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Gonadal sex determination (GSD) is a complex but poorly understood process in the early stages of embryonic development. This process determines whether the bipotential gonadal primordium (BGP) will differentiate into testes or ovaries through the activation of genetic factors related to Sertoli or Granulosa cells, respectively. The study of this developmental process remains challenging due to experimental limitations and the complexity of the underlying genetic interactions. Boolean Networks (BNs) are binary networks that simulate genetic behavior and are commonly used for modeling gene regulatory networks (GRNs) due to their simplicity when dealing with a high number of gene interactions. Reported BNs usually use a synchronous (parallel) update scheme, which means that all the nodes (representing genes) update their values simultaneously. However, the use of this update scheme has been criticized because it cannot represent biological systems that are highly regulated at a temporal scale. Asynchronous and block-sequential updating schemes appear as an alternative to tackle this issue. In the first case, the updating scheme follows a random behavior while, in the second case, the set of network nodes is partitioned into blocks such that the nodes within a block are updated simultaneously, and the blocks are considered in a specific order sequence. To assess the impact of different updating approaches in a GRN associated to GSD we first made a node reduction without losing the main dynamics of the original network which are related to the formation of testes and ovaries. Then, we tested the effect of perturbations given by the inactivation of genes on the network attractors, specifically the SRY and WNT4 genes, since the former is only present in the Y chromosome and the latter is of importance in early embryo development. We found that both genes were crucial, but WNT4 alone showed a higher percentage of attractors towards a phenotype than the SRY alone. Finally, we found that using asynchronous and block-sequential updating schemes, the attraction basins - i.e., the set of configurations that reach an attractor - remain with similar percentages to those of the original network, which supports the robustness of the model.
RESUMO
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality-a balance between change and stability, order and chaos-is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean networks-a general model of discrete dynamical systems-we show that heterogeneity-in time, structure, and function-can broaden additively the parameter region where criticality is found. Moreover, parameter regions where antifragility is found are also increased with heterogeneity. However, maximum antifragility is found for particular parameters in homogeneous networks. Our work suggests that the "optimal" balance between homogeneity and heterogeneity is non-trivial, context-dependent, and in some cases, dynamic.
RESUMO
Adaptability, heterogeneity, and plasticity are the hallmarks of macrophages. How these complex properties emerge from the molecular interactions is an open question. Thus, in this study we propose an actualized regulatory network of cytokines, signaling pathways, and transcription factors to survey the differentiation, heterogeneity, and plasticity of macrophages. The network recovers attractors, which in regulatory networks correspond to cell types, that correspond to M0, M1, M2a, M2b, M2c, M2d, M2-like, and IL-6 producing cells, including multiple cyclic attractors that are stable to perturbations. These cyclic attractors reproduce experimental observations and show that oscillations result from the structure of the network. We also study the effect of the environment in the differentiation and plasticity of macrophages, showing that the observed heterogeneity in macrophage populations is a result of the regulatory network and its interaction with the micro-environment. The macrophage regulatory network gives a mechanistic explanation to the heterogeneity and plasticity of macrophages seen in vivo and in vitro, and offers insights into the mechanism that allows the immune system to react to a complex dynamic environment.
RESUMO
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.
RESUMO
We develop a Boolean model to explore the dynamical behaviour of budding yeast in response to osmotic and pheromone stress. Our model predicts that osmotic stress halts the cell cycle progression in either of four possible arrest points. The state of the cell at the onset of the stress dictates which arrest point is finally reached. According to our study and consistent with biological data, these cells can return to the cell cycle after removal of the stress. Moreover, the Boolean model illustrates how osmotic stress alters the state transitions of the cell. Furthermore, we investigate the influence of a particular pheromone based method for the synchronisation of the cell cycles in a population of cells. We show this technique is not a suitable method to study one of the arrest points under osmotic stress. Finally, we discuss how an osmotic stress can cause some of the so called frozen cells to divide. In this case the stress can move these cells to the cell cycle trajectory, such that they will replicate again.