Modeling biological gradient formation: combining partial differential equations and Petri nets

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

A generic organ based ontology system, applied to vertebrate heart anatomy, development and physiology

We present a novel approach to modelling biological information using ontologies. The system interlinks three ontologies, comprising anatomical, developmental and taxonomical information, and includes instances of structures for different species. The framework is constructed for comparative analyses in the field of evolutionary development. We have applied the approach to the vertebrate heart and present four case studies of the functionality of the system, focusing on cross-species comparisons, developmental studies, physiological studies and 3D visualisation.

Analysis of cardiac development in the turtle Emys orbicularis (Testudines: Emidydae) using 3-D computer modeling from histological sections

In this article we present a 3-D modeling study of cardiac development in the European pond turtle, Emys orbicularis (of the reptilian order Testudines). The study is aimed at elucidating the embryonic development of the horizontal septum in the ventricle and underscoring the importance of 3-D reconstructions in studying morphogenesis. Turtles possess one common ventricle, partly divided into three cava by a vertical and a horizontal septum, of which the embryonic origins have so far not been described. We used serial sectioning and computerized high-resolution 3-D reconstructions of different developmental stages to create a chronological overview of cardiogenesis, in order to study this process. This has yielded a new understanding of the development of the horizontal septum and (directly related) the looping of the heart tube. This looping is found to be markedly different from that in the human heart, with the turtle having two clear bends in the part of the heart tube leaving the primitive ventricle, as opposed to one in humans. It is this particular looping that is responsible for the formation of the horizontal septum. In addition to our findings on the ventricular septation this study has also yielded new insights into the developmental origins of the pulmonary vein. The 3-D reconstructions were built using our platform TDR-3-D base and enabled us to study the developmental processes in specific parts of the turtle heart separately and in three dimensions, over time. The complete 3-D reconstructions have been made available to the reader via internet using our 3-D model browser application, which allows interactive viewing of the models. The browser application can be found on bio-imaging.liacs.nl/galleries/emysorbicularis/TurtleGallery.html, along with additional images of both models and histological sections and animation sequences of the models. By allowing the reader to view the material in such an interactive way, we hope to make optimal use of the new 3-D reconstruction techniques and to engage the reader in a more direct manner.