Four-dimensional realistic modeling of pancreatic organogenesis

Abstract

Organogenesis, the process by which organs develop from individual precursor stem cells, requires that the precursor cells proliferate, differentiate, and aggregate to form a functioning structure. This process progresses through changes in 4 dimensions: time and 3 dimensions of space-4D. Experimental analysis of organogenesis, by its nature, cuts the 4D developmental process into static, 2D histological images or into molecular or cellular markers and interactions with little or no spatial dimensionality and minimal dynamics. Understanding organogenesis requires integration of the piecemeal experimental data into a running, realistic and interactive 4D simulation that allows experimentation and hypothesis testing in silico. Here, we describe a fully executable, interactive, visual model for 4D simulation of organogenic development using the mouse pancreas as a representative case. Execution of the model provided a dynamic description of pancreas development, culminating in a structure that remarkably recapitulated morphologic features seen in the embryonic pancreas. In silico mutations in key signaling molecules resulted in altered patterning of the developing pancreas that were in general agreement with in vivo data. The modeling approach described here thus typifies a useful platform for studying organogenesis as a phenomenon in 4 dimensions.

Fig. 1.

Pancreatic organogenesis. (Top) Illustration. (Middle) Histological images of the pancreas. (Bottom) Snapshots of the morphogenesis emerging from model.

Fig. 2.

Morphogenesis of the pancreas at 4 time points: Illustration (Left), a 2D cross-section of the simulated structure (Center), and the 3D emerging structure (Right).

Fig. 3.

Histological cross-section image vs. the simulation at embryonic day 10 (Top), the emerging Pdx1-negative red clusters and their analysis over time (Middle), and validation by using image-processing methods (Bottom).

Fig. 4.

In silico ablation experiments: cell count over time (Left), the emerging 3D structure (Center), and histological images (Right). Red and green designate Pdx1− and Pdx1+ cells, and black designates the total.

Fig. 5.

Pancreatic organogenesis under 3 levels of expression of BMP4 (vertical axis) and FGF10 (horizontal axis) (Upper) and different shapes of pancreatic morphogenesis (Lower).

Fig. 6.

Modeling an autonomous cell. The 3 objects, cell, nucleus and membrane, accompanied by some of their statechart.

Fig. 7.

Modeling the extracellular space. (Top) An illustration of the extracellular space. (Middle) The 3D animated front end. (Bottom) The interaction scheme between the objects.