Four-Dimensional Reactive Animation Model for the
Early Stages of Pancreatic Organogenesis
Yaki Setty*+, Irun R. Cohen+ and David Harel*
*Departments of Computer Science and Applied Mathematics and
+Department of Immunology,
The Weizmann Institute of Science, Rehovot, Israel
We present a reactive animation model for the early stages of
pancreatic organogenesis. Results of simulations of the model
correspond well with previous biological knowledge. In particular, the
simulation mimics the 3-dimensional morphogenetic formation of the
pancreas. Furthermore, analysis of the model, based on in-silico
experiments, captures much of the essence of the relevant process.
Snapshots, prerecorded clips, and interactive information are
available at www.wisdom.weizmann.ac.il/~yaki/abstract.
The pancreas is an essential organ involved in metabolic and digestive pathways
[9]. Thus, modeling pancreatic organogenesis may lead to a better
understanding of this process and may reveal new insights into pancreas-related
diseases, such as diabetes. We use visual formalisms [2] and the idea of
reactive animation (RA) [1, 3] to achieve a comprehensive, realistic, and
interactive 4-dimensional model, with time being the fourth dimension.
RA enables realistic simulation of complex reactive systems by linking a reactive
engine to an animation package. In this way, the executable reactive model
drives the interactive front-end. A few years ago, a biological application of RA
was developed by Efroni et al, where a 2D interactive front-end was linked to a
reactive model of the thymus gland [8]. To facilitate the use of RA on our system
of choice, we developed a generic reactive animation platform that supports 3D
animation [4] (see www.wisdom.weizmann.ac.il/~yaki/GRA/ for details).
We employ the aforementioned platform to link three components: a reactive
model, a 3D interactive front-end and a GUI for mathematical analysis. We model
the pancreatic organogenesis as known in the literature, by formalizing
molecular processes and morphogenesis into an executable state-based
model (specified in the language of Statecharts [2] and implemented in
Rhapsody [5]). We visualize the molecular processes and interactions involved
in a 3D animated front-end in 3D game studio [10] and display mathematical
analysis in an additional GUI in Matlab [12].
Currently, our model covers the early stages of pancreatic organogenesis, which
is also known as the “primary transition”. The transition lasts for approximately
five embryonic days and involves various biological processes, such as
proliferation and specification. During this period, cells at the appropriate regions
of the flat gut evolve to form pancreatic buds, which later on generate the
lobulated form of the matured pancreas.
Next, we evaluate our simulation by comparing its results with available
illustrations and images of pancreatic development. Furthermore, the interactive
model enables in-silico knockout experiments at any stage of the simulation.
Generally, the simulation qualitatively mimics the essence of the organogenesis
and results from in-silico experiments agree with those known in literature.
Interestingly, although the model was not explicitly program to do so, the
simulation exhibits non-pancreatic clusters within the pancreatic bud that are
comprised of cells that are not specified as pancreatic cells. The clusters
correspond well with the early endocrine clusters that are observed during the
organogenesis [6].
Encouraged by our preliminary results, we now aim to model the “secondary
transition” of the organogenesis, and to achieve a comprehensive model of
pancreatic organogenesis. Such a model may lead to better understanding of
pancreatic development and pancreas-related diseases and might eventually
help in an effort to build a sort of in-silico organ.
References
[1] S. Efroni, D. Harel, and I. R. Cohen. Reactive animation: Realistic modeling of
complex dynamic systems. IEEE Computer, 38:38–47, 2005.
[2] D. Harel. Statecharts: A visual formalism for complex systems. Science of Computer
Programming, 8:231–274, 1987.
[3] D. Harel, S. Efroni, and I. R. Cohen. Reactive animation. In Formal Methods for
Components and Objects, 2852:136–153, 2002.
[4] D. Harel and Y. Setty. Generic and multi-party reactive animation. submitted, 2006.
[5] ilogix, web page. http://www.ilogix.com.
[6] J. Jensen. Gene regulatory factors in pancreatic development. Dev Dyn, 229(1):176–
200, 2004.
[7] 3D game studio A6, Web page: http://www.conitec.net/a4info.htm.
[8] S. Efroni, D. Harel and I. R. Cohen. Toward rigorous comprehension of biological
complexity: modeling, execution, and visualization of thymic T cell maturation.
Genome Res, 13(11):2485–2497, 2003.
[9] S. K. Kim and R. J. MacDonald. Signaling and transcriptional control of pancreatic
organogenesis. Curr Opin Genet Dev, 12(5):540–547, 2002.
[10] S. K. Chakrabarti and R. G. Mirmira. Transcription factors direct the development
and function of pancreatic beta cells. Trends Endocrinol Metab, 14(2):78–84, 2003.
[11] Prof. Jensen's lab, web page. http://www.uchsc.edu/cdb/faculty/jensen.htm
[12] The mathwork, Web page: http://www.mathworks.com.
Two aspects of pancreatic organogenesis: morphogenesis and
molecular processes
Pancreatic morphogenesis: illustration of the pancreatic organogenesis from the flat gut (<
embryonic day 8) to the lobulated form of the matured pancreas (> embryonic day 13.5)
(taken from [9]).
Pancreatic differentiation: Decision tree of pancreatic differentiation showing the major
transcription factors that direct a pancreatic cell towards one of its 6 matured fates (taken
from [10]).
Modelling a pancreatic cell: the basic building block of the
simulation
Illustration of a pancreatic cell: Diagram of transcription factor network within and
surrounding the pancreas. Molecular interactions (arrows) direct cell differentiation (colored
circles) (taken from [11]).
State-based model and corresponding visualization of an individual cell: a cell (brown)
is defined as an object with a sub-object for its nucleus (green). A corresponding statechart
specifies the behavior based on the known literature. Top-left: a cell as it is visualized in the
animated front-end. The sphere changes its color as it responds to changes in cell behavior
(statechart).
Modelling the biological elements involved in the pancreatic
development
The major biological elements involved in the development: Top: naïve depiction of the
elements (taken from [11]). Bottom: snapshot of the animated front-end that visualizes the
interactions in the state-based model.
State-based model for the molecular processes of the pancreas: Each biological
element is represented as an object with a corresponding statechart that specifies its
behavior.
Evaluating the simulation: comparison with previous knowledge.
Comparison between previous biological knowledge and our simulation at embryonic
day 10: Top-left: a florescent image of the pancreatic bud, (taken from [6]). Top-right: 2D
slice of the simulation. Bottom: the simulation from two perspectives. Red and green spheres
designate non pancreatic (PDX1-) and pancreatic (PDX1+) cells, respectively. Notice the
emerging non-pancreatic red clusters in the left-bottom image.
In-silico experiments: Number of cells as a function of time (left), and snapshots from the
correspondent animation (right). Top: results from the simulation under normal growth
conditions. Middle: knockout of the aorta. Bottom: knockout of the notochord. The results
generally agree with similar biological experiments.
Towards a Comprehensive and Interactive 4-Dimensional Model
of Pancreatic Organogenesis
Illustration of pancreatic RA model: The morphogenetic formation (left) and the molecular
processes (right) are combined to form a comprehensive and interactive 4D-model of the
pancreatic organogenesis.