arXiv subjects

Beatriz Pascual-Escudero

Publications and source records attributed to Beatriz Pascual-Escudero.

6 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

The generic geometry of steady state varieties

We answer several fundamental geometric questions about reaction networks with power-law kinetics, on topics such as generic finiteness of the number of steady states, robustness, and nondegenerate multistationarity. In particular, we give an ideal-theoretic characterization of generic absolute concentration robustness, as well as conditions under which a network that admits multiple steady states also has the capacity for nondegenerate multistationarity. The key tools underlying our results come from the theory of vertically parametrized systems, and include a linear algebra condition that characterizes when the steady state system has positive nondegenerate zeros.

q-bio.MN↗

arXiv2026

Optimization of sequential therapies to maximize extinction of resistant bacteria through collateral sensitivity

Antimicrobial resistance (AMR) threatens global health. A promising and underexplored strategy to tackle this problem is sequential therapies exploiting collateral sensitivity (CS), whereby resistance to one drug increases sensitivity to another. Here, we develop a four-genotype stochastic birth-death model with two bacteriostatic antibiotics to identify switching periods that maximize bacterial extinction under subinhibitory concentrations. We show that extinction probability depends nonlinearly on switching period, with stepwise increases aligned to discrete switch events: fast sequential therapies are suboptimal as they do not allow for the evolution of resistance, a key ingredient in these therapies. A geometric distribution framework accurately predicts cumulative extinction probabilities, where the per-switch extinction probability rises with switching period. We further derive a heuristic approximation for the extinction probability based on times to fixation of single-resistant mutants. Sensitivity analyses reveal that strong reciprocal CS is required for this strategy to work, and we explore how increasing antibiotic doses and higher mutation rates modulate extinction in a nonmonotonic manner. Finally, we discuss how longer therapies maximize extinction but also cause higher resistance, leading to a Pareto front of optimal switching periods. Our results provide quantitative design principles for in vitro and clinical sequential antibiotic therapies, underscoring the potential of CS-guided regimens to suppress resistance evolution and eradicate infections.

q-bio.PE↗

arXiv2024

Generic consistency and nondegeneracy of vertically parametrized systems

We determine the generic consistency, dimension and nondegeneracy of the zero locus over $\mathbb{C}^*$, $\mathbb{R}^*$ and $\mathbb{R}_{>0}$ of vertically parametrized systems: parametric polynomial systems consisting of linear combinations of monomials scaled by free parameters. These systems generalize sparse systems with fixed monomial support and freely varying parametric coefficients. As our main result, we establish the equivalence among three key properties: the existence of nondegenerate zeros, the zero set having generically the expected dimension, and the system being generically consistent. Importantly, we prove that checking whether a vertically parametrized system has these properties amounts to an easily computed matrix rank condition.

math.AG↗

arXiv2021

An algebraic approach to product-form stationary distributions for some reaction networks

Exact results for product-form stationary distributions of Markov chains are of interest in different fields. In stochastic reaction networks (CRNs), stationary distributions are mostly known in special cases where they are of product-form. However, there is no full characterization of the classes of networks whose stationary distributions have product-form. We develop an algebraic approach to product-form stationary distributions in the framework of CRNs. Under certain hypotheses on linearity and decomposition of the state space for conservative ergodic CRNs, this gives sufficient and necessary algebraic conditions for product-form stationary distributions. Correspondingly we obtain a semialgebraic subset of the parameter space that captures rates where, under the corresponding hypotheses, CRNs have product-form. We employ the developed theory to CRNs and some models of statistical mechanics, besides sketching the pertinence in other models from applied probability.

math.PR↗

arXiv2018

Nash multiplicities and isolated points of maximum multiplicity

Let $X$ be an algebraic variety defined over a field of characteristic zero, and let $ξ\in \mathrm{\underline{Max}\; mult}(X)$ be a point in the closed subset of maximum multiplicity of $X$. We provide a criterion, given in terms of arcs, to determine whether $ξ$ is isolated in $\mathrm{\underline{Max}\; mult}(X)$. More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when $ξ$ is an isolated point in $\mathrm{\underline{Max}\; mult}(X)$.

math.AG↗