproduced by a graph, we implemented a graph neural network to characterize the patterns of embryonic stem cell organoids as a whole. In addition, we implemented a multilayer perceptron model to reconstruct the fate of a given cell based on its neighbors. To train and test the models, we used synthetic data generated by our mathematical model for cell-cell communication. This interplay of deep learning and mathematical modeling in combination with summary statistics allowed us to identify a potential mechanism for cell fate determination in mouse embryonic stem cells. Our results agree with a mechanism with a dispersion of the intercellular signal that links a cell's fate to those of the local neighborhood.},
  language  = {en}
}