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تسجيل مستخدم جديدPositive Equilibria of Hill-Type Kinetic Systems
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This work introduces a novel approach to study properties of positive equilibria of a chemical reaction network $mathscr{N}$ endowed with Hill-type kinetics $K$, called a Hill-type kinetic (HTK) system $left(mathscr{N},Kright)$, 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 $left( {mathscr{N},{K_text{PY}}} right)$ 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., ${E_ + }left( {mathscr{N},K} right) = {E_ + }left( {mathscr{N},{K_text{PY}}} right)$ and ${Z_ + }left( {mathscr{N},K} right) = {Z_ + }left( {mathscr{N},{K_text{PY}}} right)$. 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 PL-equilibrated 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 Muller 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.
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