Cell division, sometimes referred to as the cell-cycle, is one of the most fundamental and highly regulated processes in biology. The decision of a cell to divide is tightly controlled integrating both extra- and intracellular signals. Extracellular signals, such as growth factors and hormones, help cells determine when there is a need to divide while intracellular cues coordinate the events leading to cell division and ensure the preceding stages in the cell-cycle have been successfully completed. Despite the existence of complex control and surveillance systems guiding cell-cycle progression, malfunctions do occur as evidenced by the uncontrolled proliferation underlying many cancers (1–3).

Not every malfunction in cell-cycle leads to cancer, thus, cell-cycle is robust to some malfunc- tions and sensitive or fragile to others. Stelling et al., have proposed that points of fragility in a network can be computationally identified by performing sensitivity analysis upon mathemat- ical models (4). Our working hypothesis is that a single-cell mathematical model of cell-cycle, which mechanistically describes the molecular events controlling cell division, could be used to computationally determine points of network fragility that correspond to known, clinically ob- served, cell-cycle malfunctions in solid and hematological malignancies. Knowledge of fragility could aid in the basic understanding of cancer progression and could serve as the basis of ther- apeutic strategies. We test our working hypothesis by analyzing published models of cell-cycle progression and compare our computationally identified fragile points with literature. Three different published cell-cycle models of varying complexity were analyzed; the skeleton mam- malian cell-cycle model of Novak and Tyson (5), the G1/S model of Qu et al., (6) and the G2/M DNA-damage model of Aguda (7). The cell-cycle models were implemented in Matlab v7.01 (The Mathworks, Natick MA) and solved using the ODE15s routine. A third-order backward difference scheme was used to solve the sensitivity equation; to capture the effect of parametric uncertainty and its impact upon the predicted points of fragility, n = 1000 independent param- eter sets were generated by randomly perturbing the published parameter sets. Overall State Sensitivity Coefficients (OSSC) were calculated for each parameter set according to Stelling et al., (4). The backward-difference method employed fast matrix update techniques that gave a 3-fold speedup over finite difference. Of the top 15 fragile points (top five from each model), 14/15 are known control or clinically observed points where malfunctions have occurred. These include global elements like translational efficiency and specific interactions like the programmed proteolysis of cyclins by the Ubiquitin Proteasome System (UPS), phosphorylation and dephos- phorylation of CDC25 in G1/S or the synthesis of 14-3-3 . When taken together, the fragility results indicate that it may be possible to computationally screen for sites of probable mal- function. Second, these results indicate that although the mathematical cell-cycle models suffer from both parametric and structural uncertainty, valuable insight may be gained in the face of this uncertainty.

References [1] C. J. Sherr. Cancer Cell Cycles. Science, 274:1672 – 1677, 1996. [2] M. Fussenegger and J.E. Bailey. Molecular Regulation of Cell-Cycle Progression and Apop- tosis in Mammalian Cells: Implications for Biotechnology. Biotechnol. Prog., 14:807 – 833, 1999. [3] K.W. Kohn. Molecular Interaction Map of the Mammalian Cell Cycle Control and DNA Repair Systems. Mol. Cell. Biol., 10:2703 – 2734, 1999. [4] 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. [5] B. Novak and J.J. Tyson. A model for restriction point control of the mammalian cell cycle. J. Theor. Biol., 230(4):563–79, 2004. [6] Z. Qu, J.N. Weiss, and W.R. MacLellan. Regulation of the Mammalian Cell Cycle: A model of the G1-to-S Transition. Am. J. Physiol., 284(2):C349–C364, 2003. [7] B. D. Aguda. A Qualitative Analysis of the Kinetics of the G2 DNA Damage Checkpoint System. Proc. Natl. Acad. Sci. USA, 96:11352–11357, 1999. Varner - 2

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