The mitigation of climate change has stood at the forefront of interest in the interface of mathematics, biology, and chemistry. Recently, direct carbon dioxide removal strategies have been examined which include direct ocean capture, as well as direct air capture. However, the structural and dynamical properties of these expanded carbon cycle models have yet to be explored. We apply methods...
Cells communicate by sending extracellular ligands such as hormones. Once recognized by their plasma membrane receptors, these ligands trigger intracellular signaling cascades. G Protein-Coupled Receptors (GPCRs) can activate such cascades both at the plasma membrane and, once internalized, from endosomal compartments. Signal kinetics and spatial organization are key determinants of cellular...
Ecosystems are commonly represented as directed graphs describing flows of energy or biomass among species. While these models highlight compartments and flows, neither provides a fundamental dynamical unit. We introduce fluxes as elementary processes that serve as building blocks of ecosystem networks. Inspired by flux balance analysis and metabolic control analysis, a flux represents the...
Polynomial dynamical systems arise in many applications (e.g., biochemistry, population dynamics) but are hard to analyze because they can display multistability, oscillations, and chaos. Mass-action systems, and in particular complex-balanced (toric) systems, are remarkably stable: they admit a unique attracting equilibrium and rule out oscillations and chaos. We study the set of rate...
An active area of research in pharmacology and drug discovery applies to biased signaling: the ability of a ligand to selectively activate some signal transduction pathways as compared to the native ligand acting at the same receptor. At the practical level, experimentalists seek to quantify ligand bias in order to classify ligands according to their selectivity. One popular method uses the...
Chemical reaction networks are mathematical tools used to model the dynamics and steady-states of intricate biochemical systems. One major obstacle in analyzing biochemical reaction networks is a lack of precise knowledge of system parameters such as reaction rates. Often, even the structure of the entire network is not accurately known and therefore simulation methods may not be sufficient in...
Network reconstruction from high-dimensional omics data remains an open challenge. While one can calculate gene-gene co-expression statistics for every pair of genes, these complete weighted graphs must then be sparsified to obtain an interpretable network. Common sparsification approaches (such as thresholding) can lead to an excessively fragmented network, masking the relationship between...
We study the long-time behaviour of a stochastic model for compartmentalised receptor signalling motivated by the trafficking of G protein-coupled receptors. The model describes the evolution of several chemical species distributed between the plasma membrane and a random population of endosomes. Chemical reactions follow deterministic dynamics inside each compartment, while stochastic events...
Reaction networks provide a framework for representing the structural form of dynamical systems. While traditionally used in systems biology and biochemistry to describe molecular interactions, the mathematical principles of reaction networks are increasingly applied across various fields such as cell biology, ecology, epidemiology, and environmental science. By viewing entities—be they...
