Abstract
In this paper we developed a Stochastic Petri Net (SPN) based model to introduce uncertainty to capture the variability of biological systems. The coagulation cascade, one of the most complex biochemical networks, has been widely analyzed in literature mostly with ordinary differential equations, outlining the general behavior but without pointing out the intrinsic variability of the system. Moreover, the computer simulation allows the assessment of the reactions over a broad range of conditions and provides a useful tool for the development and management of several observational studies, potentially customizable for each patient. We describe the SPN model for the Tissue Factor induced coagulation cascade, more intuitive and suitable than models hitherto appeared in the literature in terms of bioclinical manageability. The SPN has been simulated using Tau-Leaping Stochastic Simulation Algorithm, and in order to simulate a large number of models, to test different scenarios, we perform them using High Performance Computing. We analyze different settings for model representing the cases of “healthy” and “unhealthy” subjects, comparing their average behavior, their inter- and intra-variability in order to gain valuable biological insights.
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Breitling, R., Gilbert, D., Heiner, M., Orton, R.: A structured approach for the engineering of biochemical network models, illustrated for signalling pathways. Brief Bioinform. 9(5), 404–421 (2008)
Butenas, S., Mann, K.G.: Blood Coagulation. Biochemistry 57, 5–15 (2002)
Butenas, S., van’t Veer, C., Mann, K.G.: “Normal” Thrombin Generation. Blood 94(7), 2169–2178 (1999)
Cao, Y., Gillespie, D.T., Petzold, L.R.: Efficient stepsize selection for the tau-leaping simulation method. J. Chem. Phys. 124, 044109 (2006)
Cevenini, E., Bellavista, E., Tieri, P., Castellani, G., Lescai, F., Francesconi, M., Mishto, M., Santoro, A., Valensin, S., Salvioli, S., Capri, M., Zaikin, A., Monti, D., de Magalhaes, J.P., Franceschi, C.: Systems biology and longevity: an emerging approach to identify innovative anti-aging targets and strategies. Curr. Pharm. Des. 16(7), 802–813 (2010)
Chatterjee, M.S., Denney, W.S., Jing, H., Diamond, S.L.: Systems Biology of Coagulation Initiation: Kinetics of Thrombin Generation in Resting and Activated Human Blood. PLoS Comput. Biol. 6(9), e1000950 (2010)
Chu, A.J.: Tissue factor, blood coagulation, and beyond: an overview. Int. J. Inflam. 367284, 1–30 (2011)
Corlan, A.D., John Ross, J.: Canalization effect in the coagulation cascade and the interindividual variability of oral anticoagulant response. A simulation study. Theor. Biol. Med. Model 8, 37 (2011)
Couris, R., Tataronis, G., McCloskey, W., Oertel, L., Dallal, G., Dwyer, J., Blumberg, J.B.: Dietary vitamin K variability affects International Normalized Ratio (INR) coagulation indices. Int. J. Vitam. Nutr. Res. 76(2), 65–74 (2006)
Danforth, C.M., Orfeo, T., Mann, K.G., Brummel-Ziedins, K.E., Everse, S.J.: The impact of uncertainty in a blood coagulation model. Math. Med. Biol. 26(4), 323–336 (2009)
Dittamo, C., Cangelosi, D.: Optimized Parallel Implementation of Gillespie’s First Reaction Method on Graphics Processing Units. In: International Conference on Computer Modeling and Simulation, ICCMS 2009, pp. 156–161 (2009)
Filipovic, N., Kojic, M., Tsuda, A.: Modelling thrombosis using dissipative particle dynamics method. Philos. Transact. A Math. Phys. Eng. Sci. 366(1879), 3265–3279 (2008)
Gaffney, P.J., Edgell, T.A., Whitton, C.M.: The Haemostatic Balance – Astrup Revisited. Haemostasis 29, 58–71 (1999)
Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716–1733 (2001)
Goss, P.J.E., Peccoud, J.: Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc. Nat. Acad. Sci. USA 95, 6750–6754 (1998)
Heiner, M., Gilbert, D., Donaldson, R.: Petri Nets for Systems and Synthetic Biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 215–264. Springer, Heidelberg (2008)
Khanin, M.A., Rakov, D.V., Kogan, A.E.: Mathematical model for the blood coagulation prothrombin time test. Thromb. Res. 89(5), 227–232 (1998)
Li, H., Petzold, L.: Efficient Parallelization of the Stochastic Simulation Algorithm for Chemically Reacting Systems On the Graphics Processing Unit. Int. J. of High Perf. Comp. Appl. 24, 107–116 (2009, 2010)
Lo, K., Denney, W.S., Diamond, S.L.: Stochastic modeling of blood coagulation initiation. Pathophysiol. Haemost. Thromb. 34(2-3), 80–90 (2005)
Luan, D., Zai, M., Vamer, J.D.: Computationally Derived Points of Fragility of a Human Cascade Are Consistent with Current Therapeutic Strategies. PLoS Comput. Biol. 3(7), e142 (2007)
Mackman, N.: Role of Tissue Factor in Hemostasis, Thrombosis, and Vascular Development. Arterioscler. Thromb. Vasc. Biol. 24, 1015–1022 (2004)
Monroe, D.M., Key, N.S.: The tissue factor-factor VIIa complex: procoagulant activity, regulation, and multitasking. J. Thromb. Haemost. 5(6), 1097–1105 (2007) (review)
Ramsey, S., Orrell, D., Bolouri, H.: Dizzy: stochastic simulation of large-scale genetic regulatory networks. J. Bioinform. Comput. Biol. 3, 415–436 (2005)
Reininger, A.J., Bernlochner, I., Penz, S.M., Ravanat, C., Smethurst, P., Farndale, R.W., Gachet, C., Brandl, R., Siess, W.: A 2-Step Mechanism of Arterial Thrombus Formation Induced by Human Atherosclerotic Plaques. J. Am. Coll. Cardiol. 55, 1147–1158 (2010)
Rohr, C., Marwan, W., Heiner, M.: Snoopy—a unifying Petri net framework to investigate biomolecular networks. Bioinformatics 26(7), 974–975 (2010)
Shaw, O., Steggles, J., Wipat, A.: Automatic Parameterization of Stochastic Petri Net Models of Biological Networks. Electronic Notes in Theoretical Computer Science 151, 111–129 (2006)
Srivastava, R., Peterson, M.S., Bentley, W.E.: Stochastic kinetic analysis of the Escherichia coli stress circuit using sigma(32)-targeted antisense. Biotechnol. Bioeng. 75(1), 120–129 (2001)
Steffel, J., Lüscher, T.F., Tanner, F.C.: Tissue Factor in Cardiovascular Diseases. Molecular Mechanisms and Clinical Implications. Circulation 113, 722–731 (2006)
Wajima, T., Isbister, G.K., Duffull, S.B.: A comprehensive model for the humoral coagulation network in humans. Clin. Pharmacol. Ther. 86, 290–298 (2009)
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Castaldi, D., Maccagnola, D., Mari, D., Archetti, F. (2013). Stochastic Simulation of the Coagulation Cascade: A Petri Net Based Approach. In: Caragiannis, I., et al. Euro-Par 2012: Parallel Processing Workshops. Euro-Par 2012. Lecture Notes in Computer Science, vol 7640. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36949-0_28
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DOI: https://doi.org/10.1007/978-3-642-36949-0_28
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