Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry
We give necessary and sufficient conditions in terms of sign vectors for the injectivity of
families of polynomial maps with arbitrary real exponents defined on the positive orthant …
families of polynomial maps with arbitrary real exponents defined on the positive orthant …
A framework for deriving analytic steady states of biochemical reaction networks
BS Hernandez, PVN Lubenia… - PLoS computational …, 2023 - journals.plos.org
The long-term behaviors of biochemical systems are often described by their steady states.
Deriving these states directly for complex networks arising from real-world applications …
Deriving these states directly for complex networks arising from real-world applications …
Chemical reaction network approaches to biochemical systems theory
This paper provides a framework to represent a Biochemical Systems Theory (BST) model
(in either GMA or S-system form) as a chemical reaction network with power law kinetics …
(in either GMA or S-system form) as a chemical reaction network with power law kinetics …
Computational translation framework identifies biochemical reaction networks with special topologies and their long-term dynamics
Long-term behaviors of biochemical systems are described by steady states in deterministic
models and stationary distributions in stochastic models. Obtaining their analytic solutions …
models and stationary distributions in stochastic models. Obtaining their analytic solutions …
Reaction networks and kinetics of biochemical systems
This paper further develops the connection between Chemical Reaction Network Theory
(CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use …
(CRNT) and Biochemical Systems Theory (BST) that we recently introduced [1]. We first use …
A deficiency-based approach to parametrizing positive equilibria of biochemical reaction systems
We present conditions which guarantee a parametrization of the set of positive equilibria of a
generalized mass-action system. Our main results state that (1) if the underlying generalized …
generalized mass-action system. Our main results state that (1) if the underlying generalized …
[PDF][PDF] A deficiency zero theorem for a class of power-law kinetic systems with non-reactant-determined interactions
Abstract The Deficiency Zero Theorem (DZT) provides definitive results about the dynamical
behavior of chemical reaction networks with deficiency zero. Thus far, the available DZTs …
behavior of chemical reaction networks with deficiency zero. Thus far, the available DZTs …
Comparative analysis of carbon cycle models via kinetic representations
NT Fortun, ER Mendoza - Journal of Mathematical Chemistry, 2023 - Springer
The pre-industrial state of the global carbon cycle is a significant aspect of studies related to
climate change. In this paper, we recall the power law kinetic representations of the pre …
climate change. In this paper, we recall the power law kinetic representations of the pre …
Chemical reaction network decompositions and realizations of S-systems
HF Farinas, ER Mendoza, AR Lao - arXiv preprint arXiv:2003.01503, 2020 - arxiv.org
This paper presents novel decomposition classes of chemical reaction networks (CRNs)
derived from S-system kinetics. Based on the network decomposition theory initiated by …
derived from S-system kinetics. Based on the network decomposition theory initiated by …
A generalization of Birch's theorem and vertex-balanced steady states for generalized mass-action systems
Mass-action kinetics and its generalizations appear in mathematical models of (bio-)
chemical reaction networks, population dynamics, and epidemiology. The dynamical …
chemical reaction networks, population dynamics, and epidemiology. The dynamical …