Digit patterning during limb development as a result of the BMP-receptor interaction

Turing models have been proposed to explain the emergence of digits during limb development. However, so far the molecular components that would give rise to Turing patterns are elusive. We have recently shown that a particular type of receptor-ligand interaction can give rise to Schnakenberg-type Turing patterns, which reproduce patterning during lung and kidney branching morphogenesis. Recent knock-out experiments have identified Smad4 as a key protein in digit patterning. We show here that the BMP-receptor interaction meets the conditions for a Schnakenberg-type Turing pattern, and that the resulting model reproduces available wildtype and mutant data on the expression patterns of BMP, its receptor, and Fgfs in the apical ectodermal ridge (AER) when solved on a realistic 2D domain that we extracted from limb bud images of E11.5 mouse embryos. We propose that receptor-ligand-based mechanisms serve as a molecular basis for the emergence of Turing patterns in many developing tissues

Phase diagram of diluted Ising ferromagnet LiHoxY1−xF4

We present a systematic study of the phase diagram of LiHoxY1−xF4 (0.25≤x≤1) Ising ferromagnets obtained from neutron scattering measurements and mean-field calculations. We show that while the thermal phase transition decreases linearly with dilution, as predicted by mean-field theory, the critical transverse field at the quantum critical point is suppressed much faster. This behavior is related to competition between off-diagonal dipolar coupling and quantum fluctuations that are tuned by doping and applied field, respectively. In this paper, we quantify the deviation of the experimental results from mean-field predictions, with the aim that this analysis can be used in future theoretical efforts towards a quantitative description

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

Local stability analysis.

<p>The blue and red regions represent ranges of the dimensionless parameters for which lateral and planar bifurcation modes of branching are observed respectively. The parameter values in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a> are used as a reference point (black solid line), and each parameter was perturbed independently by a factor as indicated. The green-dashed circles mark halved and doubled parameter ranges. : * The lateral branching mode (blue) is stable up to value 2.3 times the reference value of , the bifurcation mode of branching is observed in the range from 2.3 to 7-times the reference value given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a>.</p

The FGF10 pattern is robust to changes in the domain geometry and boundary conditions.

<p>The steady state pattern of FGF10 on the computational domain has (<b>a</b>) an increased radius of epithelial bud, i.e. at the tip increased by the25%; (<b>b</b>) an increased radius of the mesenchymal bud, i.e. at the tip increased by the 10%; (<b>c</b>) a truncated stalk, i.e. at the stalk is truncated by 80%. (<b>d,e</b>) The steady state pattern of FGF10 with no flux boundary conditions at the lung boundary: (<b>d</b>) all production and degradation rate constant are equal to 0.5 and 1.7 of that presented in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a> (lateral branching mode), (<b>e</b>) constants are equal to 0.7 and 1.5 of that presented in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a> (bifurcation mode). Decrease of production rates and increase of degradation rates are imposed to compensate for the absence of morphogen flux from the epithelium and mesonchyme to the lumen and interstitial space when no-flux boundary conditions are imposed at the lung border. All parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a> unless otherwise stated.</p

A graphical summary of the modelled interactions of the signaling factors in lung bud during morphogenesis.

<p><b>a</b>) FGF10 is transcribed at high levels in the distal mesenchyme (grey) and experiments suggest that FGF10 promotes both the proliferation of the endoderm and its outward movement (green arrow). FGF10 stimulates the expression of SHH in the epithelium (red). SHH reversibly binds its receptor Ptc1 which is expressed in the mesenchyme (grey). SHH-Ptc binding results in the repression of FGF10 expression. <b>b</b>) The idealized computational domain comprises a 2D crossection along the cylinder axis of symmetry. The epithelium and the mesenchyme are shown in red and grey, correspondingly. SHH and FGF10 (but not Ptc) can diffuse freely () in the interstitial space (4) and lumen (1). The time-dependent height of the cylinder is .</p

FGF10 distribution on a growing lung tip domain.

<p>Depending on the growth speed the distribution of FGF10 is either consistent with (<b>a</b>) a lateral branching mode (fast growth speed, ), or (<b>b</b>) a bifurcating mode of branching (slow growth speed, ). Parameters values used to simulate FGF10 pattern formaton on a growing lung are as given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a>, except initial stalk length .</p

The steady state distributions of FGF10, SHH and receptor Ptc concentrations.

<p>The steady state distributions of (<b>a,d</b>) FGF10, (<b>b,e</b>) SHH, and (<b>c,f</b>) Ptc for parameter values as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi-1002377-t001" target="_blank">Table 1</a> (<b>a–c</b>) or with (<b>d–f</b>). The upper panel presents an example of FGF10 distribution during the lateral branching mode, while the lower panel provides an example for FGF10 distribution during a bifurcation branching mode. Note that the expression patterns of SHH, FGF and Ptc are shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002377#pcbi.1002377.s007" target="_blank">Figure S7</a>.</p

Dipolar Antiferromagnetism and Quantum Criticality in LiErF4

Magnetism has been predicted to occur in systems in which dipolar interactions dominate exchange. We present neutron scattering, specific heat, and magnetic susceptibility data for LiErF4, establishing it as a model dipolar coupled antiferromagnet with planar spin anisotropy and a quantum phase transition in applied field Hc 4.0 0.1 kilo oersteds. We discovered non mean field critical scaling for the classical phase transition at the antiferromagnetic transition temperature that is consistent with the two dimensional XY h4 universality class; in accord with this, the quantum phase transition at Hc exhibits three dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic frustrated nature of the dipolar interaction, which strengthens the role of fluctuations