arXiv subjects

Magalí Giaroli

Publications and source records attributed to Magalí Giaroli.

5 recordsLinked to original sources

arXiv2023

Multistationarity questions in reduced vs extended biochemical networks

We address several questions in reduced versus extended networks via the elimination or addition of intermediate complexes in the framework of chemical reaction networks with mass-action kinetics. We clarify and extend advances in the literature concerning multistationarity in this context. We establish general results about MESSI systems, which we use to compute the circuits of multistationarity for significant biochemical networks.

q-bio.MN↗

arXiv2020

Sign conditions for the existence of at least one positive solution of a sparse polynomial system

We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real root, based on degree theory and Gale duality. In the case of integer exponents, we relate our sufficient conditions to algebraic conditions that emerged in the study of toric ideals.

math.AG↗

arXiv2019

Parameter regions that give rise to 2[n/2]+1 positive steady states in the n-site phosphorylation system

The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and Sontag (2008) it is shown that for certain choices of the reaction rate constants and total conservation constants, the system can have 2[n/2]+1 positive steady states (that is, n+1 positive steady states for n even and n positive steady states for n odd). In this paper we give open parameter regions in the space of reaction rate constants and total conservation constants that ensure these number of positive steady states, while assuming in the modeling that roughly only 1/4 of the intermediates occur in the reaction mechanism. This result is based on the general framework developed by Bihan, Dickenstein, and Giaroli (2018), which can be applied to other networks. We also describe how to implement these tools to search for multistationarity regions in a computer algebra system and present some computer aided results.

q-bio.MN↗

arXiv2018

Regions of multistationarity in cascades of Goldbeter-Koshland loops

We consider cascades of enzymatic Goldbeter-Koshland loops with any number n of layers, for which there exist two layers involving the same phosphatase. Even if the number of variables and the number of conservation laws grow linearly with n, we find explicit regions in reaction rate constant and total conservation constant space for which the associated mass-action kinetics dynamical system is multistationary. Our computations are based on the theoretical results of our companion paper in arXiv:1807.05157, which are inspired by results in real algebraic geometry by Bihan, Santos and Spaenlehauer.

q-bio.MN↗

arXiv2018

Lower bounds for positive roots and regions of multistationarity in chemical reaction networks

Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan, Santos and Spaenlehauer. We apply this approach to find explicit reaction rate constants and total conservation constants in biochemical reaction networks for which the associated dynamical system is multistationary.

math.DS↗