Related papers: Chemical systems with limit cycles
Networks with absolute concentration robustness (ACR) have the property that a translation of a coordinate hyperplane either contains all steady states (static ACR) or attracts all trajectories (dynamic ACR). The implication for the…
The dominant paradigm in origin of life research is that of an RNA world. However, despite experimental progress towards the spontaneous formation of RNA, the RNA world hypothesis still has its problems. Here, we introduce a novel…
A number of simple chaotic three-dimensional dynamical systems (DSs) with quadratic polynomials on the right-hand sides are reported in the literature, containing exactly 5 or 6 monomials of which only 1 or 2 are quadratic. However, none of…
Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
Chemical reactor networks (CRNs) enable simulations of combustion reactors with detailed chemical kinetics and strongly simplified flow structure. In this paper, the implementation of a reactor component with less idealized flow structure,…
Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a…
We study the response of chemical reaction networks driven far from equilibrium to logarithmic perturbations of reaction rates. The response of the mean number of a chemical species is observed to be quantitively limited by number…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
We address the challenge of identifying all real positive steady states in chemical reaction networks (CRNs) governed by mass-action kinetics. Traditional numerical methods often require specific initial guesses and may fail to find all the…
Key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their…
Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only…
Reconstruction of biochemical reaction networks is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and…
Certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network detailed balance (RNDB) which is achieved by imposing network-related…
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…
We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…
For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We…
In this paper, we provide a detailed theoretical analysis of the numerical scheme introduced in J. Comput. Phys. 436 (2021) 110253 for the reaction kinetics of a class of chemical reaction networks that satisfies detailed balance condition.…
Timing is of fundamental importance in biology and our life. Borrowing ideas from mechanism, we map our clock signals onto a gear system, in pursuit of better depiction of a clock signal implemented with chemical reaction networks (CRNs).…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…