454 research outputs found
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
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
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
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
An analysis of B cell selection mechanisms in germinal centres
Affinity maturation of antibodies during immune responses is achieved by multiple rounds of somatic hypermutation and subsequent preferential selection of those B cells that express B cell receptors with improved binding characteristics for the antigen. The mechanism underlying B cell selection has not yet been defined. By employing an agent-based model, we show that for physiologically reasonable parameter values affinity maturation can be driven by competition for neither binding sites nor antigenâeven in the presence of competing secreted antibodies. Within the tested mechanisms, only clonal competition for T cell help or a refractory time for the interaction of centrocytes with follicular dendritic cells is found to enable affinity maturation while generating the experimentally observed germinal centre characteristics and tolerating large variations in the initial antigen density
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 âŒ45 ± 10 ”m. 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
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