This work introduces a novel approach to study properties of positive equilibria of a chemical reaction network N endowed with Hill-type kinetics K, called a Hill-type kinetic (HTK) system (N , K), including their multiplicity and concentration robustness in a species. We associate a unique positive linear combination of power-law kinetic systems called poly-PL kinetic (PYK) system (N , K PY ) to the given HTK system. The associated system has the key property that its equilibria sets coincide with those of the Hill-type system, i.e., E + (N , K) = E + (N , K PY ) and Z + (N , K) = Z + (N , K PY ). This allows us to identify two novel subsets of the Hill-type kinetics, called PL-equilibrated and PL-complex balanced kinetics, to which recent results on absolute concentration robustness (ACR) of species and complex balancing at positive equilibria of power-law (PL) kinetic systems can be applied. Our main results also include the Shinar-Feinberg ACR Theorem for PLequilibrated HT-RDK systems (i.e., subset of complex factorizable HTK systems), which establishes a foundation for the analysis of ACR in HTK systems, and the extension of the results of Müller and Regensburger on generalized mass action systems to PL-complex balanced HT-RDK systems. In addition, we derive the theory of balanced concentration robustness (BCR) in an analogous manner to ACR for PL-equilibrated systems. Finally, we provide further extensions of our results to a more general class of kinetics, which includes quotients of poly-PL functions.

This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems.

Stomatal closure is affected by various stimuli such as light, atmospheric carbon dioxide concentration, humidity and phytohormones. Our research focuses on phytohormones, specifically: abscisic acid (ABA), ethylene (ET) and methyl jasmonate (MeJA) that are responsible for the regulation of several plant processes, especially in guard cell signalling. While several studies show that these three phytohormones cause stomatal closure in plants, only two studies are notable for establishing a mathematical model of guard cell signalling involving phytohormones. Those two studies employed Boolean modelling and mechanistic ordinary differential equations modelling. In this study, we propose a new mathematical model of guard cell transduction network for stomatal closure using continuous logical modelling framework. Results showed how the different components of the network function. Furthermore, the model verified the role of antioxidants in the closure mechanism, and the diminished closure level of stomata with combined ABA-ET stimulus. The analysis was extended to ABA-ET-MeJA crosstalk.

No abstract