arXiv subjects

Diego Rojas La Luz

Publications and source records attributed to Diego Rojas La Luz.

5 recordsLinked to original sources

arXiv2026

Multistationarity in semi-open Phosphorylation-Dephosphorylation Cycles

Multistationarity underlies biochemical switching and cellular decision-making. We study how multistationarity in the sequential $n$-site phosphorylation-dephosphorylation cycle is affected when only some species are open, meaning allowed to exchange with the environment (so-called semi-open networks). Working under mass action kinetics, we obtain two complementary structural results for $n\geq$2. First, opening any nonempty subset of the substrate species preserves the network's capacity for nondegenerate multistationarity. Second, opening the enzyme species (both kinase and phosphatase), possibly together with any subset of substrates, always destroys multistationarity. The latter result is proved by a general reduction framework combining the detection of absolute concentration robustness (ACR) with projection onto the remaining species; when the projection produces a monostationary network, the full semi-open system is monostationary. We also illustrate the general method on multi-layer cascade variants and discuss biological implications.

math.DS↗

arXiv2026

A flux-based approach for analyzing the disguised toric locus of reaction networks

Dynamical systems with polynomial right-hand sides are very important in various applications, e.g., in biochemistry and population dynamics. The mathematical study of these dynamical systems is challenging due to the possibility of multistability, oscillations, and chaotic dynamics. One important tool for this study is the concept of reaction systems, which are dynamical systems generated by reaction networks for some choices of parameter values. Among these, disguised toric systems are remarkably stable: they have a unique attracting fixed point, and cannot give rise to oscillations or chaotic dynamics. The computation of the set of parameter values for which a network gives rise to disguised toric systems (i.e., the disguised toric locus of the network) is an important but difficult task. We introduce new ideas based on network fluxes for studying the disguised toric locus. We prove, under mild assumptions, that the disguised toric locus of any network $G$ is a contractible manifold with boundary, and introduce an associated graph $G^{\max}$ that characterizes its interior. These theoretical tools allow us, for the first time, to compute the full disguised toric locus for many networks of interest.

math.DS↗

arXiv2026

Stochastic Reaction Networks Within Interacting Compartments with Content-Dependent Fragmentation

Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes -- biochemical and otherwise -- in homogeneous environments. However, cellular reactions are often compartmentalized, either at the cell level or within cells, and hence non-homogeneous. We investigate a model of compartmentalization in which the rate of fragmentation of a compartment depends on the abundance of some designated species inside that compartment. The particular model of study is part of a general framework for compartmentalized chemistry with dynamic compartments that was proposed in (Duso and Zechner, PNAS, 2020). This paper builds on (Anderson and Howells, Bull. Math. Biol., 2023) where the special case where the compartment dynamics do not depend on their contents was studied mathematically. In particular, we demonstrate that the explosivity characterization from (Anderson and Howells, Bull. Math. Biol., 2023) fails in this setting and provide new sufficient conditions for non-explosivity and positive recurrence, under the assumption that the underlying CRN admits a linear Lyapunov function. These results extend the theoretical foundation for modeling content-mediated compartment dynamics, with implications for systems such as cell division and intracellular transport.

math.PR↗

arXiv2025

Asymptotic Robustness in Biochemical Systems

Living systems maintain stable internal states despite environmental fluctuations. Absolute concentration robustness (ACR) is a striking homeostatic phenomenon in which the steady-state concentration of a species remains invariant despite changes in total supply. Although experimental studies have reported approximate-but not exact-robustness in steady-state concentrations, such behavior has often been attributed to exact ACR motifs perturbed by measurement noise or minor reactions, rather than recognized as a structural property of a network itself. Here, we introduce a previously underappreciated phenomenon, namely asymptotic ACR (aACR): approximate robustness can emerge solely from the network structure, without requiring exact ACR motifs or negligible parameters. We find that aACR is more pervasive than classical ACR, as demonstrated in systems such as the Escherichia coli EnvZ-OmpR osmoregulation system and a futile cycle. Furthermore, we prove that such ubiquity stems solely from network structure without fine-tuning of kinetic parameters. The notion of aACR provides a rigorous and practical tool to analyze robust responses in broad biochemical systems.

math.DS↗

arXiv2024

Generalized Lotka-Volterra Systems and Complex Balanced Polyexponential Systems

We study the global stability of generalized Lotka-Volterra systems with generalized polynomial right-hand side, without restrictions on the number of variables or the polynomial degree, including negative and non-integer degree. We introduce polyexponential dynamical systems, which are equivalent to the generalized Lotka-Volterra systems, and we use an analogy to the theory of mass-action kinetics to define and analyze complex balanced polyexponential systems, and implicitly analyze complex balanced generalized Lotka-Volterra systems. We prove that complex balanced generalized Lotka-Volterra systems have globally attracting states, up to standard conservation relations, which become linear for the associated polyexponential systems. In particular, complex balanced generalized Lotka-Volterra systems cannot give rise to periodic solutions, chaotic dynamics, or other complex dynamical behaviors. We describe a simple sufficient condition for complex balance in terms of an associated graph structure, and we use it to analyze specific examples.

math.DS↗