Shortly before his death, Bailey suggested that perhaps the key properties of biological re-action networks could be determined solely on the basis of network structure in the absence of detailed parametric information (1). There is ample literature evidence to support the Bailey hypothesis for metabolic networks in both prokaryotes and eukaryotes (2–7). However, application of the Bailey conjecture to signaling architectures relevant to human health is less clear. To test the applicability of the Bailey hypothesis for human relevant signaling cascades, we contrast the findings of structural and parametric analysis techniques applied to a prototypical network, the extrinsic coagulation cascade. The coagulation cascade, which is activated immediately following blood vessel injury, is composed of initiator proteases, referred to as factors, that work in concert to activate a terminal protease, thrombin. To test our working hypothesis that the Bailey conjecture is correct, we contrast the parametric sensitivity of a dynamic model of the extrinsic coagulation cascade with three different structural analysis techniques; statistical network characterization, Singular Value Decomposition (SVD) (8) and Elementary Mode Decomposition (EMD) (2, 9). A dynamic mathematical model of the extrinsic coagulation cascade is formulated. Mass action kinetics are used to describe the rates of interaction of the elements of the cascade; a total of 92 proteins or protein complexes. Kinetic parameters (kon, koff or kcat) describing the 148 protein-protein interactions are taken from the literature where possible or assigned approximate values. To validate the model, simulations of thrombin formation in the presence (absence) of physiological inhibitors in quiescent synthetic plasma are compared with time-resolved in-vitro literature data. The Overall State Sensitivity Coefficients (OSSC) are computed to rank-order the fragility or sensitivity of the model parameters (10). The estimated fragile points are then compared with the results from the different structural analysis techniques to determine the similarity between the different approaches. Structural information alone gives surprising insight but does not tell the entire story of thrombin formation. We find that the extrinsic coagulation cascade is a small world architecture; Watts and Strogatz have shown this architecture to be almost ideal for signal propagation (11). Thus, the coagulation architecture is well suited for its biological role of rapidly stemming blood loss. There is at most a 60% similarity between rate constants deemed to be sensitive and the rank-ordered importance of coagulation reactions determined by SVD. However, the Spearman correlation between SVD and sensitivity analysis is at most 0.24 indicating that while SVD and sensitivity analysis produce similar lists of important reactions, they are not ranked similarly. EMD analysis yields approximately 50% similarity between the number of times a reaction is used across all elementary modes and the sensitivity of the corresponding rate constant. While EMD gives a lower similarity measure, it provides additional information about the redundancy of the cascade. When taken together, these results indicate that the Bailey complex biology with no parameters hypothesis, may be applicable to signaling architectures and that on the basis of structure alone you can expect to capture between 50-60% of the features of the network.

References [1] J. E. Bailey. Complex biology with no parameters. Nat. Biotechnol., 19:503–504, 2001. [2] J. Stelling, S. Klamt, K. Bettenbrock, S. Schuster, and E. D. Gilles. Metabolic network structure determines key aspects of functionality and regulation. Nature, 420(6912):190–3,2002. 0028-0836 Journal Article. [3] Edwards J.S. and Palsson B.O. The Escherichia coli mg1655 in silico Metabolic Genotype: Its Definition, Characteristics, and Capabilities. Proc. Natl. Acad. Sci. USA, 97(10):5528–5533, 2000. [4] J. S. Edwards, R. U. Ibarra, and B. O. Palsson. In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol, 19(2):125–30, 2001. 1087-0156 Journal Article. [5] J. S. Edwards and B. O. Palsson. Metabolic flux balance analysis and the in silico analysis of Escherichia coli k-12 gene deletions. BMC Bioinformatics, 1(1):1, 2000. 1471-2105 Journal article. [6] N.C. Duarte, M.J. Herrgard, and B.O. Palsson. Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Res., 14:1298 – 1309, 2004. [7] R. Mahadevan and B.O. Palsson. Properties of metabolic networks: structure versus function. Biophys. J., 88:L07–L09, 2005. [8] I. Famili and B.O. Palsson. Systemic Metabolic Reactions are Obtained by Singular Value Decomposition of Genome-scale Stoichiometric Matrices. J. Theo. Biol., 224:87 – 96, 2003. [9] S. Schuster, D.A. Fell, and T. Dandekar. A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat. Biotechnol., 18:326 – 332, 2000. [10] J. Stelling, E.D. Gilles, and F.J. Doyle III. Robustness properties of circadian clock architectures. Proc. Natl. Acad. Sci. USA, 101:13210 – 13215, 2004. [11] D.J. Watts and S.H. Strogatz. Collective dynamics of ‘small-world' networks. Nature, 393:440 – 442, 1998.

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