Implicit dose-response curves
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 wit...
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todo:paper_03036812_v70_n7_p1669_PerezMillan2023-10-03T15:19:42Z Implicit dose-response curves Pérez Millán, M. Dickenstein, A. 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 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. Fil:Pérez Millán, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03036812_v70_n7_p1669_PerezMillan |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Pérez Millán, M. Dickenstein, A. Implicit dose-response curves |
| topic_facet |
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 |
| description |
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. |
| format |
JOUR |
| author |
Pérez Millán, M. Dickenstein, A. |
| author_facet |
Pérez Millán, M. Dickenstein, A. |
| author_sort |
Pérez Millán, M. |
| title |
Implicit dose-response curves |
| title_short |
Implicit dose-response curves |
| title_full |
Implicit dose-response curves |
| title_fullStr |
Implicit dose-response curves |
| title_full_unstemmed |
Implicit dose-response curves |
| title_sort |
implicit dose-response curves |
| url |
http://hdl.handle.net/20.500.12110/paper_03036812_v70_n7_p1669_PerezMillan |
| work_keys_str_mv |
AT perezmillanm implicitdoseresponsecurves AT dickensteina implicitdoseresponsecurves |
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1807316987401994240 |