论文标题
山型动力学系统的正均衡
Positive Equilibria of Hill-Type Kinetic Systems
论文作者
论文摘要
这项工作介绍了一种新的方法来研究化学反应网络的正均衡$ \ MATHSCR {n} $ end赋予的山型动力学$ k $，称为山型动力学（HTK）系统$ \ left（\ Mathscr {n}，k \ right），包括他们的倍增性和浓度，包括他们的倍数和浓度。我们将称为Poly-Pl Kinetic（Pyk）系统$ \ left（{\ MathScr {n}，{K_ \ text {py}}} \ right）$的幂律动力学系统的独特正线性组合与给定的HTK系统。关联的系统具有其平衡设置的关键属性，与山坡系统的均匀属性相吻合，即$ {e_ +} \ left（{\ MathScr {n}，k} \ right）= {e_ +} \ left（{e_ +} \ left（{ +} \ left（{\ Mathscr {n}，k} \ right）= {z_ +} \ left（{\ Mathscr {n}，{k_ \ text {py}}}}}}}}} \ right）$。这使我们能够识别两个新型的山型动力学子集，称为PL平衡和PL复合体平衡动力学，最近对物种的绝对浓度鲁棒性（ACR）和复杂平衡的阳性平衡的结果可以应用到这些动力学上。我们的主要结果还包括用于PL平衡的HT-RDK系统的Shinar-Feinberg ACR定理（即，复杂的可分解HTK系统的子集），该系统为HTK Systems中ACR分析的基础建立了基础，以及Müller和Regensburger对PL-Complex Balanced HTANCESS SYSTEMS的广泛性大规模动作系统的扩展。此外，我们以类似的方式得出了平衡浓度鲁棒性（BCR）的理论。最后，我们将结果进一步扩展到更一般的动力学类别，其中包括Poly-PL功能的商。
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 $\left(\mathscr{N},K\right)$, 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 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.
