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1.  Prediction stability in a data-based, mechanistic model of σF regulation during sporulation in Bacillus subtilis 
Scientific Reports  2013;3:2755.
Mathematical modeling of biological networks can help to integrate a large body of information into a consistent framework, which can then be used to arrive at novel mechanistic insight and predictions. We have previously developed a detailed, mechanistic model for the regulation of σ F during sporulation in Bacillus subtilis. The model was based on a wide range of quantitative data, and once fitted to the data, the model made predictions that could be confirmed in experiments. However, the analysis was based on a single optimal parameter set. We wondered whether the predictions of the model would be stable for all optimal parameter sets. To that end we conducted a global parameter screen within the physiological parameter ranges. The screening approach allowed us to identify sensitive and sloppy parameters, and highlighted further required datasets during the optimization. Eventually, all parameter sets that reproduced all available data predicted the physiological situation correctly.
doi:10.1038/srep02755
PMCID: PMC3783014  PMID: 24067622
2.  The control of branching morphogenesis 
Open Biology  2013;3(9):130088.
Many organs of higher organisms are heavily branched structures and arise by an apparently similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in these organs. It is an open question whether the regulatory processes work according to a common principle and how far physical and geometrical constraints determine the branching process. Here, we review the known regulatory factors and physical constraints in lung, kidney, pancreas, prostate, mammary gland and salivary gland branching morphogenesis, and describe the models that have been formulated to analyse their impacts.
doi:10.1098/rsob.130088
PMCID: PMC3787747  PMID: 24004663
branching; computational modelling; in silico organogenesis
3.  Computational modelling of bovine ovarian follicle development 
BMC Systems Biology  2013;7:60.
Background
The development of ovarian follicles hinges on the timely exposure to the appropriate combination of hormones. Follicle stimulating hormone (FSH) and luteinizing hormone (LH) are both produced in the pituitary gland and are transported via the blood circulation to the thecal layer surrounding the follicle. From there both hormones are transported into the follicle by diffusion. FSH-receptors are expressed mainly in the granulosa while LH-receptors are expressed in a gradient with highest expression in the theca. How this spatial organization is achieved is not known. Equally it is not understood whether LH and FSH trigger distinct signalling programs or whether the distinct spatial localization of their G-protein coupled receptors is sufficient to convey their distinct biological function.
Results
We have developed a data-based computational model of the spatio-temporal signalling processes within the follicle and (i) predict that FSH and LH form a gradient inside the follicle, (ii) show that the spatial distribution of FSH- and LH-receptors can arise from the well known regulatory interactions, and (iii) find that the differential activity of FSH and LH may well result from the distinct spatial localisation of their receptors, even when both receptors respond with the same intracellular signalling cascade to their ligand.
Conclusion
The model integrates the large amount of published data into a consistent framework that can now be used to better understand how observed defects translate into failed follicle maturation.
doi:10.1186/1752-0509-7-60
PMCID: PMC3726369  PMID: 23856357
Ovarian follicle development; PDE model; Computational biology; Bovine
4.  Digit patterning during limb development as a result of the BMP-receptor interaction 
Scientific Reports  2012;2:991.
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 knockout 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.
doi:10.1038/srep00991
PMCID: PMC3524521  PMID: 23251777
5.  ECCB 2012: The 11th European Conference on Computational Biology 
Bioinformatics  2012;28(18):i303-i305.
doi:10.1093/bioinformatics/bts490
PMCID: PMC3436852  PMID: 22962444
6.  Simulations demonstrate a simple network to be sufficient to control branch point selection, smooth muscle and vasculature formation during lung branching morphogenesis 
Biology Open  2012;1(8):775-788.
Summary
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.
doi:10.1242/bio.20121339
PMCID: PMC3507219  PMID: 23213471
Lung development; Computational biology; Smooth muscles; Vasculogenesis; Branching morphogenesis
7.  Branch Mode Selection during Early Lung Development 
PLoS Computational Biology  2012;8(2):e1002377.
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 modes.
Author Summary
Most 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. While the branching sequence is identical in mice of identical genetic background it differs between mouse strains. This suggests that the positioning of branch points and the type of branching sensitively depends on information encoded in the genome. Encoding every branching point independently in the genome would require a large number of genes, and it is more likely that a recursive, self-organized process exists that determines the patterning. While many regulatory molecules have been identified an integrated understanding of the regulatory network (program) is missing. Based on available experimental data we have developed a model for lung branching. The model correctly predicts branching phenotypes in mutants and suggests that also the growth speed of the lung tip can affect the positioning and type of the next branching event.
doi:10.1371/journal.pcbi.1002377
PMCID: PMC3280966  PMID: 22359491
8.  Inferring Biological Mechanisms by Data-Based Mathematical Modelling: Compartment-Specific Gene Activation during Sporulation in Bacillus subtilis as a Test Case 
Advances in Bioinformatics  2012;2011:124062.
Biological functionality arises from the complex interactions of simple components. Emerging behaviour is difficult to recognize with verbal models alone, and mathematical approaches are important. Even few interacting components can give rise to a wide range of different responses, that is, sustained, transient, oscillatory, switch-like responses, depending on the values of the model parameters. A quantitative comparison of model predictions and experiments is therefore important to distinguish between competing hypotheses and to judge whether a certain regulatory behaviour is at all possible and plausible given the observed type and strengths of interactions and the speed of reactions. Here I will review a detailed model for the transcription factor σF, a regulator of cell differentiation during sporulation in Bacillus subtilis. I will focus in particular on the type of conclusions that can be drawn from detailed, carefully validated models of biological signaling networks. For most systems, such detailed experimental information is currently not available, but accumulating biochemical data through technical advances are likely to enable the detailed modelling of an increasing number of pathways. A major challenge will be the linking of such detailed models and their integration into a multiscale framework to enable their analysis in a larger biological context.
doi:10.1155/2011/124062
PMCID: PMC3270535  PMID: 22312331
9.  A Computational Analysis of the Dynamic Roles of Talin, Dok1, and PIPKI for Integrin Activation 
PLoS ONE  2011;6(11):e24808.
Integrin signaling regulates cell migration and plays a pivotal role in developmental processes and cancer metastasis. Integrin signaling has been studied extensively and much data is available on pathway components and interactions. Yet the data is fragmented and an integrated model is missing. We use a rule-based modeling approach to integrate available data and test biological hypotheses regarding the role of talin, Dok1 and PIPKI in integrin activation. The detailed biochemical characterization of integrin signaling provides us with measured values for most of the kinetics parameters. However, measurements are not fully accurate and the cellular concentrations of signaling proteins are largely unknown and expected to vary substantially across different cellular conditions. By sampling model behaviors over the physiologically realistic parameter range we find that the model exhibits only two different qualitative behaviors and these depend mainly on the relative protein concentrations, which offers a powerful point of control to the cell. Our study highlights the necessity to characterize model behavior not for a single parameter optimum, but to identify parameter sets that characterize different signaling modes.
doi:10.1371/journal.pone.0024808
PMCID: PMC3217926  PMID: 22110576
10.  plasticity of TGF-β signaling 
BMC Systems Biology  2011;5:184.
Background
The family of TGF-β ligands is large and its members are involved in many different signaling processes. These signaling processes strongly differ in type with TGF-β ligands eliciting both sustained or transient responses. Members of the TGF-β family can also act as morphogen and cellular responses would then be expected to provide a direct read-out of the extracellular ligand concentration. A number of different models have been proposed to reconcile these different behaviours. We were interested to define the set of minimal modifications that are required to change the type of signal processing in the TGF-β signaling network.
Results
To define the key aspects for signaling plasticity we focused on the core of the TGF-β signaling network. With the help of a parameter screen we identified ranges of kinetic parameters and protein concentrations that give rise to transient, sustained, or oscillatory responses to constant stimuli, as well as those parameter ranges that enable a proportional response to time-varying ligand concentrations (as expected in the read-out of morphogens). A combination of a strong negative feedback and fast shuttling to the nucleus biases signaling to a transient rather than a sustained response, while oscillations were obtained if ligand binding to the receptor is weak and the turn-over of the I-Smad is fast. A proportional read-out required inefficient receptor activation in addition to a low affinity of receptor-ligand binding. We find that targeted modification of single parameters suffices to alter the response type. The intensity of a constant signal (i.e. the ligand concentration), on the other hand, affected only the strength but not the type of the response.
Conclusions
The architecture of the TGF-β pathway enables the observed signaling plasticity. The observed range of signaling outputs to TGF-β ligand in different cell types and under different conditions can be explained with differences in cellular protein concentrations and with changes in effective rate constants due to cross-talk with other signaling pathways. It will be interesting to uncover the exact cellular differences as well as the details of the cross-talks in future work.
doi:10.1186/1752-0509-5-184
PMCID: PMC3227652  PMID: 22051045
11.  A quantitative study of the benefits of co-regulation using the spoIIA operon as an example 
The distribution of most genes is not random, and functionally linked genes are often found in clusters. Several theories have been put forward to explain the emergence and persistence of operons in bacteria. Careful analysis of genomic data favours the co-regulation model, where gene organization into operons is driven by the benefits of coordinated gene expression and regulation. Direct evidence that coexpression increases the individual's fitness enough to ensure operon formation and maintenance is, however, still lacking. Here, a previously described quantitative model of the network that controls the transcription factor σF during sporulation in Bacillus subtilis is employed to quantify the benefits arising from both organization of the sporulation genes into the spoIIA operon and from translational coupling. The analysis shows that operon organization, together with translational coupling, is important because of the inherent stochastic nature of gene expression, which skews the ratios between protein concentrations in the absence of co-regulation. The predicted impact of different forms of gene regulation on fitness and survival agrees quantitatively with published sporulation efficiencies.
doi:10.1038/msb4100084
PMCID: PMC1681516  PMID: 16924264
coupled gene expression; noise; operon; signalling networks; sporulation

Results 1-11 (11)