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Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select…
The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
Complex balanced mass-action systems (CBMASs) are of great importance in the filed of biochemical reaction networks. However analyzing the persistence of these networks with high dimensions and time delays poses significant challenges. To…
In many scientific fields, there is an interest in understanding the way in which complex chemical networks evolve. The chemical networks which researchers focus upon, have become increasingly complex and this has motivated the development…
A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material…
Delay mass-action systems provide a model of chemical kinetics when past states influence the current dynamics. In this work, we provide a graph-theoretic condition for delay stability, i.e., linear stability independent of both rate…
Self-assembly processes in biological and synthetic biomolecular systems are often governed by the spatial separation of biochemical processes. While previous work has focused on optimizing self-assembly through fine-tuned reaction…
Recently discovered simple quantitative relations, known as bacterial growth laws, hint on the existence of simple underlying principles at the heart of bacterial growth. In this work, we provide a unifying picture on how these known…
A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating…
Autocatalytic Sets are reaction networks theorised as networks at the basis of life. Their main feature is the ability of spontaneously emerging and self-reproducing. The Reflexively and Food-generated theory provides a formal definition of…
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
Autocatalysis is a deceptively simple concept, referring to the situation that a chemical species $X$ catalyzes its own formation. From the perspective of chemical kinetics, autocatalysts show a regime of super-linear growth. Given a…
Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of…
The realistic modeling intended to quantify precisely some biological mechanisms is a task requiering a lot of a priori knowledge and generally leading to heavy mathematical models. On the other hand, the structure of the classical Machine…