(360c) Robust Performance Analysis Of A Type 2 Apoptotic Network

Proper control of apoptosis, programmed cell death, is essential to the development of multicellular organisms and to the prevention of unmitigated cellular growth and tumorogenesis (Hanahan and Weinberg, 2000). To date, cancer therapies remain broadly ineffective as current therapies do not differentiate healthy from abnormal cell populations. Future therapeutic procedures may employ multi-targeted approaches to suitably distribute apoptotic signaling efficacy across cellular populations. To facilitate these procedures, mechanistic models of apoptosis are being developed to better understand the complex cellular processing of apoptotic stimuli. In this work, structured singular values are used to identify the parameter sets that are robust to perturbations in a Type II FasL apoptosis model (Bagci, et al. 2006).

The FasL apoptosis model accounts for the cellular internalization, processing and execution of the death signal. The signal is initiated with the binding of Fas ligand (FasL) to its receptor, leading to the activation of the caspase cascade, resulting in the production of executioner caspase, caspase 3. In Type II apoptosis, the signal is amplified via the mitochondria in a pathway parallel to the direct activation mechanism. In the Bagci, et al. model, fourth-order, Hill kinetics are assumed during the apoptosome formation, downstream of the mitochondria, to allow for bistability in the system. The model consists of 31 ordinary differential equations and 65 parameters. Since each parameter is an abstraction of several other processes (transcription, translation, diffusion, etc.), parameter values are prone to great variability. Structured singular values are used to quantify robust performance given parameter variability.

Robustness is the ability to maintain system performance despite both parameter and architectural uncertainty (Stelling, et al. 2004A). Robust systems maintain their behavior regardless of internal or external disturbances, and robustness has been identified as a key characteristic of biological systems (Kitano, 2004). In highly robust systems, even structural disturbances produce small to negligible changes in the systems performance. The counterpart to robustness is system fragility. This work seeks to identify fragilities in the apoptotic network as the intracellular conditions fluctuate. Several methods have been used to analyze the robustness of circadian rhythms (Stelling, et al. 2004B), signal transduction networks (Kikuchi, et al. 2003) and other biological systems, but these analyses do not account for simultaneous fluctuations. These results may be misleading as significant relationships between parameters may exist. Here, structured singular values are used to validate system performance given multiple, simultaneous parameter uncertainty (Doyle, 1982). The SSV is a generalization of the singular value, σ, an appropriate measure of robustness under general (unstructured) uncertainty, which determines if performance criteria are met for a specified set of real, parameter perturbations.

SSV analysis of the FasL apoptosis system reveals the heavy dependence on tight regulation of degradation and mitochondrial diffusion for proper performance during apoptotic signal rejection. Degradations parameters can tolerate an average of 12% variation in their nominal values and maintain performance. Degradation parameters are composites of several background networks (ubiquitin directed degradation, etc.) (Selvendiran, et al. 2006), and these results indicate that degradation must be highly regulated. Of the local parameters, diffusion of cyt c across the mitochondrial membrane is identified as the most sensitive in isolation (50% allowable variation) followed by parameters associated with caspase 8 activation and Bid cleavage. Mitochondrial membrane diffusion is a complex, highly variable process, whereas parameters associated with caspase 8 activation and Bid cleavage more resemble traditional kinetic parameters, are not strongly reliant on subnetworks and are less prone to variation. Thus, the system was constrained to allow 25% variation in the mitochondrial diffusion and it was found that all other local parameters must be restricted to less than 7% variation. These early results suggest several routes for a cancer to suppress apoptosis without fully disabling an interaction. SSV analysis suggests that slight disturbances in the ubiquitin network controlling degradation can successfully destroy the bistable nature of the network, negating FasL signaling, and allow for unmitigated proliferation.

This work is supported by the Institute for Collaborative Biotechnologies through grant DAAD19-03-D-0004 from the U.S. Army Research Office, IGERT NSF grant DGE02-21715, and the University of California, Board of Regents, Central Fellowship.

J. C. Doyle, 1982. Analysis of feedback systems with structured uncertainty. IEE Proceedings, Part D, 129:242?250.

E. Z. Bagci, Y. Vodovotz, T. R. Billiar, G. B. Ermentrout and I. Bahar, 2006. Bistability in apoptosis: roles of bax, bcl-2, and mitochondrial permeability transition pores. Biophys J, 90(5), 1546-59.

D. Hanahan and R. A. Weinberg, 2000. The hallmarks of cancer. Cell, 100(1):57?70.

S. Kikuchi, K. Fujimoto, N. Kitagawa, T. Fuchikawa, M. Abe, K. Oka, K. Takei, and M. Tomita, 2003. Kinetic simulation of signal transduction system in hippocampal long-term potentiation with dynamic modeling of protein phosphatase 2A. Neural Netw, 16(9):1389?98.

H. Kitano, 2002. Systems biology: a brief overview. Science, 295:1662?1664.

T. H. Landowski, N. Qu, I. Buyuksal, J. S. Painter, and W. S. Dalton, 1997. Mutations in the Fas antigen in patients with multiple myeloma. Blood, 90(11):4266?70.

F. Rieux-Laucat, F. L. Deist, and A. Fischer, 2003. Autoimmune lymphoproliferative syndromes: genetic defects of apoptosis pathways. Cell Death Differ, 10(1):124?33.

C. Scaffidi, S. Fulda, A. Srinivasan, C. Friesen, F. Li, K. J. Tomaselli, K. M. Debatin, P. H. Krammer, and M. E. Peter, 1998. Two CD95 (APO-1/Fas) signaling pathways. EMBO J, 17(6):1675?87.

J. Stelling, E. D. Gilles, and F. J. Doyle III, 2004. Robustness properties of circadian clock architectures. Proc Natl Acad Sci U S A, 101(36):13210?5.

J. Stelling, U. Sauer, Z. Szallasi, F. J. Doyle, and J. Doyle, 2004. Robustness of cellular functions. Cell, 118(6):675?85.

K. Selvendiran, H. Koga, T. Ueno, T. Yoshida, M. Maeyama, T. Torimura, H. Yano, M. Kojiro, and M. Sata, 2006. Luteolin promotes degradation in signal transducer and activator of transcription 3 in human hepatoma cells: an implication for the antitumor potential of flavonoids. Cancer Res, 66(9):4826-4834.