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]

Species-specific differences in follicular antral sizes result from diffusion-based limitations on the thickness of the granulosa cell layer

The size of mature oocytes is similar across mammalian species, yet the size of ovarian follicles increases with species size, with some ovarian follicles reaching diameters more than 1000-fold the size of the enclosed oocyte. Here we show that the different follicular sizes can be explained with diffusion-based limitations on the thickness of the hormone-secreting granulosa layer. By analysing published data on human follicular growth and granulosa cell expansion during follicular maturation we find that the 4-fold increase of the antral follicle diameter is entirely driven by an increase in the follicular fluid volume, while the thickness of the surrounding granulosa layer remains constant at about 45+/-10 mkm. Based on the measured kinetic constants, the model reveals that the observed fall in the gonadotropin concentration from peripheral blood circulation to the follicular antrum is a result of sequestration in the granulosa. The model further shows that as a result of sequestration, an increased granulosa thickness cannot substantially increase estradiol production but rather deprives the oocyte from gonadotropins. Larger animals (with a larger blood volume) require more estradiol as produced by the ovaries to downregulate FSH-secretion in the pituitary. Larger follicle diameters result in larger follicle surface areas for constant granulosa layer thickness. The reported increase in follicular surface area in larger species indeed correlates linearly both with species mass and with the predicted increase in estradiol output. In summary, we propose a structural role for the antrum in that it determines the volume of the granulosa layer and thus the level of estrogen production.Comment: Mol Hum Repr 201

B cell activation and affinity discrimination by receptor segregation?

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Simulating Organogenesis in COMSOL: Comparison Of Methods For Simulating Branching Morphogenesis

During organogenesis tissue grows and deforms. The growth processes are controlled by diffusible proteins, so-called morphogens. Many different patterning mechanisms have been proposed. The stereotypic branching program during lung development can be recapitulated by a receptor-ligand based Turing model. Our group has previously used the Arbitrary Lagrangian-Eulerian (ALE) framework for solving the receptor-ligand Turing model on growing lung domains. However, complex mesh deformations which occur during lung growth severely limit the number of branch generations that can be simulated. A new Phase-Field implementation avoids mesh deformations by considering the surface of the modelling domains as interfaces between phases, and by coupling the reaction-diffusion framework to these surfaces. In this paper, we present a rigorous comparison between the Phase-Field approach and the ALE-based simulation

Analysis of B cell selection mechanisms in the adaptive immune response

The essential task of a germinal centre reaction is the selection of those B cells that bind the antigen with high affinity. The exact mechanisms of B cell selection is still unknown and rather difficult to be accessed in experiment. With the help of an already established agent-based model for the space-time-dynamics of germinal centre reactions [1,2] we compare the most important hypotheses for what the limiting factor for B cell rescue may be. We discuss competition for antigen sites on follicular dendritic cells, a refractory time for centrocytes after every encounter with follicular dendritic cells, competition for the antigen itself, the role of antigen masking with soluble antibodies, and competition for T cell help. The unexpected result is that neither competition for interaction sites nor competition for antigen nor antigen masking are in agreement with present experimental data on germinal centre reactions. We show that these most popular selection mechanisms do not lead to sufficient affinity maturation and do not respect the observed robustness against changes of initial conditions. However, the best agreement with data was found for the newly hypothesized centrocyte refractory time and for competition for T cell help. Thus the in silico experiments point towards selection mechanisms that are not in the main focus of current germinal centre research. Possible experiments to test these hypotheses are proposed

Species-specific differences in follicular antral sizes result from diffusion-based limitations on the thickness of the granulosa cell layer

The size of mature oocytes is similar across mammalian species, yet the size of ovarian follicles increases with species size, with some ovarian follicles reaching diameters >1000-fold the size of the enclosed oocyte. Here we show that the different follicular sizes can be explained with diffusion-based limitations on the thickness of the hormone-secreting granulosa layer. By analysing published data on human follicular growth and granulosa cell expansion during follicular maturation we find that the 4-fold increase of the antral follicle diameter is entirely driven by an increase in the follicular fluid volume, while the thickness of the surrounding granulosa layer remains constant at ∼45 ± 10 µm. Based on the measured kinetic constants, the model reveals that the observed fall in the gonadotrophin concentration from peripheral blood circulation to the follicular antrum is a result of sequestration in the granulosa. The model further shows that as a result of sequestration, an increased granulosa thickness cannot substantially increase estradiol production but rather deprives the oocyte from gonadotrophins. Larger animals (with a larger blood volume) require more estradiol as produced by the ovaries to down-regulate follicle-stimulating hormone-secretion in the pituitary. Larger follicle diameters result in larger follicle surface areas for constant granulosa layer thickness. The reported increase in the follicular surface area in larger species indeed correlates linearly both with species mass and with the predicted increase in estradiol output. In summary, we propose a structural role for the antrum in that it determines the volume of the granulosa layer and thus the level of estrogen productio

Biophysical Modulations of Functional Connectivity

Resting-state low frequency oscillations have been detected in many functional magnetic resonance imaging (MRI) studies and appear to be synchronized between functionally related areas. Converging evidence from MRI and other imaging modalities suggest that this activity has an intrinsic neuronal origin. Multiple consistent networks have been found in large populations, and have been shown to be stable over time. Further, these patterns of functional connectivity have been shown to be altered in healthy controls under various physiological challenges. This review will present the biophysical characterization of functional connectivity, and examine the effects of physical state manipulations (such as anesthesia, fatigue, and aging) in healthy controls.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90432/1/brain-2E2011-2E0039.pd

Modelling affinity maturation in the immune system

The affinity of antibody for antigen increases during an immune response. This is achieved by mutation of the genes encoding for the antibody and subsequent selection of the best binder. The process takes place in a special microenvironment, the germinal centre. In this dissertation, a mathematical model is presented, which reproduces experimental data on the kinetics of this process and on the affinity maturation observed during the reaction. It further allows predictions to be made about parameters such as the selection rate of centrocytes and the recycling probability of selected centrocytes. Additionally it is shown that termination of somatic hypermutation several days before the end of the germinal centre reaction is beneficial for affinity maturation as is a start of memory cell formation well after the onset of somatic hypermutation. Selection of B cells during the germinal centre reaction is based on antigen recognition and is believed to involve interaction of B cells with membrane bound antigen. It has been shown that such encounter of membrane bound antigen leads to a re-organisation of proteins and lipids such that raft lipids are accumulating in the contact zone. In a second project possible driving forces for such a lipid re-organisation are investigated and the analysis shows that the accumulation of a special lipid sort in the contact zone can be understood by their high affinity for proteins engaged in the contact zone. Interaction between lipids themselves has no positive impact on the accumulation of lipids in the contact zone and strong interactions between lipids may even prohibit the domain formation in the contact zone by the trapping of lipids in patches elsewhere on the cell surface

Dynamic Image-Based Modelling of Kidney Branching Morphogenesis

Kidney branching morphogenesis has been studied extensively, but the mechanism that defines the branch points is still elusive. Here we obtained a 2D movie of kidney branching morphogenesis in culture to test different models of branching morphogenesis with physiological growth dynamics. We carried out image segmentation and calculated the displacement fields between the frames. The models were subsequently solved on the 2D domain, that was extracted from the movie. We find that Turing patterns are sensitive to the initial conditions when solved on the epithelial shapes. A previously proposed diffusion-dependent geometry effect allowed us to reproduce the growth fields reasonably well, both for an inhibitor of branching that was produced in the epithelium, and for an inducer of branching that was produced in the mesenchyme. The latter could be represented by Glial-derived neurotrophic factor (GDNF), which is expressed in the mesenchyme and induces outgrowth of ureteric branches. Considering that the Turing model represents the interaction between the GDNF and its receptor RET very well and that the model reproduces the relevant expression patterns in developing wildtype and mutant kidneys, it is well possible that a combination of the Turing mechanism and the geometry effect control branching morphogenesis

Branch Mode Selection during Early Lung Development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modesComment: Initially published at PLoS Comput Bio