Simulating Organogenesis in COMSOL: Tissue Mechanics

During growth, tissue expands and deforms. Given its elastic properties, stresses emerge in an expanding and deforming tissue. Cell rearrangements can dissipate these stresses and numerous experiments confirm the viscoelastic properties of tissues [1]-[4]. On long time scales, as characteristic for many developmental processes, tissue is therefore typically represented as a liquid, viscous material and is then described by the Stokes equation [5]-[7]. On short time scales, however, tissues have mainly elastic properties. In discrete cell-based tissue models, the elastic tissue properties are realized by springs between cell vertices [8], [9]. In this article, we adopt a macroscale perspective of tissue and consider it as homogeneous material. Therefore, we may use the "Structural Mechanics" module in COMSOL Multiphysics in order to model the viscoelastic behavior of tissue. Concretely, we consider two examples: first, we aim at numerically reproducing published [10] analytical results for the sea urchin blastula. Afterwards, we numerically solve a continuum mechanics model for the compression and relaxation experiments presented in [4]

A mathematical model for germinal centre kinetics and affinity maturation

We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction. We show that antigen masking by antibodies which are produced by emerging plasma cells can drive affinity maturation and provide a feedback mechanism by which the reaction is stable against variations in the initial antigen amount over several orders of magnitude. This provides a possible answer to the long-standing question of the role of antigen reduction in driving affinity maturation. By comparing model predictions with experimental results, we propose that the selection probability of centrocytes and the recycling probability of selected centrocytes are not constant but vary during the GC reaction with respect to time. It is shown that the efficiency of affinity maturation is highest if clones with an affinity for the antigen well above the average affinity in the GC leave the GC for either the memory or plasma cell pool. It is further shown that termination of somatic hypermutation several days before the end of the germinal centre reaction is beneficial for affinity maturation. The impact on affinity maturation of simultaneous initiation of memory cell formation and somatic hypermutation vs. delayed initiation of memory cell formation is discussed

Simulations demonstrate a simple network to be sufficient to control branch point selection, smooth muscle and vasculature formation during lung branching morphogenesis

Proper lung functioning requires not only a correct structure of the conducting airway tree, but also the simultaneous development of smooth muscles and vasculature. Lung branching morphogenesis is strongly stereotyped and involves the recursive use of only three modes of branching. We have previously shown that the experimentally described interactions between Fibroblast growth factor (FGF)10, Sonic hedgehog (SHH) and Patched (Ptc) can give rise to a Turing mechanism that not only reproduces the experimentally observed wildtype branching pattern but also, in part counterintuitive, patterns in mutant mice. Here we show that, even though many proteins affect smooth muscle formation and the expression of Vegfa, an inducer of blood vessel formation, it is sufficient to add FGF9 to the FGF10/SHH/Ptc module to successfully predict simultaneously the emergence of smooth muscles in the clefts between growing lung buds, and Vegfa expression in the distal sub-epithelial mesenchyme. Our model reproduces the phenotype of both wildtype and relevant mutant mice, as well as the results of most culture conditions described in the literature.Comment: Initially published at Biology Ope