Artículo
Abstract:
We develop tools from computational algebraic geometry for the study of steady state features of autonomous polynomial dynamical systems via elimination of variables. In particular, we obtain nontrivial bounds for the steady state concentration of a given species in biochemical reaction networks with mass-action kinetics. This species is understood as the output of the network and we thus bound the maximal response of the system. The improved bounds give smaller starting boxes to launch numerical methods. We apply our results to the sequential enzymatic network studied in Markevich et al. (J Cell Biol 164(3):353–359, 2004) to find nontrivial upper bounds for the different substrate concentrations at steady state. Our approach does not require any simulation, analytical expression to describe the output in terms of the input, or the absence of multistationarity. Instead, we show how to extract information from effectively computable implicit dose-response curves, with the use of resultants and discriminants. We moreover illustrate in the application to an enzymatic network, the relation between the exact implicit dose-response curve we obtain symbolically and the standard hysteresis diagram provided by a numerical ode solver. The setting and tools we propose could yield many other results adapted to any autonomous polynomial dynamical system, beyond those where it is possible to get explicit expressions. © 2014, Springer-Verlag Berlin Heidelberg.
Registro:
| Documento: | Artículo |
| Título: | Implicit dose-response curves |
| Autor: | Pérez Millán, M.; Dickenstein, A. |
| Filiación: | Dto. de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, Buenos Aires, C1428EGA, Argentina Dto. de Ciencias Exactas, CBC, Universidad de Buenos Aires, Ramos Mejía 841, Buenos Aires, C1405CAE, Argentina IMAS, CONICET, Ciudad Universitaria, Pab. I, Buenos Aires, C1428EGA, Argentina |
| Palabras clave: | Bounds; Chemical reaction networks; Maximal response; Resultants; Steady states; enzyme; biological model; dose response; kinetics; mathematical phenomena; metabolism; phosphorylation; signal transduction; systems biology; Dose-Response Relationship, Drug; Enzymes; Kinetics; MAP Kinase Signaling System; Mathematical Concepts; Metabolic Networks and Pathways; Models, Biological; Phosphorylation; Systems Biology |
| Año: | 2015 |
| Volumen: | 70 |
| Número: | 7 |
| Página de inicio: | 1669 |
| Página de fin: | 1684 |
| DOI: | http://dx.doi.org/10.1007/s00285-014-0809-4 |
| Título revista: | Journal of Mathematical Biology |
| Título revista abreviado: | J. Math. Biol. |
| ISSN: | 03036812 |
| CAS: | Enzymes |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03036812_v70_n7_p1669_PerezMillan |
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Citas:
---------- APA ----------
Pérez Millán, M. & Dickenstein, A. (2015) . Implicit dose-response curves. Journal of Mathematical Biology, 70(7), 1669-1684.http://dx.doi.org/10.1007/s00285-014-0809-4
---------- CHICAGO ----------
Pérez Millán, M., Dickenstein, A. "Implicit dose-response curves" . Journal of Mathematical Biology 70, no. 7 (2015) : 1669-1684.http://dx.doi.org/10.1007/s00285-014-0809-4
---------- MLA ----------
Pérez Millán, M., Dickenstein, A. "Implicit dose-response curves" . Journal of Mathematical Biology, vol. 70, no. 7, 2015, pp. 1669-1684.http://dx.doi.org/10.1007/s00285-014-0809-4
---------- VANCOUVER ----------
Pérez Millán, M., Dickenstein, A. Implicit dose-response curves. J. Math. Biol. 2015;70(7):1669-1684.http://dx.doi.org/10.1007/s00285-014-0809-4
