On applicability of category theory to the description of ontogeny events |
Gudimenko A.I., Guzev M.A., Zhuravlev Yu.N. |
2016, issue 2, P. 147-159 |
Abstract |
The possibility of application of the category-theoretical formalism to the description of the fundamental molecular events of ontogeny (transcription, translation and the protein combination formation) is studied. It is shown that a correspondence between these events and the well-known category operations, pull-back and push-out, can be established. The naturalness of application of the geometrical idea of fibration to the analyses of these events is demonstrated. |
Keywords: ontogeny, biological objects, mathematical modelling, category theory, fiber bundles |
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References |
[1] Handbook of Statistical Systems Biology, eds. M. Stumpf, D. Balding, M. Girolami, Wiley, 2011. [2] F. Hoppensteadt, Mathematical theories of populations: demographics, genetics, and epidemics, Society for Industrial Mathematics, Philadelphia, 1997. [3] J. Pastor, Mathematical Ecology of Populations and Ecosystems, Wiley-Blackwell, 2008. [4] Zh. Setubal, Zh. Meidanis, Vvedenie v vychislitel'nuiu molekuliarnuiu biologiiu, RKhD, 2007. [5] R. Rosen, Essays on Life Itself, Colmbia University Press, New York, 2000. [6] M. Mesarovich, Ia. Takakhara, Obshchaia teoriia sistem: matematicheskie osnovy, Mir, M., 1978. [7] S. Eilenberg, S. MacLane, “General Theory of Natural Equivalences”, Transactions of the American Mathematical Society, 58:2 (1945), 231–294. [8] S. MacLane, Categories for the Working Mathematician, Springer, New York, 1998. [9] R. Rosen, “A relational theory of biological systems”, Bulletin of Mathematical Biology, 20:3 (1958), 245–260. [10] R. Rosen, “The representation of biological systems from the standpoint of the theory of categories”, Bulletin of Mathematical Biology, 20:4 (1958), 317–341. [11] A.C. Ehresmann, J.-P. Vanbremeersch, “Hierarchical evolutive systems: A mathematical model for complex systems”, Bulletin of Mathematical Biology, 49:1 (1987), 13–50. [12] O. Wolkenhauer, J.-H. S. Hofmeyr, “An abstract cell model that describes the self- organization of cell function in living systems”, Journal of Theoretical Biology, 246 (2007), 461–476. [13] T. Haruna, “Theory of interface: Category theory, directed networks and evolution of biological networks”, Biosystems, 114:2 (2013), 125–148. [14] N. Rashevsky, “Topology and life: In search of general mathematical principles in biology and sociology”, Bulletin of Mathematical Biology, 16:4 (1954), 317–348. [15] N. Rashevskyk, Organismic Sets: Some Reflections on the Nature of Life and Society, Grosse Pointe, Michigan, 1972. |