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WIREs Syst Biol Med
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Integrating multi‐scale knowledge on cardiac development into a computational model of ventricular trabeculation

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Insights into the mechanisms of development of the mammalian four‐chambered heart are based on biological observations at organ, tissue, cell, and molecular levels, but the full integration of these experimental data awaits a systems biology approach. Such an approach can be employed to formulate and test conceptual models in a computational simulation. To illustrate how this can be applied to heart development, we used the process of trabeculation, which is the formation of muscular strands during chamber development. We selected this process because it is localized, involves a restricted number of cell types, and a range of experimental data is available. Trabeculation of the ventricles is based on the interplay between endocardial and myocardial cells and involves molecular pathways underlying cell–cell interactions and tissue‐specific cell behavior. A cellular Potts model was used for the simulation of these multi‐scale processes. With fairly simple inputs, of which the relative contributions are unknown, an iterative exploration achieved an outcome that resembles the trabeculation process and allows further investigation of contributing factors. The systems biology pipeline from biological observations and conceptual modeling to a mathematical model and computational algorithms is described and discussed. The multi‐level biological observations provide the components and their connections of the conceptual model. However, the true strength of systems biology must be found in the biological test of the predictions that result from an experimental change in the computational model. These validated predictions will ultimately elucidate the functional role of a component or interaction in the process of heart development. WIREs Syst Biol Med 2014, 6:389–397. doi: 10.1002/wsbm.1285 This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models
From biological observation to computational model. Biological observations form the basis of a conceptual model at molecular, cellular, and tissue levels. This model is translated into a mathematical model and computational algorithms. A feedback loop is needed in which the model parameters are tuned to obtain initial values which enable the simulation to mimic the morphogenetic process. Validation of the computational model has to be done, for example, by testing the predicted morphology resulting from the simulation of a treatment with known observed biological effects.
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Computational model, signal gradients, and first trabecula formation. Delta (a, a') and Notch (b, b') activity gradients show a lateral inhibition pattern in the endocardial protrusions that occurs after 350 Monte Carlo steps. The activated Notch is then driving the secretion of Nrg1 which signals to the myocardium (c, c'). White dashed lines in panels a, b, and c show the position of the sections of panels a', b', and c' and vice versa. After approximately 700 steps (d), the model produces dividing cells (magenta) and trabecular ridges of extruded myocardial cells (cyan‐blue cells). In the absence of Notch the model fails to form these trabecular ridges (e compared with d) and Delta expression loses its lateral inhibition pattern (f compared with a'). In all panels, the endocardium is represented as the top layer and the myocardium as the bottom layer.
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Model initiation. A two‐dimensional (2D) and a three‐dimensional (3D) views of the computational framework that was created, including the tissue types involved in trabeculation. The initial framework consists of regular cubic cells (left). This model was relaxed for 50 Monte Carlo steps to minimize the local energy of the model which results in a stable, more natural, tissue architecture (right).
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Conceptual model of trabecular development. An overview of the tissue components, molecules, and interactions involved in the cell behavior that leads to trabecular formation.
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(a) Three‐dimensional reconstructions of human embryonic hearts at carnegie stage (CS) 12, 13, and 18, kindly provided by Dr. Aleksander Sizarov. Trabecular ridges appear around stages 12–13 and transform into a complex trabecular mesh at stage 18 (scalebars 500 µm). (b) Confocal image of the floor of the right ventricle of an embryonic day 9.5 mouse heart showing the myocardium (shown in red, using a transgene driving Tomato expression) and endocardium (shown in green, using Flk1 and Pecam antibodies). At the dotted line (100 µm) a virtual cross section, perpendicular to the blood flow, (panel c) shows endocardial protrusions (EP) that touch the myocardium next to a trabecular ridge (TR).
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Analytical and Computational Methods > Computational Methods
Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

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