Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2504.14700

Curvature-Induced Saturation in Catalytic Reaction Networks: A Differential Geometrical Framework for Modeling Chemical Complexity

Anderson M. Rodriguez
View original source ↗Read source document ↗Export metadata ↓

Abstract

The evolution of chemical reaction networks is often analyzed through kinetic models and energy landscapes, but these approaches fail to capture the deeper structural constraints governing complexity growth. In chemical reaction networks, emergent constraints dictate the organization of reaction pathways, limiting combinatorial expansion and determining stability conditions. This paper introduces a novel approach to modeling chemical reaction networks by incorporating differential geometry into the classical framework of reaction kinetics. By utilizing the Riemannian metric, Christoffel symbols, and a system-specific entropy-like term, we provide a new method for understanding the evolution of complex reaction systems. The approach captures the interdependence between species, the curvature of the reaction network's configuration space, and the tendency of the system to evolve toward more probable states. The interaction topology constrains the accessible reaction trajectories and the introduced differential geometrical approach allows analysis of curvature constraints which help us to understand pathway saturation and transition dynamics. Rather than treating reaction space as an unconstrained combinatorial landscape, we frame it as a structured manifold with higher order curvature describing a geodesic for system evolution under intrinsic constraints. This geometrical perspective offers a unique insight into pathway saturation, self-interruption, and emergent behavior in reaction networks, and provides a scalable framework for modeling large biochemical or catalytic systems.

Explore related subjects

q-bio.MN

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anderson M. Rodriguez. 2025-04-20. Curvature-Induced Saturation in Catalytic Reaction Networks: A Differential Geometrical Framework for Modeling Chemical Complexity. https://arxiv.org/abs/2504.14700

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Minimality in Reflexive and Stoichiometric Autocatalysis

Autocatalysis, the ability of a chemical subsystem to sustain its own constituents when supplied with sufficient food molecules, has been closely related to the origin of life on Earth. Emerging from Wilhelm Ostwald's considerations about an explicit autocatalytic reaction, different notions of autocatalysis have been developed over the years. The two most prominent are reflexively autocatalytic F-generated sets (RAFs) and stoichiometric autocatalysis. After having shown that each RAFs is, under reasonable conditions, in general stoichiometrically autocatalytic, we examine here the relationship between the two notions of minimality: irreducible RAFs and autocatalytic cores. To this end, we overcome the obstacle that RAFs and stoichiometric autocatalysis have been formalized in distinct systems of chemical reactions, i.e., catalytic reaction systems (CRS) and chemical reaction networks (CRNs), respectively. We show that reactions in a CRS constitute equivalence classes of reactions of the corresponding CRNs w.r.t. their specific catalyzations. Using the fact that CRN and CRS can be canonically identified whenever each CRS reaction is associated with a single catalyzation, we demonstrate that the Kőnig graph of a monocatalyzed, irreducible RAF is composed of strong blocks devoid of food and waste species that are separated by reaction vertices, each of which contains an autocatalytic core. In fact, a single irreducible RAF can, in general, contain exponentially many autocatalytic cores.

q-bio.MN↗
arXiv2026

Implementation of Linear Regression and Linear Interpolation using Reaction Networks

Statistical inference is a fundamental component of data science. In this work, we focus on two classical inference techniques: regression and interpolation. We propose a reaction-network-based framework for implementing linear regression, including both univariate and multivariate settings, as well as linear interpolation. Our approach encodes the outputs of these inference techniques in the steady-state concentrations of species within the reaction network. A key ingredient of the construction is a novel generalized division module capable of handling division involving negative numbers. We validate the proposed framework through in silico implementations on standard synthetic datasets and obtain the expected regression and interpolation outputs.

q-bio.MN↗
arXiv2026

Mapping disease-regulatory flux through eQTL-based causal gene networks: a complex-trait framework applied to coronary artery disease

A substantial proportion of inherited susceptibility to common diseases is mediated through tissue-specific regulatory variation. The omnigenic model hypothesizes that much of this risk arises from distant (trans) regulatory effects that are propagated via gene-regulatory networks (GRNs) from numerous regulatory genes onto a relatively small set of core genes. Two major challenges have hindered an empirical assessment of this model. First, transcriptome-wide association studies primarily assess gene expression that is regulated locally (in cis), and thus miss trans-acting effects. Second, trans regulation has so far been examined only in aggregate, without identifying which regulatory genes transmit disease-associated signals to which target genes. Here, we present a framework that decomposes each gene's disease association into a local cis component and a set of trans components attributable to its upstream regulators, propagated along a directed causal GRN. For each gene, we estimate sparse Bayesian expression models and we assess model performance using out-of-sample prediction. Propagating trans signals through the inferred network yields a disease-regulatory flux map: a directed, signed representation that quantifies the contribution of each regulator to the disease association of each target gene. Applying this framework to seven tissues relevant to coronary artery disease, we demonstrate how genetic variation flows through the GRN to affect disease risk. Outgoing regulatory influences from individual genes are directionally heterogeneous, whereas disease-associated genes tend to integrate convergent input from multiple regulators; these convergent targets are enriched for cardiovascular-related biological processes. Consequently, each gene's disease association can be reinterpreted as a detailed allocation of the disease signal among its contributing regulators.

q-bio.MN↗