Related papers: Discreteness-induced Transition in Catalytic React…
To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however,…
Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the…
Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…
To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the…
Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…
The number of molecules involved in a cell or subcellular structure is sometimes rather small. In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
We study an autocatalytic system consisting of several interacting chemical species. We observe a strong dependence of the concentrations of the chemicals on the size of the system. This dependence is caused by the discrete nature of the…
A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be…
A simple cell model consisting of a catalytic reaction network with intermediate complex formation is numerically studied. As nutrients are depleted, the transition from the exponential growth phase to the growth-arrested dormant phase…
The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study…
Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…
A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers…
Slowing down of the relaxation of the fluctuations around equilibrium is investigated both by stochastic simulations and by analysis of Master equation of reversible reaction networks consisting of resources and the corresponding products…
This paper analyses of a stochastic model of a chemical reaction network with three types of chemical species ${\cal R}$, ${\cal M}$ and ${\cal U}$ that interact to transform a flow of external resources, the chemical species ${\cal Q}$, to…
We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory…
All life, including cells and artificial protocells, must integrate diverse molecules into a single unit in order to reproduce. Despite expected pressure to evolve a simple system with the fastest replication speed, the mechanism by which…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
In this paper I show that, for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the…