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oai:recercat.cat:10459.1/571232024-12-05T22:19:19Zcom_2072_3622col_2072_479130

2024-12-05T22:19:19Z urn:hdl:10459.1/57123 Cooperativity and Saturation in Biochemical Networks: A Saturable Formalism Using Taylor Series Approximations Sorribas Tello, Albert Hernández Bermejo, Benito Vilaprinyo Terré, Ester Alves, Rui System Biology Mathematical modeling Cooperativity Biochemical System Theory Cooperative and saturable systems are common in molecular biology. Nevertheless, common canonical formalisms for kinetic modeling that are theoretically well justified do not have a saturable form. Modeling and fitting data from saturable systems are widely done using Hill-like equations. In practice, there is no theoretical justification for the generalized use of these equations, other than their ability to fit experimental data. Thus it is important to find a canonical formalism that is (a) theoretically well supported, (b) has a saturable functional form, and (c) can be justifiably applicable to any biochemical network. Here we derive such a formalism using Taylor approximations in a special transformation space defined by power-inverses and logarithms of power-inverses. This formalism is generalized for processes with n-variables, leading to a useful mathematical representation for molecular biology: the Saturable and Cooperative Formalism (SC formalism). This formalism provides an appropriate representation that can be used for modeling processes with cooperativity and saturation. We also show that the Hill equation can be seen as a special case within this formalism. Parameter estimation for the SC formalism requires information that is also necessary to build Power-Law models, Metabolic Control Analysis descriptions or (log)linear and Lin-log models. In addition, the saturation fraction of the relevant processes at the operating point needs to be considered. The practical use of the SC formalism for modeling is illustrated with a few examples. Similar models are built using different formalisms and compared to emphasize advantages and limitations of the different approaches. A.S., E.V., and R.A. want to acknowledge the financial support of the Spanish Ministerio de Educación y Ciencia (grant BFU2005-0234). B.H.-B. would like to thank the other authors and the Universitat de Lleida for the kind hospitality and financial support provided in 2005 during a stay in which part of this work was done. RA was supported by a Ramon y Cajal award from the Spanish Ministerio de Educacion y Ciencia. 2024-12-05T22:19:19Z 2024-12-05T22:19:19Z 2016-05-31T08:20:18Z 2025-01-01 2007 article publishedVersion http://hdl.handle.net/10459.1/57123 MIECI/PN2004-2007/BFU2005-00234/BMC Reproducció del document publicat a https://doi.org/10.1002/bit.21316 Biotechnology and Bioengineering, 2007, vol. 97, núm. 5, p. 1259-1277 (c) Wiley Periodicals, Inc., 2007 info:eu-repo/semantics/restrictedAccess Wiley