Fig 1.
Variety of morphologies observed in in vitro organoids.
Cross-sectional view of different organoids with the lumen surface labeled in red. (a) Snapshot of an Madin-Darby canine kidney (MDCK) cyst with a single lumen labeled with F-actin (red) and DAPI (blue). Scale bar: 10 μm. (b) Snapshot of a pancreatic organoid with multiple lumens labeled with Ezrin (red) and Hoescht (blue). Scale bar: 40 μm. (c) Snapshot of a murine epidermal organoid with a single lumen surrounded by multiple cell layers labeled with F-actin (red), DAPI (blue), and Keratin-5 (yellow). Adapted with permission from Boonekamp KE et al. [13]. Scale bar: 50 μm. (d) Human breast adenocarcinoma tumor spheroid with metabolically viable cells shown in green and the central cells of the spheroid remained viable. Adapted with permission from Gong X et al. [3]. Scale bar: 100 μm.
Fig 2.
Cells and lumen represented by field variables
represents each cell for
, and u0 represents the lumen. Color codes are shown for cells and lumen.
Fig 3.
Overview of the morphologies produced by this model.
The final states of (a) star shape organoid formed when , (b) monolayer cyst organoid formed when
, (c) branched multilayer organoid formed when
, (d) multilayer multi-lumen organoid formed when
, (e) multilayer no-stable-lumen organoid formed when
, and (f) multilayer single-stable-lumen organoid formed when
. The blue and yellow regions in (a–f) represent the cells and lumen, respectively. (g) Phase diagram of the organoid morphology and typical pattern of each phase. Each domain corresponds to; star shape (yellow), monolayer cyst (green), branched multi-lumen (blue), multilayer multi-lumen (red), multilayer no-stable-lumen (purple), and multilayer single-stable-lumen (gray). The black diamond markers correspond to the parameter sets where the organoids of (a-f) emerge.
Fig 4.
Time evolution of the organoid growth process.
The blue and yellow regions in (a-f) represent the cells and lumen, respectively. (a) star-shape , (b) monolayer cyst
, (c) branched multi-lumen
, (d) multilayer multi-lumen
, (e) multilayer no-stable-lumen
, and (f) multilayer single-stable-lumen
. See S1-S6 Movies.
Table 1.
Summary of the behaviors of the indices to characterize the organoid morphology.
Fig 5.
(a) Time evolution of the lumen occupancy at the various td and . (b) Time variation rate of lumen occupancy for the various values of the minimum cell division time td and lumen pressure
. The black dashed line serves as a visual guide to indicate zero rate. The lumen occupancy increases and decreases with time to above and below the black dashed line, respectively. (c) Value of the lumen occupancy at the final state for the various td and
. The black dashed line here corresponds to the one in (b), demonstrating regions of increasing and decreasing lumen occupancy. (d) Snapshot of each parameter set of (a). The number labels represent the class of the organoid morphology: (i) star-shape, (ii) monolayer cyst, (iii) branched multi-lumen, (iv) multilayer multi-lumen, (v) multilayer single-stable-lumen, and (vi) multilayer no-stable-lumen.
Fig 6.
(a) Number of lumens present at the various values of the minimum cell division time td and lumen pressure . The brown region with a star marker, *, represents zero. The black dashed lines serve as visual guides to demarcate the boundaries between regions with single and multiple lumens (b-d) Time evolution of the number of lumen at the various td and
. See their morphology in Fig 5d.
Fig 7.
(a) Sphericity of organoids at various values of the minimum cell division time td and lumen pressure . The brown region with a star marker, *, represents the zero lumen region. The black solid, dashed, and dotted lines are included as visual guides. The solid and dashed lines suggest regions of single and multi-lumen formations, respectively, while the dotted line provides a reference for distinguishing between star-shaped and monolayer cyst structures. (b-d) Time evolution of the sphericity at various values of td and
. See their morphology in Fig 5d.
Fig 8.
Morphologies resulting from the addition of noise to the volume condition for cell division.
The final states of (a) star shape organoid formed when , (b) monolayer cyst organoid formed when
, (c) branched multilayer organoid formed when
, (d) multilayer multi-lumen organoid formed when
, (e) multilayer no-stable-lumen organoid formed when
, and (f) multilayer single-stable-lumen organoid formed when
. (g) A phase diagram of the organoid morphology and typical pattern of each phase with added noise to the volume condition for cell division. Each domain corresponds to: star shape (yellow), monolayer cyst (green), branched multi-lumen (blue), multilayer multi-lumen (red), multilayer no-stable-lumen (purple), and multilayer single-stable-lumen (gray). The black diamond markers correspond to the parameter sets where the organoids of (a–f) emerge.
Fig 9.
Process of maintaining monolayers;
(a) Lumen perimeter and the number of cells N were plotted as a function of time for the 2D simulation with
and td = 300. Note that N(t) has been multiplied by a constant factor of a = 1.6 to align with the curve of
on the right vertical axis. Inset: An enlarged view of the two curves. Inset: N(t) shows a step-wise increase while
exhibits a rapid increase followed by a decay. (b) Micro-lumens were generated just after cell division and merged into a central lumen at
and td = 300. (c) Lumen index, defined by a = 1.6 and td = 300, was plotted for various values of
. (d) The lumen perimeter
and the number of cells multiplied by the short axis of a cell
were plotted as a function of time for the 2D simulation with noise added to the volume condition at
and td = 300. Inset: Variation of the typical cell width
as a function of time. (e) A kymograph of the cell division events was plotted as a function of the angle coordinate. The color indicates the elapsed time since the cell was generated through a cell division. (f) The lumen index measured at td = 300 with added noise to the volume condition, was plotted for various values of
. (g) The lumen surface, defined by Eq (8), Sl, and the number of cells N multiplied by a constant a were plotted as a function of time for the 3D simulation at
, where a = 0.05. (h) The evolution of the organoid shape (top row) and the lumen shape (bottom row) are shown for the 3D simulation with
. (i) Cross-sectional images of organoids from 3D simulations at different lumen pressures, with a constant cell division time (td) of 10. (j) The lumen index, Sl/aN, was plotted for the 3D simulation with various lumen pressure values
, 0.35, 0.40, and 0.45 and td = 10.
Fig 10.
Mechanism for the formation of a star-shaped organoid.
(a) Snapshot of the typical morphology of a star-shaped organoid formed at . Red arrows indicate cells extruding into the lumen, and white arrows show the branches of the organoid. (b) Time evolution of a branch tip. (c) Time-integrated distribution of cell volume of the cells for angular coordinates of the cells appearing in a star-shaped organoid at
. The vertical lines represent the angles of the lumen branches. The black dot line represents the volume of the cells required for cell division,
. (d) Relations between the cell volume and position of the representative cells in a star-shaped organoid at
. The black dot line represents the volume of the cells required for cell division,
. Cell 1, Cell 2, and Cell 3 represent typical cells in the center, on a branch, and at the tip of the branch, respectively. The orange, green, and blue markers in the inset represent the final positions of Cell 1, Cell 2, and Cell 3, respectively. (e-g) Historical positions of each cell. All cells at various times are overlaid in the same figure, and the color indicates the elapsed time from the generation of each cell at each time tcell. (h-j) Histograms of the frequencies of the number of divisions from the initial cells. Simulation conditions for panels (e-j) are as follows: (e) and (h) are without added noise to
and at
; (f) and (i) are with added noise to
and at
; and (g) and (j) are with noise to
and at
.
Fig 11.
Comparison between simulation and experiments;
(a) and (b) are adapted from Fig 2 in [77] and represent experimental measurements of lumen occupancy and lumen sphericity, respectively, for MDCK-II cells. Blue markers indicate wild-type (WT), green markers represent claudin knockout (CLDN-KO), and red markers correspond to ZO1/2 knockout (ZO-KO) MDCK-II cells. WT and CLDN-KO cysts exhibit round lumen shapes, while ZO-KO cysts exhibit lumen morphologies with folds. Data are based on 3D segmentation of lumen and cyst surfaces as a function of total cell number per cyst. Error bars represent SEM, and statistical significance was determined using one-way ANOVA. (c) and (d) show simulation results for lumen occupancy and sphericity, respectively, based on our model. The x-axis represents the cell count, where 2D values were converted to 3D equivalents. Different markers correspond to simulations with varying combinations of and td. As in Fig 8, noise was added to the volume conditions. Green markers represent parameter combinations classified as Monolayer Cysts:
(circle), (0.5,240) (triangle), and (0.45,300) (square). Red markers represent parameter combinations classified as Branched Multilumen:
(star), (0.5,240) (cross), and (0.4,300) (plus). Monolayer Cysts show behavior similar to WT and CLDN-KO cysts in (a) and (b), while Branched Multilumen resembles the behavior of ZO-KO cysts.
Fig 12.
Figure illustrating force balance and water transport across cell layer.
Fig 13.
Figure illustrating the conditions that need to be met for cell division to occur in the model used for this study.
(a) Time evolution of the cell volume of a daughter cell that was generated through cell division. The horizontal dashed line represents , which is the minimum volume required for cell division to occur. The vertical dotted line indicates the time when the cell satisfies the volume condition for cell division. (b) When the time condition is dominant, the cell divides immediately after the time condition is satisfied. (c) When the volume condition is dominant, the cell divides immediately after the volume condition is satisfied.
Table 2.
Typical values of physical parameters in experiments and simulation. *1) It was estimated as 103 (Pa) in [74], while it was estimated as 105 (Pa) in [73]. *2) It is not a control parameter but estimated by the fitting simulation data. *3) Water permeability can be adjusted by modifying the characteristic timescale specific to the lumen (), as
. However, in the simulation, the same parameter
is used for both the cells and the lumen, as described in Eq 3.