One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

Stem cell maintenance in multilayered shoot apical meristems (SAMs) of plants requires strict regulation of cell growth and division. Exactly how the complex milieu of chemical and mechanical signals interact in the central region of the SAM to regulate cell division plane orientation is not well understood. In this paper, simulations using a newly developed multiscale computational model are combined with experimental studies to suggest and test three hypothesized mechanisms for the regulation of cell division plane orientation and the direction of anisotropic cell expansion in the corpus. Simulations predict that in the Apical corpus, WUSCHEL and cytokinin regulate the direction of anisotropic cell expansion, and cells divide according to tensile stress on the cell wall. In the Basal corpus, model simulations suggest dual roles for WUSCHEL and cytokinin in regulating both the direction of anisotropic cell expansion and cell division plane orientation. Simulation results are followed by a detailed analysis of changes in cell characteristics upon manipulation of WUSCHEL and cytokinin in experiments that support model predictions. Moreover, simulations predict that this layer-specific mechanism maintains both the experimentally observed shape and structure of the SAM as well as the distribution of WUSCHEL in the tissue. This provides an additional link between the roles of WUSCHEL, cytokinin, and mechanical stress in regulating SAM growth and proper stem cell maintenance in the SAM.

Biological systems are inherently complex, and the increasing level of detail with which we are able to experimentally probe such systems continually reveals new complexity. Fortunately, mathematical models are uniquely positioned to provide a tool suitable for rigorous analysis, hypothesis generation, and connecting results from isolated in vitro experiments with results from in vivo and whole-organism studies. However, developing useful mathematical models is challenging because of the often different domains of knowledge required in both math and biology. In this work, we endeavor to provide a useful guide for researchers interested in incorporating mathematical modeling into their scientific process. We advocate for the use of conceptual diagrams as a starting place to anchor researchers from both domains. These diagrams are useful for simplifying the biological process in question and distinguishing the essential components. Not only do they serve as the basis for developing a variety of mathematical models, but they ensure that any mathematical formulation of the biological system is led primarily by scientific questions. We provide a specific example of this process from our own work in studying prion aggregation to show the power of mathematical models to synergistically interact with experiments and push forward biological understanding. Choosing the most suitable model also depends on many different factors, and we consider how to make these choices based on different scales of biological organization and available data. We close by discussing the many opportunities that abound for both experimentalists and modelers to take advantage of collaborative work in this field.

Spatial patterns in microbial colonies are the consequence of cell-division dynamics coupled with cell-cell interactions on a physical media. Agent-based models (ABMs) are a powerful tool for understanding the emergence of large scale structure from these individual cell processes. However, most ABMs have focused on fission, a process by which cells split symmetrically into two daughters. The yeast, Saccharomyces cerevisiae, is a model eukaryote which commonly undergoes an asymmetric division process called budding. The resulting mother and daughter cells have unequal sizes and the daughter cell does not inherit the replicative age of the mother. In this work, we develop and analyze an ABM to study the impact of budding cell division and nutrient limitation on yeast colony structure. We find that while budding division does not impact large-scale properties of the colony (such as shape and size), local spatial organization of cells with respect to spatial layout of mother-daughter cell pairs and connectivity of subcolonies is greatly impacted. In addition, we find that nutrient limitation further promotes local spatial organization of cells and changes global colony organization by driving variation in subcolony sizes. Moreover, resulting differences in spatial organization, coupled with differential growth rates from nutrient limitation, create distinct sectoring patterns within growing yeast colonies. Our findings offer novel insights into mechanisms driving experimentally observed sectored yeast colony phenotypes. Furthermore, our work illustrates the need to include relevant biophysical mechanisms when using ABMs to compare to experimental studies.