Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial.

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, which combines solid mechanics and growth, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the final model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples.

AcAxl2 and AcMst1 regulate arthrospore development and stress resistance in the cephalosporin C producer Acremonium chrysogenum.

The filamentous fungus Acremonium chrysogenum is the primordial producer of the ß-lactam antibiotic cephalosporin C. This antibiotic is of major biotechnological and medical relevance because of its antibacterial activity against Gram-positive and Gram-negative bacteria. Antibiotic production during the lag phase of fermentation is often accompanied by a typical morphological feature of A. chrysogenum, the fragmentation of the mycelium into arthrospores. Here, we sought to identify factors that regulate the hyphal septation process and present the first comparative functional characterization of the type I integral plasma membrane protein Axl2 (axial budding pattern protein 2), a central component of the bud site selection system (BSSS) and Mst1 (mammalian Sterile20-like kinase), a septation initiation network (SIN)-associated germinal center kinase (GCK). Although an Acaxl2 deletion strain showed accelerated arthrospore formation after 96 h in liquid culture, deletion of Acmst1 led to a 24 h delay in arthrospore development. The overexpression of Acaxl2 resulted in an arthrospore formation similar to the A3/2 strain. In contrast to this, A3/2::Acmst1 OE strain displayed an enhanced arthrospore titer. Large-scale stress tests revealed an involvement of AcAxl2 in controlling osmotic, endoplasmic reticulum, and cell wall stress response. In a similar approach, we found that AcMst1 plays an essential role in regulating growth under osmotic, cell wall, and oxidative stress conditions. Microscopic analyses and plating assays on media containing Calcofluor White and NaCl showed that arthrospore development is a stress-dependent process. Our results suggest the potential for identifying candidate genes for strain improvement programs to optimize industrial fermentation processes.

Mechanical and cell-to-cell adhesive properties of aggregated Methanosarcina.

The mechanical and adhesive properties as well as the turgor pressure of microbes play an important role in cell growth and aggregation. By applying AFM together with finite element modelling, one can determine the cell wall structural homogeneity, mechanical and cell-to-cell adhesive properties for aggregated Methanosarcina barkeri cells. This also allows a novel approach to determine in-aggregate turgor pressure determination. Analyzing the AFM force-indentation response of the aggregates under loads less than 10 nN, our study reveals structural inhomogeneity of the polymeric part of the cell wall material and suggests that the cell wall consists of two layers of methanochondroitin (external: with a thickness of 3 ± 1 nm and internal: with a thickness of 169 ± 30 nm). On average, the hyperelastic finite element model showed that the internal layer is more rigid (µ = 14 ± 4 MPa) than the external layer (µ = 2.8 ± 0.9 MPa). To determine the turgor pressure and adhesiveness of the cells, a specific mode of indentation (under a load of 45 nN), aimed towards the centre of the individual aggregate, was performed. By modelling the AFM induced decohesion of the aggregate, the turgor pressure and the cell-to-cell adhesive interface properties could be determined. On average, the turgor pressure is estimated to be 59 ± 22 kPa, the interface strength is 78 ± 12 kPa and the polymer network extensibility is 2.8 ± 0.9 nm. We predict that internal cell wall comprised highly compressed methanochondroitin chains and we are able to identify a conceptual model for stress dependent inner cell wall growth.