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. 2018 Jul 26;16(7):e2002842.
doi: 10.1371/journal.pbio.2002842. eCollection 2018 Jul.

Deconstructing the Principles of Ductal Network Formation in the Pancreas

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Free PMC article

Deconstructing the Principles of Ductal Network Formation in the Pancreas

Svend Bertel Dahl-Jensen et al. PLoS Biol. .
Free PMC article

Abstract

The mammalian pancreas is a branched organ that does not exhibit stereotypic branching patterns, similarly to most other glands. Inside branches, it contains a network of ducts that undergo a transition from unconnected microlumen to a mesh of interconnected ducts and finally to a treelike structure. This ductal remodeling is poorly understood, both on a microscopic and macroscopic level. In this article, we quantify the network properties at different developmental stages. We find that the pancreatic network exhibits stereotypic traits at each stage and that the network properties change with time toward the most economical and optimized delivery of exocrine products into the duodenum. Using in silico modeling, we show how steps of pancreatic network development can be deconstructed into two simple rules likely to be conserved for many other glands. The early stage of the network is explained by noisy, redundant duct connection as new microlumens form. The later transition is attributed to pruning of the network based on the flux of fluid running through the pancreatic network into the duodenum.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Digitized pancreas networks.
Presented both in (A) their raw image format and (B) digitized. The red dots represent the mapped nodes, while the blue lines represent the mapped links. The green circle represents the exit from the pancreas (the organoids do not have an exit). The yellow box shows the mapped section of the E18.5 pancreas. Digitized data and code files “Import_Experimental_data”, “PlotNetwork” are provided in supporting information (S1 Data). E, embryonic day; Muc1, mucin1
Fig 2
Fig 2. Network properties for the in vivo samples.
< …> denotes the average of a value for every node in the network. C is the clustering coefficient for a given node. k is node degree. Droot is a node's distance to the root node through the network. D is the average distance of a node to every other node. Ltot is the total amount of link length in the entire network. Digitized data and code files “Import_Experimental_data”, “ConvertToAdjMat”, “ConvertToAdjList”, “NetworkProp”, “NetworkShapes”, “FindTriangles”, “Remove_kinks” are provided in supporting information (S1 Data). DP, dorsal pancreas; VP, ventral pancreas.
Fig 3
Fig 3. Time evolution of pancreas network features.
(A) Distribution of network degree for the different pancreas stages. A node of degree 1 corresponds to a terminal end. (B) Distribution of polygonal features for the different pancreas stages. (C) Average distance of all nodes to the exit scaled by the average distance between all nodes for the different pancreas stages. The absence of nodes with degree 2 is a result of the technique used to digitize the pancreas network, as those nodes merely represent a continuation of ducts. Error bars represent SEM. Digitized data and code files “Import_Experimental_data”, “ConvertToAdjMat”, “ConvertToAdjList”, “NetworkProp”, “NetworkShapes”, “FindTriangles”,”Remove_kinks” are provided in supporting information (S1 Data). E, embryonic day; ns, not significant; VP, ventral pancreas.
Fig 4
Fig 4. In silico network creation of ventral E12.5 networks.
(A) Schematic of the in silico model. Step I: A node is created in the neighborhood of the existing network. Step II: The created node links to M nodes drawn from a pool of the nearest M + Δ nodes. Step III: The model reiterates until the desired node amount has been reached. (B) Network evolution of the in silico model from 2 nodes to 320 nodes. (C) Distribution of polygonal features for the in silico network nodes and the E12.5 pancreas network. Error bars represent SEM. Code files “NetworkCreation”, “ConvertToAdjMat”, “ConvertToAdjList”, “PlotNetwork”, “NetworkShapes”, “NetworkProp”, “FindTriangles”,”Remove_kinks” are provided in supporting information (S1 Data). E, embryonic day; ns, not significant; VP, ventral pancreas.
Fig 5
Fig 5. Flux-based pruning of the VP14.5 networks.
(A) The logarithm of the normalized flux at steady state of the E14.5 2 pancreas network. Thicker links indicate a higher flux. The highest flux is closest to the exit, with some interlinking nodes having very low flux. The links highlighted red are pruned by the pruning mechanism of least flux. (B) The pruning event's distance from the exit as pruning progresses for flux-based pruning and random pruning. (C) Average distance of all nodes to the exit scaled by the average distance between all nodes shown for the networks of E14.5, E18.5, the in silico pruned E14.5, and the E14.5 MST. Error bars represent SEM. Code files “Import_Experimental_data”, “DiffusionOnNetwork”, “PruneBasedOnFlux”, “SnapShot”, “ConvertToAdjMat”, “ConvertToAdjList”, “NetworkProp”, “NetworkShapes”, “FindTriangles”, “Remove_kinks” are provided in supporting information (S1 Data). E, embryonic day; MST, minimum spanning tree; ns, not significant; VP, ventral pancreas.
Fig 6
Fig 6. Swelling assays reveal forskolin-induced secretion.
(A) E12.5 pancreata cultured in vitro for 1 day and submitted to forskolin treatment activating the CFTR channels undergo lumen swelling. The lumen appears as a dark shadow, and some are highlighted with arrows (B). Ductal spheres generated from E12.5 pancreata swell upon treatment with forskolin, as compared to untreated controls. CFTR, cystic fibrosis transmembrane conductance regulator; E, embryonic day.

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Grant support

Danish National Research Foundation https://dg.dk/en/ (grant number DNRF 116). Received by AGB. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Danish National Research Foundation https://dg.dk/en/ (grant number Center for Models of life). Received by KS. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Novo Nordisk Foundation http://novonordiskfonden.dk/en (grant number NNF17CC0027852). Received by AGB. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. European Union's Seventh Framework Programme ERC Grant https://erc.europa.eu/funding/advanced-grants (grant number 740704). Received by KS. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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