Abstract
The experimental actualization of organoids modelling organs from brains to pancreases has revealed that much of the diverse morphologies of organs are emergent properties of simple intercellular 'rules' and not the result of top-down orchestration. In contrast to other organs, the initial plexus of the vascular system is formed by aggregation of cells in the process known as vasculogenesis. Here we study this self-assembling process of blood vessels in three dimensions through a set of simple rules that align intercellular apical-basal and planar cell polarity. We demonstrate that a fully connected network of tubes emerges above a critical initial density of cells. Through planar cell polarity, our model demonstrates convergent extension, and this polarity furthermore allows for both morphology-maintaining growth and growth-induced buckling. We compare this buckling with the special vasculature of the islets of Langerhans in the pancreas and suggest that the mechanism behind the vascular density-maintaining growth of these islets could be the result of growth-induced buckling.
Highlights
Tubes are ubiquitous features of numerous biological systems
While lumen formation in blood vessels is its own research field [5,24,25,26], we introduce a simple mechanism for lumen formation by describing the evolution of the apical–basal polarity of cells, yielding a fully emergent approach to tubulogenesis
A simple feedback mechanism where the proliferation rate inversely depends on the density can keep vascular density constant during growth. While this effect would definitely be co-occurring with angiogenesis, it is intriguing that it simultaneously gives an explanation for the tortuousness of the vascular network
Summary
Tubes are ubiquitous features of numerous biological systems. In humans, they form the gastrointestinal tract, the ductal network of the pancreas, the fallopian tubes, the urinary tract and so on, with the most obvious example being the entire vascular network of blood vessels. Q’s orthogonal and S3 favours Note that, in reality, cells can deform based on the polarities, but we model them as point particles. If we turn on AB polarity in the present model, that is, we let λ0 → 0.0 and λ1 → 1.0, the solid structure tube of figure 2a opens up into a sheet-like structure as shown in figure 2b This behaviour occurs because of the random initialization of the AB polarity (as illustrated in figure 2a). There will naturally be culture medium, extracellular matrix, pericytes, etc., present, and the system will perhaps be embedded in, for example, matrigel and collagen [29] These components mitigate their own interactions between one another and with the cells and could be explicitly modelled in a similar manner to our cell–cell interactions. We have tested such effects and our results remain qualitatively unchanged
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