Fig 1.
Experimental images and computational approach of bile duct lumen formation.
(A) The bile ducts mature from the hilum (right panel) to the periphery of the liver lobes (left panel), as illustrated with sections made at several distances from the hilum in mouse embryonic day (E) 18.5 liver. Nascent lumina are identified with Mucin-1 staining. White arrowheads point to SOX9-expressing cholangiocytes; red arrowheads point to hepatoblasts delineating nascent lumina. Size bar is 20 μm. (B) Snapshot of the equivalent in silico model showing the CBM and DCM regions. The initial cholangiocyte is marked by a dashed circle. The yellow arrows indicate the background pressure forces. (C) Tissular organization of the developing liver. The portal vein (PV) is delineated by an endothelium and is surrounded by mesenchyme. Cholangiocytes form a discontinuous layer of cells called ductal plate. When lumina start to form they are delineated by cholangiocytes and Hepatocyte Nuclear Factor 4 (HNF4)-expressing hepatoblasts (red). Epithelial cells are identified by beta-catenin staining (green); DAPI stains nuclei (blue). The left panel illustrates a section through a mouse liver at E18.5; the right panel (D) shows the tissular architecture in a close-up of the in silico model.
Table 1.
Antibodies used for immunostaining.
Fig 2.
(A) Cell surface element (triangle) with nodal force. (B) Horizontal cut section through the DCM model plane, indicating cytoplasm and cortex of the cells. C-E are cross sections through individual cells. C) 2D sketch defining the polarity vector (PCP) formed by the two cones with opening angle α. Note that the zone of polarity is assumed to be symmetric. (D) Definition of the Apical-Basal vector (ABP). (E) Tracer Particles (TP) moving across the apical surface of the cell. (F) Tight junctions between two cells in contact represented by red colored triangles. (G) Overview of the different stages for the DCM cell division algorithm, extended from [37] 1: A cell with arbitrary shape. 2: just before cell division, the cell rounds up. A division plane is chosen. 3: Two new smaller spherical cells are created on both sides of the plane inside the mother envelope. Both daughter cells first grow artificially fast (“sub-simulation”) within the boundaries of the mother envelope, to reach their target initial volume. 4: Shortly after, the mother envelope is removed. The cells adapt to their new environment. 5: Two new growing and adhering cells have been created (nuclei are shown).
Table 2.
Nominal physical parameter values for the model.
An (*) denotes parameter variability meaning that the individual cell parameters are picked from a Gaussian distribution with ±10% on their mean value. CR: Calibration Runs. Unless indicated, the cell parameters for the CBM and DCM are identical. PC: Personal communication.
Fig 3.
Morphological features of cells delineating developing biliary lumen.
(A) Tight junctions are detected between HNF4- cholangiocytes and between cholangiocytes and HNF4+ hepatoblasts; but not between adjacent hepatoblasts. (B) Proliferating SOX9+ cholangiocytes and HNF4+ hepatoblasts are detected by Ki67-staining in E16.5 embryonic livers. E-cad: E-cadherin. (C) Apical constriction in cholangiocytes. Developing ducts are delineated by white dotted lines. White size bar, 20 micrometer; yellow size bar 10 micrometer. PV: portal vein.
Fig 4.
Expression of ion transporters and water channels during biliary lumenogenesis.
Expression of ion transporters and aquaporins was measured by RNA sequencing of total RNA extracted from purified developing cholangiocytes. Bars are standard deviation (SD).
Fig 5.
Possible mechanisms of lumen formation in a cell bi-layer.
(A) Cell division. 1: double layer of cells with 4 dividing cells (indicated by orange dashed line). Cell division goes along PCP. 2: random directed cell division. (B) Apical constriction on the same 4 cells. Note the wedge-like shape of the four center cells with apical membrane marked in red in configuration 2 compared to configuration 1. (C) Osmosis initiated by 4 cells inducing hydrostatic pressure in extracellular space.
Fig 6.
Detail image of the lumen with indicated cell surface areas.
White numbering: hepatoblasts, red numbering: cholangiocytes, green numbering: mesenchyme. The picture is from an E18.5 mouse liver expressing eYFP in the mesenchyme. Red membrane staining of hepatoblasts and cholangiocytes: E-cadherin; green staining of mesenchyme: eYFP.
Fig 7.
Simulation results for Models 1 and 2.
(A) Immediately after the initial state, where a cholangiocyte divides in two daughter cells. The division direction is indicated by the arrow. (B) Snapshot of a simulation for Model 0 (t = 12). (C) Lumen area versus time for models 1 and 2, for different runs (no osmotic effects present). The solid lines are the average of 5 stochastic realizations of the same parameter set, while the shadowed regions indicate the two times standard deviation interval of these realizations. (D) Snapshot of a simulation for Model 1 (t = 12). (E) Snapshot of a simulation for Model 2 (t = 12). The red, grey and blue cells indicate hepatocytes, cholangiocytes and the mesenchyme respectively. (F) simulation snapshots for model 2 showing TP’s (yellow) and apical sites of the cholangiocytes (red).
Table 3.
Models and the feature they represent.
Fig 8.
Simulation results for Model 3.
(A) lumen area versus time for different osmotic pressures. The solid lines are the average of 5 stochastic realizations of the same parameter set, while the shadowed regions indicate the minimum and maximum values of these realizations. (B-C) Snapshot of a simulation for Model 3 (PL = 50Pa and PL = 100Pa respectively). In B, the red zones indicate increased cell-cell adhesion due to presence of TJ. (D) Picture of typical bile duct lumen for an embryo at E18.5 (SOX9, blue; beta-catenin, green).
Fig 9.
Simulation results for Model 3, assuming Pl = 50Pa: Lumen area versus time.
(A) influence of cell-to-cell signalling times Tsig. (B) influence of absence or presence of Apical constriction (AC). The solid lines are the average of 5 stochastic realizations of the same parameter set, while the shadowed regions indicate the two times standard deviation interval of these realizations. An increase in lumen area from zero to ∼ 350μm2 in 24 hours is realistic since the area of lumina near the hilum ranged from 7 to 36 μm2 at E16.5 and from 116 to 674 μm2 at E18.5 (n = 10 at each stage) (C) Microscopic picture of small lumen with cholangiocytes (white arrowheads) and hepatoblasts (red arrowheads). Tissue section is stained to detect SOX9 (red), beta-catenin (green) and nuclei (DAPI, blue). (D) Snapshot of simulation showing a configuration comparable to that in panel C. The yellow arrows indicate the direction of cell-cell signalling during the formation.
Fig 10.
Simulation results compared to Model 3 with nominal parameters.
(A) Effect of a higher global cell-cell adhesion energy value. (B-C) Effect of an apical adhesion energy value equal to the global cell-cell adhesion energy (Wap = W), for Pl = 50Pa and Pl = 70Pa respectively. In the last figure, only the individual realizations are shown for clarity reasons.