A Mathematical model for cephalostatin 1-induced apoptosis in leukemic cells - Rodriquez, Eva M.
The mechanisms involved in apoptosis have been an area of extensive study because of the importance of maintaining a homeostatic balance in response to pro-or anti-apoptotic stimuli. Cephalostatin 1 has been found to induce apoptosis in leukemia Jurkat T cells in a dose-and time-dependent manner even at nanomolar concentrations using a novel pathway that excludes the receptor-mediated pathway and includes not only the mitochondrial pathway but also the ER-mediated pathway. In this paper, the methods and tools of Petri net theory were used to construct, validate and analyze a Petri net model for cephalostatin 1-induced apoptosis in leukemic cells. Based on actual experimental results from the Vollmar laboratory and literature search, we have constructed a Petri net consisting of 43 places and 57 transitions using a software tool called Snoopy. Standard Petri net techniques of analysis such as structural and invariant analyses and analysis using abstract dependent transition sets or ADT-sets were employed with the help of another software tool, Charlie. Results of these analyses revealed consistency with known biological behavior of apoptosis induced by cephalostatin 1. By its inherent readability, the Petri net model showed that the apoptosis of leukemic cells due to cephalostatin 1 is primarily mediated by the ER pathway and is particularly involved in 3 upstream events: PIDDosome formation, JNK phosphorylation and release of calcium from the ER lumen. It also reveals that the mitochondrial pathway induced by cephalostatin 1 contributes to apoptosis principally through its release of Smac, which counteract the inhibiting effect of the IAPs on caspases-2, -9 and -3. Calpain and Smac are also shown to be important elements that are crucial for the possible crosstalk of mitochondrial-and ER-mediated apoptotic pathways. These insights can be verified further by experimentation. Results of structural analysis indicate that the Petri net model is pure, ordinary, homogenous, live, connected, unbounded and is covered by semi-positive t-invariants. Computation of T-invariants gave 16 solutions, forming subnets of the apoptotic network that represent sound biological interpretations consistent with the known behavior of apoptosis induced by cephalostatin 1. In this paper, we conclude that the computation of maximal ADT-sets is a mathematically reliable method of partially modularizing the Petri net model for cephalostatin 1-induced apoptosis since its 27 computed maximal ADT-sets partition the entire network into its smallest functional biological units. Maximal ADT-sets with only one transition, though not exactly representing functional subunits, also gave additional insights on the behavior of the system.
Computer print out.