Angiogenesis is an important adaptation mechanism of the blood vessels to the changing requirements of the body during development, aging, and wound healing. Angiogenesis allows existing blood vessels to form new connections or to reabsorb existing ones. Blood vessels are composed of a layer of endothelial cells (ECs) covered by one or more layers of mural cells (smooth muscle cells or pericytes). We constructed a computational Boolean model of the molecular regulatory network involved in the control of angiogenesis. Our model includes the ANG/TIE, HIF, AMPK/mTOR, VEGF, IGF, FGF, PLCγ/Calcium, PI3K/AKT, NO, NOTCH, and WNT signaling pathways, as well as the mechanosensory components of the cytoskeleton. The dynamical behavior of our model recovers the patterns of molecular activation observed in Phalanx, Tip, and Stalk ECs. Furthermore, our model is able to describe the modulation of EC behavior due to extracellular micro-environments, as well as the effect due to loss- and gain-of-function mutations. These properties make our model a suitable platform for the understanding of the molecular mechanisms underlying some pathologies. For example, it is possible to follow the changes in the activation patterns caused by mutations that promote Tip EC behavior and inhibit Phalanx EC behavior, that lead to the conditions associated with retinal vascular disorders and tumor vascularization. Moreover, the model describes how mutations that promote Phalanx EC behavior are associated with the development of arteriovenous and venous malformations. These results suggest that the network model that we propose has the potential to be used in the study of how the modulation of the EC extracellular micro-environment may improve the outcome of vascular disease treatments.

Over the last few decades, the Arabidopsis thaliana root stem cell niche (RSCN) has become a model system for the study of plant development and stem cell niche dynamics. Currently, many of the molecular mechanisms involved in RSCN maintenance and development have been described. A few years ago, we published a gene regulatory network (GRN) model integrating this information. This model suggested that there were missing components or interactions. Upon updating the model, the observed stable gene configurations of the RSCN could not be recovered, indicating that there are additional missing components or interactions in the model. In fact, due to the lack of experimental data, GRNs inferred from published data are usually incomplete. However, predicting the location and nature of the missing data is a not trivial task. Here, we propose a set of procedures for detecting and predicting missing interactions in Boolean networks. We used these procedures to predict putative missing interactions in the A. thaliana RSCN network model. Using our approach, we identified three necessary interactions to recover the reported gene activation configurations that have been experimentally uncovered for the different cell types within the RSCN: (1) a regulation of PHABULOSA to restrict its expression domain to the vascular cells, (2) a self-regulation of WOX5, possibly by an indirect mechanism through the auxin signaling pathway, and (3) a positive regulation of JACKDAW by MAGPIE. The procedures proposed here greatly reduce the number of possible Boolean functions that are biologically meaningful and experimentally testable and that do not contradict previous data. We believe that these procedures can be used on any Boolean network. However, because the procedures were designed for the specific case of the RSCN, formal demonstrations of the procedures should be shown in future efforts.

Endothelial cells (ECs) form the lining of lymph and blood vessels. Changes in tissue requirements or wounds may cause ECs to behave as tip or stalk cells. Alternatively, they may differentiate into mesenchymal cells (MCs). These processes are known as EC activation and endothelial-to-mesenchymal transition (EndMT), respectively. EndMT, Tip, and Stalk EC behaviors all require SNAI1, SNAI2, and Matrix metallopeptidase (MMP) function. However, only EndMT inhibits the expression of VE-cadherin, PECAM1, and VEGFR2, and also leads to EC detachment. Physiologically, EndMT is involved in heart valve development, while a defective EndMT regulation is involved in the physiopathology of cardiovascular malformations, congenital heart disease, systemic and organ fibrosis, pulmonary arterial hypertension, and atherosclerosis. Therefore, the control of EndMT has many promising potential applications in regenerative medicine. Despite the fact that many molecular components involved in EC activation and EndMT have been characterized, the system-level molecular mechanisms involved in this process have not been elucidated. Toward this end, hereby we present Boolean network model of the molecular involved in the regulation of EC activation and EndMT. The simulated dynamic behavior of our model reaches fixed and cyclic patterns of activation that correspond to the expected EC and MC cell types and behaviors, recovering most of the specific effects of simple gain and loss-of-function mutations as well as the conditions associated with the progression of several diseases. Therefore, our model constitutes a theoretical framework that can be used to generate hypotheses and guide experimental inquiry to comprehend the regulatory mechanisms behind EndMT. Our main findings include that both the extracellular microevironment and the pattern of molecular activity within the cell regulate EndMT. EndMT requires a lack of VEGFA and sufficient oxygen in the extracellular microenvironment as well as no FLI1 and GATA2 activity within the cell. Additionally Tip cells cannot undergo EndMT directly. Furthermore, the specific conditions that are sufficient to trigger EndMT depend on the specific pattern of molecular activation within the cell.

Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.

The vulva of Caenorhabditis elegans has been long used as an experimental model of cell differentiation and organogenesis. While it is known that the signaling cascades of Wnt, Ras/MAPK, and NOTCH interact to form a molecular network, there is no consensus regarding its precise topology and dynamical properties. We inferred the molecular network, and developed a multivalued synchronous discrete dynamic model to study its behavior. The model reproduces the patterns of activation reported for the following types of cell: vulval precursor, first fate, second fate, second fate with reversed polarity, third fate, and fusion fate. We simulated the fusion of cells, the determination of the first, second, and third fates, as well as the transition from the second to the first fate. We also used the model to simulate all possible single loss- and gain-of-function mutants, as well as some relevant double and triple mutants. Importantly, we associated most of these simulated mutants to multivulva, vulvaless, egg-laying defective, or defective polarity phenotypes. The model shows that it is necessary for RAL-1 to activate NOTCH signaling, since the repression of LIN-45 by RAL-1 would not suffice for a proper second fate determination in an environment lacking DSL ligands. We also found that the model requires the complex formed by LAG-1, LIN-12, and SEL-8 to inhibit the transcription of eff-1 in second fate cells. Our model is the largest reconstruction to date of the molecular network controlling the specification of vulval precursor cells and cell fusion control in C. elegans. According to our model, the process of fate determination in the vulval precursor cells is reversible, at least until either the cells fuse with the ventral hypoderm or divide, and therefore the cell fates must be maintained by the presence of extracellular signals.

BackgroundThere are recent experimental reports on the cross-regulation between molecules involved in the control of the cell cycle and the differentiation of the vulval precursor cells (VPCs) of Caenorhabditis elegans. Such discoveries provide novel clues on how the molecular mechanisms involved in the cell cycle and cell differentiation processes are coordinated during vulval development. Dynamic computational models are helpful to understand the integrated regulatory mechanisms affecting these cellular processes.ResultsHere we propose a simplified model of the regulatory network that includes sufficient molecules involved in the control of both the cell cycle and cell differentiation in the C. elegans vulva to recover their dynamic behavior. We first infer both the topology and the update rules of the cell cycle module from an expected time series. Next, we use a symbolic algorithmic approach to find which interactions must be included in the regulatory network. Finally, we use a continuous-time version of the update rules for the cell cycle module to validate the cyclic behavior of the network, as well as to rule out the presence of potential artifacts due to the synchronous updating of the discrete model. We analyze the dynamical behavior of the model for the wild type and several mutants, finding that most of the results are consistent with published experimental results.ConclusionsOur model shows that the regulation of Notch signaling by the cell cycle preserves the potential of the VPCs and the three vulval fates to differentiate and de-differentiate, allowing them to remain completely responsive to the concentration of LIN-3 and lateral signal in the extracellular microenvironment.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0498-z) contains supplementary material, which is available to authorized users.

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