Pattern formation analysis by colored Petri nets with quantitative manipulation of a gene We propose a new approach of modeling and simulation for analyzing multicellular biological events by combining colored hybrid Petri nets (CoIHPNs) with newly devised biological experiments that can control the level of a gene quantitatively. We analyzed the patterning of boundary cells in the Drosophila large intestine, where onecellwide domain of boundary cells differentiate through DeltaNotch signaling. Biological experiments regulating the level of Delta result in six distinct patterns of boundary cells corresponding with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling.

Disentangling a complex response in cell reprogramming and probing the Waddington landscape by automatic construction of Petri nets. Abstract   We analyzed the developmental switch to sporulation of a multinucleate Physarum polycephalum plasmodial cell, a complex response to phytochrome photoreceptor activation. Automatic construction of Petri nets representing finite state machines assembled from trajectories of differential gene expression in single cells revealed alternative, genotypedependent interconnected developmental routes and identified reversible steps, metastable states, commitment points, and subsequent irreversible steps together with molecular signatures associated with cell fate decision and differentiation. Formation of cyclic transits identified by transition invariants in mutants that are locked in a proliferative state is remarkable considering the view that oncogenic alterations may cause the formation of cancer attractors. We conclude that the Petri net approach is useful to probe the Waddington landscape of cellular reprogramming, to disentangle developmental routes for the reconstruction of the gene regulatory network, and to understand how genetic alterations or physiological conditions reshape the landscape eventually creating new basins of attraction. Unraveling the complexity of pathogenesis, disease progression, drug response or the analysis of attractor landscapes in other complex systems of uncertain structure might be additional fields of application.