After a brief overview of the thermodynamic framework for open chemical reaction networks (CRNs) \cite{Rao2016}, I will introduce a circuit-theoretic approach that provides thermodynamically consistent schemes for coarse-graining CRNs \cite{Avanzini2023}. I will then illustrate how this framework can be used to analyse energy transduction in metabolic networks, emphasising how network...
Random graph models have been instrumental in characterizing
complex networks, but chemical reaction networks (CRNs) are better
represented as hypergraphs. Traditional models of random CRNs often
reduce CRNs to bipartite graphs, representing species and reactions as
distinct nodes, or simpler derived graphs, which can obscure the
relationship between the statistical properties of...
Power-law dynamical systems are widely used as models in chemistry and biology (e.g., in ecology and epidemiology), as well as in economics and engineering. We study positive solutions to parametrized systems of generalized polynomial equations (with real exponents) in abstract terms. In particular, we identify the relevant geometric objects: the coefficient polytope, the monomial difference,...
Understanding self-organized pattern formation is fundamental to biology. In 1952, Alan Turing proposed a pattern-enabling mechanism in reaction-diffusion systems containing chemical species later conceptualized as activators and inhibitors that are involved in feedback loops. However, identifying pattern-enabling regulatory systems with the concept of feedback loops has been a long-standing...
We consider the system of differential equations describing genetic recombination, which is well known to be equivalent to the law of mass action of a chemical reaction network \cite{Mueller_Hofbauer_15,Alberti_21}. It is equally well known that this nonlinear system can be solved via its dual process backward in time (see \cite{Baake_Baake_21} for a review). This dual process is a (linear)...
I will introduce a graph grammar-based formalism to handle (bio)chemical reaction networks. The formalism provides a set of powerful techniques to specify, construct and analyze chemical reaction spaces. A chemical space is defined by a set of compounds and a "reaction chemistry" defined as a collection of graph transformation rules. This algebraic model of chemical transformation in...
Biological systems must maintain stable functions despite environmental perturbations and intrinsic molecular noise. Robust perfect adaptation (RPA) enables biological networks to restore their output to a desired level after disturbances. While antithetic integral feedback can guarantee adaptation of the mean output, it often amplifies stochastic fluctuations and therefore fails to control...
Reaction networks form a foundational mathematical framework for modelling complex biological systems, from intracellular biochemical interactions to multiscale dynamics at the ecological scale. Recent advances in stochastic and deterministic theory, nonequilibrium thermodynamics, and multiscale analysis have significantly deepened our understanding of noise-driven phenomena, biochemical...
