Programmed cell death or apoptosis is an important process in development and tissue home- ostasis. Dysfunctional apoptosis contributes to autoimmune and neurodegenerative disorders as well as to cancer. Designing targeted therapies for these diseases could perhaps benefit from a molecular understanding of the cell death process, including the activation of a group of pro- teolytic enzymes referred to as Caspases (Cysteine Containing Aspartate Specific Proteases). Caspases, once activated, dismantle the cell by seeking out and selectively cleaving specific pro- tein targets after aspartate residues. Cytosolic calcium ions play a key role in stress induced caspase activation; procaspase-12 and 4, resident on the surface of the Endoplasmic Reticulum (ER), are activated, via an unknown mechanism, in the presence of cytosolic Ca2+ (1). Caspase- 12 and 4, which we assume remain localized on the surface of the ER, are then free to activate downstream initiator and executioner caspases.

A Ca2+ ER module is embedded into a larger model of apoptosis to explore the impact of Ca2+ release upon cell-death. The release of Ca2+ from the ER is mediated by activated feedback sensitive Ca2+ channels on the surface of the ER. Inositol 1,4,5-triphosphate (IP3), generated by activation of the G-protein cascade, binds the ER receptor IP3R to form a nonspecific feedback sensitive Ca2+ channel that transports Ca2+ from the ER to the cytosol. The 4- state IP3R-IP3 feedback-activation model of Tang and Othmer is employed to describe the formation and regulation of active IP3R-IP3 channels (2). The Tang-Othmer model assumes a sequential binding scheme: first IP3 binds IP3R at which time cytosolic Ca2+ binds one of three regulatory sites on the IP3-IP3R complex. Binding of Ca2+ to the positive regulatory site activates the IP3R-IP3 channel while binding of Ca2+ to the remaining two negative regulatory sites downregulates the transport activity of the channel. IP3 is generated as a product of the receptor couple G-protein cascade. Activated receptor binds inactive G-protein (G-GDP) resulting in the generation of G -GTP (the activated fragment of the G-protein) and the G fragment after exchanging GDP. G -GTP binds Phospholipase C (PLC) and cytosolic Ca2+ to generate an active enzyme which converts the precursor molecule Phosphatidylinositol 4,5- bisphosphate (PIP2) to IP3. G -GTP-PLC can also regenerate inactive G-protein; the PLCsubunit can hydrolyze G -GTP to G -GDP which in turn reversibly binds the G G-protein subunits generated during G-protein activation. Cytosolic Ca2+ can be transported into the ER via localized ATP dependent pumps or to the extracellular environment via several different ion transport channels. In this study we assume exchange of Ca2+ with the extracellular environment is inhibited by the addition of channel specific blockers present in excess. In addition, we assume a high and low affinity Ca2+ pumping capacity on the ER and we ignore the ATP dependence of the pump. Lastly, we assume, consistent with the earlier models of Othmer and coworkers (3) and Bennett et.al., (4) that Ca2+ is reversibly transported between the ER and cytosol via leakage and that all the ER Ca2+ channels are of the three-regulatory site IP3R-IP3 type and neglect possible direct G activation of IP3R (5).

The apoptosis-ER model, which contains 738 species and 1145 interactions, is analyzed us- ing sensitivity analysis to determine points of robustness and fragility as defined by Stelling et al., (6). To combat the issue of model size, a new technique for the computation of sensitivity coefficients which relies upon network decomposition is presented; the apoptotic network is de- composed into minimally connected modules using the hMETIS k-way hypergraph partitioning algorithm (7). Sensitivity analysis is then conducted on each of the subnetworks for random families of parameters and initial conditions. The sensitivity results for each module are re- combined to yield Overall State Sensitivity Coefficients (OSSC) for all 1145 kinetic parameters. Sensitivity results for several treatment cases will be presented and compared with literature in solid and hematological malignancies to access their validity.

References [1] R.V. Rao, H.M. Ellerby, and D.E. Bredesen. Coupling endoplasmic reticulum stress to the cell death program. Cell Death Differ., 11:372 – 380, 2004. [2] Y. Tang. Theoretical studies on second messenger dynamics. PhD thesis, University of Michigan, 1993. [3] Y. Tang, J.L. Stephenson, and H. G. Othmer. Simplification and Analysis of Models of Calcium Dynamics Based on IP3 Sensitive Calcuim Channel Kinetics. Biophys J., 70:246 – 263, 1996. [4] G. Lemon, W.G. Gibson, and M.R. Bennett. Metabotropic receptor activation, desensi- tization and sequestration I - Modeling calcium and inositol 1,4,5-triphosphate dynamics following receptor activation. J. Theo. Biol., 223:93 – 111, 2003. [5] W. Zeng, D-O. D. Mak, Q. Li, D.M. Shin, J.K. Foskett, and S. Muallem. A new mode of Ca2+ signaling by G protein-coupled receptors - Gating of IP3 receptor Ca2+ release channels by G . Curr. Biol., 13:872 – 876, 2003. [6] J. Stelling, E.D. Gilles, and F.J. Doyle III. Robustness properties of circadian clock archi- tectures. Proc. Natl. Acad. Sci. USA, 101:13210 – 13215, 2004. [7] G. Karypis and V.Kumar. Multilevel k-way Hypergraph Partitioning. VLSI Design, 11:285 – 300, 2000.

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